By Ralph E. Christoffersen (Eds.)

ISBN-10: 0841203717

ISBN-13: 9780841203716

ISBN-10: 0841203768

ISBN-13: 9780841203761

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**Sample text**

I f more than h a l f the e n t r i e s are zero i t i s more e f f i c i e n t t o omit zero e n t r i e s and include the index as a l a b e l ( i f the word length i s long and the matrix i s small enough, t h i s l a b e l may be packed i n t o the i n s i g n i f i c a n t b i t s of the matrix element). The e l e c t r o n r e p u l s i o n i n t e g r a l s are more com p l i c a t e d t o store i f point group symmetry i s used t o reduce t h e i r number. In general the i n t e g r a l s may be c l a s s i f i e d i n t o blocks depending on the symmetry of the four o r b i t a l s involved i n the i n t e g r a l [ i , | | .

Further, many of the i n t e g r a l s can be eliminated by a t e s t based only on one charge d i s t r i b u t i o n . Thus, although ^ d i n t e g r a l s need to be done f o r small molecules, only ^ d i n t e g r a l s are needed f o r large molecules. Those i n t e g r a l s which remain to be done can be w r i t t e n so they i n v o l v e one exponential, one square root, and e i t h e r F ( T ) or e r f ( / T ) . Each of these three functions i n v o l v e about the same amount of time althougl the square root can be made 30% f a s t e r than the stan dard square root r o u t i n e furnished with the computer software package.

Several algorithms e x i s t which are s u i t a b l e f o r f i n d i n g a l l of the eigenvalues of any matrix of dimen sion d which can be kept i n c e n t r a l memory. The Jacobi plane r o t a t i o n method i s by f a r the simplest t o program and i s reasonably e f f i c i e n t ( 3 4 ) . As i t i s an i t e r a t i v e method the running time cannot be r i g o r o u s l y defined, but times p r o p o r t i o n a l t o d are expected. Other methods u s u a l l y begin w i t h a n o n - i t e r a t i v e transforma t i o n t o t r i d i a g o n a l form followed by c a l c u l a t i o n of the eigenvalues and eigenvectors and a back transformation to the o r i g i n a l problem ( 3 4 , 3 5 ) .

### Algorithms for Chemical Computations by Ralph E. Christoffersen (Eds.)

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