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  • 1
    Online Resource
    Online Resource
    Wiley ; 1972
    In:  International Journal of Quantum Chemistry Vol. 6, No. 2 ( 1972-03), p. 353-366
    In: International Journal of Quantum Chemistry, Wiley, Vol. 6, No. 2 ( 1972-03), p. 353-366
    Abstract: A new expression is given for the electron repulsion integral over Slater‐type orbitals on four different centers. It is based on the asymptotic expansion derived from the bipolar expansion of a previous paper. The expression has the form where q p = { n p , l p , m p }. Both F and σ are closed expressions. The quantity F is a combination of incomplete gamma functions, Laguerre polynomials and spherical harmonics. It depends upon the relative coordinates of a point P on the AB axis and a point Q on the CD axis. The functions σ nlm ( A , B ) depend on the charge distribution (χ A χ B ); they have the character of overlap integrals and are of the form
    Type of Medium: Online Resource
    ISSN: 0020-7608 , 1097-461X
    URL: Issue
    Language: English
    Publisher: Wiley
    Publication Date: 1972
    detail.hit.zdb_id: 241655-4
    detail.hit.zdb_id: 1475014-4
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  • 2
    Online Resource
    Online Resource
    Wiley ; 1969
    In:  International Journal of Quantum Chemistry Vol. 3, No. 4 ( 1969-07), p. 493-501
    In: International Journal of Quantum Chemistry, Wiley, Vol. 3, No. 4 ( 1969-07), p. 493-501
    Abstract: Expansions in terms of the spherical coordinates of two particles are given for the interparticle distance and its inverse. The expansions are characterized in that each term is a product of analytical one‐variable functions. While it is possible to find acceptable expansions for r 12 , those obtained for r exhibit extremely slow convergence, unacceptable for practical use. The same objections must be raised against related expansions of multi‐centered molecular integrals.
    Type of Medium: Online Resource
    ISSN: 0020-7608 , 1097-461X
    URL: Issue
    Language: English
    Publisher: Wiley
    Publication Date: 1969
    detail.hit.zdb_id: 241655-4
    detail.hit.zdb_id: 1475014-4
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  • 3
    Online Resource
    Online Resource
    Elsevier BV ; 2009
    In:  Chemical Physics Vol. 356, No. 1-3 ( 2009-02), p. 64-75
    In: Chemical Physics, Elsevier BV, Vol. 356, No. 1-3 ( 2009-02), p. 64-75
    Type of Medium: Online Resource
    ISSN: 0301-0104
    Language: English
    Publisher: Elsevier BV
    Publication Date: 2009
    detail.hit.zdb_id: 184594-9
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  • 4
    Online Resource
    Online Resource
    Elsevier BV ; 1982
    In:  Chemical Physics Vol. 71, No. 1 ( 1982-9), p. 51-64
    In: Chemical Physics, Elsevier BV, Vol. 71, No. 1 ( 1982-9), p. 51-64
    Type of Medium: Online Resource
    ISSN: 0301-0104
    Language: English
    Publisher: Elsevier BV
    Publication Date: 1982
    detail.hit.zdb_id: 184594-9
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  • 5
    Online Resource
    Online Resource
    AIP Publishing ; 2010
    In:  The Journal of Chemical Physics Vol. 132, No. 7 ( 2010-02-21)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 132, No. 7 ( 2010-02-21)
    Abstract: In the first paper of this series, a very accurate ab initio potential energy curve of the Σ3g− ground state of O2 has been determined in the approximation that all valence shell electron correlations were calculated at the complete basis set limit. In the present study, the corrections arising from core electron correlations and relativity effects, viz., spin-orbit coupling and scalar relativity, are determined and added to the potential energy curve. From the 24 points calculated on this curve, an analytical expression in terms of even-tempered Gaussian functions is determined and, from it, the vibrational and rotational energy levels are calculated by means of the discrete variable representation. We find 42 vibrational levels. Experimental data (from the Schumann–Runge band system) only yield the lowest 36 levels due to significant reduction in the transition intensities of higher levels. For the 35 term values G(v), the mean absolute deviation between theoretical and experimental data is 12.8 cm−1. The dissociation energy with respect to the lowest vibrational energy is calculated within 25 cm−1 of the experimental value of 41 268.2±3 cm−1. The theoretical crossing between the Σ3g− state and the Σ1g+ state is found to occur at 2.22 Å and the spin-orbit coupling in this region is analyzed.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2010
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 6
    Online Resource
    Online Resource
    AIP Publishing ; 2008
    In:  The Journal of Chemical Physics Vol. 128, No. 21 ( 2008-06-07)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 128, No. 21 ( 2008-06-07)
