Manual
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A practical guide to Grasp2K
P. Jönsson, G. Gaigalas, J. Bieroń,
C. Froese Fischer, and I.P. Grant
COMPutational Atomic Structure Group 2012
2
Preface
This is a practical guide to Grasp2K, version version 1_1 [P. Jönsson, G. Gaigalas, J. Bieroń,
C. Froese Fischer, and I.P. Grant, Comput. Phys. Commun xxxxx]. The guide assumes that the
Grasp2K package has been correctly installed according to the instructions in the README file
in the main directory of the package and that the executables are on the path. All calculations
are done with non-interacting blocks of given parity and Jvalue. The programs used (Version
2 and Version 3) all adhere to this format. Only the operation of scalar programs is discussed.
For a description on how to run the Message Passing Interface (MPI) codes see previous write-up
[P. Jönsson, X. He, C. Froese Fischer, and I. P. Grant Comput. Phys. Commun. 177, 597-692
(2007)].
To run the scripts the GRASP environment variable must be set. If you are using the gfortran
compiler this is done by issuing the command
source ./make_environment_gfort
in the Grasp2K installation directory (issue similar command if you use the ifort or Portland
compiler).
Sample Disclaimer: Certain commercial equipment, instruments, software, or materials are identi-
fied in this paper in order to specify the computational procedure adequately. Such identification is
not intended to imply recommendation or endorsement by the National Institute of Standards and
Technology, nor is it intended to imply that the materials or equipment identified are necessarily
the best available for the purpose.
3
4
Contents
1 The GRASP2K package 7
1.1 Application programs and tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 File naming conventions, program and data flow . . . . . . . . . . . . . . . . . . . 10
1.3 Generating lists of configuration state functions . . . . . . . . . . . . . . . . . . . . 13
1.4 Providing initial estimates of the radial functions . . . . . . . . . . . . . . . . . . . 13
1.5 Spectroscopicorbitals .................................. 13
1.6 Transverse photon interaction and self-energy correction . . . . . . . . . . . . . . . 13
1.7 Trouble shooting: convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.8 Trouble shooting: angular data from the biotra,bioscl and rhfs3 programs . . . 14
2 Running the application programs 15
2.1 First example: 1s22s2Sand 1s22p2PinLiI..................... 15
2.2 Second example: 1s22s2p3P0,1,2,1P1inBII ..................... 38
2.3 Third example: 2s22p3and 2p5inSiVIII ....................... 46
3 Running the tools 63
3.1 Extractingandcondensing................................ 63
3.2 Extract radial orbitals for printing . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 Description of output files 69
4.1 Output files from the first example . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Output files from the third example . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Case study: 2s22p,2s2p2in Mo XXXVIII using scripts 83
5.1 Runningscriptfiles.................................... 83
5.2 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Transitionrates...................................... 96
5
6CONTENTS
Chapter 1
The GRASP2K package
1.1 Application programs and tools
The new version of the Grasp2K package consists of a number of application programs and tools.
The application programs and tools, along with the underlying theory, are described in the original
write-ups [1 – 6]. The new Grasp2K contains three program versions for backward compatibility.
Version 1 (V1) programs retain all the previous Grasp92 formats. In order to deal more efficiently
with large scale calculations Version 2 (V2) codes were developed where the interaction matrix
is considered to be a series of non-interacting blocks of given parity and Jvalue, with selected
eigenvalues determined from each. In the new version of Grasp2K programs are referred to as
Version 3 (V3) programs [3]. They have the same block format as in V2, but angular integrations
are based on second quantization in the coupled tensorial form, angular momentum theory in
three spaces (orbital, spin and quasispin), and a generalized graphical technique. The theoretical
background can be found in [7 – 9]. Also the new version implements a fast program jj2lsj that
transforms a portion of the wave function in jj-coupling to a basis of LSJ-coupled configuration
state functions. In the default mode, at least 99 % is transformed but the user can readily request
that 99.9 % is transformed, see [10 – 11]. Labels in LSJ-coupling are used by several programs in
the package. This will be discussed in detail later on.
When available, calculations using Version 3 programs are recommended. In order to distinguish
V1, V2, and V3 executables, the Makefiles produce binary files with ’version number’ at the end
of filename, i.e., mcp1,mcp2,mcp3,mcp2_mpi, etc. The programs which exist in only one version
do not have a ’version number’. MPI codes are available mainly for Version 2 parts of the package.
These have names such as mcp2_mpi. Below is a partial list of programs in the package:
1. iso – define nuclear properties
2. Routines that generate a configuration state list (CSL):
(a) csl – generate a configuration state list (CSL) from lists of reference configurations
(b) jjgen – generate a CSL using rules
(c) jjreduce3 – include only CSFs that have at least one non-zero matrix element with a
CSF of a reference list
(d) xcsl – discard the CSFs defined in the second configuration symmetry list file from the
first one and output the rest
(e) mrgcsl – merge two configuration lists to one list weeding out all duplicates
3. mcp3 – compute angular coefficients
4. erwf – estimate relativistic wave functions
7
8CHAPTER 1. THE GRASP2K PACKAGE
5. rscf2 – determine orbitals and mixing coefficients
6. rci3 – perform CI calculation with Breit and other corrections
7. jj2lsj – a program for converting a portion of the wave function expansion in jj-coupled
configuration states to LSJ-coupled CSFs.
8. Routines for computing transition probabilities:
(a) oscl – perform transition calculations in a single orthonormal basis
(b) biotra3, biotra2_mpi – perform biorthogonal transformations between states.
(c) bioscl3, bioscl2_mpi – compute oscillator strengths between biorthogonal states. If
the program jj2lsj has been run the labels of the states in the output files are in
LSJ-coupling.
9. rhfs3 – compute hyperfine interactions and Landé gJfactors
10. sms2 – compute isotope shifts (this program is obsolete and should be replaced by the ris3
program [C. Nazé et al. Comput. Phys. Commun. (2012) submitted]
A number of generally short programs have been developed as tools to facilitate a computational
procedure. Some are routines for converting files from V2 to V1 form (for backward compatibility)
or from parallel to serial versions.
1. cndens2 – condense a mixing file and associated .c file by deleting configuration states with
a mixing coefficient below a cut-off, for block-format.
2. extmix – prints the numerical values of the expansion coefficients ( in block format), above
a cut-off value) along with the corresponding configuration states, in descending order of
magnitude, if requested.
3. jsplit – split a configuration state list into blocks by Jand parity.
4. mchfmcdf – convert an multiconfiguration Hartree-Fock (MCHF) radial orbital file wfn.inp
file to grasp2K orbital file rwfn.out that can be used with erwf.
5. plotmcdf – extracts a single radial orbital from a radial orbital file(.w) and prints out in
format for plot.
6. readrwf – convert a file of binary radial wave functions to ASCII form (for porting to other
environments), or vice versa.
7. rlevels – list the levels in a series of mixing files, in the order of increasing energy and
report levels (in cm−1) relative to the lowest. If the program jj2lsj has been run the levels
are given in LSJ-coupling notation.
8. rsave – a script file such that the command rsave name moves rwfn.out to name.w,
rmix.out to name.m,rcsl.inp to name.c and rscf.sum to name.s .
9. rotate_pair – a routine that rotates orbitals, useful for testing purposes.
A number of small scripts with self-explanatory names are included in directory ${GRASP}/src:
1. Cleanup.oa — remove object and auxiliary files in all subdirectories
2. Cleanup.oaexe — remove object, auxiliary, and executable files
3. Grep — issue a grep command through all fortran files in all subdirectories
4. Grepall — issue a grep command through all files in all subdirectories
1.1. APPLICATION PROGRAMS AND TOOLS 9
5. qcompile — quick recompile (equivalent to make)
6. recompile — remove object, executable, and auxiliary files, and recompile from scratch
7. Search — search for a file in all ${GRASP} subdirectories (equivalent to find .. -name)
The script recompile includes a feature to generate soft-links (via ln -s linux command) which
link the latest version of each program (i.e. executable file with ’version number’) to the generic
name (executable file without ’version number’), as explained in the second paragraph of this
section.
References
1. Grasp92: F. A. Parpia, C. Froese Fischer, I. P. Grant, Comput. Phys. Commun. 94,
249-271 (1996)
2. Grasp2K: P. Jönsson, X. He, C. Froese Fischer, and I. P. Grant. Comput. Phys. Commun.
176, 597-692 (2007)
3. Grasp2K new version: P. Jönsson, G. Gaigalas, J. Bieroń, C. Froese Fischer, I.P. Grant,
Comput. Phys. Commun xxxxx
4. HFS92: P. Jönsson F.A. Parpia and C. Froese Fischer, Comput. Phys. Commun. 96, 301
(1996)
5. SMS92: P. Jönsson and C. Froese Fischer, Comput. Phys. Commun. 94, 249 (1997)
6. JJGEN: L. Sturesson, P. Jönsson and C. Froese Fischer, Comput. Phys. Commun. 177,
539 (2007)
7. G. Gaigalas, Z.B. Rudzikas and C. Froese Fischer, Journal of Physics B At. Mol. Phys. 30,
3747 (1997)
8. G. Gaigalas, S. Fritzsche and I.P. Grant, Comput. Phys. Commun. 139, 263 (2001)
9. G. Gaigalas, S. Fritzsche, Z. Rudzikas, Atomic Data and Nuclear Data Tables. 76, 235
(2000)
10. G. Gaigalas, T. Žalandauskas, and Z. Rudzikas, At. Data and Nucl. Data Tables 84, 99
(2003)
11. G. Gaigalas, T. Žalandauskas, and S. Fritzsche, Comput. Phys. Commun. 157, 239 (2004)
10 CHAPTER 1. THE GRASP2K PACKAGE
1.2 File naming conventions, program and data flow
Passing of information between different programs is done through files. This process is greatly
facilitated through file naming conventions. Consider transition probability calculations between
two groups of results, say one odd group and one even group. Three files are needed for each group
in such a calculation - the configuration state list, the radial wave functions, and the expansion
(or mixing) coefficients - or a total of six files. The Grasp2K package uses a convention similar to
the one for the MCHF package [C. Froese Fischer, G. Tachiev, G. Gaigalas, and M.R. Godefroid,
Comput. Phys. Commun. 176, 559 (2007)]. A name is associated with the results for each group
and an extension that defines the contents and format of the file. Thus the file name becomes
name.extension. Common extensions are listed in Table 1. The tool rsave makes use of these
default extensions.
To run Grasp2K a number of programs need to be run in a pre-determined sequence. Figure 2
displays a typical sequence of block version program calls to evaluate different expectation values.
The resulting flow of files is displayed in Figure 3.
Table 1.1: Table of common extensions.
Extension Type of file
cConfiguration state list.
wBinary file of radial functions.
mBinary file of expansion or mixing coefficients produced by rscf or its variants.
cm Binary file of mixing coefficients produced by rci or its variants.
bw A.w file after biorthogonal transformation using biotra or its variants.
bm A.m file after biorthogonal transformation using biotra or its variants.
cbm A.cm file after biorthogonal transformation using biotra or its variants.
lsj.lbl File containing composition of wave functions in LSJ -coupling.
tTransition probability data from rscf mixing coefficients or its variants.
t.lsj Transition probability data from rscf mixing coefficients or its variants. Labels in
in LSJ -coupling.
ct Transition probability data from rci mixing coefficients or its variants.
ct.lsj Transition probability data from rci mixing coefficients or its variants. Labels in
in LSJ -coupling.
hHyperfine structure data and Landé factors from rscf mixing coefficients or its variants.
ch Hyperfine structure data and Landé factors from rci mixing coefficients or its variants.
hoffd Off-diagonal hyperfine structure data from rscf mixing coefficients or its variants.
choffd Off-diagonal hyperfine structure data from rci mixing coefficients or its variants.
iIsotope shift data from rscf mixing coefficients or its variants.
ci Isotope shift data from rci mixing coefficients or its variants.
1.2. FILE NAMING CONVENTIONS, PROGRAM AND DATA FLOW 11
iso (Generation of nuclear data)
?
jjgen (Generation of configuration state list)
?
jjreduce3 (Reduction of configuration state list)
?
jsplit (Re-arrangement of configuration state list to block form)
?
mcp3 (Angular integration)
?
erwf (Generation of initial radial orbitals)
?
rscf2 (Self-consistent field procedure)
?
rci3 (Relativistic CI with optional Breit interaction)
?
jj2lsj (Transform representation from jj- to LSJ-coupling)
PPPPPPPPPP
Pq
biotra3 (Biorthonormal transf.)
?
bioscl3 (Eval. of expect. values)
rhfs3,sms2 (Eval. of expect. values )
Figure 1.1: Typical sequence of block version program calls to evaluate different expectation values.
12 CHAPTER 1. THE GRASP2K PACKAGE
iso
?
Output; isodata
jjgen
?
Output; rcsl.out
jjreduce3
?
Input; mrlist, rcsl.inp
Output; rcsl.out
jsplit
?
Input; rcsl.inp
Output; rcsl.out
mcp3
?
Input; rcsl.inp
Output; mcp.xx where xx = 30, 31, 32, ...
erwf
?
Input; rcsl.inp, optional radial function file(s)
Output; rwfn.inp
rscf2
?
Input; rcsl.inp,rwfn.inp,mcp.xx
Output; rmix.out,rwfn.out,rscf.sum
rci3
?
Input; name.c,name.w
Output; name.cm,name.csum
jj2lsj
?
Input; name.c,name.(c)m
Output; name.lsj.lbl
biotra2
?
Input; name1.c,name1.(c)m,name1.w,name2.c,name2.(c)m,name2.w
Input; name1.TB,name2.TB (if available)
Output; name1.(c)bm,name1.(c)bw,name2.(c)bm,name2.(c)bw
Output; name1.TB,name2.TB
bioscl2 Input; name1.c,name1.(c)bm,name1.(c)bw
name2.c,name2.(c)bm,name2.(c)bw
Input; name1.name2.xT (if available)
Output; name1.name2.(c)t, name1.name2.(c)t.lsj (in LS J -coupling)
Output; name1.name2.xT
Figure 1.2: Flow of files for a normal sequence of program runs in the block version. Extensions
(c) indicate data files from rci3 mixing coefficients.
1.3. GENERATING LISTS OF CONFIGURATION STATE FUNCTIONS 13
1.3 Generating lists of configuration state functions
Exploring different correlation models and generating lists of configuration state functions (CSFs)
is a major task of the computation. The Grasp2K provides several programs for performing this
task. For generating small lists of CSFs it is often best to use the CSL program. To generate
expansion based on the notion of excitations from subshells to an active set of orbitals it is often
advantageous to use the jjgen program. Different restrictions can be put on the excitations
and it is possible to describe core-valence correlation where at most one excitation is allowed
from subshells of the core. To make sure that the generated CSFs interacts with the CSFs in
multireference the program jjreduce3 should be used. Before continuing the reader is advised
to study the write-up of the jjgen program [L. Sturesson, P. Jönsson and C. Froese Fischer,
Comput. Phys. Commun. 177, 539 (2007)]. The write-up provides a number of examples on how
to generate expansions capturing different correlation effects.
1.4 Providing initial estimates of the radial functions
The program application erwf generates initial estimates for radial orbitals. These estimates
may be generated using a Thomas-Fermi potential. Alternatively, the initial radial functions can
be taken as screened hydrogenic functions. Converted Hartree-Fock (HF) or multiconfiguration
Hartree-Fock (MCHF) or radial functions from previous runs may also be used. It is the experience
of the authors that the use of converted HF or MCHF functions generally give very good starting
values and that this may cut down on the number of needed iterations in the self-consistent-field
procedure. The conversion of HF or MCHF radial functions is done by mchfmcdf. In the present
implementation, prior to normalization,
P(nκ;r) = PMCHF (nl;r)
Q(nκ;r) = α
2d
dr +κ
rP(nκ;r),
which means that the relativistic orbital pair is strictly kinetically matched [I.P. Grant, Relativistic
Quantum Theory of Atoms and Molecules, Springer 2007, p. 291].
1.5 Spectroscopic orbitals
The “spectroscopic orbitals” are those where node counting is required to ensure that the self-
consistent field procedure converges to the desired solution [C. Froese Fischer, T. Brage, P. Jönsson,
Computational Atomic Structure - an MCHF approach, IoP, 1997]. Spectroscopic orbitals build
the reference CSFs and often have occupation numbers near unity or more. All other orbitals are
“correlation orbitals”. If the self-consistent field procedure fails for spectroscopic orbitals, i.e. the
wrong number of nodes are obtained with a subsequent program halt, it is often helpful to start
from converted HF or MCHF radial orbitals rather than orbitals generated in a Thomas-Fermi
potential or the simple screened hydrogenic orbitals.
