메뉴 건너뛰기




Volumn 35, Issue 45, 2002, Pages 9685-9698

Convergence properties of the SD̄ transformation and a fast and accurate numerical evaluation of molecular integrals

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037111804     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/45/314     Document Type: Article
Times cited : (7)

References (43)
  • 1
    • 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
  • 2
    • 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
  • 3
    • 0023427925 scopus 로고
    • An algorithm for a generalization of the Richardson extrapolation process
    • Ford W F and Sidi A 1987 An algorithm for a generalization of the Richardson extrapolation process SIAM J. Numer. Anal. 24 1212
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1212
    • Ford, W.F.1    Sidi, A.2
  • 4
    • 0000950740 scopus 로고    scopus 로고
    • The H D and HD̄ methods for accelerating the convergence of three-center nuclear attraction and four-center two-electron Coulomb integrals over B functions and their convergence properties
    • Safouhi H 2000 The H D and HD̄ 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
    • (2000) J. Comput. Phys. , vol.165 , pp. 473
    • Safouhi, H.1
  • 5
    • 0035536410 scopus 로고    scopus 로고
    • Numerical evaluation of three-center two-electron Coulomb and hybrid integrals over B functions using the H D and HD̄ methods and convergence properties
    • Safouhi H 2000 Numerical evaluation of three-center two-electron Coulomb and hybrid integrals over B functions using the H D and HD̄ methods and convergence properties J. Math. Chem. 29 213-32
    • (2000) J. Math. Chem. , vol.29 , pp. 213-232
    • Safouhi, H.1
  • 6
    • 0035815604 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-center nuclear attraction integrals over B functions
    • 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-center nuclear attraction integrals over B functions J. Phys. A: Math. Gen. 34 2801
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 2801
    • Safouhi, H.1
  • 9
    • 0037050816 scopus 로고    scopus 로고
    • Efficient and rapid numerical evaluation of the two-electron four-center Coulomb integrals using nonlinear transformations and practical properties of sine and Bessel functions
    • 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
    • (2002) J. Comput. Phys. , vol.176 , pp. 1-19
    • Safouhi, H.1
  • 10
    • 2342430094 scopus 로고
    • New developments in molecular orbital theory
    • Roothaan C C 1951 New developments in molecular orbital theory Rev. Mod. Phys. 23 69
    • (1951) Rev. Mod. Phys. , vol.23 , pp. 69
    • Roothaan, C.C.1
  • 11
    • 10844264917 scopus 로고
    • Basis set selection for molecular calculations
    • Davidson E R and Feller D 1986 Basis set selection for molecular calculations Chem. Rev. 86 681
    • (1986) Chem. Rev. , vol.86 , pp. 681
    • Davidson, E.R.1    Feller, D.2
  • 12
    • 84980086883 scopus 로고
    • On the eigenfunctions of many-particle systems in quantum mechanics
    • Kalo 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
    • Kalo, T.1
  • 14
    • 0002665562 scopus 로고
    • Bounds on exponential decay of eigenfunctions of Schrödinger operators
    • ed S Graffi (Berlin: Springer)
    • Agmon S 1985 Bounds on exponential decay of eigenfunctions of Schrödinger operators Schrödinger Operators ed S Graffi (Berlin: Springer) pp 1-38
    • (1985) Schrödinger Operators , pp. 1-38
    • Agmon, S.1
  • 15
    • 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 Vol 2. Quantum Mechanics ed B Alder, S Fernbach and M Rotenberg (New York: Academic)
    • (1963) Methods in Computational Physics Vol 2. Quantum Mechanics , vol.2
    • Shavitt, I.1
  • 16
    • 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
  • 17
    • 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
  • 18
    • 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
  • 20
    • 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
  • 22
    • 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
  • 23
    • 36149002029 scopus 로고
    • Atomic shielding constants
    • Slater J C 1930 Atomic shielding constants Phys. Rev. 36 51
    • (1930) Phys. Rev. , vol.36 , pp. 51
    • Slater, J.C.1
  • 24
    • 0040053100 scopus 로고
    • Analytic atomic wave functions
    • Slater J C 1932 Analytic atomic wave functions Phys. Rev. 42 33
    • (1932) Phys. Rev. , vol.42 , pp. 33
    • Slater, J.C.1
  • 25
    • 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
  • 26
    • 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
  • 27
    • 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
  • 28
    • 0000609316 scopus 로고    scopus 로고
    • Efficient evaluation of integrals for density functional theory: Non-linear D-transformations to evaluate three-center nuclear attraction integrals over B functions
    • Safouhi H, Pinchon D and Hoggan P E 1998 Efficient evaluation of integrals for density functional theory: non-linear D-transformations to evaluate three-center nuclear attraction integrals over B functions Int. J. Quantum Chem. 70 181
    • (1998) Int. J. Quantum Chem. , vol.70 , pp. 181
    • Safouhi, H.1    Pinchon, D.2    Hoggan, P.E.3
  • 29
    • 0032491356 scopus 로고    scopus 로고
    • Efficient evaluation of Coulomb integrals: The non-linear D- and D̄-transformations
    • Safouhi H and Hoggan P E 1998 Efficient evaluation of Coulomb integrals: the non-linear D- and D̄-transformations J. Phys. A: Math. Gen. 31 8941
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 8941
    • Safouhi, H.1    Hoggan, P.E.2
  • 30
    • 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
  • 31
    • 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
  • 32
    • 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
  • 33
    • 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
  • 35
    • 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
  • 36
    • 0033609676 scopus 로고    scopus 로고
    • Three-center two electron Coulomb and hybrid integrals evaluated using nonlinear D and D̄-transformations
    • Safouhi H and Hoggan P E 1999 Three-center 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
  • 42
    • 0035793525 scopus 로고    scopus 로고
    • An extremely efficient approach for accurate and rapid evaluation of three-center two-electron Coulomb and hybrid integral over B functions
    • Safouhi H 2001 An extremely efficient approach for accurate and rapid evaluation of three-center two-electron Coulomb and hybrid integral over B functions J. Phys. A: Math. Gen. 34 881
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 881
    • Safouhi, H.1
  • 43
    • 0001293659 scopus 로고
    • Some properties of a generalization of the Richardson process
    • Sidi A 1979 Some properties of a generalization of the Richardson process J. Inst. Math. Appl. 24 327
    • (1979) J. Inst. Math. Appl. , vol.24 , pp. 327
    • Sidi, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.