A program for generating configuration state lists in many-electron atoms

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Computer Physics Communications 157 (2004) 217–225

www.elsevier.com/locate/cp

A program for generating configuration state lists inmany-electron atoms✩

P. Bogdanovich∗, A. Momkauskaite

Institute of Theoretical Physics and Astronomy, Goštauto 12, Vilnius 2600, Lithuania

Received 31 October 2002; accepted 29 April 2003

Abstract

This program written in FORTRAN is aimed at generating configuration state list of the set of complex atomic configuThe program generates a list of configuration states obtained by taking into account many additional constraints oftypes for minimizing the orders of matrices, as proposed in [Bogdanovich et al., Comput. Phys. Comm. 143 (2002) 1generated list file complies with the requirements of codes [Hibbert et al., Comput. Phys. Comm. 64 (1991) 455; FischComput. Phys. Comm. 64 (1991) 486] and other related programs.

Program summary

Title of program: ATOTERMCatalogue identifier:ADTMProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTMProgram obtainable from:CPC Program Library, Queen’s University of Belfast, N. IrelandLicensing provisions:NoneComputers:Any computer with a FORTRAN 77 compilerOperating systems under which the program has been tested:LinuxProgramming language used:FORTRAN 77Memory required to execute with typical data:2 MBNo. of lines in distributed program, including text data, etc.:2368No. of bytes in distributed program, including test data, etc.:15 446Distribution format: tar gzip fileKeywords: Complex atom, configuration interaction, configuration state,LS-couplingNature of physical problem:Generating the list of configuration states with taking into account multiple additional constof different types.Method of solution:Building the configuration state list for the set of the given configurations with further selection of necconfiguration states by applying a set of restrictions on each configuration.

✩ This paper and its associated program are available via the Computer Physics Communications homepage on Sci(http://www.sciencedirect.com/science/journal/00104655).

* Corresponding author.E-mail address:[email protected] (P. Bogdanovich).

0010-4655/$ – see front matter 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0010-4655(03)00519-8

http://www.elsevier.com/locate/cpc

http://cpc.cs.qub.ac.uk/summaries/ADTM

http://www.sciencedirect.com/science/journal/00104655

218 P. Bogdanovich, A. Momkauskait˙e / Computer Physics Communications 157 (2004) 217–225

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Restrictions onto the complexity of the problem:For atomic configurations containing any electron shells withl � 3; momentaof the electron shells withl > 3 andN � 2 is restricted byLmax= 6. The number of the active shells can not exceed sevenUnusual features of the program:Possibility to select configuration states.Typical running time: Seconds to minutes. Depends on the size of the problem: of the order of a few seconds forconfigurations to minutes for a large set of very complex admixed configurations withf -electron shells. 2003 Elsevier B.V. All rights reserved.

PACS:31.25.Eb; 31.25.Jf

Keywords:Complex atom; Configuration interaction; Configuration state;LS-coupling

1. Theoretical aspects

The theoretical background of this program is given in our previous paper [1], where the method for rethe number of configuration states (CSs) has been proposed, allowing one to decrease significantly thematrices of the energy operator while calculating energy spectra by the method of configuration interactionloss of accuracy in the obtained results. The background of the usage of this method is a selection of onCSs with orbital and spin momenta satisfying the given constraints from the list of all possible CSs. This pgenerates the CSs and selects according to these constraints.

2. Program description

The program ATOTERM enables one to generate the list of CSs from the list of configurations, takinaccount different types of additional constraints. The program allows one to impose well-founded restrictthe total orbital and spin momenta of admixed configurations, on the momenta of separate shells as wellintermediate momenta.

The program consists of a main routine and four subroutines ATOM, KLAI, TERMAI, VARDAS. The tof the main routine are: reading the input data, generating the CS list, then processing the informatiothe restrictions on CSs, and writing the resulting list to the file “cfg.inp”. This routine also prints on the sintermediate and final information about the number of generated and selected CSs. ATOM sets the corresbetween the atom numberZ and atom name, KLAI prints messages about errors in the input information. TERgives the number of terms of shells withs-, p-, d- andf -electrons and the table with 2L and 2S. Notations of theterms of shells withf -electrons correspond to those proposed in [2]; and for the remaining shells, includingwith l > 3, notations correspond to those adopted in [3]. VARDAS prints the text in a large format. The pruses only the standard library of the FORTRAN language.

