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New expansion of the Boys function
Author(s) -
Primorac Miljenko
Publication year - 1998
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1998)68:5<305::aid-qua2>3.0.co;2-z
Subject(s) - taylor series , power series , asymptotic expansion , series (stratigraphy) , series expansion , gaussian , truncation (statistics) , edgeworth series , function (biology) , mathematics , expression (computer science) , range (aeronautics) , mathematical analysis , matrix (chemical analysis) , statistical physics , computational chemistry , physics , chemistry , statistics , computer science , materials science , paleontology , evolutionary biology , biology , chromatography , composite material , programming language
We propose a new expansion for the Boys function ∫ 0 1 t 2 j exp(− r 2 t 2 ) dt appearing in the calculation of molecular two‐electron matrix elements if Gaussian basis sets are employed. This expansion involves a power series involving the terms C i , j (τ) ( r 2 − R 2 ) i multiplied by exp(−τ r 2 ), where τ is an optimized parameter τ∈[0, 1]. The performances of the introduced expansion are discussed and illustrated by some numerical experiments. It appears that the proposed expansion is considerably shorter than the customary Taylor series, which in turn is the special case for τ=0. This is of some importance, particularly for higher j values. Further, the proposed expansion enables a single expression for calculating erf( x ) for the whole range of variable x . The recursive relations for the expansion coefficients are derived and the truncation errors are estimated. A new method for calculating the Boys function by means of asymptotic series is represented too. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 305–315, 1998