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Volumn 34, Issue 4, 2001, Pages 881-902

An extremely efficient approach for accurate and rapid evaluation of three-centre two-electron Coulomb and hybrid integrals over B functions

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EID: 0035793525     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/4/314     Document Type: Article
Times cited : (27)

References (51)
  • 1
    • 0038868353 scopus 로고    scopus 로고
    • 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
    • submitted
    • Safouhi H 2000 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. submitted
    • (2000) J. Phys. A: Math. Gen.
    • Safouhi, H.1
  • 2
    • 0039461213 scopus 로고    scopus 로고
    • Efficient and rapid numerical evaluation of the two-electron four-centre Coulomb integrals using nonlinear transformations and practical properties of sine and bessel functions
    • submitted
    • Safouhi H 2000 Efficient and rapid numerical evaluation of the two-electron four-centre Coulomb integrals using nonlinear transformations and practical properties of sine and Bessel functions J. Comput. Phys. submitted
    • (2000) J. Comput. Phys.
    • Safouhi, H.1
  • 3
    • 36149002029 scopus 로고
    • Atomic shielding constants
    • Slater J C 1930 Atomic shielding constants Phys. Rev. 36 57
    • (1930) Phys. Rev. , vol.36 , pp. 57
    • Slater, J.C.1
  • 5
    • 2342430094 scopus 로고
    • New development in molecular orbital theory
    • Roothaan C C 1951 New development in molecular orbital theory Rev. Mod. Phys. 23 69
    • (1951) Rev. Mod. Phys. , vol.23 , pp. 69
    • Roothaan, C.C.1
  • 6
    • 0000570413 scopus 로고
    • The integral formulae for the variational solution of the molecular many-electron wave equation in terms of Gaussian functions with direct electronic correlation
    • Boys S F 1960 The integral formulae for the variational solution of the molecular many-electron wave equation in terms of Gaussian functions with direct electronic correlation Proc. R. Soc. A 258 402
    • (1960) Proc. R. Soc. A , vol.258 , pp. 402
    • Boys, S.F.1
  • 9
    • 84980086883 scopus 로고
    • On the eigenfunctions of many-particle systems in quantum mechanics
    • Kato T 1957 On the eigenfunctions of many-particle systems in quantum mechanics Commun. Pure Appl. Math. 10 151
    • (1957) Commun. Pure Appl. Math. , vol.10 , pp. 151
    • Kato, T.1
  • 11
    • 0002708849 scopus 로고
    • The Gaussian function in calculation of statistical mechanics and quantum mechanics
    • ed B Alder, S Fernbach and M Rotenberg (New York: Academic)
    • 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)
    • (1963) Methods in Computational Physics: 2. Quantum Mechanics
    • Shavitt, I.1
  • 12
    • 0002973752 scopus 로고
    • Translations of fields represented by spherical-harmonics expansions for molecular calculations: III. Translations of reduced bessel functions, Slater-type s-orbitals and other functions
    • 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
    • (1975) Theor. Chim. Acta. , vol.38 , pp. 273
    • Steinborn, E.O.1    Filter, E.2
  • 13
    • 0001777261 scopus 로고
    • Extremely compact formulas for molecular one-electron integrals and Coulomb integrals over Slater-type orbitals
    • 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
    • (1978) Phys. Rev. A , vol.18 , pp. 1
    • Filter, E.1    Steinborn, E.O.2
  • 16
    • 0001071778 scopus 로고
    • Addition theorems for B functions and other exponentially declining functions
    • Weniger E J and Steinborn E O 1989 Addition theorems for B functions and other exponentially declining functions J. Math. Phys. 30 774
    • (1989) J. Math. Phys. , vol.30 , pp. 774
    • Weniger, E.J.1    Steinborn, E.O.2
  • 17
    • 0000767655 scopus 로고
    • Numerical properties of the convolution theorems of B functions
    • Weniger E J and Steinborn E O 1983 Numerical properties of the convolution theorems of B functions Phys. Rev. A 28 2026
