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Hartree forck slater self consistent field calculations
C-26 COMPUTER PHYSICS COMMUNICATIONS 1 (1969) 216-222. NORTH-HOLLAND PUBLISHING COMP., AMSTERDAM
HARTREE
FOCK
SLATER
SELF
CONSISTENT
FIELD
CALCULATIONS
J . P. D E S C L A U X
Commissarial h l'Energie .Alomique, C . E . L . , B . P . 27, 94 Villeneuve-St-Georges, France Received 23 S e p t e m b e r 1969
PROGRAM
SUMMARY
Title of program (32 c h a r a c t e r s m a x i m u m ) : H . F . S . S E L F CONSISTENT F I E L D Catalogue number: ACQI Computer f o r which the program is designed and others upon which it is operable Computer: IBM 300/50. Inslallation:C. E. L.. B . P . n ° . 27. 9 4 - V i l l e n e u v e - S t - G e o r g e s , F r a n c e Operating s y s l e m or monitor under which the program is executed: O S MFT 2 Programming languages used: FORTRAN High speed slore required: 22 160 w o r d s . No. of bits in a word: 32 Is the program overlaid? No No. of magnetic tapes required: None What olher peripherals are used? 2540 Card Reader; 2540 Card Pmlch; 1403 P r i n t e r No. of cards in combined program and tesl deck: 635 Keywords descriptive of problem and method of solution: Atomic, H a r t r e e Fock e q u a t i o n s , F r e e e l e c t r o n exchange potential. Eigenfunctions, E i g e n v a l u e s , N u m e r o v Method, P r a t t i m p r o v e m e n t s c h e m e .
Nature of the physical problem With p r e s e n t p r o g r a m s the t l a r t r e e - F o c k (H. F.) e q u a t i o n s can be t r e a t e d for n e a r l y all c o n f i g u r a t i o n s . It h a s been shown [1], h o w e v e r , that a c c u r a t e e l e c t r o n binding e n e r g i e s can be obtained without use of the c o m p a r a t i v e l y c o m p l i c a t e d H. F. s c h e m e . Since the main difficulty posed by the It. F. e q u a t i o n s is the t r e a t m e n t of the non local exchange potential it would be d e s i r a b l e to find a good local a p p r o x i m a t i o n to the H. F. potential. The a p p r o x i m a t i o n s u g g e s t e d by S l a t e r [2] is u s e d in this prol~ram as it has been in m a n y a t o m i c o r e n e r g y ban(I c a l c u l a t i o n s .
matched s p i n s a r e not c o n s i d e r e d . The e l e c t r o n i c c o n figuration is specified by the o r b i t a l occupation n u m b e r s only. The p r o g r a m is r e s t r i c t e d to f r e e a t o m s o r positive ions and the m a x i m u m n u m b e r of one e l e c t r o n o r b i t a l s is 20.
Typical running time The test c a s e ( n e u t r a l m e r c u r y atom) r e q u i r e s 110 s e c o n d s to c o m p i l e and 151 s e c o n d s to run on the IBM 360/50 c o m p u t e r . The s t a r t i n g potential being the T h o m a s F e r m i potential f o r t h e f r e e a t o m , an a n a l y t i cal a p p r o x i m a t i o n of which is included in the p r o g r a m .
Method of sohdion
References
The FI. F. equations a r e solved by the " I N - O U T " method d e s c r i b e d by l l a r t r e e [31 . The n u m e r i c a l p r o c e d u r e is that of N u m e r o v with the "tail p r o c e d u r e " int r o d u c e d by F r o e s e [4 I. The i m p r o v e m e n t s c h e m e of P r a t t , as d e s c r i b e d in [11 page 4-8, is used to a c c e l e r a t e the c o n v e r g e n c e .
[1] F. H e r m a n and S . S k i l l m a n , Atomic s t r u c t u r e c a l culations ( P r e n t i c e Hall, Englewood Cliffs, New J e r s e y , 1963). [2] J . C . S l a t e r , P h y s . Rev. 81 (1951) 385. [3] D . R . H a r t r e e , The calculation of a t o m i c s t r u c t u r e (John Wiley, New York, 1957). [41 Ch. F r o e s e , Can. J . P h y s . 41 (1963) 1895.