The main restriction of the program is a number of active shells in the configuration: this number is equand cannot be changed without changing the program itself. In the present version of the program the oinformation is carried out for the case of five or fewer active shells, which corresponds to the possibilitiesprogram [3] and can be used for codes [4,5] and other related programs. The maximum number of CSs oconfiguration (or alternatively the first two or three configurations) is defined by the parameterMTPK = 50 000and can be changed by the user. The parameterMK = 3000, setting the maximum number of configurations,also be changed.

3. Input data

The input of information is carried out interactively, though it is more convenient and simple to useprepared earlier. The information is entered similarly to the analogous program [3]:

P. Bogdanovich, A. Momkauskait˙e / Computer Physics Communications 157 (2004) 217–225 219

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(1) the first row: if empty or “N” (“n”) is at its first three positions—no output with help on the screen; if “(“y”) is at its first three positions—all information about the program is printed;

(2) the second row contains the assigned problem name /FORMAT(A11)/; if the point is in the first elpositions, this information is treated as the decimal number of nucleus charge and will be changedname of the atom;

(3) the third row describes closed shells /FORMAT(19A4)/, e.g.:

1s 2s 2p

(4) the next rows contain active shells of the separate configurations, written down as program [3] re/FORMAT(A160)/, e.g.:

3s(2)3p(4)3d(1),

3s(2)3p(2)3d(3).

The additional information about the rules by which CSs are selected for the specified configuration isafter the list of active shells. The figure braces {} mark out each separate constraint (there must be no blanthe figure braces). CSs, satisfying all the given constraints, will be selected.

There are two modes of setting the constraints, which can be conditionally divided into “simple” and “stanThe following variants of setting “simple” constraints are possible:

{∗comments} — if “*” is at the first position, all the following information is treated as comments and the gconstraint is ignored;

{%} — the configuration is neglected (the strongest feature);{!}, {!!}, {!!!} — only those CSs will be selected for which the final momentaL and S coincide with the final

momenta of the first one, first two or first three configurations, respectively; and at the same tthe restrictions are imposed on the final momenta of the first configurations, then these restrictiautomatically applied to the remaining configurations as well with the help of the prescribed constrainconstraints with two or three “!” should be used if several very strongly mixing configurations are studThey must be placed at the beginning of the list of configurations and all admixed ones have to influthe terms of such configurations. The mixing of 3dN , 3dN−14s and 3dN−24s2 configurations in the energspectra of atoms and first ions can be mentioned as an example of such a case;

{+} — blocks checking the previous presence of the configuration in the input data; one should use this covery carefully in order that two identical CSs do not appear in the list of CSs.

All other constraints belong to the “standard”. The maximum number of such constraints for each configis MITE = 12. It can be increased by changing this parameter. In this case, the width of the format heldinformation input, which is equal to 160 in the present version and is prescribed by the parameterILEIL, may alsohave to be increased. The “standard” constraint is of the form{M?X}. M denotes the momenta pair to which tconstraint is applied, “?” is a mathematical sign of equality or inequality,X sets the values of the momenta. Seveconstraints can be imposed on the same pair of momenta.

To explain the use of this notation, we number the pairs of momenta (LS), in the order used in [3]: firstly thpairs associated with each shell, and then the pairs associated with the intermediate and final angular mobtained through the consecutive coupling of the separate shells. Hence the order of the pairs is that of thto the file “cfg.inp”: if there areK shells specified in the configuration, there will be(2K − 1) pairs of angularmomenta, with the firstK pairs corresponding to the (LS) of theK shells.

In the constraint{M?X}, if M is a positive integer, it refers to the angular momentum pair of shellM, while ifM is a negative integer (M < 0), |M| refers to theMth intermediate (or final) angular momentum pair, the reof coupling the angular momenta of the first (M + 1) shells.


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M can also possess the following values:LL—a restriction is imposed on the final orbital momentum;SS—a restriction is imposed on the final spin momentum;JJ—a restriction is imposed on the final orbital and smomenta, which can be coupled to the indicated total momentum.