    • (1983) Phys. Rev. A , vol.28 , pp. 2026
    • Weniger, E.J.1    Steinborn, E.O.2
  • 18
    • 36749114381 scopus 로고
    • The fourier transforms of some exponential-type functions and their relevance to multicenter problems
    • 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
    • (1983) J. Chem. Phys. , vol.78 , pp. 6121
    • Weniger, E.J.1    Steinborn, E.O.2
  • 19
    • 36849122172 scopus 로고
    • On the calculation of multicenter two-electron repulsion integrals involving Slater functions
    • 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
    • (1964) J. Chem. Phys. , vol.40 , pp. 3083
    • Bonham, R.A.1    Peacher, J.L.2    Cox, H.L.3
  • 20
    • 0000808234 scopus 로고
    • Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals
    • 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
    • (1983) Phys. Rev. A , vol.27 , pp. 670
    • Trivedi, H.P.1    Steinborn, E.O.2
  • 21
    • 6244235267 scopus 로고
    • Numerical evaluation of molecular one-and tow-electron multicenter integrals with exponential-type orbitals via the fourier transform method
    • Grotendorst J and Steinborn E O 1988 Numerical evaluation of molecular one-and tow-electron multicenter integrals with exponential-type orbitals via the Fourier transform method Phys. Rev. A 38 3857
    • (1988) Phys. Rev. A , vol.38 , pp. 3857
    • Grotendorst, J.1    Steinborn, E.O.2
  • 22
    • 0033609676 scopus 로고    scopus 로고
    • Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinear D- and D̄-transformations
    • Safouhi H and Hoggan P E 1999 Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinear D-and D̄-transformations J. Phys. A: Math. Gen. 32 6203
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 6203
    • Safouhi, H.1    Hoggan, P.E.2
  • 24
    • 0001449239 scopus 로고
    • Two new classes of non-linear transformations for accelerating the convergence of infinite integrals and series
    • Levin D and Sidi A 1981 Two new classes of non-linear transformations for accelerating the convergence of infinite integrals and series Appl. Math. Comput. 9 175
    • (1981) Appl. Math. Comput. , vol.9 , pp. 175
    • Levin, D.1    Sidi, A.2
  • 25
    • 0003054141 scopus 로고
    • Extrapolation methods for oscillating infinite integrals
    • Sidi A 1980 Extrapolation methods for oscillating infinite integrals J. Inst. Math. Appl. 26 1
    • (1980) J. Inst. Math. Appl. , vol.26 , pp. 1
    • Sidi, A.1
  • 26
    • 84968492712 scopus 로고
    • The numerical evaluation of very oscillatory infinite integrals by extrapolation
    • Sidi A 1982 The numerical evaluation of very oscillatory infinite integrals by extrapolation Math. Comput. 38 517
    • (1982) Math. Comput. , vol.38 , pp. 517
    • Sidi, A.1
  • 28
    • 84948301871 scopus 로고
    • Developement of non-linear transformations for improving convergence of sequences
    • Levin D 1973 Developement of non-linear transformations for improving convergence of sequences Int. J. Comput. Math. B 3 371
    • (1973) Int. J. Comput. Math. B , vol.3 , pp. 371
    • Levin, D.1
  • 29
    • 0000199191 scopus 로고    scopus 로고
    • Efficient and rapid evaluation of three-center two-electron Coulomb and hybrid integrals using nonlinear transformations
    • Safouhi H and Hoggan P E 1999 Efficient and rapid evaluation of three-center two-electron Coulomb and hybrid integrals using nonlinear transformations J. Comput. Phys. 155 331
    • (1999) J. Comput. Phys. , vol.155 , pp. 331
    • Safouhi, H.1    Hoggan, P.E.2
  • 30
    • 0040646517 scopus 로고    scopus 로고
    • Numerical evaluation of three-center two-electron Coulomb and hybrid integrals over B functions using the H D and H D̄ methods and convergence properties
    • submitted
    • Safouhi H 2000 Numerical evaluation of three-center two-electron Coulomb and hybrid integrals over B functions using the H D and H D̄ methods and convergence properties J. Math. Chem. submitted
    • (2000) J. Math. Chem.