1.6 Transverse photon interaction and self-energy correction
Relativistic corrections beyond the Dirac-Coulomb approximation for a many-electron system are
implemented using assumptions based on one-electron concepts. For example, the transverse
photon frequency is assumed to be the difference between the diagonal energy parameters. This
may be an appropriate assumption for singly occupied orbitals but is not correct for multiply
occupied ones and certainly is not true for correlation orbitals. For these reasons transverse photon
interaction is often computed in the low-frequency limit by multiplying the frequency with a scale
factor. The scale factor is often set to 10−6. Similarly, the self-energy correction is computed from
a screened-hydrogenic approximation, a model that does not apply well to correlation orbitals that
14 CHAPTER 1. THE GRASP2K PACKAGE
are far from hydrogenic. The rci3 code allows the user to specify the largest principal quantum
number for which CSFs are to be considered in the self-energy corrections. For small calculations
with a few correlation orbitals this cut-off is set to the largest principal quantum number of the
included orbitals. In large calculations with many correlation orbitals the cut-off is typically set
to a number somewhat larger than the highest principal quantum number of the spectroscopic
orbitals.
1.7 Trouble shooting: convergence
Convergence in the self-consistent field procedure is a major issue. It is advisable to first do
a calculation with the most important configuration state functions defining the multireference.
If there are problems converging spectroscopic orbitals then start from converted HF or MCHF
radial functions. If convergence problems remain the user may increase the nuclear charge Z
and perform the calculation for some more highly charged ion. The, hopefully, converged radial
functions from this run can then be used for another calculation, where the nuclear charge has
been slightly decrease. The radial functions from this run are, provided they are converged, used
in a new calculation where the nuclear charge has been decreased further etc. If this still does not
led to convergence the user may override the default options in the self-consistent field procedure.
There a number of options to aid convergence such as increasing the orbital damping. After the
calculation for the multireference has been successfully finished the user may introduce correlation
orbitals layer by layer. Each time only the outermost layer is optimized and the remaining orbitals
are kept frozen.
1.8 Trouble shooting: angular data from the biotra,bioscl
and rhfs3 programs
The biotra and bioscl programs and their variants as well as the hfs3 program save angular
data on file. If angular files are available the programs read these files and the execution time
is reduced considerably. If, for some reason, there are incomplete files with angular coefficients
these programs will end with some error message when trying to process the angular data files.
In these cases the user should remove the angular files (they all have a capital Tin the extension)
and rerun the case again.
Chapter 2
Running the application programs
In this chapter we demonstrate the use of the application programs of Grasp2K in three cases
described below. The use of the tools of the Grasp2K package is described in the next chapter.
The data written to the output files are explained and discussed in chapter 4. Output files from
the runs are available in the directories manual\example1,manual\example2,manual\example3.
Scripts for running the examples can be found there, too. Please note that the executable all must
be on the path! Also, to run the scripts the environment variable GRASP needs to be set. If you
have set up the package with the gfortran compiler this is done by issuing the command
source ./make_environment_gfort
in the Grasp2K installation directory. A simpilar command should be issued if you have used
the ifort or portland compilers.
2.1 First example: 1s22s2Sand 1s22p2Pin Li I
The first example is for 1s22s2S1/2and 1s22p2P1/2,3/2in Li.
Overview
1. Define nuclear data.
2. Generate configuration list containing three CSFs: 1s22s2S1/2,1s22p2P1/2,3/2.
3. Perform angular integration.
4. Generate initial estimates of radial orbitals.
5. Perform self-consistent field calculation on the weighted average (EOL) of 1s22s2S1/2,1s22p2P1/2,3/2.
6. Save output to 2s_2p_DF.
7. Generate n= 3 complete active space configuration expansion for 1s22s2S1/2.
8. Perform angular integration.
9. Generate initial estimates of radial orbitals.
10. Perform self-consistent field calculation on 1s22s2S1/2.
11. Save output to 2s_3.
12. Perform CI calculations in which Breit and QED effects are added.
13. Generate n= 3 complete active space configuration expansion for 1s22p2P1/2,3/2.
15
16 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
14. Perform angular integration.
15. Generate initial estimates of radial orbitals.
16. Perform self-consistent field calculation on the weighted average (EOL) of 1s22p2P1/2,3/2.
17. Save output to 2p_3.
18. Perform CI calculations in which Breit and QED effects are added.
19. Run rlevels to view energy separations.
20. Calculate isotope and hyperfine calculations using the CI wave functions.
21. Compute the transition rates from the CI wave functions. Calculation in two steps: biorthog-
onal transformation and evaluation of transition matrix elements using standard Racah al-
gebra methods.
Program input
In the test-runs input is marked by >> and >>3, for example, indicate that the user should input
3 and then strike the return key. When >> is followed by blanks just strike the return key.
*******************************************************************************
* RUN ISO TO GENERATE NUCLEAR DATA *
* OUTPUT FILE: isodata *
*******************************************************************************
>>iso
Enter the atomic number:
>>3
Enter the mass number (0 if the nucleus is to be modelled as a point source:
>>7
The default root mean squared radius is 2.16921046879772 fm;
the default nuclear skin thickness is 2.30000000000000 fm;
Revise these values?
>>n
Enter the mass of the neutral atom (in amu) (0 if the nucleus is to be static):
>>6.941
Enter the nuclear spin quantum number (I) (in units of h / 2 pi):
>>1.5
Enter the nuclear dipole moment (in nuclear magnetons):
>>3.2564268
Enter the nuclear quadrupole moment (in barns):
>>-0.040
*******************************************************************************
* RUN JJGEN TO GENERATE CONFIGURATION LIST FOR 2S AND 2P WITH *
* THREE CSFs: 1s(2)2s J=1/2, 1s(2)2p- J=1/2, 1s(2)2p J=3/2 *
* OUTPUT FILES: clist.out, clist.log *
* *
* DETAILED INFORMATION ON HOW TO RUN THE JJGEN PROGRAM IS AVAILABLE *
* FROM THE ORIGINAL ARTICLE *
* L. Sturesson, P. Jönsson and C. Froese Fischer *
* JJGEN: A flexible program for generating lists of jj-coupled *
* configuration state functions. *
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 17
* Computer Physics Communications, 177, 539 (2007). *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>2
Highest orbital angular momentum, l? (s..p)
>>p
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..2)
>>2
Predefine open, closed or no core? (o/c/*)
>>
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>1
Number of electrons in 2p? (0..6)
>>0
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,1
Number of excitations = ? (0..3)
>>0
One configuration state has been generated.
One configuration state in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>y
Highest n-number? (1..15)
>>2
Highest l-number? (s..p)
>>p
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..2)
>>2
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
18 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
>>0
Number of electrons in 2p? (0..6)
>>1
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,3
Number of excitations = ? (0..3)
>>0
2 configuration states have been generated.
3 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
* IT IS ADVISABLE TO SAVE THE JJGEN LOG-FILE TO HAVE A RECORD ON *
* HOW THE CONFIGURATION LISTS GENERATION WAS DONE *
*******************************************************************************
>>cp clist.log 2s_2p_DF.log
>>cp clist.out rcsl.inp
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
* *
* NOTE: IF JJGEN IS USED FOR GENERATION CHECKS ON DUPLICATES *
* GENERALLY NOT NEEDED *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
3 blocks were found
nb J/P ncf
1 1/2+ 1
2 1/2- 1
3 3/2- 1
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 19
>>mcp3
====================================================
MCP3: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Block 1 , ncf = 1
Block 2 , ncf = 1
Block 3 , ncf = 1
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
......
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
30 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/20
Time (Hr/Min/Sec): 23/55/47.390
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN ERWF TO GENERATE INITIAL ESTIMATES FOR RADIAL FUNCTIONS *
* OUTPUT FILE: rwfn.inp *
*******************************************************************************
>>erwf
ERWF: Execution begins ...
Estimating Relativistic Wave Functions: Output file = rwfn.inp
Default settings ?
>>y
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
The following subshell radial wavefunctions remain to be estimated:
1s 2s 2p- 2p
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>2
Enter the list of relativistic subshells:
>>*
20 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
All required subshell radial wavefunctions have been estimated:
Shell e p0 gamma P(2) Q(2) MTP SRC
1s 0.2476D+01 0.9246D+01 0.1000D+01 0.9481D-06 -0.3767D-10 310 T-F
2s 0.2895D+00 0.2308D+01 0.1000D+01 0.2366D-06 -0.9404D-11 333 T-F
2p- 0.2173D+00 0.1444D-03 0.1000D+01 0.7276D-13 0.1353D-08 336 T-F
2p 0.2173D+00 0.1204D+01 0.2000D+01 0.1266D-13 -0.5029D-18 336 T-F
ERWF: Execution complete.
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
* NOTE: ORBITALS BUILDING REFERENCE STATES ARE REQUIRED TO HAVE *
* THE CORRECT NUMBER OF NODES. THEY ARE REFERRED TO AS SPECTROSCOPIC *
* ORBITALS. IN THIS RUN WE VARY 1s, 2s, 2p AND THEY ARE ALL *
* SPECTROSCOPIC. WE CAN USE WILD CARDS FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Date and Time:
Date: 20070603 Time: 161709.150 Zone: +0200
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
Loading CSL File for ALL blocks
There are 3 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 3 blocks (block J/Parity NCF):
1 1/2+ 1 2 1/2- 1 3 3/2- 1
Enter ASF serial numbers for each block
Block 1 ncf = 1 id = 1/2+
>>1
Block 2 ncf = 1 id = 1/2-
>>1
Block 3 ncf = 1 id = 3/2-
>>1
level weights (1 equal; 5 standard; 9 user)
>>5
Radial functions
1s 2s 2p- 2p
Enter orbitals to be varied (Updating order)
>>*
Which of these are spectroscopic orbitals?
>>*
Enter the maximum number of SCF cycles:
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 21
>>100
..........
Generalised occupation numbers:
2.0000D+00 2.5000D-01 2.5000D-01 5.0000D-01
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
21 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/20
Time (Hr/Min/Sec): 23/57/51.642
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2s_2p_DF
Created 2s_2p_DF.w, 2s_2p_DF.c, 2s_2p_DF.m and 2s_2p_DF.sum
*******************************************************************************
* RUN JJGEN TO GENERATE n=3 CAS CONFIGURATION LIST FOR 2S *
* OUTPUT FILES: clist.out, clist.log *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>3
Highest orbital angular momentum, l? (s..d)
>>d
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..3)
>>2
Predefine open, closed or no core? (o/c/*)
>>
22 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>1
Number of electrons in 2p? (0..6)
>>0
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,1
Number of excitations = ? (0..3)
>>3
79 configuration states have been generated.
79 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
* IT IS ADVISABLE TO SAVE THE JJGEN LOG-FILE TO HAVE A RECORD ON *
* HOW THE CONFIGURATION LISTS GENERATION WAS DONE *
*******************************************************************************
>>cp clist.log 2s_3.log
>>cp clist.out rcsl.inp
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
1 blocks were found
nb J/P ncf
1 1/2+ 79
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
>>mcp3
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 23
====================================================
MCP3: Execution Begins ...
====================================================
Date and Time:
Date: 20070603 Time: 162634.101 Zone: +0200
Default settings? (y/n)
>>y
Block 1 , ncf = 79
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
........
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
9 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/00/46.466
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN ERWF TO GENERATE INITIAL ESTIMATES FOR RADIAL FUNCTIONS *
* OUTPUT FILE: rwfn.inp *
*******************************************************************************
>>erwf
ERWF: Execution begins ...
Estimating Relativistic Wave Functions: Output file = rwfn.inp
Default settings ?
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
The following subshell radial wavefunctions remain to be estimated:
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>1
Enter the file name (Null then "rwfn.out")
>>2s_2p_DF.w
Enter the list of relativistic subshells:
>>*
24 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
The following subshell radial wavefunctions remain to be estimated:
3s 3p- 3p 3d- 3d
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>2
Enter the list of relativistic subshells:
>>*
All required subshell radial wavefunctions have been estimated:
Shell e p0 gamma P(2) Q(2) MTP SRC
1s 0.2518D+01 0.9281D+01 0.1000D+01 0.9517D-06 -0.3781D-10 333 2s_
2s 0.1963D+00 0.1453D+01 0.1000D+01 0.1489D-06 -0.5918D-11 339 2s_
2p- 0.1287D+00 0.5116D-04 0.1000D+01 0.2578D-13 0.4793D-09 344 2s_
2p 0.1287D+00 0.4265D+00 0.2000D+01 0.4485D-14 -0.1782D-18 344 2s_
3s 0.9128D-01 0.9784D+00 0.1000D+01 0.1003D-06 -0.3987D-11 347 T-F
3p- 0.7531D-01 0.6592D-04 0.1000D+01 0.3321D-13 0.6175D-09 349 T-F
3p 0.7531D-01 0.5495D+00 0.2000D+01 0.5777D-14 -0.2296D-18 349 T-F
3d- 0.6228D-01 0.3234D-05 0.2000D+01 0.3342D-21 0.6213D-17 351 T-F
3d 0.6228D-01 0.3237D-01 0.3000D+01 0.3491D-22 -0.1387D-26 351 T-F
ERWF: Execution complete.
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
* NOTE: FOR CORRELATION ORBITALS THERE ARE NO RESTRICTIONS ON THE *
* NUMBER OF NODES, I.E. THEY ARE NOT SPECTROSCOPIC. IN THIS RUN WE *
* VARY THE CORRELATION ORBITALS 3s,3p, 3d. NONE OF THESE ARE *
* SPECTROSCOPIC. WE CAN USE WILD CARDS FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Date and Time:
Date: 20070603 Time: 162752.521 Zone: +0200
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Loading CSL File for ALL blocks
There are 79 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 1 blocks (block J/Parity NCF):
1 1/2+ 79
Enter ASF serial numbers for each block
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 25
Block 1 ncf = 79 id = 1/2+
>>1
Radial functions
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Enter orbitals to be varied (Updating order)
>>3*
Which of these are spectroscopic orbitals?
>>
Enter the maximum number of SCF cycles:
>>100
..........
Generalised occupation numbers:
1.9940D+00 9.9996D-01 3.8609D-05 7.7191D-05 2.5018D-03 1.1036D-03
2.2074D-03 5.9745D-05 8.9702D-05
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
18 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/02/42.794
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2s_3
Created 2s_3.w, 2s_3.c, 2s_3.m and 2s_3.sum
*******************************************************************************
* RUN RCI3 TO INCLUDE BREIT AND QED EFFECTS *
* OUTPUT FILE: 2s_3.cm, 2s_3.csum *
* *
* THE TRANSVERSE PHOTON FREQUENCIES CAN BE SET TO THE LOW FREQUENCY *
* LIMIT. RECOMMENDED IN CASES WHERE YOU HAVE CORRELATION ORBITALS *
* THE SELF ENERGY CORRECTION MAY FAIL FOR CORRELATION ORBITALS WITH *
* HIGH N. *
*******************************************************************************
>>rci3
====================================================
RCI3: Execution Begins ...
====================================================
Default settings?
26 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
>>y
Name of state:
>>2s_3
isofile = isodata
name = 2s_3
Calling CHKPLT...
Calling SETDBG...
Calling SETMC...
Calling SETCON...
Calling SETSUM...
Calling setcsl...
Block 1 , ncf = 79
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Calling SETRES...
Calling SETISO ...
Include contribution of H (Transverse)?
>>y
Modify all transverse photon frequencies?
>>y
Enter the scale factor:
>>1d-6
Include H (Vacuum Polarisation)?
>>y
Include H (Normal Mass Shift)?
>>n
Include H (Specific Mass Shift)?
>>n
Estimate self-energy?
>>y
Largest n quantum number for including self-energy for orbital
n should be less or equal 8
>>3
Loading Radial WaveFunction File ...
Calling SETMIX...
There are 1 blocks (block J/Parity NCF):
1 1/2+ 79
Enter ASF serial numbers for each block
Block 1 ncf = 79 id = 1/2+
>>1
..............
Finish time, Statistics
====================================================
RCI3: Execution Finished ...
====================================================
Wall time:
79 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 27
Time (Hr/Min/Sec): 00/04/56.426
Zone: +0200
RCI3: Execution complete.
*******************************************************************************
* RUN JJGEN TO GENERATE n=3 CAS CONFIGURATION LIST FOR 2P *
* OUTPUT FILES: clist.out, clist.log *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>3
Highest orbital angular momentum, l? (s..d)
>>d
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..3)
>>2
Predefine open, closed or no core? (o/c/*)
>>
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>0
Number of electrons in 2p? (0..6)
>>1
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,3
Number of excitations = ? (0..3)
>>3
186 configuration states have been generated.
186 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
* *
* IT IS ADVISABLE TO SAVE THE JJGEN LOG-FILE TO HAVE A RECORD ON *
28 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
* HOW THE CONFIGURATION LISTS GENERATION WAS DONE *
*******************************************************************************
>>cp clist.log 2p_3.log
>>cp clist.out rcsl.inp
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
2 blocks were found
nb J/P ncf
1 1/2- 76
2 3/2- 110
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
>>mcp3
====================================================
MCP3: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Block 1 , ncf = 76
Block 2 , ncf = 110
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
.................
