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  • American Institute of Physics (AIP)  (5)
  • 1
    Electronic Resource
    Electronic Resource
    General formula evaluation of the electron-repulsion integrals and the first and second integral derivatives over Gaussian-type orbitals (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 5198-5205 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Recurrence relations between auxiliary functions to calculate the electron-repulsion integrals (ERIs) over Cartesian Gaussian-type orbitals (GTOs) can be derived. With the use of the Rys polynomials, this serves as a general formula method for evaluating ERIs and the ERI analytical derivatives. The computer code of the present method is quite general (i.e., it has no limitation for the shell type of GTOs), very compact (i.e., it has no coding difficulty), and extremely rapid (e.g., 2.1 μs per one ERI, 0.51 μs per one ERI first derivative, and 0.40 μs per one ERI second derivative for the [II||II] shell block). It is found that the present method is especially efficient for evaluating ERIs including g-type or higher GTOs, the first derivatives including f-type or higher GTOs, and the second derivatives including d-type or higher GTOs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461688
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  • 2
    Electronic Resource
    Electronic Resource
    General formula evaluation of the electron-repulsion integral (ERI) and its derivatives over Gaussian-type orbitals. II. ERI evaluation improved (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 2176-2181 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The general recurrence relation (RR) of paper I [J. Chem. Phys. 95, 5198 (1991)] can be improved. This improved RR, with the use of the Head–Gordon–Pople (HGP), is able to take the contraction of Gaussian-type orbitals (GTO's) efficiently into account for the electron-repulsion-integral (ERI) evaluation. With the use of the RR by Hamilton and Schaefer and by Lindh, Ryu, and Liu (HSLRL), this improved RR makes the evaluation more rapid. Furthermore, the calculation of the roots and weights of the Rys polynomial can be improved. As a result, an extremely rapid code can be obtained for a vector computer. For example, the measured time is 135 ns per one ERI for [HH||HH] shell block of the uncontracted GTO's, which is 16 times faster than that of paper I. When the degree of contraction K=2 for (HH||HH) shell block of the contracted GTO's, the measured time is 40 ns per one primitive ERI. It is confirmed that the present method is most efficient for the ERI evaluation of GTO's higher than or equal to f. It is found that both the HGP and the HSLRL RR's are numerically unstable in their bad cases. Several procedures to avoid their instabilities are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.464196
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  • 3
    Electronic Resource
    Electronic Resource
    Rigorous algorithm for the electron repulsion integral over the generally contracted solid harmonic Gaussian-type orbitals (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 7818-7829 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A rigorous general formula can be derived for the electron repulsion integral (ERI) over the generally contracted (GC) solid harmonic (SH) Gaussian-type orbitals by the use of the "reducing triply mixed solid harmonics" defined in this article. A general algorithm is obtained inductively from the general formula by the use of the "triply mixed solid harmonics" defined in this article. This algorithm is named as ACEb3k3-SH-GC. This ACEb3k3-SH-GC is rigorous and capable of computing the above SH-ERI very fast. Numerical assessment can be performed for (LL|LL) class of SH-ERIs (L=2–5). It is found that the present ACEb3k3-SH-GC is severalfold to a thousandfold faster than the ACEb3k3 algorithm for the usual segment contraction (which is named as ACEb3k3-SH-SC and is the fastest algorithm of all methods in the literature) for the generally contracted (LL|LL) class of SH-ERIs. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1316013
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  • 4
    Electronic Resource
    Electronic Resource
    Rigorous and rapid calculation of the electron repulsion integral over the uncontracted solid harmonic Gaussian-type orbitals (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4913-4922 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A rigorous general formula for calculating the electron repulsion integral (ERI) over the uncontracted solid harmonic (SH) Gaussian-type orbitals (GTOs) can be derived by the use of the "reducing mixed solid harmonics" defined in this paper. A general algorithm can be obtained inductively from this formula with the use of the "mixed solid harmonics" also defined in this paper. This algorithm is named as accompanying coordinate expansion (ACE) b1k1. This ACE-b1k1 is capable of computing very fast SH-ERIs. The floating-point operation (FLOP) count assessment is shown for the (LL|LL) class of SH-ERIs (L=2–5). It is found that the present ACE-b1k1 algorithm is the fastest among all algorithms in the literature for the ERI over the uncontracted SH-GTOs. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479785
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  • 5
    Electronic Resource
    Electronic Resource
    Rigorous formula for the fast calculation of the electron repulsion integral over the solid harmonic Gaussian-type orbitals (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 881-890 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A rigorous general formula for calculating the electron repulsion integral (ERI) over the solid harmonic (SH) Gaussian-type orbitals (GTOs) can be derived. A general algorithm can be obtained from this formula named as accompanying coordinate expansion (ACE) b3k3. This algorithm is capable of computing very fast SH-ERIs, especially for SH contracted GTOs. Numerical assessment is shown for the (LL|LL) class of SH-ERIs (L=2–5). It is found that the present ACE-b3k3 algorithm is the fastest among all algorithms in the literature in the floating-point-opration (FLOP) count assessment when the degree of contraction is large. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476628
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