Possible meanings of the symbol “?” are the following:

= means equal;# means unequal;> always denotes more or equal;< always denotes less or equal.

X can acquire the following values:

(1) the pair ofSL, whereS is the multiplicity, L is the spectroscopic notation of the orbital momentum, e3P, 2D; bearing in mind that only such CSs will be selected, for which both multiplicity and ormomentum satisfy the given constraint (=, <, >, #);

(2) the shellnlN , wherenl are the usual orbital labels,N is the number of electrons; this format is used only w“=”; bearing in mind that only those momenta which are possible for that shell will be selected;

(3) an integer, depending on the meaning ofM, setting various quantities: the value of orbital momentum (incase, whenM equals toLL), the value of multiplicity (in the case, whenM equals toSS), the doubled value othe total momentumJ (in the case, whenM equals toJJ).

Below, examples of constraints with the description of their effect are given:

{1 = 3D} — only those CSs will be selected, for which the first pair of momenta makes up the term3D;{2 < 1G} — only those CSs will be selected, for which the second pair of momenta satisfies the restrictionL � 4

andS = 0;{6 = np3} — only those CSs will be selected, for which the sixth pair of momenta coincides with the

possible for thenp3-shell;{−1#3F } — only those CSs will be selected, for which the first pair of intermediate momenta satisfi

restrictionsL = 3 andS = 1;{−2 = nd2} — only those CSs will be selected, for which the second pair of intermediate momenta coincid

the terms possible for thend2-shell;{LL < 3} — only those CSs will be selected, for which the final orbital momentum satisfies the restrictionL � 3;{SS> 4} — only those CSs will be selected, for which multiplicity is greater or equal 4 and so the fina

momentum satisfies the restrictionS � 1.5;{JJ= 4} — only those CSs will be selected, for which the final orbital and spin momenta can be coupled

total momentumJ satisfying the restrictionJ = 2;{JJ< 3} — only those CSs will be selected, for which the final orbital and spin momenta can be coupled

total momentumJ satisfying the restrictionJ � 1.5.

An empty row interrupts the work of the program.

4. Output data

The selected CSs are written to the file “cfg.inp”, completely corresponding to the respective file geby the program [3]. Moreover, in the process of the work the program prints on the screen the entry infoand the intermediate information about the number of selected CSs, their total number, the maximum ord


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matrix for a certain value of the total momentumJ , the largest number of repeatedly appearing final momLS and other useful information. If the program receives mistaken or incomprehensible information, it pmessage, but does not stop. The total number of errors met in the work of the program is printed on the scrcompletion of the program. At the end, the program prints some general information concerning the featurcreated set of CSs.

TEST RUN INPUT

The real tasks of calculations of spectra require the input of a very large amount of information,is impossible to illustrate in this publication. Therefore, in this work a simple model example is givendemonstrates the main possibilities of the program. At the same time, in the input information one erintentionally introduced.

Input file

n20.1s2s(2)2p(3)3d(1) {LL#0}4d(2)2s(2)2p(1)3d(1) {!} {1=np2}{6=np3} {*2p(2) excitations}4f(2)2s(2)2p(1)3d(1) {!} {1=np2}{-2=np3}{1>1D}4f(2)2s(2)2p(1)3d(1) {!} {+}{1=np2}{-2=np3}{1<3P}3d(1)5d(1)2s(2)2p(1)3d(1) {!} {-1=np2}{-3=np3}4d(1)5d(1)2s(2)2p(1)3d(1) {!} {-1=np2}{-3=np3}4p(1)2s(2)2p(1)3p(1)3d(1) {!} {-3=np3}2s(2)2p(1)3d(3) {!}4d(1)4f(1)2s(1)2p(2)3d(1) {!} {-1<3P}{-3=np3} {*2s(1)2p(1)excitation}4f(2)2s(1)2p(3) {!} {1=1D} {*2s(1)3d(1)excitations}4f(1)5f(1)2s(1)2p(3) {!} {-1<3D}{-1>1D}4d(2)2p(3)3d(1) {!} {1=1S} {*2s(2)excitation}4d(1)4f(1)2s(2)2p(2) {!} {-1<3F}{-1>1P} {*2p(1)3d(1)excitation}

As seen from the given input file example a number of restrictions have been introduced. The virtuallyelectrons, used to obtain the admixed configurations, determine all these restrictions. They are selected tothose CSs of the admixed configurations, which have the interconfigurational matrix elements with tconfiguration equal to zero. Below, we explain the constraints appearing in the input file, using Roman nto number the configurations following their sequence in the input file.