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
12 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/07/01.366
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 29
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN ERWF TO GENERATE INITIAL ESTIMATES FOR RADIAL FUNCTIONS *
* OUTPUT FILE: rwfn.inp *
*******************************************************************************
>>erwf
ERWF: Execution begins ...
Estimating Relativistic Wave Functions: Output file = rwfn.inp
Default settings ?
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
The following subshell radial wavefunctions remain to be estimated:
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>1
Enter the file name (Null then "rwfn.out")
>>2s_2p_DF.w
Enter the list of relativistic subshells:
>>*
The following subshell radial wavefunctions remain to be estimated:
3s 3p- 3p 3d- 3d
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>2
Enter the list of relativistic subshells:
>>*
All required subshell radial wavefunctions have been estimated:
Shell e p0 gamma P(2) Q(2) MTP SRC
1s 0.2518D+01 0.9281D+01 0.1000D+01 0.9517D-06 -0.3781D-10 333 2s_
2s 0.1963D+00 0.1453D+01 0.1000D+01 0.1489D-06 -0.5918D-11 339 2s_
2p- 0.1287D+00 0.5116D-04 0.1000D+01 0.2578D-13 0.4793D-09 344 2s_
2p 0.1287D+00 0.4265D+00 0.2000D+01 0.4485D-14 -0.1782D-18 344 2s_
3s 0.9128D-01 0.9784D+00 0.1000D+01 0.1003D-06 -0.3987D-11 347 T-F
3p- 0.7531D-01 0.6592D-04 0.1000D+01 0.3321D-13 0.6175D-09 349 T-F
3p 0.7531D-01 0.5495D+00 0.2000D+01 0.5777D-14 -0.2296D-18 349 T-F
3d- 0.6228D-01 0.3234D-05 0.2000D+01 0.3342D-21 0.6213D-17 351 T-F
3d 0.6228D-01 0.3237D-01 0.3000D+01 0.3491D-22 -0.1387D-26 351 T-F
ERWF: Execution complete.
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
30 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
* NOTE: FOR CORRELATION ORBITALS THERE ARE NO RESTRICTIONS ON THE *
* NUMBER OF NODES, I.E. THEY ARE NOT SPECTROSCOPIC. IN THIS RUN WE *
* VARY THE CORRELATION ORBITALS 3s,3p, 3d. NON OF THESE ARE *
* SPECTROSCOPIC. WE CAN USE WILD CARDS FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Loading CSL File for ALL blocks
There are 186 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 2 blocks (block J/Parity NCF):
1 1/2- 76 2 3/2- 110
Enter ASF serial numbers for each block
Block 1 ncf = 76 id = 1/2-
>>1
Block 2 ncf = 110 id = 3/2-
>>1
level weights (1 equal; 5 standard; 9 user)
>>5
Radial functions
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Enter orbitals to be varied (Updating order)
>>3*
Which of these are spectroscopic orbitals?
>>
Enter the maximum number of SCF cycles:
>>100
...............
Generalised occupation numbers:
1.9939D+00 2.0158D-04 3.3333D-01 6.6667D-01 2.5203D-03 1.0853D-03
2.1709D-03 6.4805D-05 9.7285D-05
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
38 seconds
Finish Date and Time:
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 31
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/08/57.582
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2p_3
Created 2p_3.w, 2p_3.c, 2p_3.m and 2p_3.sum
*******************************************************************************
* RUN RCI3 TO INCLUDE BREIT AND QED EFFECTS *
* OUTPUT FILE: 2p_3.cm, 2p_3.csum *
* *
* THE TRANSVERSE PHOTON FREQUENCIES CAN BE SET TO THE LOW FREQUENCY *
* LIMIT. RECOMMENDED IN CASES WHERE YOU HAVE CORRELATION ORBITALS *
* THE SELF ENERGY CORRECTION MAY FAIL FOR CORRELATION ORBITALS WITH *
* HIGH N. *
*******************************************************************************
>>rci3
====================================================
RCI3: Execution Begins ...
====================================================
Default settings?
>>y
Name of state:
>>2p_3
isofile = isodata
name = 2p_3
Calling CHKPLT...
Calling SETDBG...
Calling SETMC...
Calling SETCON...
Calling SETSUM...
Calling setcsl...
Block 1 , ncf = 76
Block 2 , ncf = 110
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Calling SETRES...
Calling SETISO ...
Include contribution of H (Transverse)?
>>y
Modify all transverse photon frequencies?
>>y
Enter the scale factor:
>>1.d-6
Include H (Vacuum Polarisation)?
>>y
32 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
Include H (Normal Mass Shift)?
>>n
Include H (Specific Mass Shift)?
>>n
Estimate self-energy?
>>y
Largest n quantum number for including self-energy for orbital
n should be less or equal 8
>>3
Loading Radial WaveFunction File ...
Calling SETMIX...
There are 2 blocks (block J/Parity NCF):
1 1/2- 76 2 3/2- 110
Enter ASF serial numbers for each block
Block 1 ncf = 76 id = 1/2-
>>1
Block 2 ncf = 110 id = 3/2-
>>1
.................
====================================================
RCI3: Execution Finished ...
====================================================
Wall time:
60 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/10/55.223
Zone: +0200
RCI3: Execution complete.
*******************************************************************************
* RUN RLEVELS TO VIEW ENERGIES AND ENERGY SEPARATIONS *
*******************************************************************************
>> rlevels
You can also use command-line option:
%rlevels file1 file2 (wild cards allowed)...
Now, carry on
Type the input file name, one for each line (NULL to terminate)
File name ?
>>2s_3.cm
File name ?
>>2p_3.cm
File name ?
>>
nblock = 1 ncftot = 79 nw = 9 nelec = 3
nblock = 2 ncftot = 186 nw = 9 nelec = 3
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 33
Energy levels for ...
Rydberg constant is 109737.31534
No - Serial number of the state; Pos - Position of the state within the
J/P block; Splitting is the energy difference with the lower neighbor
-------------------------------------------------------------------------
No Pos J Parity Energy Total Levels Splitting
(a.u.) (cm^-1) (cm^-1)
-------------------------------------------------------------------------
1 1 1/2 + -7.4719740 0.00 0.00
2 1 1/2 - -7.4042610 14861.28 14861.28
3 1 3/2 - -7.4042597 14861.57 0.29
------------------------------------------------------------
*******************************************************************************
* RUN SMS2 FOR 2s_3 *
* OUTPUT FILE: 2s_3.ci *
*******************************************************************************
>>sms2
====================================================
SMS2: Execution Begins ...
====================================================
Default settings?
>>y
Name of state
>>2s_3
Mixing coefficients from a CI calc.?
>>y
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 79 relativistic CSFs;
... load complete;
Loading Radial WaveFunction File ...
..........
====================================================
SMS2: Execution Finished ...
====================================================
Wall time:
50 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/12/13.537
Zone: +0200
SMS2: Execution complete.
34 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
*******************************************************************************
* RUN SMS2 FOR 2p_3 *
* OUTPUT FILE: 2p_3.ci *
*******************************************************************************
>>sms2
====================================================
SMS2: Execution Begins ...
====================================================
Default settings?
>>y
Name of state
>>2p_3
Mixing coefficients from a CI calc.?
>>y
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 186 relativistic CSFs;
... load complete;
Loading Radial WaveFunction File ...
.................
====================================================
SMS2: Execution Finished ...
====================================================
Wall time:
26 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/13/08.567
Zone: +0200
SMS2: Execution complete.
*******************************************************************************
* RUN RHFS2 FOR 2s_3 *
* OUTPUT FILE: 2s_3.ch, 2s_3.choffd *
*******************************************************************************
>>rhfs3
====================================================
RHFS2: Execution Begins ...
====================================================
THIS VERSION COMPUTES GJ FACTORS
ANGULAR DATA, IF AVAILABLE, ARE READ FROM FILE
Default settings?
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 35
>>y
Name of state
>>2s_3
Mixing coefficients from a CI calc.?
>>y
NPLANTS: 215 590 214 54
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 79 relativistic CSFs;
... load complete;
Loading Radial WaveFunction File ...
nelec = 3
ncftot = 79
nw = 9
nblock = 1
block ncf nev 2j+1 parity
1 79 1 2 1
Angular file not available
====================================================
RHFS2: Execution Finished ...
====================================================
Wall time:
34 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/14/13.820
Zone: +0200
RHFS2: Execution complete.
*******************************************************************************
* RUN RHFS2 FOR 2p_3 *
* OUTPUT FILE: 2p_3.ch, 2p_3.choffd *
*******************************************************************************
>>rhfs3
====================================================
RHFS2: Execution Begins ...
====================================================
THIS VERSION COMPUTES GJ FACTORS
ANGULAR DATA, IF AVAILABLE, ARE READ FROM FILE
Default settings?
>>y
Name of state
>>2p_3
36 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
Mixing coefficients from a CI calc.?
>>y
NPLANTS: 215 590 214 54
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 186 relativistic CSFs;
... load complete;
Loading Radial WaveFunction File ...
nelec = 3
ncftot = 186
nw = 9
nblock = 2
block ncf nev 2j+1 parity
1 76 1 2 -1
2 110 1 4 -1
Column 100 complete;
====================================================
RHFS2: Execution Finished ...
====================================================
Wall time:
5 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/15/42.608
Zone: +0200
RHFS2: Execution complete.
*******************************************************************************
* RUN BIOTRA3 FOR 2s_3 AND 2p_3 TO TRANSFORM WAVE FUNCTIONS *
* OUTPUT FILES: 2s_3.cbm, 2s_3.bw, 2p_3.cbm, 2p_3.bw *
*******************************************************************************
>>biotra3
====================================================
BIOTRA3: Execution Begins ...
====================================================
Default settings?
>>y
Input from a CI calculation?
>>y
Name of the Initial state
>>2s_3
Name of the Final state
>>2p_3
Transformation of all J symmetries?
>>y
2.1. FIRST EXAMPLE: 1S22S2SAND 1S22P2PIN LI I 37
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 79 relativistic CSFs;
... load complete;
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 186 relativistic CSFs;
... load complete;
.......
====================================================
BIOTRA3: Execution Finished ...
====================================================
Wall time:
31 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/17/00.136
Zone: +0200
BIOTRA3: Execution complete.
*******************************************************************************
* RUN BIOSCL3 FOR 2s_3 and 2p_3 TO COMPUTE TRANSITION PARAMETERS *
* OUTPUT FILE: 2s_3.2p_3.ct *
*******************************************************************************
>>bioscl3
====================================================
BIOSCL3: Execution Begins ...
====================================================
Input from a CI calculation?
>>y
Generate debug output?
>>n
Name of the Initial state
>>2s_3
Name of the Final state
>>2p_3
MRGCSL: Execution begins ...
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 79 relativistic CSFs;
... load complete;
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
38 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
There are 186 relativistic CSFs;
... load complete;
1 s
2 s
2 p-
2 p
3 s
3 p-
3 p
3 d-
3 d
1
79
2
76 186
Loading Configuration Symmetry List File ...
there are 9 relativistic subshells;
there are 265 relativistic CSFs;
... load complete;
Enter the list of transition specifications
e.g., E1,M2 or E1 M2 or E1;M2 :
>>E1
.................
====================================================
BIOSCL3: Execution Finished ...
====================================================
Wall time:
54 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/18/45.036
Zone: +0200
BIOSCL3: Execution complete.
2.2 Second example: 1s22s2p3P0,1,2,1P1in B II
The second example is 1s22s2p3P0,1,2,1P1in B II.
Overview
1. Define nuclear data
2. Generate configuration list containing 4 CSFs belonging to 1s22s2p1,3P
3. Perform angular integration
4. Perform HF calculation
5. Convert HF orbitals to relativistic orbitals. We do not need to run erwf since all orbitals
have been estimated
2.2. SECOND EXAMPLE: 1S22S2P3P0,1,2,1P1IN B II 39
6. Perform self-consistent field calculation on the weighted average (EOL) on the state belonging
to 1s22s2p1,3P
7. Save output to 2s2p_DF
8. Transform from jj- to LSJ-coupling
9. Run rlevels to view energy separations.
Program input
In the test-runs input is marked by >> and >>3, for example, indicate that the user should input
3 and then strike the return key. When >> is followed by blanks just strike the return key.
*******************************************************************************
* RUN ISO TO GENERATE NUCLEAR DATA *
* OUTPUT FILE: isodata *
*******************************************************************************
>>iso
Enter the atomic number:
>>5
Enter the mass number (0 if the nucleus is to be modelled as a point source:
>>11
The default root mean squared radius is 2.42924735571595 fm;
the default nuclear skin thickness is 2.30000000000000 fm;
Revise these values?
>>n
Enter the mass of the neutral atom (in amu) (0 if the nucleus is to be static):
>>10.81
Enter the nuclear spin quantum number (I) (in units of h / 2 pi):
>>1.5
Enter the nuclear dipole moment (in nuclear magnetons):
>>2.6886489
Enter the nuclear quadrupole moment (in barns):
>>1
*******************************************************************************
* RUN JJGEN TO GENERATE CONFIGURATION LIST FOR 1P_1 AND 3P_0,1,2 *
* WITH FOUR CSFs: 2s2p- J=0, 2s2p- J=1, 2s2p J=1, 2s2p J = 2 *
* OUTPUT FILES: clist.out, clist.log *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>2
Highest orbital angular momentum, l? (s..p)
40 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
>>p
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..2)
>>2
Predefine open, closed or no core? (o/c/*)
>>
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>1
Number of electrons in 2p? (0..6)
>>1
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>0,4
Number of excitations = ? (0..4)
>>0
4 configuration states have been generated.
4 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp clist.log 2s2p_DF.log
>>cp clist.out rcsl.inp
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
3 blocks were found
nb J/P ncf
1 0- 1
2 1- 2
3 2- 1
*******************************************************************************
* COPY FILES *
*******************************************************************************
2.2. SECOND EXAMPLE: 1S22S2P3P0,1,2,1P1IN B II 41
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
>>mcp3
====================================================
MCP3: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Block 1 , ncf = 1
Block 2 , ncf = 2
Block 3 , ncf = 1
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
.................
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
9 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/28/23.256
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN HF PROGRAM TO GENERATE NON-RELATIVISTIC RADIAL ORBITALS *
* THAT CAN BE CONVERTED TO RELATIVISTIC ORBITALS *
* OUTPUT FILE: wfn.out *
*******************************************************************************
>>HF
=============================
HARTREE-FOCK.96
=============================
THE DIMENSIONS FOR THE CURRENT VERSION ARE:
NWF= 20 NO=220
42 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
START OF CASE
=============
Enter ATOM,TERM,Z
Examples: O,3P,8. or Oxygen,AV,8.
>>B,AV,5.
List the CLOSED shells in the fields indicated (blank line if none)
... ... ... ... ... ... ... ... etc.
>> 1s (Note that the closed shells should be entered right-centered with
respect to the dots on the line above!!!)
Enter electrons outside CLOSED shells (blank line if none)
Example: 2s(1)2p(3)
>>2s(1)2p(1)
There are 3 orbitals as follows:
1s 2s 2p
Orbitals to be varied: ALL/NONE/=i (last i)/comma delimited list/H
>>all
Default electron parameters ? (Y/N/H)
>>y
Default values for remaining parameters? (Y/N/H)
>>y
WEAK ORTHOGONALIZATION DURING THE SCF CYCLE= T
SCF CONVERGENCE TOLERANCE (FUNCTIONS) = 1.00D-08
NUMBER OF POINTS IN THE MAXIMUM RANGE = 220
ITERATION NUMBER 1
----------------
................
ITERATION NUMBER 6
----------------
SCF CONVERGENCE CRITERIA (SCFTOL*SQRT(Z*NWF)) = 1.2D-06
C( 1s 2s) = 0.00000 V( 1s 2s) = -7.06535 EPS = 0.000000
E( 2s 1s) = 0.02654 E( 1s 2s) = 0.01327
EL ED AZ NORM DPM
1s 16.3418222 20.8332819 1.0000000 1.93D-08
2s 1.8579695 4.7336947 1.0000000 1.38D-08
2p 1.4015370 4.0799511 1.0000000 1.74D-08
2.2. SECOND EXAMPLE: 1S22S2P3P0,1,2,1P1IN B II 43
< 1s| 2s>= 8.0D-09
TOTAL ENERGY (a.u.)
----- ------
Non-Relativistic -24.06678870 Kinetic 24.06678852
Relativistic Shift -0.00587815 Potential -48.13357722
Relativistic -24.07266685 Ratio -2.000000008
Additional parameters ? (Y/N/H)
>>n
Do you wish to continue along the sequence ?