Reslriclions on the complexity of the problem In the p r e s e n t work s i n g l e e l e c t r o n i c c o n f i g u r a t i o n s having one o r m o r e open s h e l l s a r e t r e a t e d on the s a m e b a s i s as closed s h e l l s c o n f i g u r a t i o n s . The d i s tinctive f e a t u r e s introcluced by the p r e s e n c e of u n -
HARTREE
FOCK
SLATER
SELF
CONSISTENT
FIELD
CALCULATIONS
J . P. D E S C L A U X
Commissarial h l'Energie .Alomique, C . E . L . , B . P . 27, 94 Villeneuve-St-Georges, France Received 23 S e p t e m b e r 1969
PROGRAM
SUMMARY
Title of program (32 c h a r a c t e r s m a x i m u m ) : H . F . S . S E L F CONSISTENT F I E L D Catalogue number: ACQI Computer f o r which the program is designed and others upon which it is operable Computer: IBM 300/50. Inslallation:C. E. L.. B . P . n ° . 27. 9 4 - V i l l e n e u v e - S t - G e o r g e s , F r a n c e Operating s y s l e m or monitor under which the program is executed: O S MFT 2 Programming languages used: FORTRAN High speed slore required: 22 160 w o r d s . No. of bits in a word: 32 Is the program overlaid? No No. of magnetic tapes required: None What olher peripherals are used? 2540 Card Reader; 2540 Card Pmlch; 1403 P r i n t e r No. of cards in combined program and tesl deck: 635 Keywords descriptive of problem and method of solution: Atomic, H a r t r e e Fock e q u a t i o n s , F r e e e l e c t r o n exchange potential. Eigenfunctions, E i g e n v a l u e s , N u m e r o v Method, P r a t t i m p r o v e m e n t s c h e m e .
Nature of the physical problem With p r e s e n t p r o g r a m s the t l a r t r e e - F o c k (H. F.) e q u a t i o n s can be t r e a t e d for n e a r l y all c o n f i g u r a t i o n s . It h a s been shown [1], h o w e v e r , that a c c u r a t e e l e c t r o n binding e n e r g i e s can be obtained without use of the c o m p a r a t i v e l y c o m p l i c a t e d H. F. s c h e m e . Since the main difficulty posed by the It. F. e q u a t i o n s is the t r e a t m e n t of the non local exchange potential it would be d e s i r a b l e to find a good local a p p r o x i m a t i o n to the H. F. potential. The a p p r o x i m a t i o n s u g g e s t e d by S l a t e r [2] is u s e d in this prol~ram as it has been in m a n y a t o m i c o r e n e r g y ban(I c a l c u l a t i o n s .
matched s p i n s a r e not c o n s i d e r e d . The e l e c t r o n i c c o n figuration is specified by the o r b i t a l occupation n u m b e r s only. The p r o g r a m is r e s t r i c t e d to f r e e a t o m s o r positive ions and the m a x i m u m n u m b e r of one e l e c t r o n o r b i t a l s is 20.
Typical running time The test c a s e ( n e u t r a l m e r c u r y atom) r e q u i r e s 110 s e c o n d s to c o m p i l e and 151 s e c o n d s to run on the IBM 360/50 c o m p u t e r . The s t a r t i n g potential being the T h o m a s F e r m i potential f o r t h e f r e e a t o m , an a n a l y t i cal a p p r o x i m a t i o n of which is included in the p r o g r a m .
Method of sohdion
References
The FI. F. equations a r e solved by the " I N - O U T " method d e s c r i b e d by l l a r t r e e [31 . The n u m e r i c a l p r o c e d u r e is that of N u m e r o v with the "tail p r o c e d u r e " int r o d u c e d by F r o e s e [4 I. The i m p r o v e m e n t s c h e m e of P r a t t , as d e s c r i b e d in [11 page 4-8, is used to a c c e l e r a t e the c o n v e r g e n c e .
[1] F. H e r m a n and S . S k i l l m a n , Atomic s t r u c t u r e c a l culations ( P r e n t i c e Hall, Englewood Cliffs, New J e r s e y , 1963). [2] J . C . S l a t e r , P h y s . Rev. 81 (1951) 385. [3] D . R . H a r t r e e , The calculation of a t o m i c s t r u c t u r e (John Wiley, New York, 1957). [41 Ch. F r o e s e , Can. J . P h y s . 41 (1963) 1895.
Reslriclions on the complexity of the problem In the p r e s e n t work s i n g l e e l e c t r o n i c c o n f i g u r a t i o n s having one o r m o r e open s h e l l s a r e t r e a t e d on the s a m e b a s i s as closed s h e l l s c o n f i g u r a t i o n s . The d i s tinctive f e a t u r e s introcluced by the p r e s e n c e of u n -