    • Safouhi, H.1
  • 33
    • 84987157199 scopus 로고
    • Improved quadrature methods for the Fourier transform of a two-center product of exponential-type basis functions
    • Homeier H H H and Steinborn E O 1992 Improved quadrature methods for the Fourier transform of a two-center product of exponential-type basis functions Int. J. Quantum Chem. 41 399
    • (1992) Int. J. Quantum Chem. , vol.41 , pp. 399
    • Homeier, H.H.H.1    Steinborn, E.O.2
  • 34
    • 84987138354 scopus 로고
    • Möbius-type quadrature of electron repulsion integrals with B functions
    • Steinborn E O and Homeier H H H 1990 Möbius-type quadrature of electron repulsion integrals with B functions Int. J. Quantum. Chem. 24 349
    • (1990) Int. J. Quantum. Chem. , vol.24 , pp. 349
    • Steinborn, E.O.1    Homeier, H.H.H.2
  • 35
    • 0001920396 scopus 로고
    • Numerical integration of a function with a sharp peak at or near one boundary using Möbius transformations
    • Homeier H H H and Steinborn E O 1990 Numerical integration of a function with a sharp peak at or near one boundary using Möbius transformations J. Comput. Phys. 87 61
    • (1990) J. Comput. Phys. , vol.87 , pp. 61
    • Homeier, H.H.H.1    Steinborn, E.O.2
  • 36
    • 84987143786 scopus 로고
    • Improved quadrature methods for three-center nuclear attraction integrals with exponential-type basis functions
    • Homeier H H H and Steinborn E O 1991 Improved quadrature methods for three-center nuclear attraction integrals with exponential-type basis functions Int. J. Quantum. Chem. 39 625
    • (1991) Int. J. Quantum. Chem. , vol.39 , pp. 625
    • Homeier, H.H.H.1    Steinborn, E.O.2
  • 37
    • 36749112175 scopus 로고
    • New representations for the spherical tensor gradient and the spherical delta function
    • Weniger E J and Steinborn E O 1983 New representations for the spherical tensor gradient and the spherical delta function J. Math. Phys. 24 2553
    • (1983) J. Math. Phys. , vol.24 , pp. 2553
    • Weniger, E.J.1    Steinborn, E.O.2
  • 43
    • 0002712936 scopus 로고    scopus 로고
    • Some properties of the coupling coefficients of real spherical harmonics and their relation to Gaunt coefficients
    • 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. 368 31
    • (1996) J. Mol. Struct. , vol.368 , pp. 31
    • Homeier, H.H.H.1    Steinborn, E.O.2
  • 44
    • 0040005593 scopus 로고    scopus 로고
    • On the computation of the integrated product of three spherical harmonics
    • Sébilleau D 1998 On the computation of the integrated product of three spherical harmonics J. Phys. A: Math. Gen. 31 7157
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 7157
    • Sébilleau, D.1
  • 45
  • 46
    • 0030514936 scopus 로고    scopus 로고
    • Fast evaluation of Gaunt coefficients
    • Yu-Lin Xu 1996 Fast evaluation of Gaunt coefficients Math. Comput. 65 1601
    • (1996) Math. Comput. , vol.65 , pp. 1601
    • Xu, Y.-L.1
  • 47
    • 0031556622 scopus 로고    scopus 로고
    • Fast evaluation of gaunt coefficients: Recursive approach
    • Yu-Lin Xu 1997 Fast evaluation of Gaunt coefficients: recursive approach J. Comput. Appl. Math. 85 53
    • (1997) J. Comput. Appl. Math. , vol.85 , pp. 53
    • Xu, Y.-L.1
  • 48
    • 0000577165 scopus 로고    scopus 로고
    • Efficient evaluation of vector translation coefficients in multiparticle light-scattering theories
    • Yu-Lin Xu 1998 Efficient evaluation of vector translation coefficients in multiparticle light-scattering theories J. Comput. Phys. 139 137
    • (1998) J. Comput. Phys. , vol.139 , pp. 137
    • Xu, Y.-L.1
  • 50
    • 0343863901 scopus 로고
    • Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
    • Weniger E J 1989 Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series Comput. Phys. Rep. 10 189
    • (1989) Comput. Phys. Rep. , vol.10 , pp. 189
    • Weniger, E.J.1


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