>>n
END OF CASE
===========
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp wfn.out wfn.inp
*******************************************************************************
* RUN MCHFMCDF TO CONVERT NON-RELATIVISTIC RADIAL ORBITALS TO *
* RELATIVISTIC ONES *
* OUTPUT FILE: rwfn.out *
*******************************************************************************
>>mchfmcdf
===============
MCHF to MCDF
===============
Input: wfn.inp
Output: rwfn.out
*******************************************************************************
* COPY FILES *
* WE DONT NEED TO INVOKE ERWF SINCE ALL ORBIATALS HAVE BEEN ESTIMATED *
*******************************************************************************
>>cp rwfn.out rwfn.inp
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
44 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
* NOTE: ORBITALS BUILDING REFERENCE STATES ARE REQUIRED TO HAVE *
* THE CORRECT NUMBER OF NODES. THEY ARE REFERRED TO AS SPECTROSCOPIC *
* ORBITALS. IN THIS RUN WE VARY 1s, 2s, 2p AND THEY ARE ALL *
* SPECTROSCOPIC. WE CAN USE WILD CARDS FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
Loading CSL File for ALL blocks
There are 4 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 3 blocks (block J/Parity NCF):
1 0- 1 2 1- 2 3 2- 1
Enter ASF serial numbers for each block
Block 1 ncf = 1 id = 0-
>>1
Block 2 ncf = 2 id = 1-
>>1,2
Block 3 ncf = 1 id = 2-
>>1
level weights (1 equal; 5 standard; 9 user)
>>5
Radial functions
1s 2s 2p- 2p
Enter orbitals to be varied (Updating order)
>>*
Which of these are spectroscopic orbitals?
>>*
Enter the maximum number of SCF cycles:
>>100
...................
Generalised occupation numbers:
2.0000D+00 1.0000D+00 3.3333D-01 6.6667D-01
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
8 seconds
Finish Date and Time:
2.2. SECOND EXAMPLE: 1S22S2P3P0,1,2,1P1IN B II 45
Date (Yr/Mon/Day): 2011/09/21
Time (Hr/Min/Sec): 00/32/20.913
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2s2p_DF
Created 2s2p_DF.w, 2s2p_DF.c, 2s2p_DF.m and 2s2p_DF.sum
*******************************************************************************
* RUN JJ2LSJ TO GET THE LSJ-COMPOSITION *
* OUTPUT FILE: 2s2p_DF.lsj.lbl *
*******************************************************************************
>>jj2lsj
====================================================
jj2lsj: Execution Begins ...
====================================================
jj2lsj: Transformation of ASFs from a jj-coupled CSF basis
into an LS-coupled CSF basis (Fortran 95 version)
(C) Copyright by G. Gaigalas and Ch. F. Fischer,
NIST (2011).
Name of state
>>2s2p_DF
Loading Configuration Symmetry List File ...
There are 4 relativistic subshells;
There are 4 relativistic CSFs;
... load complete;
Mixing coefficients from a CI calc.?
>>n
nelec = 4
ncftot = 4
nw = 4
nblock = 3
block ncf nev 2j+1 parity
1 1 1 1 -1
2 2 2 3 -1
3 1 1 5 -1
Default settings? (y/n)
>>y
...............
====================================================
jj2lsj: Execution Finished ...
46 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
====================================================
Wall time:
7 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 08/58/10.774
Zone: +0200
jj2lsj: Execution complete.
*******************************************************************************
* RUN RLEVELS TO VIEW ENERGIES AND ENERGY SEPARATIONS *
* NOTE: SINCE LSJ-INFORMATION NOW IS AVAILABLE OUTPUT LABELS *
* WILL BE IN LSJ-COUPLING *
*******************************************************************************
>> rlevels
You can also use command-line option:
%rlevels file1 file2 (wild cards allowed)...
Now, carry on
Type the input file name, one for each line (NULL to terminate)
File name ?
>>2s2p_DF.m
File name ?
>>
nblock = 3 ncftot = 4 nw = 4 nelec = 4
Energy levels for ...
Rydberg constant is 109737.31534
Splitting is the energy difference with the lower neighbor
------------------------------------------------------------------------------------------
No Pos J Parity Energy Total Levels Splitting Configuration
(a.u.) (cm^-1) (cm^-1)
------------------------------------------------------------------------------------------
1 1 0 - -24.1270877 0.00 0.00 1s(2).2s_2S.2p_3P
2 1 1 - -24.1270404 10.39 10.39 1s(2).2s_2S.2p_3P
3 1 2 - -24.1269457 31.17 20.79 1s(2).2s_2S.2p_3P
4 2 1 - -23.9154061 46458.75 46427.58 1s(2).2s_2S.2p_1P
------------------------------------------------------------------------------------------
2.3 Third example: 2s22p3and 2p5in Si VIII
The third example is 2s22p3and 2p5in Si VIII.
Overview
1. Define nuclear data
2. Generate configuration list belonging to 2s22p3and 2p5
3. Perform angular integration
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 47
4. Generate initial estimates of radial orbitals
5. Perform self-consistent field calculation on the weighted average (EOL) of all states belonging
to 2s22p3and 2p5(there are 2 states with J= 1/2, 4 states with J= 3/2and 1 state with
J= 5/2, see NIST Tables)
6. Save output to 2s22p3_2p5_DF
7. Generate CSF list from SD-excitations from 2s22p3and 2p5to n= 3
8. Run jjreduce3 to extract CSFs that interacts with CSFs belonging to 2s22p3and 2p5
9. Perform angular integration
10. Generate initial estimates of radial orbitals
11. Perform self-consistent field calculation on the weighted average (EOL) of all states belonging
to 2s22p3and 2p5
12. Save output to 2s22p3_2p5_3
13. Perform CI calculations in which Breit and QED effects are added.
14. Transform from jj- to LSJ-coupling
15. Run rlevels to view energy separations.
16. Compute the M1 transition rates from the CI wave functions. Biorthogonal transformation
not needed in this case since the states are described using the same orthogonal orbital set.
Copy files and run the transition program.
Program input
In the test-runs input is marked by >> and >>3, for example, indicate that the user should input
3 and then strike the return key. When >> is followed by blanks just strike the return key.
*******************************************************************************
* RUN ISO TO GENERATE NUCLEAR DATA *
* OUTPUT FILE: isodata *
*******************************************************************************
>>iso
Enter the atomic number:
>>14
Enter the mass number (0 if the nucleus is to be modelled as a point source:
>>28
The default root mean squared radius is 3.1085883804880532 fm;
the default nuclear skin thickness is 2.2999999999999998 fm;
Revise these values?
>>n
Enter the mass of the neutral atom (in amu) (0 if the nucleus is to be static):
>>27.9769271
Enter the nuclear spin quantum number (I) (in units of h / 2 pi):
>>0
Enter the nuclear dipole moment (in nuclear magnetons):
>>0
Enter the nuclear quadrupole moment (in barns):
>>0
48 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
*******************************************************************************
* RUN JJGEN TO GENERATE CONFIGURATION LIST FOR ALL STATES OF *
* 2s(2)2p(3) + 2p(5) *
* OUTPUT FILES: clist.out, clist.log *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>2
Highest orbital angular momentum, l? (s..p)
>>p
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..2)
>>2
Predefine open, closed or no core? (o/c/*)
>>
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>2
Number of electrons in 2p? (0..6)
>>3
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,5
Number of excitations = ? (0..7)
>>0
5 configuration states have been generated.
5 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>y
Highest n-number? (1..15)
>>2
Highest l-number? (s..p)
>>p
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..2)
>>2
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 49
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>0
Number of electrons in 2p? (0..6)
>>5
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,5
Number of excitations = ? (0..7)
>>0
2 configuration states have been generated.
7 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
* NOTE THAT WE COPY AN UNSPLIT FILE TO MRLIST FOR FUTURE USE *
* TOGETHER WITH JJREDUCE *
*******************************************************************************
>>cp clist.log 2s22p3_2p5_DF.log
>>cp clist.out rcsl.inp
>>cp clist.out mrlist
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
3 blocks were found
nb J/P ncf
1 1/2- 2
2 3/2- 4
3 5/2- 1
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
50 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
>>mcp3
====================================================
MCP3: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Block 1 , ncf = 2
Block 2 , ncf = 4
Block 3 , ncf = 1
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
0 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 09/15/43.865
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN ERWF TO GENERATE INITIAL ESTIMATES FOR RADIAL FUNCTIONS *
* OUTPUT FILE: rwfn.inp *
*******************************************************************************
>>erwf
ERWF: Execution begins ...
Estimating Relativistic Wave Functions: Output file = rwfn.inp
Default settings ?
>>y
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
The following subshell radial wavefunctions remain to be estimated:
1s 2s 2p- 2p
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>3
Enter the list of relativistic subshells:
*
***** Screening parameters ******
1s 0.00
2s 0.00
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 51
2p- 0.00
2p 0.00
All required subshell radial wavefunctions have been estimated:
Shell e p0 gamma P(2) Q(2) MTP SRC
1s 0.9826D+02 0.1033D+03 0.1000D+01 0.1153D-04 -0.5903D-06 275 Hyd
2s 0.2458D+02 0.3670D+02 0.1000D+01 0.4094D-05 -0.2097D-06 291 Hyd
2p- 0.2458D+02 0.8338D-01 0.1000D+01 0.9303D-08 0.1816D-06 291 Hyd
2p 0.2452D+02 0.1492D+03 0.2000D+01 0.1636D-11 -0.4182D-13 291 Hyd
ERWF: Execution complete.
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
* NOTE: FOR CORRELATION ORBITALS THERE ARE NO RESTRICTIONS ON THE *
* NUMBER OF NODES, I.E. THEY ARE NOT SPECTROSCOPIC. IN THIS RUN WE *
* VARY 1s,2s,2p ALL OF THESE ARE SPECTROSCOPIC. WE CAN USE WILD CARDS *
* FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 4 relativistic subshells;
Loading CSL File for ALL blocks
There are 7 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 3 blocks (block J/Parity NCF):
1 1/2- 2 2 3/2- 4 3 5/2- 1
Enter ASF serial numbers for each block
Block 1 ncf = 2 id = 1/2-
>>1,2
Block 2 ncf = 4 id = 3/2-
>>1,2,3,4
Block 3 ncf = 1 id = 5/2-
>>1
level weights (1 equal; 5 standard; 9 user)
>>5
Radial functions
1s 2s 2p- 2p
Enter orbitals to be varied (Updating order)
>>*
Which of these are spectroscopic orbitals?
>>*
52 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
Enter the maximum number of SCF cycles:
>>100
..................
Generalised occupation numbers:
2.0000D+00 1.5385D+00 1.1538D+00 2.3077D+00
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
53 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 09/20/21.495
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2s22p3_2p5_DF
Created 2s22p3_2p5_DF.w, 2s22p3_2p5_DF.c, 2s22p3_2p5_DF.m and 2s22p3_2p5_DF.sum
*******************************************************************************
* RUN JJGEN TO GENERATE LIST OBTAINED BY SD EXCITATIONS FROM *
* 2s(2)2p(3) + 2p(5) TO n = 3 *
* OUTPUT FILES: clist.out, clist.log *
*******************************************************************************
>>jjgen
Version 2
* : new list
e : expand existing list
q : quit
>>
Default, reverse, symmetry or user specified ordering? (*/r/s/u)
>>
Highest principal quantum number, n? (1..15)
>>3
Highest orbital angular momentum, l? (s..d)
>>d
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..3)
>>2
Predefine open, closed or no core? (o/c/*)
>>
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 53
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>2
Number of electrons in 2p? (0..6)
>>3
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,5
Number of excitations = ? (0..7)
>>2
1968 configuration states have been generated.
1968 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>y
Highest n-number? (1..15)
>>3
Highest l-number? (s..d)
>>d
Are all these nl-subshells active? (n/*)
>>
Limitations on population of n-subshells? (y/*)
>>
Highest n-number in reference configuration? (1..3)
>>2
Number of electrons in 1s? (0..2)
>>2
Number of electrons in 2s? (0..2)
>>0
Number of electrons in 2p? (0..6)
>>5
Resulting 2*J-number? lower, higher (J=1 -> 2*J=2 etc.)
>>1,5
Number of excitations = ? (0..7)
>>2
751 configuration states have been generated.
2356 configuration states in the final list.
You have the possibility to generate another list
This list must have the same 2*J values as
previous lists of the same parity
Generate another list? (y/*)
>>
The merged file is called clist.out.
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp clist.out rcsl.inp
54 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
*******************************************************************************
* RUN JJREDUCE3 PROGRAM TO DETERMINE WHICH OF THE CSFs IN THE LIST *
* rcsl.inp LIST THAT INTERACTS WITH THE CSFs IN THE mrlist *
* THE INTERACTING CSFs ARE WRITTEN TO rcsl.out *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jjreduce3
JJREDUCE: Execution begins ...
Default settings?
>>y
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 2356 relativistic CSFs;
... load complete;
JJREDUCE: Execution complete.
The reduced list is in rcsl.out
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN JSPLIT *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>jsplit
Perform duplicate check and remove them ?
>>n
3 blocks were found
nb J/P ncf
1 1/2- 274
2 3/2- 590
3 5/2- 300
*******************************************************************************
* COPY FILES *
*******************************************************************************
>>cp rcsl.out rcsl.inp
*******************************************************************************
* RUN MCP3 TO GENERATE ENERGY EXPRESSION *
* OUTPUT FILES: mcp.xxx *
*******************************************************************************
>>mcp3
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 55
====================================================
MCP3: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Block 1 , ncf = 274
Block 2 , ncf = 590
Block 3 , ncf = 300
................
====================================================
MCP3: Execution Finished ...
====================================================
Wall time:
1 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 09/38/08.109
Zone: +0200
MCP3: Execution complete.
*******************************************************************************
* RUN ERWF TO GENERATE INITIAL ESTIMATES FOR RADIAL FUNCTIONS *
* OUTPUT FILE: rwfn.inp *
*******************************************************************************
>>erwf
ERWF: Execution begins ...
Estimating Relativistic Wave Functions: Output file = rwfn.inp
Default settings ?
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
The following subshell radial wavefunctions remain to be estimated:
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>1
Enter the file name (Null then "rwfn.out")
>>2s22p3_2p5_DF.w
Enter the list of relativistic subshells:
>>*
The following subshell radial wavefunctions remain to be estimated:
3s 3p- 3p 3d- 3d
56 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
Read subshell radial wavefunctions. Choose one below
1 -- GRASP92 File
2 -- Thomas-Fermi
3 -- Screened Hydrogenic
>>3
Enter the list of relativistic subshells:
>>*
***** Screening parameters ******
3s 0.00
3p- 0.00
3p 0.00
3d- 0.00
3d 0.00
All required subshell radial wavefunctions have been estimated:
Shell e p0 gamma P(2) Q(2) MTP SRC
1s 0.7698D+02 0.1056D+03 0.1000D+01 0.1082D-04 -0.9224D-09 294 2s2
2s 0.1236D+02 0.3088D+02 0.1000D+01 0.3167D-05 -0.3599D-09 298 2s2
2p- 0.1089D+02 0.5761D-01 0.1000D+01 0.1477D-10 0.1157D-06 299 2s2
2p 0.1086D+02 0.1007D+03 0.2000D+01 0.1059D-11 -0.1204D-15 300 2s2
3s 0.1092D+02 0.1998D+02 0.1000D+01 0.2229D-05 -0.1142D-06 301 Hyd
3p- 0.1092D+02 0.4942D-01 0.1000D+01 0.5514D-08 0.1076D-06 301 Hyd
3p 0.1090D+02 0.8855D+02 0.2000D+01 0.9710D-12 -0.2482D-13 301 Hyd
3d- 0.1090D+02 0.4311D-01 0.2000D+01 0.4729D-15 0.1850D-13 300 Hyd
3d 0.1089D+02 0.9250D+02 0.3000D+01 0.1026D-18 -0.1747D-20 300 Hyd
ERWF: Execution complete.
*******************************************************************************
* RUN RSCF2 TO OBTAIN SELF CONSISTENT SOLUTIONS *
* OUTPUT FILES: rwfn.out, rmix.out, rscf.sum *
* *
* NOTE: FOR CORRELATION ORBITALS THERE ARE NO RESTRICTIONS ON THE *
* NUMBER OF NODES, I.E. THEY ARE NOT SPECTROSCOPIC. IN THIS RUN WE *
* VARY THE CORRELATION ORBITALS 3s,3p, 3d. NONE OF THESE ARE *
* SPECTROSCOPIC. WE CAN USE WILD CARDS FOR SPECIFYING ORBITALS *
*******************************************************************************
>>rscf2
====================================================
RSCF2: Execution Begins ...
====================================================
Default settings? (y/n)
>>y
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Loading CSL File for ALL blocks
There are 1164 relativistic CSFs... load complete;
Loading Radial WaveFunction File ...
(E)OL type calculation? (y/n)
>>y
There are 3 blocks (block J/Parity NCF):
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 57
1 1/2- 274 2 3/2- 590 3 5/2- 300
Enter ASF serial numbers for each block
Block 1 ncf = 274 id = 1/2-
>>1,2
Block 2 ncf = 590 id = 3/2-
>>1,2,3,4
Block 3 ncf = 300 id = 5/2-
>>1
level weights (1 equal; 5 standard; 9 user)
>>5
Radial functions
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
Enter orbitals to be varied (Updating order)
>>3*
Which of these are spectroscopic orbitals?
