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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Intrinsic reaction coordinate for the gas-phase pyrolysis of ethyl formate (1983)
    Springer
    Theoretical chemistry accounts 62 (1983), S. 245-255 
    Details
    ISSN: 1432-2234
    Keywords: Intrinsic reaction coorinate ; Ethyl formate ; Gas phase pyrolysis ; Activation entropy ; MNDO molecular orbital calculations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Fukui's IRC is obtained for the pyrolysis of ethyl formate within the level of MNDO molecular orbital calculations. The activation enthalpy and entropy can be evaluated from the calculated partition functions and compared with the observed values. It is suggested that the pyrolysis would be significantly promoted when it occurs in an aprotic polar solvent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00548838
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  • 7
    Electronic Resource
    Electronic Resource
    ACE algorithm for the rapid evaluation of the electron-repulsion integral over Gaussian-type orbitals (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 59 (1996), S. 209-218 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new series of general formulas to evaluate the electron-repulsion integral (ERI) can be derived from modifying the Gauss-Rys quadrature formula. These named as “accompanying coordinate expansion (ACE) formulas” are capable of evaluating very fast ERIs, especially for contracted Gaussian-type orbitals (GTOs). According to the degree of the contraction of GTOs, the optimum formula can be selected among these ACEs. Numerical examples are shown for (ps|ps) and (pp|pp) ERIs as typical examples. It is found that the present ACE algorithm is numerically stable and is most efficient among all algorithms in the literature in the floating-point-operation (FLOP) count for all varieties of the degree of contraction. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Spin and charge densities from Hiller-Sucher-Feinberg identities. Test calculations for He, B, C, N, O, and F atoms and H2O, N2, and CH3 molecules (1988)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 195-197 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560340212
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  • 9
    Electronic Resource
    Electronic Resource
    Charge density by the use of the hiller-sucher-feinberg identity. Perturbative corrections and configuration interaction effects (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 36 (1989), S. 213-223 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Configuration interaction (CI) calculations are carried out for He atom and H2, LiH, and BH molecules in order to obtain the value of the charge density at the nucleus by the use of the Hiller-Sucher-Feinberg (HSF) identity. The HSF density also can be calculated with the double perturbation theory based on the Møller-Plesset-type theory and also on the Epstein-Nesbet type. It is found that each value of the HSF density for these perturbative corrections is very similar to the corresponding value by the CI with single- and double-electron excitations. Especially for the He atom, the HSF density value by the full-CI wave function coincides with the exact value of the charge density in three significant figures. The electron correlation effects are found to be small but cannot be ignored in the HSF density. It can be shown that the superiority of the HSF density over the usual delta-function-type density is excellently confirmed.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560360306
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  • 10
    Electronic Resource
    Electronic Resource
    Calculation in k space of integrals arising in the theory of Van der Waals forces. II. Formulas for arbitrary atoms (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 633-649 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Basic integrals arising in the momentum space formulation of the van der Waals forces are derived for arbitrary two atoms. These integrals are essentially the matrix elements of the Fourier transformed Coulomb operator and the Fourier transformed square of the Coulomb operator between any two Slater orbitals. The derivation is completely analytic and the results are expressed as finite series expansions in terms of auxiliary integrals. Recursion relations among the auxiliary integrals are developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560240610
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