The CSs of the first configuration will not contain the terms with the final orbital momentum equal to zerlist of CSs of all remaining configurations will have only those CSs, for which the final momentaL andS willcoincide with the final momenta of the first configuration. The momenta of the first active shell of the configuII, III and IV have to coincide with the momenta possible fornp2-shell. The same restriction is imposed on the fiintermediate momenta of the V and VI configurations, so the terms of 3d5d and 4d5d have to be only3P , 1D and1S. The pairs of the intermediate momenta of the first three shells 4d22s22p of the configuration II are allowed tcouple only to4S, 2P and2D. The restriction of the same meaning is presented for the configurations III an(Notice that, in these configurations,{6 = np3} is equivalent to{−2 = np3} since there are four active shellsThe similar restrictions are presented for the third pair of the intermediate momenta of the configuration


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VII and IX. The configuration IV has{+}, so it will be left if even it coincides with the configuration III. Threstrictions for the pair of momenta of the first active shells of these two configurations avoid repeating CSwas performed only to demonstrate the usage of the restriction{+}. If the configuration III does not have the larestriction and the configuration IV is absent, the same CSs are obtained. The first pair of intermediate mof the 4d4f shells of the configuration IX must satisfy such inequalities:L � 1, S � 1. The similar restrictions arpresented for the same momenta of the configurations XI and XIII. In these cases the momenta are restriby the maximum and minimum values. The list of CSs of the configuration X contains only those states whithe first pair of momenta equal to1D. The similar restriction is presented for CSs of the configuration XII.

TEST RUN OUTPUT

As mentioned above, two kinds of the output information are obtained from running the programinformation printed on the screen of a PC and/or to an output file and the file cfg.inp containing the list of geCSs. Even in this simple example file cfg.inp contains a large number of CSs, therefore only its initial anrows are given in this paper. The testing of the results of the control example can be quite effectively reathe data given in the output file.

Output file

AA TTTTT OOO TTTTT EEEEE RRRR M MA A T O O T E R R MM MMA A T O O T E R R M M M

A A T O O T EEE RRRR M M MAAAAAA T O O T E RR M MA A T O O T E R R M MA A T O O T E R R M MA A T OOO T EEEEE R R M M

Is the help necessary? Y?n

Enter the name. F-T(A78)20.

FNT= the number of CSs of all configurationsMO(J)= the maximum order of J-matricesMO(LS)= the maximum number of the same final momenta LSQ at the end of line - the number of chosen CSs > 99QQ at the end of line - the number of chosen CSs > 499

Enter the closed shells. F-T(19A4)1s

Enter the open shells and the restrictions on CSs.------------------------------------------------------------Configuration No. 1


2s(2)2p(3)3d(1) {LL#0}16 CSs are chosen from 18. FNT= 16. MO(J)= 10. MO(LS)= 3

------------------------------------------------------------Configuration No. 24d(2)2s(2)2p(1)3d(1) {!} {1=np2}{6=np3} {*2p(2)excitations}

36 CSs are chosen from 158. FNT= 52. MO(J)= 32. MO(LS)= 9------------------------------------------------------------Configuration No. 34f(2)2s(2)2p(1)3d(1) {!} {1=np2}{-2=np3}{1>1D}

14 CSs are chosen from 248. FNT= 66. MO(J)= 40. MO(LS)= 11------------------------------------------------------------Configuration No. 44f(2)2s(2)2p(1)3d(1) {!} {+}{1=np2}{-2=np3}{1<3P}

22 CSs are chosen from 248. FNT= 88. MO(J)= 54. MO(LS)= 15------------------------------------------------------------Configuration No. 53d(1)5d(1)2s(2)2p(1)3d(1) {!} {-1=np2}{-3=np3}

The quantum numbers of the shells have coincided.The incomprehensible information.Please repeat the input.------------------------------------------------------------Configuration No. 54d(1)5d(1)2s(2)2p(1)3d(1) {!} {-1=np2}{-3=np3}