>>
Enter the maximum number of SCF cycles:
>>100
......................
Generalised occupation numbers:
1.9998D+00 1.5371D+00 1.1513D+00 2.3027D+00 5.8239D-04 4.8570D-04
9.6735D-04 2.8070D-03 4.2144D-03
====================================================
RSCF2: Execution Finished ...
====================================================
Wall time:
195 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 09/44/11.007
Zone: +0200
RSCF2: Execution complete.
*******************************************************************************
* RUN RSAVE TO SAVE OUTPUT FILES *
*******************************************************************************
>>rsave 2s22p3_2p5_3
Created 2s22p3_2p5_3.w, 2s22p3_2p5_3.c, 2s22p3_2p5_3.m and 2s22p3_2p5_3.sum
*******************************************************************************
* RUN RCI3 TO INCLUDE BREIT AND QED EFFECTS *
* OUTPUT FILE: 2s22p3_2p5_3.cm, 2s22p3_2p5_3.csum *
* *
* THE TRANSVERSE PHOTON FREQUENCIES CAN BE SET TO THE LOW FREQUENCY *
* LIMIT. RECOMMENDED IN CASES WHERE YOU HAVE CORRELATION ORBITALS *
* THE SELF ENERGY CORRECTION MAY FAIL FOR CORRELATION ORBITALS WITH *
* HIGH N. *
58 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
*******************************************************************************
>>rci3
====================================================
RCI3: Execution Begins ...
====================================================
Default settings?
>>y
Name of state:
>>2s22p3_2p5_3
isofile = isodata
name = 2s22p3_2p5_3
Calling CHKPLT...
Calling SETDBG...
Calling SETMC...
Calling SETCON...
Calling SETSUM...
Calling setcsl...
Block 1 , ncf = 274
Block 2 , ncf = 590
Block 3 , ncf = 300
Loading CSL file ... Header only
There are/is 9 relativistic subshells;
Calling SETRES...
Calling SETISO ...
Include contribution of H (Transverse)?
>>y
Modify all transverse photon frequencies?
>>y
Enter the scale factor:
>>1.d-6
Include H (Vacuum Polarisation)?
>>y
Include H (Normal Mass Shift)?
>>n
Include H (Specific Mass Shift)?
>>n
Estimate self-energy?
>>y
Largest n quantum number for including self-energy for orbital
n should be less or equal 8
>>3
Loading Radial WaveFunction File ...
Calling SETMIX...
There are 3 blocks (block J/Parity NCF):
1 1/2- 274 2 3/2- 590 3 5/2- 300
Enter ASF serial numbers for each block
Block 1 ncf = 274 id = 1/2-
>>1,2
Block 2 ncf = 590 id = 3/2-
>>1,2,3,4
Block 3 ncf = 300 id = 5/2-
>1
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 59
...........................
Finish time, Statistics
====================================================
RCI3: Execution Finished ...
====================================================
Wall time:
233 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/18
Time (Hr/Min/Sec): 17/13/28.331
Zone: +0200
RCI3: Execution complete.
*******************************************************************************
* RUN JJ2LSJ TO GET THE LSJ-COMPOSITION *
* OUTPUT FILE: 2s22p3_2p5_3.lsj.lbl *
*******************************************************************************
>>jj2lsj
====================================================
jj2lsj: Execution Begins ...
====================================================
jj2lsj: Transformation of ASFs from a jj-coupled CSF basis
into an LS-coupled CSF basis (Fortran 95 version)
(C) Copyright by G. Gaigalas and Ch. F. Fischer,
NIST (2011).
Name of state
>>2s22p3_2p5_3
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 1164 relativistic CSFs;
... load complete;
Mixing coefficients from a CI calc.?
>>y
nelec = 7
ncftot = 1164
nw = 9
nblock = 3
block ncf nev 2j+1 parity
1 274 2 2 -1
2 590 4 4 -1
3 300 1 6 -1
Default settings? (y/n)
60 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
>>y
............
====================================================
jj2lsj: Execution Finished ...
====================================================
Wall time:
58 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 09/52/21.594
Zone: +0200
jj2lsj: Execution complete.
*******************************************************************************
* RUN RLEVELS TO VIEW ENERGIES AND ENERGY SEPARATIONS *
* NOTE: SINCE LSJ-INFORMATION NOW IS AVAILABLE OUTPUT LABELS *
* WILL BE IN LSJ-COUPLING *
*******************************************************************************
>>rlevels
You can also use command-line option:
%rlevels file1 file2 (wild cards allowed)...
Now, carry on
Type the input file name, one for each line (NULL to terminate)
File name ?
>>2s22p3_2p5_3.cm
File name ?
>>
nblock = 3 ncftot = 1164 nw = 9 nelec = 7
Energy levels for ...
Rydberg constant is 109737.31534
Splitting is the energy difference with the lower neighbor
------------------------------------------------------------------------------------------
No Pos J Parity Energy Total Levels Splitting Configuration
(a.u.) (cm^-1) (cm^-1)
------------------------------------------------------------------------------------------
1 1 3/2 - -263.2797816 0.00 0.00 1s(2).2s(2).2p(3)4S3_4S
2 2 3/2 - -262.9550531 71269.67 71269.67 1s(2).2s(2).2p(3)2D3_2D
3 1 5/2 - -262.9538181 71540.71 271.04 1s(2).2s(2).2p(3)2D3_2D
4 1 1/2 - -262.7906314 107356.05 35815.34 1s(2).2s(2).2p(3)2P1_2P
5 3 3/2 - -262.7882718 107873.93 517.89 1s(2).2s(2).2p(3)2P1_2P
6 4 3/2 - -259.5241162 824273.28 716399.35 1s(2).2p(5)_2P
7 2 1/2 - -259.4979382 830018.67 5745.39 1s(2).2p(5)_2P
------------------------------------------------------------------------------------------
*******************************************************************************
2.3. THIRD EXAMPLE: 2S22P3AND 2P5IN SI VIII 61
* WE WILL NOW COMPUTE THE M1 TRANSITION RATES *
* IN THIS CASE THE INITIAL AND FINAL STATE FILES ARE THE SAME *
* AND WE DO NOT NEED TO PERFORM A BIORTHOGONAL TRANSFORMATION *
* USING BIOTRA. JUST COPY FILES TO NAME.bw AND NAME.cbm *
*******************************************************************************
>>cp 2s22p3_2p5_3.w 2s22p3_2p5_3.bw
>>cp 2s22p3_2p5_3.cm 2s22p3_2p5_3.cbm
*******************************************************************************
* RUN BIOSCL3 FOR 2s22p3_2p5_3 TO COMPUTE M1 TRANSITION PARAMETERS *
* OUTPUT FILE: 2s22p3_2p5_3.2s22p3_2p5_3.ct, *
* 2s22p3_2p5_3.2s22p3_2p5_3.ct.lsj *
* *
* NOTE THAT THE LATTER OUTPUT FILE HAS ALL THE LABELS IN LSJ- *
* COUPLING WHICH IS VERY CONVENIENT *
* *
* PLEASE OBSERVE!! IF WE ARE GOING TO RUN BIOSCL FOR AN RCI WAVE *
* FUNCTIONS THEN THE LSJ-INFORMATION SHOULD BE AVAILABLE FOR THE SAME *
* WAVE FUNCTION. IF FOR EXAMPLE THE LSJ-INFORMATION FROM JJ2LSJ IS *
* IS AVAILABLE FROM AN RSCF RUN AND WE RUN BIOSCL ON THE RCI WAVE *
* FUNCTION THEN BIOSCL3 WILL STOP. In THIS CASE JUST RERUN JJ2LSJ *
* FOR THE RCI WAVE FUNCTION AND START BIOSCL AGAIN FOR THE SAME *
* WAVE FUNCTION. IN OUR EXAMPLE JJ2LJS AND BIOSCL3 ARE RUN FOR RCI *
* WAVE FUNCTIONS AND EVERYTHING IS OK. *
*******************************************************************************
>>bioscl3
====================================================
BIOSCL3: Execution Begins ...
====================================================
Input from a CI calculation?
>>y
Generate debug output?
>>n
Name of the Initial state
>>2s22p3_2p5_3
Name of the Final state
>>2s22p3_2p5_3
MRGCSL: Execution begins ...
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 1164 relativistic CSFs;
... load complete;
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 1164 relativistic CSFs;
... load complete;
1 s
62 CHAPTER 2. RUNNING THE APPLICATION PROGRAMS
2 s
2 p-
2 p
3 s
3 p-
3 p
3 d-
3 d
3
274 864 1164
3
274 864 1164
Loading Configuration Symmetry List File ...
there are 9 relativistic subshells;
1
2 2
there are 2328 relativistic CSFs;
... load complete;
Enter the list of transition specifications
e.g., E1,M2 or E1 M2 or E1;M2 :
>>M1
M1 transitions only between levels with different J?
>>n
.......................
====================================================
BIOSCL3: Execution Finished ...
====================================================
Wall time:
88 seconds
Finish Date and Time:
Date (Yr/Mon/Day): 2012/07/17
Time (Hr/Min/Sec): 10/02/34.969
Zone: +0200
BIOSCL3: Execution complete.
Chapter 3
Running the tools
3.1 Extracting and condensing
We first demonstrate how to extract mixing coefficients from a wave functions and also how to
condense an expansion.
Overview
1. Extract mixing coefficients for the CI wave function 2p_3
2. Condense the CI wave function 2p_3. The files containing the condensed configuration list
and the mixing coefficients will have letter D appended in their names.
Program input
In the test-runs input is marked by >> and >>3, for example, indicate that the user should input
3 and then strike the return key. When >> is followed by blanks just strike the return key.
*******************************************************************************
* RUN EXTMIX TO EXTRACT MIXING COEFFICIENTS FOR 2p_3 *
* OUTPUT FILE: rcsl.out *
*******************************************************************************
>>extmix
extmix - Extract mixing coefficients and CSF
Files to be read :
<name>.c, <name>.m / <name>.cm
Files to be written :
rcsl.out, screen output
Enter the file <name>
>>2p_3
Mixing coefficients from CI or RSCF calc. ?
a -- CI ; b -- RSCF
>>a
Enter the cut-off value for the coefficients [0--1]
>>0.01
Sort the eigen vector components ? (y/n)
>>y
63
64 CHAPTER 3. RUNNING THE TOOLS
nblock = 2 ncftot = 186 nw = 9 nelec = 3
===========================================================================
nb = 1 ncfblk = 76 nevblk = 1 2J+1 = 2 parity = -1
nb = 1 ncfblk = 76 nevblk = 1 2J+1 = 2 parity = -1
===========================================================================
Average Energy = 8.4326214447012884 ncf_reduced = 5
Energy = -7.4042610306325809 Coefficients and CSF :
1 0.99844919818571742
1s ( 2) 2p-( 1)
1/2
1/2-
2 -3.43284268055015288E-002
2p-( 1) 3s ( 2)
1/2
1/2-
3 3.25958079398396758E-002
2p-( 1) 3p ( 2)
1/2 0
1/2-
4 2.30630117289014891E-002
2p-( 1) 3p-( 2)
1/2
1/2-
5 1.07509560347749163E-002
2s ( 1) 2p-( 1) 3s ( 1)
1/2 1/2 1/2
1 1/2-
===========================================================================
nb = 2 ncfblk = 110 nevblk = 1 2J+1 = 4 parity = -1
nb = 2 ncfblk = 110 nevblk = 1 2J+1 = 4 parity = -1
===========================================================================
Average Energy = 9.6081891369267218 ncf_reduced = 4
Energy = -7.4042597183271539 Coefficients and CSF :
1 0.99844920108615898
1s ( 2) 2p ( 1)
3/2
3/2-
2 -3.43284268104856322E-002
2p ( 1) 3s ( 2)
3/2
3/2-
3 3.25895578847494038E-002
2p ( 1) 3p ( 2)
3/2 0
3/2-
4 2.30718743933811983E-002
2p ( 1) 3p-( 2)
3/2
3/2-
3.2. EXTRACT RADIAL ORBITALS FOR PRINTING 65
STOP Successful
*******************************************************************************
* RUN CNDENS2 TO CONDENSE THE 2p_3 EXPANSION *
* OUTPUT FILES 2p_3D.c, 2P_3D.cm *
* *
* NOTE THAT THE LETTER D INDICATES THAT CSFs HAVE BEEN DELETED *
* (WHICH AMOUNTS TO A CONDENSATION) *
*******************************************************************************
>>cndens2
Default settings?
>>y
Name of state
>>2p_3
2p_3
Mixing coefficients from a CI calc.?
>>y
2p_3.c
filnam2p_3
Loading Configuration Symmetry List File ...
There are 9 relativistic subshells;
There are 186 relativistic CSFs;
... load complete;
2
76 186
What is the value below which an
eigenvector component is to be
neglected?
>>0.001
nelec = 3
ncftoti = 186
nwi = 9
nblocki = 2
9 relativistic subshells;
22 relativistic CSFs.
CNDENS: Execution complete.
3.2 Extract radial orbitals for printing
The program plotmcdf extracts a specified orbital from the binary radial orbital file and prints
in ASCII format, in three columns, the grid, the large component, and the small component of
the orbital. The input file containing the radial orbital should have the name mcdf.w. The ASCII
output file has the name mcdf.w.dat. In this example we extract the 1sand 2porbitals from
66 CHAPTER 3. RUNNING THE TOOLS
2p_3.w. In the input the orbitals are labeled by nand l. In addition the user should supply a
number that is 1 or −1depending whether nl(j=l+ 1/2) or nl(j=l−1/2) is to be extracted. To
extract the 2p3/2orbital the input string is 2,1,1. To extract the 2p1/2orbital the input string is
2,1,-1.
Program input
In the test-runs input is marked by >> and >>3, for example, indicate that the user should input
3 and then strike the return key. When >> is followed by blanks just strike the return key.
*******************************************************************************
* COPY 2p_3.w TO mcdf.w WHICH IS THE INPUT FILE TO PLOTMCDF *
*******************************************************************************
>>cp 2p_3.w mcdf.w
*******************************************************************************
* RUN PLOTMCDF TO EXTRACT THE 1s ORBITAL *
* OUTPUT: mcdf.w.dat *
*******************************************************************************
>>plotmcdf
****** PLOTMCDF ******
Convert one orbital to ASCII form for plotting
Enter the n, l, J(1 or -1)
>>1,0,1
1 -1 2.5177395462822258 333
*******************************************************************************
* COPY mcdf.w.dat TO plot_1s.dat *
*******************************************************************************
>>cp mcdf.w.dat plot_1s.dat
*******************************************************************************
* RUN PLOTMCDF TO EXTRACT THE 2p ORBITAL *
* OUTPUT: mcdf.w.dat *
*******************************************************************************
>>plotmcdf
****** PLOTMCDF ******
Convert one orbital to ASCII form for plotting
Enter the n, l, J(1 or -1)
>>2,1,1
1 -1 2.5177395462822258 333
2 -1 0.19634308440517523 339
2 1 0.12867248391836894 344
3.2. EXTRACT RADIAL ORBITALS FOR PRINTING 67
2 -2 0.12866992751269327 344
*******************************************************************************
* COPY mcdf.w.dat TO plot_2p.dat *
*******************************************************************************
>>cp mcdf.w.dat plot_2p.dat
Given the two ASCII files it is easy to invoke a program, e.g. Matlab, for plotting, see figure 3.1.
0 5 10 15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
r in a.u.
Large components of the 1s and 2p+ orbitals in Li
1s
2p+
Figure 3.1: Plot of the large components of the 1sand 2p3/2orbitals in Li I. The plot has been
produced by editing the ASCII files.
68 CHAPTER 3. RUNNING THE TOOLS
Chapter 4
Description of output files
In this chapter we describe in detail what information can be found in the different output files
and how this information should be interpreted.
4.1 Output files from the first example
The isodata file
Below is the isodata file for the Li example.
Atomic number:
3.0000000000000000
Mass number (integer) :
7.0000000000000000
Fermi distribution parameter a:
0.52338755531043146
Fermi distribution parameter c:
1.2520789669753825
Mass of nucleus (in amu):
6.9393542602910001
Nuclear spin (I) (in units of h / 2 pi):
1.5000000000000000
Nuclear dipole moment (in nuclear magnetons):
3.2564267999999998
Nuclear quadrupole moment (in barns):
-4.00000000000000008E-002
The calculation was for 7Li with Z= 3 and M= 7. The nuclear charge distribution ρ(r)was
modeled as an extended Fermi distribution with
ρ(r) = ρ0
1 + e(r−b)/a (4.1)
The parameters aand bare set by default and depend on the mass of the isotope. In this case we
have a= 0.52338755531043146 fm and c= 1.2520789669753825 fm. At the end of the isodata
file the nuclear spin Iis displayed along with the nuclear magnetic dipole moment µin nuclear
magnetons and the nuclear quadrupole moment Qin barns.
