Journal ArticleDOI
Evaluation of molecular integrals over Gaussian basis functions
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TLDR
This method is computationally simple and numerically well behaved, and has been incorporated into a new molecular SCF program HONDO, and preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.Abstract:
This paper is concerned with the efficient computation of the ubiquitous electron repulsion integral in molecular quantum mechanics. Differences and similarities in organization of existing Gaussian integral programs are discussed, and a new strategy is developed. An analysis based on the theory of orthogonal polynomials yields a general formula for basis functions of arbitrarily high angular momentum. (ηiηj∥ηkηl) = Σα=1,nIx(uα) Iy(uα) I*z(uα) By computing a large block of integrals concurrently, the same I factors may be used for many different integrals. This method is computationally simple and numerically well behaved. It has been incorporated into a new molecular SCF program HONDO. Preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.read more
Citations
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Advances in methods and algorithms in a modern quantum chemistry program package
Yihan Shao,Laszlo Fusti Molnar,Yousung Jung,Jörg Kussmann,Christian Ochsenfeld,Shawn T. Brown,Andrew T. B. Gilbert,Lyudmila V. Slipchenko,Sergey V. Levchenko,Darragh P. O’Neill,Robert A. DiStasio,Rohini C. Lochan,Tao Wang,Gregory J. O. Beran,Nicholas A. Besley,John M. Herbert,Ching Yeh Lin,Troy Van Voorhis,Siu Hung Chien,Alexander J. Sodt,Ryan P. Steele,Vitaly A. Rassolov,Paul E. Maslen,Prakashan P. Korambath,Ross D. Adamson,Brian Austin,Jon Baker,Edward F. C. Byrd,Holger Dachsel,Robert J. Doerksen,Andreas Dreuw,Barry D. Dunietz,Anthony D. Dutoi,Thomas R. Furlani,Steven R. Gwaltney,Andreas Heyden,So Hirata,Chao-Ping Hsu,Gary S. Kedziora,Rustam Z. Khalliulin,Phil Klunzinger,Aaron M. Lee,Michael S. Lee,WanZhen Liang,Itay Lotan,Nikhil Nair,Baron Peters,Emil Proynov,Piotr A. Pieniazek,Young Min Rhee,Jim Ritchie,Edina Rosta,C. David Sherrill,Andrew C. Simmonett,Joseph E. Subotnik,H. Lee Woodcock,Weimin Zhang,Alexis T. Bell,Arup K. Chakraborty,Daniel M. Chipman,Frerich J. Keil,Arieh Warshel,Warren J. Hehre,Henry F. Schaefer,Jing Kong,Anna I. Krylov,Peter Gill,Martin Head-Gordon,Martin Head-Gordon +68 more
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References
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Journal ArticleDOI
Methods in Computational Physics
Journal ArticleDOI
Electronic Wave Functions. I. A General Method of Calculation for the Stationary States of Any Molecular System
TL;DR: In this paper, it was shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation, and that all necessary integrals can be explicitly evaluated.
Journal ArticleDOI
Coulombic potential energy integrals and approximations
TL;DR: Theorems are derived which establish a method of approximating two‐particle Coulombic potential energy integrals, [φa(1) r12−1 |φb(2)], in terms of approximate charge densities φa′ and φb′, and a simple method of optimizing charge density approximations such that δ is minimized is derived.
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General contraction of Gaussian atomic orbitals: Core, valence, polarization, and diffuse basis sets; Molecular integral evaluation
TL;DR: The basis is compared with standard methods in current use and is shown to be superior in terms of energy lowering obtained per additional basis function beyond a minimal number.