    Abstract: A close approximation to the empirical potential energy curve of the neon dimer is obtained by coupled-cluster singles plus doubles plus noniterative triples calculations by using nonaugmented correlation-consistent basis sets without counterpoise corrections and complementing them by three-term extrapolations to the complete basis set limit. The potential energy is resolved into a self-consistent-field Hartree–Fock contribution and a correlation contribution. The latter is shown to decay in the long-range region in accordance with the empirical dispersion expansion.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2008
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 7
    Online Resource
    Online Resource
    AIP Publishing ; 1965
    In:  The Journal of Chemical Physics Vol. 43, No. 10 ( 1965-11-15), p. S88-S90
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 43, No. 10 ( 1965-11-15), p. S88-S90
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1965
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 8
    Online Resource
    Online Resource
    AIP Publishing ; 1999
    In:  The Journal of Chemical Physics Vol. 111, No. 19 ( 1999-11-15), p. 8825-8831
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 111, No. 19 ( 1999-11-15), p. 8825-8831
    Abstract: Recurrence relations are derived for constructing rotation matrices between complex spherical harmonics directly as polynomials of the elements of the generating 3×3 rotation matrix, bypassing the intermediary of any parameters such as Euler angles. The connection to the rotation matrices for real spherical harmonics is made explicit. The recurrence formulas furnish a simple, efficient, and numerically stable evaluation procedure for the real and complex representations of the rotation group. The advantages over the Wigner formulas are documented. The results are relevant for directing atomic orbitals as well as multipoles.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1999
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 9
    Online Resource
    Online Resource
    AIP Publishing ; 1994
    In:  The Journal of Chemical Physics Vol. 100, No. 8 ( 1994-04-15), p. 5836-5848
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 100, No. 8 ( 1994-04-15), p. 5836-5848
    Abstract: While contour plots provide conceptual pictures of potential energy surfaces and exhibit their critical points, quantitative determinations of critical points and reaction paths as well as dynamical calculations require a knowledge of the gradient fields. The corresponding orthogonal trajectory maps are more complex than contour maps, but they provide additional insights. They are found to contain certain frequently occurring structural elements and these patterns are here examined. It is shown that many of them result from local confluences of orthogonal trajectory bundles with gradient extremals. The analysis leads to the distinction between eight different kinds of such gradient extremal channels. The most important ones are the streambeds and ridges, the former being typical conceptual prototypes of reaction channels, the latter being prototypes of reaction barriers. Gradient extremal channels emanate from second order critical points in the directions of all normal modes, but they do not necessarily follow along the entire reaction path of any one reaction. They can also exist unrelated to critical points. The conclusions are exemplified on a number of model potential energy surfaces.  
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1994
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 10
    Online Resource
    Online Resource
    AIP Publishing ; 1991
    In:  The Journal of Chemical Physics Vol. 95, No. 3 ( 1991-08-01), p. 1862-1876
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 95, No. 3 ( 1991-08-01), p. 1862-1876
    Abstract: The topographies of two potential energy surfaces are examined in the vicinity of their intersection. A brief account of the basic theory is given and the possible surface types are discussed explicitly. Two main patterns are found. One of these (‘‘peaked’’) has the character of a tilted double cone in that the lower (upper) surface decreases (increases) in all directions from the intersection which is a point where an infinite number, in fact, all orthogonal trajectories emanate. The other pattern (‘‘sloped’’) results when both surfaces are monotonically sloped and touch each other along the slope, with most orthogonal trajectories bypassing the intersection. When the latter pattern prevails, the intersection can lie on a steepest descent line which originates at a transition state and hence may qualify as a reaction path model. An intermediate pattern, involving a horizontal slope on both surfaces, is also possible. The topographical patterns also differ markedly with respect to the bunching of the steepest descent lines. In general, the latter tend to veer away from the intersection on the lower surface favoring bifurcations, but are funneled towards the intersection on the upper surface, making the vicinity of the intersection a region favoring radiationless transitions. The various cases are classified and illustrated through quantitative graphs of contours and orthogonal trajectories.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1991
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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