The jjgen log file
After each jjgen run there is a log file displaying the response to the different questions. Below
is the log file 2p_3.log from the n= 3 complete active space expansion for 1s22p2P1/2,3/2.
69
70 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
Option :
Standard ordering.
3 Highest principal quantum number.
2 Highest orbital angular momentum.
T all subshells active.
F limitations on population of n-subshells.
2 highest n-number.
Predefined core:
2 number of electrons in 1 s
0 number of electrons in 2 s
1 number of electrons in 2 p
1 to 3 is the resulting term.
3 number of excitations.
F Generate another list.
We see that the highest principal quantum number for the active set was n= 3. The highest orbital
quantum number was l= 2. This corresponds to an active set of orbitals {1s, 2s, 2p, 3s, 3p, 3d}
in non-relativistic notation. All subshells are active and there is no limitations on the population
of the subshells (see write-up of the jjgen program). The highest principal quantum number for
orbitals in the reference configuration was n= 2. The reference configuration contains 2 electrons
in 1sand 1 electron in 2p, i.e. the reference configuration is 1s22p. The resulting values of 2J
range from 1 to 3, i.e. we generate CSFs that have J= 1/2and J= 3/2. The number of
excitations from the reference configuration 1s22pto the active set of orbitals is 3, i.e. we allow
SDT-excitations.
The configuration state list file
The jjgen program produces a configuration state list file. The file has a header with information
about the radial orbitals and the closed shells (core shells). After this information there is a list
of configuration state functions (CSFs). After running jsplit the configuration state functions
are ordered in blocks with specified value of J. Each block is separated by a line with asterisk.
Below is the file 2p_3.c.
Core subshells:
Peel subshells:
1s 2s 2p- 2p 3s 3p- 3p 3d- 3d
CSF(s):
1s ( 2) 2p-( 1)
1/2
1/2-
1s ( 2) 3p-( 1)
1/2
1/2-
1s ( 1) 2s ( 1) 2p ( 1)
1/2 1/2 3/2
1 1/2-
..............
3p-( 1) 3d-( 1) 3d ( 1)
1/2 3/2 5/2
2 1/2-
3p-( 1) 3d-( 2)
4.1. OUTPUT FILES FROM THE FIRST EXAMPLE 71
1/2 0
1/2-
*
1s ( 2) 2p ( 1)
3/2
3/2-
1s ( 2) 3p ( 1)
3/2
3/2-
1s ( 1) 2s ( 1) 2p ( 1)
1/2 1/2 3/2
0 3/2-
............
3p-( 1) 3d-( 1) 3d ( 1)
1/2 3/2 5/2
2 3/2-
3p-( 1) 3d-( 2)
1/2 2
3/2-
The line with core subshells is empty and in this case we have no closed core. The radial orbitals
are 1s, 2s, 2p−,2p, 3s, 3p−,3p, 3d−,3d. After the radial orbitals there are lists of CSFs arranged
in blocks. The first block of CSFs has J= 1/2. The second block has J= 3/2. An asterisk is
separating the blocks. In the file each CSF occupies three lines. On the first line the subshells
and their occupations are listed in a linear form where, for example, 1s2becomes 1s ( 2). The
second line shows the coupling of each subshell to a Jquantum number and the third line shows
how the Jquantum numbers of each subshell are coupled from left to right to a final J.
The rscf2 summary file
The self-consistent field program rscf2 produces a summary file. After running rsave this file is
saved in name.sum. Below is the summary file 2p_3.sum from the run on weighted average (EOL)
of the 1s22p2P1/2,3/2states.
There are 3 electrons in the cloud
in 186 relativistic CSFs
based on 9 relativistic subshells.
The atomic number is 3.0000000000;
the mass of the nucleus is 1.264966897439D+04 electron masses;
Fermi nucleus:
c = 2.366086344330D-05 Bohr radii,
a = 9.890591408973D-06 Bohr radii;
there are 53 tabulation points in the nucleus.
Speed of light = 137.0359990840D+00 atomic units.
Radial grid: R(I) = RNT*(exp((I-1)*H)-1), I = 1, ..., N;
RNT = 2.000000000000D-06 Bohr radii;
H = 5.000000000000D-02 Bohr radii;
N = 590;
72 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
R(1) = 0.000000000000D+00 Bohr radii;
R(2) = 1.025421927520D-07 Bohr radii;
R(N) = 1.233111896689D+07 Bohr radii.
EOL calculation.
2 levels will be optimised;
their indices are: 1, 1.
Each is assigned its statistical weight;
Radial wavefunction summary:
Self
Subshell e p0 gamma P(2) Q(2) Consistency MTP
1s 2.5177395463D+00 9.281D+00 1.00 9.517D-07 -3.781D-11 0.000D+00 333
2s 1.9634308441D-01 1.453D+00 1.00 1.489D-07 -5.918D-12 0.000D+00 339
2p- 1.2867248392D-01 5.116D-05 1.00 2.578D-14 4.793D-10 0.000D+00 344
2p 1.2866992751D-01 4.265D-01 2.00 4.485D-15 -1.782D-19 0.000D+00 344
3s 8.0600845411D+00 1.179D+01 1.00 1.507D-06 -8.686D-12 8.965D-08 338
3p- 8.7786094243D+00 2.853D-03 1.00 2.042D-12 2.677D-08 8.942D-07 342
3p 8.7823538492D+00 2.381D+01 2.00 2.508D-13 -3.787D-17 1.303D-06 342
3d- 1.6298092508D+01 8.146D-03 2.00 8.417D-19 1.565D-14 6.785D-06 336
3d 1.6306599830D+01 8.170D+01 3.00 8.809D-20 -3.503D-24 8.699D-06 336
-3 -1 2 4 Generalised
Subshell < r > < r > < r > < r > < r > occupation
1s 0.00000D+00 2.68556D+00 5.73199D-01 4.47081D-01 5.33751D-01 1.99386D+00
2s 0.00000D+00 3.45596D-01 3.87317D+00 1.77347D+01 5.65669D+02 2.01584D-04
2p- 0.00000D+00 2.65023D-01 4.79564D+00 2.78265D+01 1.47509D+03 3.33335D-01
2p 5.85643D-02 2.65011D-01 4.79578D+00 2.78280D+01 1.47522D+03 6.66669D-01
3s 0.00000D+00 3.09463D+00 8.79428D-01 1.76019D+00 3.83411D+01 2.52035D-03
3p- 0.00000D+00 1.94750D+00 6.74894D-01 8.40900D-01 2.20221D+01 1.08534D-03
3p 1.72790D+01 1.94712D+00 6.74750D-01 8.40046D-01 2.19775D+01 2.17087D-03
3d- 1.01792D+01 1.82956D+00 6.31485D-01 4.57970D-01 4.14736D-01 6.48046D-05
3d 1.01575D+01 1.82935D+00 6.31441D-01 4.57852D-01 4.14179D-01 9.72851D-05
Eigenenergies:
Level J Parity Hartrees Kaysers eV
1 1/2 - -7.404577002212D+00 -1.625116808015D+06 -2.014887871281D+02
1 3/2 - -7.404574142856D+00 -1.625116180459D+06 -2.014887093211D+02
Weights of major contributors to ASF:
Block Level J Parity CSF contributions
1 1 1/2 - 0.9985 -0.0343 0.0326 0.0230 0.0107
1 56 58 60 30
2 1 3/2 - 0.9985 -0.0343 0.0326 0.0230 0.0099
1 62 67 71 32
4.1. OUTPUT FILES FROM THE FIRST EXAMPLE 73
The first lines of the file tell us that the calculation was for a three electron system and that there
were in total 186 CSFs built on 9 relativistic radial orbitals. After this there is information about
the nucleus. In this case the nucleus has Z= 3 and a mass of 1.264966897439×104electron masses.
The nuclear charge distribution is modeled by a Fermi distribution with c= 2.366086344330×10−5
Bohr radii, and a= 9.890591408973 ×10−6Bohr radii. There is information about the radial grid
used in the calculation. The grid is given by
R(I) = RN T (exp((I−1)H)−1), I = 1, . . . , N
with RNT = 2 ×10−6Bohr radii and H= 5 ×10−2Bohr radii. There are N= 590 grid points.
We see that it is an EOL calculation and that the calculation was on the lowest state (first
eigenvalue) of each block (J= 1/2and J= 3/2). In the optimization each state is weighted
according to the statistical weight 2J+ 1.
The information on optimization is followed by a radial orbital summary. Important characteristics
of a radial orbital are the orbital energy eigenvalue and parameters that determine the behavior
near r= 0. The radial amplitudes
u(r) = P(r)
Q(r),
can be expanded in power series
u(r) = rγ[u0+u1r+u2r2+. . .], uk=pk
qk
near the origin where the index γ,pk, and qkare constants that depend on the nuclear potential
model. In the radial orbital summary eis orbital energy eigenvalue, p0 is a parameter related
to the leading expansion coefficients of the radial amplitudes and gamma is the exponent γ, for
details see I.P. Grant, Relativistic Quantum Theory of Atoms and Molecules, Springer 2007, p
272 - 273 and also the subroutine start in lib92.P(2) and Q(2) are the values of the radial
amplitudes at the first grid point R(2) away from zero. Then the self consistency (weighted change
of an orbital during an iteration) is given for each orbital. In this case the orbitals 1s, 2s, 2p−,2p
were keep frozen and they thus have a self consistency of zero. The orbitals 3s, 3p−,3p, 3d−,3d
were optimized and the self consistency is between 8.699 ×10−6for 3dand 8.965 ×10−8for 3s.
Finally, the value MTP gives the number of the outermost grid point used for representing the radial
amplitudes of the orbital. At remaining grid points the radial amplitudes of the orbital are set to
zero. Around 340 of the available 590 grid points are utilized.
Different radial expectation values
hrki=hnlj|r−k|nlji
of the orbitals are given along with the generalized occupation numbers. The generalized occupa-
tion number q(nlj)of an orbital nlj is defined as
q(nlj) =
NCSF
X
r=1
d2
rqr(nlj),
where qr(nlj)is the number of electrons in subshell nlj in CSF rand d2
ris the generalized weight
d2
r=PnL
i=1(2Ji+ 1)c2
ri
PnL
i=1(2Ji+ 1) .
In the expression for the generalized weight the sum is over all levels in the EOL calculation.
cri, r = 1, . . . , NCSF are the mixing coefficients of level iin the basis of the CSFs. An orbital
with a small generalized occupation number is associated with CSFs that have small expansion
coefficients.
At the end of the summary file the eigenenergies for the states are displayed in different energy
units. The weights of the major CSF contributers are also given. Note that the CSFs in this case
are counted blockwise.
74 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
The specific mass shift file
The sms2 program computes isotope shift data. Below is the output file 2p_3.ci from the sms2
run of the relativistic CI wave function, given in the 2p_3.c,2p_3.w and 2p_3.cm files, of the
1s22p2P1/2,3/2states.
Level J Parity Specific mass shift (au)
1 1/2 - 0.2425644705D+00
1 3/2 - 0.2425741117D+00
Electron density in atomic units
Level J Parity DENS (a.u.)
1 1/2 - 0.1372387504D+02
1 3/2 - 0.1372387755D+02
Kinetic energy
Level J Parity T (a.u.)
1 1/2 - 0.7405495457D+01
1 3/2 - 0.7405486537D+01
Radial expectationvalue
Level J Parity <r> (a.u.)
1 1/2 - 0.5942052019D+01
1 3/2 - 0.5942191269D+01
Radial expectationvalue
Level J Parity <r2> (a.u.)
1 1/2 - 0.2871844755D+02
1 3/2 - 0.2871990038D+02
Radial expectationvalue
Level J Parity <r-1> (a.u.)
1 1/2 - 0.5636518702D+01
1 3/2 - 0.5636507661D+01
Radial expectationvalue
Level J Parity <r-2> (a.u.)
1 1/2 - 0.2991265967D+02
1 3/2 - 0.2991265070D+02
4.1. OUTPUT FILES FROM THE FIRST EXAMPLE 75
Presented in the file is, for each level or state, the specific mass shift parameter
Ssms =hΓP JMJ|
N
X
i<j
pi·pj|ΓP JMJi
the electron density at the nucleus
ρ(0) = hΓP JMJ|
N
X
i=1
δ(ri)|ΓP JMJi
and the kinetic energy Tparameter, or Snms parameter,
T=Snms =hΓP JMJ|
N
X
i=1
[cαi·pi+ (βi−1)c2]|ΓP JMJi
The mass and field shift corrected energy for an isotope of mass Mis then
EM=E0+1
MSnms +1
MSsms +2
3πZρ(0)hr2
Mi,
where hr2
Miis the mean square radius of the nuclear charge density.
At the end of the file different radial expectation values are given
hrki=hΓP JMJ|
N
X
i=1
rk
i|ΓP JMJi
See the original write-up by P. Jönsson and C. Froese Fischer Comput. Phys. Commun. 94, 249
(1997) for details.
The hyperfine structure files
The rhfs3 program computes hyperfine structure data. In addition the Landé gJfactor is com-
puted. Below is the output file 2p_3.ch from the rhfs3 run for the relativistic CI wave function,
given in the 2p_3.c,2p_3.w and 2p_3.cm files, of the 1s22p2P1/2,3/2states.
Nuclear spin 1.500000000000000D+00 au
Nuclear magnetic dipole moment 3.256426800000000D+00 n.m.
Nuclear electric quadrupole moment -4.000000000000000D-02 barns
Interaction constants:
Level1 J Parity A (MHz) B (MHz) g_J
1 1/2 - 4.4822178884D+01 -0.0000000000D+00 6.6588395646D-01
1 3/2 - -3.5381701048D+00 -1.7729096404D-01 1.3340987050D+00
At the top the nuclear spin and moments are displayed. Then, for each level, the Aand Bhyperfine
interaction constants are given in MHz along with the Landé gJfactor.
The rhfs3 program gives another file 2p_3.choffd which contains off-diagonal hyperfine data
Nuclear spin 1.500000000000000D+00 au
Nuclear magnetic dipole moment 3.256426800000000D+00 n.m.
Nuclear electric quadrupole moment -4.000000000000000D-02 barns
76 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
Interaction constants:
Level1 J Parity Level2 J Parity A (MHz) B (MHz)
1 1/2 - 1 1/2 - 4.4822178884D+01 -0.0000000000D+00
1 3/2 - 1 1/2 - 1.1768858007D+01 -3.8388220252D-02
1 3/2 - 1 3/2 - -3.5381701048D+00 -1.7729096404D-01
Matrix elements:
Level1 J Parity Level2 J Parity F Matrix element (a.u.)
1 1/2 - 1 1/2 - 1 -8.5152606539D-09
1 1/2 - 1 1/2 - 2 5.1091563924D-09
Matrix elements:
Level1 J Parity Level2 J Parity F Matrix element (a.u.)
1 3/2 - 1 1/2 - 1 4.0297076210D-09
1 3/2 - 1 1/2 - 2 5.3525246272D-09
Matrix elements:
Level1 J Parity Level2 J Parity F Matrix element (a.u.)
1 3/2 - 1 3/2 - 0 1.9828496847D-09
1 3/2 - 1 3/2 - 1 1.4720532420D-09
1 3/2 - 1 3/2 - 2 4.2351514680D-10
1 3/2 - 1 3/2 - 3 -1.2166550207D-09
Given are diagonal and off-diagonal hyperfine interaction constants Aand Bin MHz and the
Fdependent hyperfine matrix elements in atomic units. The above quantities are defined in P.
Jönsson F.A. Parpia and C. Froese Fischer Comput. Phys. Commun. 96, 301 (1996), Eq (13-17)
and Eq (7-8).
The transition file
The bioscl3 program computes transition data. Below is the output file 2s_4.2p_3.ct from the
bioscl3 electric dipole E1 run for the relativistic CI wave functions given in the 2s_3.c,2s_3.w,
2s_3.cm and 2p_3.c,2p_3.w and 2p_3.cm files.
Transition between files:
f1 = 2s_3
f2 = 2p_3
Electric 2**( 1)-pole transitions
=================================
Upper Lower
File Lev J P File Lev J P E (Kays) A (s-1) gf S
4.2. OUTPUT FILES FROM THE THIRD EXAMPLE 77
f2 1 1/2 - f1 1 1/2 + 14861.28 C 3.81311D+07 5.17671D-01 1.14676D+01
B 3.74756D+07 5.08773D-01 1.12705D+01
f2 1 3/2 - f1 1 1/2 + 14861.57 C 3.81334D+07 1.03537D+00 2.29353D+01
B 3.74782D+07 1.01758D+00 2.25413D+01
The first lines of the file gives the name of the files defining the wave functions. Then data are
given for the electric dipole transition E1. The first transition is from the upper level 1 with
J= 1/2and negative parity in file f2, i.e. 1s22p2P1/2to the lower level 1 with J= 1/2and
positive parity in file f1, i.e. 1s22s2S1/2. The second transition is from the upper level 1 with
J= 3/2and negative parity in file f2, i.e. 1s22p2P3/2to the lower level 1 with J= 1/2and
positive parity in file f1, i.e. 1s22s2S1/2. For each transition the transition energy Eis given in
Kays (cm−1). Also the transition rate A, the weighted oscillator strength gf and the line strength
Sare given in Coulomb (velocity) and Babushkin (length) gauge.
