Optimal use of the recurrence relations for the evaluation of molecular integrals over Cartesian Gaussian basis functions

1993 ◽  
Vol 14 (1) ◽  
pp. 30-36 ◽  
Author(s):  
Ungsik Ryu ◽  
Myeongcheol Kim ◽  
Yoon Sup Lee
Keyword(s):  
Recurrence Relations ◽  
Basis Functions ◽  
Molecular Integrals ◽  
Gaussian Basis Functions

Evaluation of molecular integrals over Gaussian basis functions

1976 ◽  
Vol 65 (1) ◽  
pp. 111-116 ◽  
Author(s):  
Michel Dupuis ◽  
John Rys ◽  
Harry F. King
Keyword(s):  
Basis Functions ◽  
Molecular Integrals ◽  
Gaussian Basis Functions

scholarly journals On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

2020 ◽  
Vol 76 (2) ◽  
pp. 172-179 ◽  
Author(s):  
Alessandro Genoni
Keyword(s):  
Recurrence Relations ◽  
Basis Functions ◽  
Future Perspectives ◽  
Recurrence Formulas ◽  
Atomic Nuclei ◽  
Structure Factors ◽  
Modern Methods ◽  
Molecular Integrals ◽  
Chemical Strategies ◽  
Quantum Crystallography

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two-centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.

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