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Implementation of gradient formulas for correlated gaussians: He, ∞ He, Ps 2 , 9 Be, and ∞ Be test results
Author(s) -
Kinghorn Donald B.,
Poshusta R. D.
Publication year - 1997
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(1997)62:2<223::aid-qua10>3.0.co;2-c
Subject(s) - subroutine , conjugate gradient method , mathematics , gaussian , basis (linear algebra) , energy (signal processing) , exponential function , matrix (chemical analysis) , newton's method , set (abstract data type) , nonlinear system , algorithm , computer science , mathematical analysis , physics , quantum mechanics , statistics , geometry , programming language , operating system , materials science , composite material
New formulas in the basis of explicitly correlated Gaussian basis functions, derived in a previous article using powerful matrix calculus, are implemented and applied to find variational upper bounds for nonrelativistic ground states of 4 He, ∞ He, Ps 2 , 9 Be, and ∞ Be. Analytic gradients of the energy are included to speed optimization of the exponential variational parameters. Five different nonlinear optimization subroutines (algorithms) are compared: TN, truncated Newton; DUMING, quasi‐Newton; DUMIDH, modified Newton; DUMCGG, conjugate gradient; and POWELL, direction set (nongradient). The new analytic gradient formulas are found to significantly accelerate optimizations that require gradients. We found that the truncated Newton algorithm out‐performs the other optimizers for the selected test cases. Computer timings and energy bounds are reported. © 1997 John Wiley & Sons, Inc.