4.2 Output files from the third example
The third example case was the extended optimal level (EOL) calculations of the states belonging
to the 1s22s22p3and 1s22p5configurations in Si VIII.
The jj2lsj file
The jj2lsj program transforms from jj- to LSJ-coupling and gives the LSJ-composition of the
states. Below is the output file 2s22p3_2p5_3.lsj.lbl from the jj2lsj run of the relativistic CI
wave functions given in the 2s22p3_2p5_3.c,2s22p3_2p5_3.w,2s22p3_2p5_3.cm files. For each
case, the first line gives the position (number) of the eigenstate in the interaction matrix, parity,
total energy and the percentage of the atomic state function (ASF) that has been transformed.
Thus 99.946 % implies that 0.054 % has not been transformed.
Pos J Parity Energy Total Comp. of ASF
1 1/2 - -262.790631446 99.946%
0.98656029 0.97330120 1s(2).2s(2).2p(3)2P1_2P
0.15010909 0.02253274 1s(2).2p(5)_2P
-0.03364614 0.00113206 1s(2).2s_2S.2p(3)2P1_1P.3d_2P
2 1/2 - -259.497938232 99.613%
0.98251139 0.96532864 1s(2).2p(5)_2P
-0.14989839 0.02246953 1s(2).2s(2).2p(3)2P1_2P
-0.06893364 0.00475185 1s(2).2s_2S.2p(3)2D3_3D.3d_2P
-0.03674439 0.00135015 1s(2).2s_2S.2p(3)2D3_1D.3d_2P
0.03527443 0.00124429 1s(2).2s_2S.2p(3)2P1_3P.3d_2P
1 3/2 - -263.279781588 99.951%
0.99652486 0.99306180 1s(2).2s(2).2p(3)4S3_4S
-0.06051742 0.00366236 1s(2).2s_2S.2p(3)2D3_3D.3d_4S
0.03703206 0.00137137 1s(2).2s(2).2p(3)2P1_2P
2 3/2 - -262.955053092 99.950%
0.98954099 0.97919137 1s(2).2s(2).2p(3)2D3_2D
-0.12139915 0.01473775 1s(2).2s(2).2p(3)2P1_2P
0.04260716 0.00181537 1s(2).2s_2S.2p(3)2D3_1D.3d_2D
-0.03690740 0.00136216 1s(2).2s_2S.2p(3)4S3_3S.3d_2D
3 3/2 - -262.788271788 99.956%
0.97818838 0.95685251 1s(2).2s(2).2p(3)2P1_2P
0.15010555 0.02253168 1s(2).2p(5)_2P
0.12276481 0.01507120 1s(2).2s(2).2p(3)2D3_2D
-0.03672209 0.00134851 1s(2).2s(2).2p(3)4S3_4S
78 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
-0.03335975 0.00111287 1s(2).2s_2S.2p(3)2P1_1P.3d_2P
4 3/2 - -259.524116164 99.612%
0.98234136 0.96499454 1s(2).2p(5)_2P
-0.15102027 0.02280712 1s(2).2s(2).2p(3)2P1_2P
-0.06882345 0.00473667 1s(2).2s_2S.2p(3)2D3_3D.3d_2P
-0.03662955 0.00134172 1s(2).2s_2S.2p(3)2D3_1D.3d_2P
0.03537697 0.00125153 1s(2).2s_2S.2p(3)2P1_3P.3d_2P
1 5/2 - -262.953818133 99.429%
0.99713868 0.99428554 1s(2).2s(2).2p(3)2D3_2D
There is a total of seven states. For each state the file gives the LSJ-composition. The lowest J=
1/2state (pos 1) with negative parity and energy −262.790631446 a.u. has the LSJ-composition
0.98656029 1s(2).2s(2).2p(3)2P1_2P
0.15010909 1s(2).2p(5)_2P
-0.03364614 1s(2).2s_2S.2p(3)2P1_1P.3d_2P
The second lowest J= 1/2state (pos 2) with negative parity and energy −259.497938232 a.u.
has the LSJ-composition
0.98251139 1s(2).2p(5)_2P
-0.14989839 1s(2).2s(2).2p(3)2P1_2P
-0.06893364 1s(2).2s_2S.2p(3)2D3_3D.3d_2P
-0.03674439 1s(2).2s_2S.2p(3)2D3_1D.3d_2P
0.03527443 1s(2).2s_2S.2p(3)2P1_3P.3d_2P
We see that the states are close to pure LSJ-coupling and the file provides meaningful labels that
match labels given in, for example, the NIST data tables.
The transition file in LSJ-coupling
The bioscl3 program computes transition data. Below is the output file 2s22p3_2p5_3.2s22p3_2p5_3.ct
from the bioscl3 magnetic dipole M1 run of the relativistic CI wave functions given in the
2s22p3_2p5_3.c,2s22p3_2p5_3.w,2s22p3_2p5_3.cm files giving the states belonging to the
1s22s22p3and 1s22p5configurations
Transition in file:
f = 2s22p3_2p5_3
Magnetic 2**( 1)-pole transitions
=================================
Upper Lower
File Lev J P File Lev J P E (Kays) A (s-1) gf S
f 2 1/2 - f 1 1/2 - 722662.63 M 6.00625D-05 3.44842D-16 1.18002D-11
f 3 3/2 - f 1 1/2 - 517.89 M 1.22718D-03 2.74385D-08 1.31018D+00
f 4 3/2 - f 1 1/2 - 716917.24 M 4.29996D+00 5.01700D-11 1.73053D-06
f 1 1/2 - f 1 3/2 - 107356.05 M 3.11300D+01 8.09869D-09 1.86549D-03
f 2 1/2 - f 1 3/2 - 830018.68 M 4.56696D+00 1.98765D-11 5.92184D-07
f 1 1/2 - f 2 3/2 - 36086.38 M 1.27613D+01 2.93830D-08 2.01353D-02
f 2 1/2 - f 2 3/2 - 758749.01 M 4.24419D+00 2.21048D-11 7.20432D-07
f 2 1/2 - f 3 3/2 - 722144.74 M 1.09838D+01 6.31527D-11 2.16258D-06
f 2 1/2 - f 4 3/2 - 5745.39 M 3.40761D+00 3.09527D-07 1.33224D+00
f 2 3/2 - f 1 3/2 - 71269.67 M 1.41119D+00 1.66607D-09 5.78087D-04
4.2. OUTPUT FILES FROM THE THIRD EXAMPLE 79
f 3 3/2 - f 1 3/2 - 107873.93 M 7.52313D+01 3.87689D-08 8.88734D-03
f 4 3/2 - f 1 3/2 - 824273.28 M 1.25265D+01 1.10562D-10 3.31695D-06
f 3 3/2 - f 2 3/2 - 36604.27 M 2.11595D+01 9.47020D-08 6.39783D-02
f 4 3/2 - f 2 3/2 - 753003.62 M 9.62936D+00 1.01841D-10 3.34448D-06
f 4 3/2 - f 3 3/2 - 716399.35 M 7.21349D-02 8.42854D-13 2.90939D-08
f 1 5/2 - f 1 3/2 - 71540.71 M 1.99972D-02 3.51456D-11 1.21485D-05
f 1 5/2 - f 2 3/2 - 271.04 M 2.11530D-04 2.59004D-08 2.36306D+00
f 3 3/2 - f 1 5/2 - 36333.22 M 1.17594D+01 5.34187D-08 3.63575D-02
f 4 3/2 - f 1 5/2 - 752732.58 M 5.41425D+00 5.73026D-11 1.88252D-06
The structure of the file is the same as for the 2s_3.2p_3.ct file discussed above. If the information
of LSJ-coupling is available from a jj2lsj run bioscl3 also produces a file 2s22p3_2p5_3.2s22p3_2p5_3.ct.lsj
Transition between files:
2s22p3_2p5_3
2s22p3_2p5_3
1 -262.79063145 1s(2).2s(2).2p(3)2P1_2P
1 -259.49793823 1s(2).2p(5)_2P
722662.63 CM-1 138.38 ANGS(VAC) 138.38 ANGS(AIR)
M1 S = 1.18002D-11 GF = 3.44842D-16 AKI = 6.00625D-05
1 -262.79063145 1s(2).2s(2).2p(3)2P1_2P
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
517.89 CM-1 193093.04 ANGS(VAC) 193073.07 ANGS(AIR)
M1 S = 1.31018D+00 GF = 2.74385D-08 AKI = 1.22718D-03
1 -262.79063145 1s(2).2s(2).2p(3)2P1_2P
3 -259.52411616 1s(2).2p(5)_2P
716917.24 CM-1 139.49 ANGS(VAC) 139.49 ANGS(AIR)
M1 S = 1.73053D-06 GF = 5.01700D-11 AKI = 4.29996D+00
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
1 -262.79063145 1s(2).2s(2).2p(3)2P1_2P
107356.05 CM-1 931.48 ANGS(VAC) 931.48 ANGS(AIR)
M1 S = 1.86549D-03 GF = 8.09869D-09 AKI = 3.11300D+01
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
1 -259.49793823 1s(2).2p(5)_2P
830018.68 CM-1 120.48 ANGS(VAC) 120.48 ANGS(AIR)
M1 S = 5.92184D-07 GF = 1.98765D-11 AKI = 4.56696D+00
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
1 -262.79063145 1s(2).2s(2).2p(3)2P1_2P
36086.38 CM-1 2771.13 ANGS(VAC) 2770.83 ANGS(AIR)
M1 S = 2.01353D-02 GF = 2.93830D-08 AKI = 1.27613D+01
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
1 -259.49793823 1s(2).2p(5)_2P
758749.01 CM-1 131.80 ANGS(VAC) 131.80 ANGS(AIR)
M1 S = 7.20432D-07 GF = 2.21048D-11 AKI = 4.24419D+00
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
80 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
1 -259.49793823 1s(2).2p(5)_2P
722144.74 CM-1 138.48 ANGS(VAC) 138.48 ANGS(AIR)
M1 S = 2.16258D-06 GF = 6.31527D-11 AKI = 1.09838D+01
3 -259.52411616 1s(2).2p(5)_2P
1 -259.49793823 1s(2).2p(5)_2P
5745.39 CM-1 17405.25 ANGS(VAC) 17403.45 ANGS(AIR)
M1 S = 1.33224D+00 GF = 3.09527D-07 AKI = 3.40761D+00
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
71269.67 CM-1 1403.12 ANGS(VAC) 1403.12 ANGS(AIR)
M1 S = 5.78087D-04 GF = 1.66607D-09 AKI = 1.41119D+00
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
107873.93 CM-1 927.01 ANGS(VAC) 927.01 ANGS(AIR)
M1 S = 8.88734D-03 GF = 3.87689D-08 AKI = 7.52313D+01
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
3 -259.52411616 1s(2).2p(5)_2P
824273.28 CM-1 121.32 ANGS(VAC) 121.32 ANGS(AIR)
M1 S = 3.31695D-06 GF = 1.10562D-10 AKI = 1.25265D+01
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
36604.27 CM-1 2731.92 ANGS(VAC) 2731.63 ANGS(AIR)
M1 S = 6.39783D-02 GF = 9.47020D-08 AKI = 2.11595D+01
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
3 -259.52411616 1s(2).2p(5)_2P
753003.62 CM-1 132.80 ANGS(VAC) 132.80 ANGS(AIR)
M1 S = 3.34448D-06 GF = 1.01841D-10 AKI = 9.62936D+00
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
3 -259.52411616 1s(2).2p(5)_2P
716399.35 CM-1 139.59 ANGS(VAC) 139.59 ANGS(AIR)
M1 S = 2.90939D-08 GF = 8.42854D-13 AKI = 7.21349D-02
3 -263.27978159 1s(2).2s(2).2p(3)4S3_4S
5 -262.95381813 1s(2).2s(2).2p(3)2D3_2D
71540.71 CM-1 1397.81 ANGS(VAC) 1397.81 ANGS(AIR)
M1 S = 1.21485D-05 GF = 3.51456D-11 AKI = 1.99972D-02
3 -262.95505309 1s(2).2s(2).2p(3)2D3_2D
5 -262.95381813 1s(2).2s(2).2p(3)2D3_2D
271.04 CM-1 368946.28 ANGS(VAC) 368908.14 ANGS(AIR)
M1 S = 2.36306D+00 GF = 2.59004D-08 AKI = 2.11530D-04
5 -262.95381813 1s(2).2s(2).2p(3)2D3_2D
3 -262.78827179 1s(2).2s(2).2p(3)2P1_2P
36333.22 CM-1 2752.30 ANGS(VAC) 2752.01 ANGS(AIR)
M1 S = 3.63575D-02 GF = 5.34187D-08 AKI = 1.17594D+01
4.2. OUTPUT FILES FROM THE THIRD EXAMPLE 81
5 -262.95381813 1s(2).2s(2).2p(3)2D3_2D
3 -259.52411616 1s(2).2p(5)_2P
752732.58 CM-1 132.85 ANGS(VAC) 132.85 ANGS(AIR)
M1 S = 1.88252D-06 GF = 5.73026D-11 AKI = 5.41425D+00
Here labels of the upper and lower states in the transition are in LSJ-notation. In addition to
transition energies in cm−1also the wave lengths (vacuum and air) are given in Angstrom. On the
next line the line strength S, the weighted oscillator strength gf and the transition rate Aare given.
The format is the same as the one produced by the transition program of the ATSP2K package
[C. Froese Fischer, G. Tachiev, G. Gaigalas, and M. R. Godefroid, Comput. Phys. Commun. 176,
559-579 (2007).]
82 CHAPTER 4. DESCRIPTION OF OUTPUT FILES
Chapter 5
Case study: 2s22p,2s2p2in
Mo XXXVIII using scripts
In this case study we use script files to perform systematic calculations for all the states of the
2s22pand 2s2p2configurations in Mo XXXVIII. The 10 states are as follows:
odd: 2s22p2P1/2,3/2
even: 2s2p2 4P1/2,3/2,5/2,2s2p2 2D3/2,5/2,2s2p2 2P1/2,3/2,2s2p2 2S1/2
The script files can be found in manual\casestudy. Output files from the runs are available in
the same directory.
In a real application a correlation model should be defined, i.e. some rule to generate the CSFs
from an orbital set. The convergence of computed properties is then monitored as the orbital set is
increased. For the odd state a reasonable correlation model is to start from the {1s22s22p, 1s22p3}
multireference and then generate all CSFs that can be obtained by single- and double- excitations
from the multireference to an active set of orbitals. The active set of orbitals is then systematically
increased. Following the normal conventions the orbital set is denoted by the highest principal
quantum number. For example n= 3 means the orbital set {1s, 2s, 2p, 3s, 3p, 3d}. In this study
we increase the active set of orbitals up to n= 6. For the even states we start from the 1s22s2p2
reference and generate all CSFs that can be obtained by single- and double- excitations from the
multireference to the active sets of orbitals. The correlation model can be easily be extended by
adding CSFs to the multireference.
5.1 Running script files
To automate the calculations we use script files. For convenience we have a main script that calls
subscripts to perform different tasks. The construction of the scripts is greatly simplified if the
names of the files are chosen in a simple and systematic way. In the case study we use the names
odd2, odd3, odd4, odd5, odd6 and even2, even3, even4, even5, even6 to denote files for
the odd and even parity states, respectively. The digit indicates which orbital set has been used
to generate the expansion.
Before starting please note that the scripts assume that the environment variable GRASP has been
set. If you compiled grasp2K with the gfortran compiler this is done by issuing the command
source ./make_environment_gfort
in the Grasp2K installation directory. Issue similar commands if you have compiled with the ifort
or portland compiler.
83
84 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
The main script sh_grasp2K_case is shown below. This script controls the computational flow
and calls several subscripts.
#!/bin/sh
set -x
# Main script for 2s(2)2p and 2s2p(2)
# 1. Generate the expansions
./sh_files_c
# 2. Get the nuclear data
./sh_iso
# 3. Get screened hydrogenic orbitals as initial estimates
./sh_initial
# 4. Perform scf calculations and a final rci calculation that
# includes the Breit correction and QED
./sh_scf
# 5. Transform ASF from jj-coupling to LSJ-coupling
./sh_jj2lsj
# 6. Perform a transition calculation
./sh_tr
Each of the subscripts are given below together with some comments.
If all script files are available with execute permission (use the command chmod +x) we start the
computation by typing the name of the main script
./sh_grasp2K_case
Please note that these calculations will take several hours to finish!
1. Generate expansions
The expansions are generated by the script sh_files_c. This is by far the most complicated
script. Once the scripts for the smallest expansions (odd2, odd3 and even2, even3) are tested and
running the remaining part can be obtained by cut and paste with minor modifications.
