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  • Articles  (18)
  • Atomic, Molecular and Optical Physics  (18)
  • 1970-1974  (18)
  • 1960-1964
  • 1
    Electronic Resource
    Electronic Resource
    Stability conditions for the solutions of the hartree-fock equations. VII. Stability of some closed-shell nonalternant systemsQTG Publication M-121. (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 87-108 
    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 instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070110
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  • 2
    Electronic Resource
    Electronic Resource
    Padé approximants to physical properties via inner projections (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 133-134 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070114
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  • 3
    Electronic Resource
    Electronic Resource
    On the validity of Hamilton-Jacobi mechanics in the mean in quantum mechanics (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 449-453 
    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: It is shown that under certain conditions the time-dependent Hamilton-Jacobi equation (TDHJE) is satisfied in the mean in quantum mechanics provided the classical action is replaced by Dirac's complex quantal action. This may be regarded as the equivalent of Ehrenfest's theorem for the TDHJE. Expectation values of operators are discussed in a similar manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060306
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  • 4
    Electronic Resource
    Electronic Resource
    Gaussian representations of charge overlap effects in intermolecular forcesThis research was supported by a grant from the National Research Council of Canada. (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 501-508 
    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 ground state H—H+ and H—H interactions are used as model interactions for investigating the feasibility of using Gaussian basis sets for representing charge overlap effects in intermolecular forces. The non-expanded charge-induced dipole energy and the non-expanded dipole-dipole dispersion energy, respectively, for these interactions are calculated using two types of Gaussian basis functions to represent the first order wave function, Ψ(1). Very good results for these interaction energies, which include charge overlap effects, are obtained for all interatomic separations by using small Gaussian basis sets to represent the interaction, that is Ψ(1), and/or the isolated atoms (the zeroth order wave function).
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060311
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  • 5
    Electronic Resource
    Electronic Resource
    Integrals of quantum chemical interest in bases of laguerre functions. I. Functions of order 2l+2 (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 285-300 
    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: Formulae are presented for the evaluation of some definite integrals in which the Laguerre orthogonal functions are contained. In some cases mechanical quadratures are to be preferred, and a scheme is presented for generating such a quadrature as it is needed.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070211
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  • 6
    Electronic Resource
    Electronic Resource
    Long range interaction energies using Gaussian basis sets and a one center methodThis research was supported by a grant from the National Research Council of Canada. (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 201-209 
    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 one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R-8), for the H(ls) - H+ interaction employing two types of Gaussian basis sets constructed from functions of the form {rje-αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) - H(ls) interaction, through O(R-10), and the R-9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060202
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  • 7
    Electronic Resource
    Electronic Resource
    Gaussian orbitals optimized for lower bounds of hydrogenic atoms (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 951-958 
    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: Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson-Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1s, 2s, 2p, 3s, 3p, and 3d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070510
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  • 8
    Electronic Resource
    Electronic Resource
    Branch point singularities in the energy of the delta-function model of one-electron diatoms (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 131-142 
    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: Two different perturbation series (the polarization expansion and a united-atom expansion) of the ground state energy of the delta-function model for one-electron diatoms are studied and the radii of convergence are determined. For both expansions the singularity in the energy which limits the radius of convergence is a branch point with exponent one-half. The physical significance of the branch point is that for particular values of the perturbation parameter, two different energy eigenvalues coalesce. The positions of the branch points are computed as a function of the internuclear separation R. For all values of R, both series converge for all physical values of the perturbation parameters. A lower bound to the radius of convergence of the polarization expansion has been computed previously by Claverie. It is proved in the present paper that the lower bound calculation is in fact an exact determination of the radius of convergence. The results of the model study are applied to real one-electron diatoms to suggest the possible location of a branch point singularity in the energy of the ground state.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060110
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  • 9
    Electronic Resource
    Electronic Resource
    The non-crossing rule in molecular quantum mechanics (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 271-279 
    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: Previous mathematical proofs of the non-crossing rule concerning the potential energy curves of a diatomic molecule are examined and criticised. A new treatment is presented which is simple and mathematically rigorous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060206
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  • 10
    Electronic Resource
    Electronic Resource
    The cusp condition: Constraint on the electron density matrix (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 519-523 
    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: Attention is called to the attractive cusp conditions as useful constraints in fixing the elements of the electron density matrix. An equation for determination of pure state densities satisfying arbitrary constraints is reviewed, and a detailed formalism for using cusp conditions with this equation is displayed. A calculation is done using the nitrogen molecule as an example.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060313
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