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  • 1
    Electronic Resource
    Electronic Resource
    Convergence analysis of the addition theorem of Slater orbitals and its application to three-center nuclear attraction integrals (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 5718-5729 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The mathematical foundation of the methods using addition theorems to evaluate multicenter integrals over Slater-type orbitals is actually well understood. However, many numerical aspects of such approaches still require further investigations. In the framework of these methods, multicenter integrals are generally represented by infinite series which under certain circumstances are very slowly convergent. Accordingly, the determination of the convergence type of such series is of great importance since it allows one to choose adequately the convergence accelerator to be used in the summation procedure. In this work, the convergence of the two-range addition theorem proposed by Barnett and Coulson [Philos. Trans. R. Soc. London, Ser. A 243, 221 (1951)] is analyzed. The results obtained from this study are then applied to study the convergence of three-center nuclear integrals, and most importantly, to discuss the choice of the convergence accelerator to be used in the summation procedure. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477194
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  • 2
    Electronic Resource
    Electronic Resource
    Comprehensive strategy for the calculation of overlap integrals with Slater-type orbitals (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 881-889 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A strategy is presented for the calculation of two-center overlap integrals over Slater-type orbitals. Displaced orbitals are expanded in spherical harmonics with Löwdin α-functions as coefficients. The exponentials in the α-functions are expanded, leading to representation in terms of stored E and F matrices. For a given precision, the number of terms needed for each orbital for a specified harmonic, and its displacement multiplied by its screening constant, is predetermined and stored. A survey of these data is presented. The one-dimensional integration needed for the overlap is done by Gauss-Legendre numerical integration over the interior region and analytically over the exterior. Complete stability is achieved and excellent results obtained. Implications for all multicenter molecular integrals are apparent. © 1997 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Computer-generated formulas for two-center coulomb integrals over slater- type orbitals (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 1217-1224 
    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: Formulas can be automatically generated for all two-center Coulomb integrals over Slater-type orbitals by means of the “C-matrix” single-center expansion method with use of “computer algebra.” The formula coefficients may be stored in two-dimensional arrays.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560200606
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  • 4
    Electronic Resource
    Electronic Resource
    Formulas for three-center exchange integrals by computer implementation of the Löwdin α-function method (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 61-66 
    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: By use of computer algebra and expansions of orbitals about a single center in spherical harmonics with a matrix representation for the α-function coefficients it is possible to produce formulas for each term of an infinite series that represents the value of a three-center exchange integral. Only seven terms are required to get six decimal digits for triatomic hydrogen. This method is readily generalized to solve all three-center exchange integrals over Slater-type orbitals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260810
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  • 5
    Electronic Resource
    Electronic Resource
    Löwdin α-function, overlap integral, and computer algebra (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 749-754 
    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 commercial computer algebra program, Mathematica, is used to generate the C matrix that characterizes our implementation of the Löwdin α-function method as applied to Slater-type orbitals. An example of a two-center overlap integral is done to show how the arbitrary precision capability of Mathematica can overcome severe cancellation errors encountered with programming in FORTRAN. This strategy is capable of being generalized to other multicenter molecular integrals. Mathematica programs are included.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410511
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  • 6
    Electronic Resource
    Electronic Resource
    Restricted basis functions for H2+ with use of overlap integrals of Slater-type orbitals (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 265-270 
    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: The Löwdin α-function method, augmented by the computer-generated C matrix, is applied to the H2+ molecule. A LCAO (linear combination of atomic orbitals) method is employed using several s-orbitals with equal screening constants. Precautions are taken to avoid cancellation errors, thereby achieving convergence with increasingly higher orbitals. © 1992 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560440823
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  • 7
    Electronic Resource
    Electronic Resource
    Accurate LCAO ground state calculations of HeH2+ using slater-type orbitals (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 755-758 
    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 linear combination of atomic orbitals (LCAO) of the Slater type is used in a variational treatment of the HeH2+ ion to achieve excellent results for the ground state energy of this heteronuclear diatomic system. As in our recent treatment of H2+, we use orbitals with identical screening constants but with increasing principal quantum numbers and angular momentum. This strategy was feasible because of our ability to accurately evaluate all overlap integrals. Unlike even tempered Gaussian-type LCAO, our results become more accurate at large interatomic separations. Using two different screening constants (one type associated with each atom) proved to be unnecessary. © 1993 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560480867
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  • 8
    Electronic Resource
    Electronic Resource
    Exact formulas for overlap integrals of Slater-type orbitals with equal screening constants (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 19 (1981), S. 567-574 
    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: Exact formulas for 147 overlap integrals between Slater-type orbitals with equal screening constants are presented in the most simplified form. This represents all combinations of orbitals with quantum numbers: 1 ≤ N ≤ 5, 0 ≤ L ≤ 3, and M ≤ L. The formulas are automatically generated by computer using the “C-matrix” single-center expansion method. There are no limitations to the applicability of this method to orbitals of higher quantum numbers.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560190410
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  • 9
    Electronic Resource
    Electronic Resource
    Computer-generated formulas for overlap integrals of slater-type orbitals (1980)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 18 (1980), S. 709-713 
    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: Using a modified form of Sharma's method for the expansion of a Slater-type orbital in spherical harmonics about a displaced center, a general expression for the overlap integral between two orbitals is derived that is equivalent to that given by Sharma. By use of a simple kind of “computer algebra” this expression is developed here into a formula that is equivalent to earlier known ones and may have computational advantages when the generated formula coefficients are stored. This method is capable of extension to more complicated integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560180306
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  • 10
    Electronic Resource
    Electronic Resource
    Evaluation of two-center overlap and coulomb integrals derived from slater-type orbitals (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 1079-1089 
    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: The strategy for the evaluation of two-center overlap and Coulomb integrals is illustrated by using computer-generated formulas produced from 1s orbitals. There is no loss in generality as these formulas have the same structure for higher quantum numbers. For small parameter values, singularities may be removed from the formulas by expanding exponential functions and collecting coefficients of like powers by machine. Suitable terminated expansions, along with exact formulas, permit high accuracy throughout the entire possible range of parameter values.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210612
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