#!/bin/sh
set -x
# 1. Generate grasp2K expansions
# 1.1 HF for 2s(2)2p
$GRASP/bin/jjgen << EOF
*
*
2
p
*
*
5.1. RUNNING SCRIPT FILES 85
2
*
2
2
1
1,3
0
y
2
p
*
*
2
2
0
3
1,3
0
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit << EOF
n
EOF
mv rcsl.out odd2.c
# 1.2 SD-MR for n=3
$GRASP/bin/jjgen <<EOF
*
*
3
d
*
*
2
*
2
2
1
1,3
2
y
3
d
*
*
2
2
0
3
1,3
86 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out odd3.c
# 1.3 SD-MR for n=4
$GRASP/bin/jjgen <<EOF
*
*
4
f
*
*
2
*
2
2
1
1,3
2
y
4
f
*
*
2
2
0
3
1,3
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out odd4.c
# 1.4 SD-MR for n=5
$GRASP/bin/jjgen <<EOF
*
*
5
5.1. RUNNING SCRIPT FILES 87
g
*
*
2
*
2
2
1
1,3
2
y
5
g
*
*
2
2
0
3
1,3
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out odd5.c
# 1.5 SD-MR for n=6
$GRASP/bin/jjgen <<EOF
*
*
6
h
*
*
2
*
2
2
1
1,3
2
y
6
h
*
*
2
2
88 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
0
3
1,3
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out odd6.c
# 1. Generate grasp2K expansions
# 1.6 HF for 2s2p(2)
$GRASP/bin/jjgen << EOF
*
*
2
p
*
*
2
*
2
1
2
1,5
0
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit << EOF
n
EOF
mv rcsl.out even2.c
# 1.7 SD-MR for n=3
$GRASP/bin/jjgen <<EOF
*
*
3
d
*
*
2
*
2
1
5.1. RUNNING SCRIPT FILES 89
2
1,5
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out even3.c
# 1.8 SD-MR for n=4
$GRASP/bin/jjgen <<EOF
*
*
4
f
*
*
2
*
2
1
2
1,5
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out even4.c
# 1.9 SD-MR for n=5
$GRASP/bin/jjgen <<EOF
*
*
5
g
*
*
2
*
2
1
2
1,5
90 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out even5.c
# 1.10 SD-MR for n=6
$GRASP/bin/jjgen <<EOF
*
*
6
h
*
*
2
*
2
1
2
1,5
2
*
EOF
mv clist.out rcsl.inp
$GRASP/bin/jsplit <<EOF
n
EOF
mv rcsl.out even6.c
2. Get nuclear data
Nuclear data are defined by the script sh_iso. Since we are not interested in hyperfine structure
the nuclear spin and moments have all been set to 1.
#!/bin/sh
set -x
# 2. Get isodata
$GRASP/bin/iso <<S1
42
96
n
96
1
1
1
5.1. RUNNING SCRIPT FILES 91
S1
cat isodata
3. Get initial estimates
The script sh_initial performs angular integration, gets initial estimates and performs scf calcu-
lations for the odd and even reference states (odd2 and even2). As initial estimates we use screened
hydrogenic functions. For the reference states all orbitals are required to be spectroscopic, i.e. they
should have the correct number of nodes.
#!/bin/sh
set -x
# 3. For n=2, Get initial estimates for odd.
cp odd2.c rcsl.inp
$GRASP/bin/mcp3 <<S4
y
S4
# Get initial estimates of wave functions
$GRASP/bin/erwf <<S5
y
3
*
S5
# Perform self-consistent field calculations
$GRASP/bin/rscf2 <<S6
y
y
1
1
5
*
*
100
S6
# Save the result to odd2
$GRASP/bin/rsave odd2
# 3. For n=2, Get initial estimates for even
cp even2.c rcsl.inp
$GRASP/bin/mcp3 <<S4
y
S4
# Get initial estimates of wave functions
$GRASP/bin/erwf <<S5
y
3
92 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
*
S5
# Perform self-consistent field calculations
$GRASP/bin/rscf2 <<S6
y
y
1,2,3
1,2,3
1,2
5
*
*
100
S6
# Save the result to even2
$GRASP/bin/rsave even2
4. Scf calculations and rci
The script sh_scf performs angular integration, estimates the new radial functions and performs
self-consistent field calculations for the odd and even states up to n= 6. At the end CI calculations
are performed for the largest expansions. The CI calculations include Breit interaction and QED
corrections. In the script, note how we loop over the digit nthat indicates the size of the orbital
set.
#!/bin/sh
set -x
# 4. Get results for odd n=3,4,5,6
for n in 3 4 5 6
do
(cp odd${n}.c rcsl.inp
# Get angular data
$GRASP/bin/mcp3 <<S4
y
S4
# Get initial estimates of wave functions
m=‘expr $n - 1‘
echo m=$m n=$n
$GRASP/bin/erwf <<S5
y
1
odd${m}.w
*
3
*
S5
# Perform self-consistent field calculations
5.1. RUNNING SCRIPT FILES 93
$GRASP/bin/rscf2 > out_rscf2_${n} <<S6
y
y
1
1
5
${n}*
100
S6
$GRASP/bin/rsave odd${n}
echo)
done
# Perform Breit-correction using CI for n=6
n=6
$GRASP/bin/rci3 <<S7
y
odd${n}
y
y
1.d-6
y
n
n
y
4
1
1
S7
# 4. Get results for even n=3,4,5,6
for n in 3 4 5 6
do
(cp even${n}.c rcsl.inp
# Get angular data
$GRASP/bin/mcp3 <<S4
y
S4
# Get initial estimates of wave functions
m=‘expr $n - 1‘
echo m=$m n=$n
$GRASP/bin/erwf <<S5
y
1
even${m}.w
*
3
94 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
*
S5
# Perform self-consistent field calculations
$GRASP/bin/rscf2 > out_rscf2_${n} <<S6
y
y
1,2,3
1,2,3
1,2
5
${n}*
100
S6
$GRASP/bin/rsave even${n}
echo)
done
# Perform Breit-correction using CI for n=6
n=6
$GRASP/bin/rci3 <<S7
y
even${n}
y
y
1.d-6
y
n
n
y
4
1,2,3
1,2,3
1,2
S7
5. Transform to LSJ-coupling
The script sh_jj2lsj transforms from jj- to LSJ-coupling.
#!/bin/sh
set -x
# 5. Get LSJ coupling
n=6
$GRASP/bin/jj2lsj > out_jj2lsj_odd${n} <<S1
odd${n}
y
y
5.2. COMPARISON WITH EXPERIMENT 95
S1
$GRASP/bin/rlevels odd${n}.cm > out_rlevels_odd${n} <<S2
S2
n=6
$GRASP/bin/jj2lsj > out_jj2lsj_even${n} <<S1
even${n}
y
y
S1
$GRASP/bin/rlevels even${n}.cm > out_rlevels_even${n} <<S2
S2
6. Perform a transition calculation
The script sh_tr computes the E1 transition rates between the odd and even states. First we
perform a biorthogonal transformation and then we perform the transition calculation itself.
#!/bin/sh
set -x
# 6. Perform transition calculation for the n=6 CI results
n=6
# First the biorthogonal rotations
$GRASP/bin/biotra3 > out_biotra <<EOF
y
y
odd$n
even$n
y
EOF
# Then the transition calculations
$GRASP/bin/bioscl3 > out_bioscl <<EOF
y
n
odd$n
even$n
E1
EOF
5.2 Comparison with experiment
To display the computed energies we give the command
rlevels odd6.cm even6.cm
The computer returns the energies together with labels in LSJ-coupling for all the states.
96 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
nblock = 2 ncftot = 20641 nw = 36 nelec = 5
nblock = 3 ncftot = 36290 nw = 36 nelec = 5
Energy levels for ...
Rydberg constant is 109737.31534
Splitting is the energy difference with the lower neighbor
------------------------------------------------------------------------------------------
No Pos J Parity Energy Total Levels Splitting Configuration
(a.u.) (cm^-1) (cm^-1)
------------------------------------------------------------------------------------------
1 1 1/2 - -2386.3192492 0.00 0.00 1s(2).2s(2).2p_2P
2 1 1/2 + -2382.2384104 895640.59 895640.59 1s(2).2s_2S.2p(2)3P2_4P
3 1 3/2 - -2381.9234302 964770.76 69130.17 1s(2).2s(2).2p_2P
4 1 3/2 + -2378.9978407 1606863.43 642092.67 1s(2).2s_2S.2p(2)3P2_4P
5 1 5/2 + -2378.1468367 1793637.20 186773.77 1s(2).2s_2S.2p(2)3P2_4P
6 2 3/2 + -2376.7262038 2105430.10 311792.89 1s(2).2s_2S.2p(2)1D2_2D
7 2 1/2 + -2376.5304790 2148386.73 42956.63 1s(2).2s_2S.2p(2)3P2_2P
8 2 5/2 + -2373.9005645 2725586.24 577199.51 1s(2).2s_2S.2p(2)1D2_2D
9 3 1/2 + -2371.8997599 3164712.08 439125.84 1s(2).2s_2S.2p(2)1S0_2S
10 3 3/2 + -2371.8553153 3174466.55 9754.47 1s(2).2s_2S.2p(2)3P2_2P
------------------------------------------------------------------------------------------
The Mo XXXVIII transitions have been observed in the JET Tokamak, Myrnäs et al. 1993
http://www.iop.org/Jet/fulltext/JETP93072.pdf. In the table below the experimental tran-
sition energies are compared with the calculated energies. Please note that the quantum labels
for the 2s2p2 2P1/2and 2s2p2 2S1/2seem to have been swapped in the experimental paper, i.e.
the highest J= 1/2state should be 2s2p2 2S1/2and not 2s2p2 2P1/2. We see that the odd
states are somewhat too high. This is due to an imbalance in the multireference. As discussed
in the beginning of the chapter the correlation model can be refined by extending the multiref-
erence. Adopting the multireferences {2s22p, 2p3,2s2p3d, 2p33d}and {2s22p, 2p23d, 2s23d, 2s3d2}
for, respectively, the odd and even parity states improves the energy separations considerably
[P. Rynkun, P. Jönsson, and G. Gaigalas, Atomic Data and Nuclear Data Tables, 98 481 (2012)].
A careful investigation of the effects of increasing the multireference is part of any systematic
calculation.
State Experiment Calculation
2s22p2P1/20 0
2s2p2 4P1/2894 050 ±400 895 848
2s22p2P3/2964 050 ±90 964 715
2s2p2 4P3/21 606 863
2s2p2 4P5/21 790 130 ±200 1 793 682
2s2p2 2D3/22 102 900 ±900 2 106 354
2s2p2 2P1/22 147 300 ±900 2 149 456
2s2p2 2D5/22 725 586
2s2p2 2S1/23 164 770 ±1500 3 166 168
2s2p2 2P3/23 171 300 ±1500 3 175 559
5.3 Transition rates
Below are the transition rates as given in the file odd6.even6.ct.lsj. The agreement between
calculated values in the two gauges is quite good, specially for the strong transitions. Expansions
based on a larger multireference will further improve the agreement.
Transition between files:
5.3. TRANSITION RATES 97
odd6
even6
1-2386.31924920 1s(2).2s(2).2p_2P
1-2382.23841041 1s(2).2s_2S.2p(2)3P2_4P
895640.59 CM-1 111.65 ANGS(VAC) 111.65 ANGS(AIR)
E1 S = 4.42136D-03 GF = 1.20286D-02 AKI = 3.21806D+09 dT = 0.05151
4.66146D-03 1.26818D-02 3.39281D+09
1-2386.31924920 1s(2).2s(2).2p_2P
1-2376.53047897 1s(2).2s_2S.2p(2)3P2_2P
2148386.74 CM-1 46.55 ANGS(VAC) 46.55 ANGS(AIR)
E1 S = 1.87909D-02 GF = 1.22627D-01 AKI = 1.88766D+11 dT = 0.00414
1.88691D-02 1.23137D-01 1.89551D+11
1-2386.31924920 1s(2).2s(2).2p_2P
1-2371.89975994 1s(2).2s_2S.2p(2)1S0_2S
3164712.09 CM-1 31.60 ANGS(VAC) 31.60 ANGS(AIR)
E1 S = 1.51562D-05 GF = 1.45696D-04 AKI = 4.86664D+08 dT = 0.06894
1.62784D-05 1.56485D-04 5.22700D+08
1-2386.31924920 1s(2).2s(2).2p_2P
3-2378.99784066 1s(2).2s_2S.2p(2)3P2_4P
1606863.44 CM-1 62.23 ANGS(VAC) 62.23 ANGS(AIR)
E1 S = 1.11563D-04 GF = 5.44535D-04 AKI = 2.34458D+08 dT = 0.01688
1.13479D-04 5.53886D-04 2.38485D+08
1-2386.31924920 1s(2).2s(2).2p_2P
3-2376.72620380 1s(2).2s_2S.2p(2)1D2_2D
2105430.10 CM-1 47.50 ANGS(VAC) 47.50 ANGS(AIR)
E1 S = 2.45759D-02 GF = 1.57172D-01 AKI = 1.16182D+11 dT = 0.00643
2.47350D-02 1.58190D-01 1.16934D+11
1-2386.31924920 1s(2).2s(2).2p_2P
3-2371.85531532 1s(2).2s_2S.2p(2)3P2_2P
3174466.55 CM-1 31.50 ANGS(VAC) 31.50 ANGS(AIR)
E1 S = 6.34291D-04 GF = 6.11623D-03 AKI = 1.02780D+10 dT = 0.00528
6.30940D-04 6.08392D-03 1.02237D+10
1-2382.23841041 1s(2).2s_2S.2p(2)3P2_4P
3-2381.92343016 1s(2).2s(2).2p_2P
69130.17 CM-1 1446.55 ANGS(VAC) 1446.55 ANGS(AIR)
E1 S = 5.06276D-04 GF = 1.06311D-04 AKI = 8.47221D+04 dT = 0.18819
4.11000D-04 8.63046D-05 6.87783D+04
3-2381.92343016 1s(2).2s(2).2p_2P
1-2376.53047897 1s(2).2s_2S.2p(2)3P2_2P
1183615.97 CM-1 84.49 ANGS(VAC) 84.49 ANGS(AIR)
E1 S = 2.36462D-03 GF = 8.50151D-03 AKI = 3.97219D+09 dT = 0.05226
2.49501D-03 8.97033D-03 4.19124D+09
3-2381.92343016 1s(2).2s(2).2p_2P
1-2371.89975994 1s(2).2s_2S.2p(2)1S0_2S
2199941.33 CM-1 45.46 ANGS(VAC) 45.46 ANGS(AIR)
98 CHAPTER 5. CASE STUDY: 2S22P,2S2P2IN MO XXXVIII USING SCRIPTS
E1 S = 1.48021D-02 GF = 9.89142D-02 AKI = 1.59659D+11 dT = 0.00260
1.47635D-02 9.86566D-02 1.59243D+11
3-2381.92343016 1s(2).2s(2).2p_2P
3-2378.99784066 1s(2).2s_2S.2p(2)3P2_4P
642092.68 CM-1 155.74 ANGS(VAC) 155.74 ANGS(AIR)
E1 S = 1.00858D-03 GF = 1.96712D-03 AKI = 1.35241D+08 dT = 0.11530
1.14003D-03 2.22350D-03 1.52867D+08
3-2381.92343016 1s(2).2s(2).2p_2P
3-2376.72620380 1s(2).2s_2S.2p(2)1D2_2D
1140659.34 CM-1 87.67 ANGS(VAC) 87.67 ANGS(AIR)
E1 S = 2.73256D-03 GF = 9.46782D-03 AKI = 2.05421D+09 dT = 0.04984
2.87589D-03 9.96443D-03 2.16195D+09
3-2381.92343016 1s(2).2s(2).2p_2P
3-2371.85531532 1s(2).2s_2S.2p(2)3P2_2P
2209695.79 CM-1 45.26 ANGS(VAC) 45.26 ANGS(AIR)
E1 S = 4.49451D-02 GF = 3.01675D-01 AKI = 2.45633D+11 dT = 0.00388
4.51204D-02 3.02851D-01 2.46591D+11
3-2381.92343016 1s(2).2s(2).2p_2P
5-2378.14683675 1s(2).2s_2S.2p(2)3P2_4P
828866.45 CM-1 120.65 ANGS(VAC) 120.65 ANGS(AIR)
E1 S = 9.97374D-03 GF = 2.51112D-02 AKI = 1.91790D+09 dT = 0.08157
1.08596D-02 2.73415D-02 2.08825D+09
3-2381.92343016 1s(2).2s(2).2p_2P
5-2373.90056450 1s(2).2s_2S.2p(2)1D2_2D
1760815.48 CM-1 56.79 ANGS(VAC) 56.79 ANGS(AIR)
E1 S = 1.52579D-02 GF = 8.16083D-02 AKI = 2.81289D+10 dT = 0.01678
1.55183D-02 8.30007D-02 2.86088D+10