36 CSs are chosen from 330. FNT= 124. MO(J)= 76. MO(LS)= 21------------------------------------------------------------Configuration No. 64p(1)2s(2)2p(1)3p(1)3d(1) {!} {-3=np3}

70 CSs are chosen from 150. FNT= 194. MO(J)= 118. MO(LS)= 32------------------------------------------------------------Configuration No. 72s(2)2p(1)3d(3) {!}

35 CSs are chosen from 48. FNT= 229. MO(J)= 139. MO(LS)= 38------------------------------------------------------------Configuration No. 84d(1)4f(1)2s(1)2p(2)3d(1) {!} {-1<3P}{-3=np3} {*2s(1)2p(1)excitation}

88 CSs are chosen from 1706. FNT= 317. MO(J)= 193. MO(LS)= 53------------------------------------------------------------Configuration No. 94f(2)2s(1)2p(3) {!} {1=1D} {*2s(1)3d(1)excitations}

16 CSs are chosen from 166. FNT= 333. MO(J)= 203. MO(LS)= 56------------------------------------------------------------Configuration No. 104f(1)5f(1)2s(1)2p(3) {!} {-1<3D}{-1>1D}

44 CSs are chosen from 344. FNT= 377. MO(J)= 234. MO(LS)= 65------------------------------------------------------------Configuration No. 114d(2)2p(3)3d(1) {!} {1=1S} {*2s(2)excitation}

16 CSs are chosen from 470. FNT= 393. MO(J)= 244. MO(LS)= 68


------------------------------------------------------------Configuration No. 124d(1)4f(1)2s(2)2p(2) {!} {-1<3F}{-1>1P} {*2p(1)3d(1)excitation}

55 CSs are chosen from 116. FNT= 448. MO(J)= 280. MO(LS)= 78

The orders of J-matrices:J Order0 811 2152 2803 2464 1375 29

The final momenta and their numbers:

3D 5D 1P 1D 1F 3P 3F 1G 3G78 20 56 59 57 61 62 26 29

448 CSs HAVE BEEN MADE.

MO(J)= 280. MO( 3D)= 78

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ATTENTION!!! THERE WERE ERRORS ( 1) !!!XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

File “cfg.inp”

Ca Calcium1s2s( 2) 2p( 3) 3d( 1)

1S0 4S3 2D1 4S0 3D02s( 2) 2p( 3) 3d( 1)

1S0 4S3 2D1 4S0 5D02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 1P02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 1D02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 1F02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 3P02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 3D02s( 2) 2p( 3) 3d( 1)

1S0 2P1 2D1 2P0 3F0


2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 1P0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 1D0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 1F0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 1G0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 3P0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 3D0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 3F0

2s( 2) 2p( 3) 3d( 1)1S0 2D3 2D1 2D0 3G0

4d( 2) 2s( 2) 2p( 1) 3d( 1)1S0 1S0 2P1 2D1 1S0 2P0 1P0

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . .4d( 1) 4f( 1) 2s( 2) 2p( 2)

2D1 2F1 1S0 1D2 3F0 3F0 3P04d( 1) 4f( 1) 2s( 2) 2p( 2)

2D1 2F1 1S0 1D2 3F0 3F0 3D04d( 1) 4f( 1) 2s( 2) 2p( 2)

2D1 2F1 1S0 1D2 3F0 3F0 3F04d( 1) 4f( 1) 2s( 2) 2p( 2)

2D1 2F1 1S0 1D2 3F0 3F0 3G0

References

[1] P. Bogdanovich, P. Karpuškiene, A. Momkauskaite, Comput. Phys. Comm. 143 (2002) 174.[2] G. Gaigalas, C.F. Fischer, Comput. Phys. Comm. 98 (1996) 255.[3] C.F. Fischer, B. Liu, Comput. Phys. Comm. 64 (1991) 406.[4] A. Hibbert, R. Glass, C.F. Fischer, Comput. Phys. Comm. 64 (1991) 455.[5] C.F. Fischer, M.R. Godefroid, A. Hibbert, Comput. Phys. Comm. 64 (1991) 486.

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A program for generating configuration state lists in many-electron atoms