Multicentre two-electron Coulomb and exchange integrals over Slater functions evaluated using a generalized algorithm based on nonlinear transformations

Journal of Physics A: Mathematical and General

Volumn 37, Issue 10, 2004, Pages 3393-3410

  Berlu, Lilian ^a   Safouhi, Hassan ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642619001     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/10/006     Document Type: Article

References (44)

1. Safouhi H 2001 The properties of sine, spherical Bessel and reduced Bessel functions for improving convergence of semi-infinite very oscillatory integrals: the evaluation of three-centre nuclear attraction integrals over B functions J. Phys. A: Math. Gen. 34 2801
2. Safouhi H 2002 Efficient and rapid numerical evaluation of the two-electron four-center Coulomb integrals using nonlinear transformations and practical properties of sine and Bessel functions J. Comput. Phys. 176 1-19
3. Safouhi H 2001 An extremely efficient approach for accurate and rapid evaluation of three-centre two-electron Coulomb and hybrid integral over B functions J. Phys. A: Math. Gen. 34 881
4. Berlu L and Safouhi H 2003 An extremely efficient and rapid algorithm for a numerical evaluation of three-centre nuclear attraction integrals over Slater type functions J. Phys. A: Math. Gen. 36 11791
5. Berlu L and Safouhi H 2003 A new algorithm for accurate and fast numerical evaluation of hybrid and three-centre two-electron Coulomb integrals over Slater type functions J. Phys. A: Math. Gen. 36 11267
6. Slater J C 1930 Atomic shielding constants Phys. Rev. 36 57
7. Slater J C Analytic atomic wave functions Phys. Rev. 42 33
8. Roothaan C C 1951 New developments in molecular orbital theory Rev. Mod. Phys. 23 69
9. AMSTERDAM DENSITY FUNCTIONAL program Theoretical Chemistry, Vrije Universiteit, Amsterdam http://www.scm.com
10. Kutzelnigg W 1988 Present and future trends in quantum chemical calculations J. Mol. Struct. (THEOCHEM) 50 33
11. Bouferguene A, Fares M and Hoggan P E 1996 STOP: a Slater type orbitals package for molecular electronic structure determination Int. J. Quantum Chem. 57 801
12. Watson M A, Handy N C and Cohen A J 2003 Density functional calculations, using basis sets, with exact exchange J. Chem. Phys. 119 6475
13. Shavitt I 1963 The Gaussian function in calculation of statistical mechanics and quantum mechanics Methods in Computational Physics: 2. Quantum Mechanics ed B Alder, S Fernbach and M Rotenberg (New York: Academic)
14. Filter E and Steinborn E O 1978 Extremely compact formulas for molecular one-electron integrals and Coulomb integrals over Slater-type orbitals Phys. Rev. A 18 1
15. Steinborn E O and Filter E 1975 Translations of fields represented by spherical-harmonics expansions for molecular calculations: III. Translations of reduced Bessel functions, Slater-type s-orbitals, and other functions Theor. Chim. Acta. 38 273
16. Filter E 1978 Analytische Methoden zur Auswertung von Mehrzentren-Matrixelementen in der Theorie der Molekülorbitale bei Verwendung exponentialartiger Basissätze PhD Thesis Universität Regensburg
17. Weniger E J and Steinborn E O 1989 Addition theorems for B functions and other exponentially declining functions J. Math. Phys. 30 774
18. Weniger E J and Steinborn E O 1983 Numerical properties of the convolution theorems of B functions Phys. Rev. A 28 2026
19. Weniger E J 1982 Reduzierte Bessel-Funktionen als LCAO-Basissatz: Analytische und numerische Untersuchungen PhD Thesis Universität Regensburg
20. Weniger E J and Steinborn E O 1983 The Fourier transforms of some exponential-type functions and their relevance to multicenter problems J. Chem. Phys. 78 6121
21. Bonham R A, Peacher J L and Cox H L 1964 On the calculation of multicenter two-electron repulsion integrals involving Slater functions J. Chem. Phys. 40 3083
22. Trivedi H P and Steinborn E O 1983 Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals Phys. Rev. A 27 670
23. Grotendorst J and Steinborn E O 1988 Numerical evaluation of molecular one- and two-electron multicenter integrals with exponential-type orbitals via the Fourier-transform method Phys. Rev. A 38 3857
24. Davis P J and Rabinowitz P 1994 Methods of Numerical Integration (Orlando, FL: Academic)
25. Evans G 1993 Practical Numerical Integration (Chichester: Wiley)
26. Brezinski C and Zaglia M R 1991 Extrapolation Methods: Theory and Practice (Amsterdam: North-Holland)
27. Shanks D 1955 Non-linear transformations of divergent and slowly convergent sequences J. Math. Phys. 34 1
28. Sidi A 1997 Computation of infinite integrals involving Bessel functions of arbitrary order by the ̄D-transformation J. Comput. Appl. Math. 78 125
29. Sidi A 1980 Extrapolation methods for oscillating infinite integrals J. Inst. Math. Appl. 26 1
30. Sidi A 1982 The numerical evaluation of very oscillatory infinite integrals by extrapolation Math. Comput. 38 517
31. Sidi A 1982 An algorithm for a special case of a generalization of the Richardson extrapolation process Numer. Math. 38 299
32. Ford W F and Sidi A 1987 An algorithm for a generalization of the Richardson extrapolation process SIAM J. Numer. Anal. 24 1212
33. Fernèndez Rico J, Lòpez R, Ema I and Ramìrez G 1997 Calculation of many centre two-electron molecular integrals with STO Comput. Phys. Commun. 105 216
34. Yoshimine M, Lengsfield B H, Bagus P S, McLean A D and Liu B 1990 Alchemy II (San Jose, NM: International Business Machines) MOTECC-90
35. Bouferguene A, Fares M and Hoggan P E 1996 STOP: a Slater type orbitals package for molecular electronic structure determination Int. J. Quantum Chem. 57 801
36. Condon E U and Shortley G H 1970 The Theory of Atomic Spectra (Cambridge: Cambridge University Press)
37. Arfken G B and Weber H J 1995 Mathematical Methods for Physicists 4th edn (New York: Academic)
38. Gel'fand I M and Shilov G E 1964 Generalized Functions: I. Properties and Operations (New York: Academic)
39. Safouhi H and Hoggan P E 1998 Efficient evaluation of Coulomb integrals: the non-linear D- and ̄D-transformations J. Phys. A: Math. Gen. 31 8941
40. Safouhi H 2000 The HD and H̄D methods for accelerating the convergence of three-center nuclear attraction and four-center two-electron Coulomb integrals over B functions and their convergence properties J. Comput. Phys. 165 473
41. Levin D 1973 Developement of non-linear transformations for improving convergence of sequences Int. J. Comput. Math. B 3 371
42. Homeier H H H and Steinborn E O 1996 Some properties of the coupling coefficients of real spherical harmonics and their relation to Gaunt coefficients J. Mol. Struct. (THEOCHEM) 368 31
43. Weniger E J and Steinborn E O 1982 Programs for the coupling of spherical harmonics Comput. Phys. Commun. 25 149
44. Xu Y-L 1997 Fast evaluation of Gaunt coefficients: recursive approach J. Comput. Appl. Math. 85 53