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  • Atomic, Molecular and Optical Physics  (22)
  • Wiley-Blackwell  (22)
  • National Academy of Sciences
  • 1970-1974  (22)
  • 1
    Electronic Resource
    Electronic Resource
    Direct minimization of the energy functional in LCAO-MO calculations (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 459-473 
    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: In this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO-MO-MC-SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed- and open-shell problems as special cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070304
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  • 2
    Electronic Resource
    Electronic Resource
    SCF equations for pure spin states with many-particle interactions (1974)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 539-546 
    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: SCF equations for any pure spin state are given for a spin-free system with many-particle interactions. The equations are very simple and explicit. Due to the use of different antisymmetric requirement our equations are different from some of the other methods. In our method, the abstract group theory formalism is converted into some explicit and straightforward equations which makes the many-particle interaction problem easier to handle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560080405
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  • 3
    Electronic Resource
    Electronic Resource
    Approximate valence-shell electron unrestricted Hartree-Fock calculations with orthogonalized atomic orbitals: Proton hyperfine splittings in benzyl and related radicalsPaper presented at the First International Congress of Quantum Chemistry, Menton, France, July 4-10, 1973. (1974)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 451-465 
    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 modified INDO procedure has been used to calculate the proton hyperfine splittings in benzyl and the isoelectronic anilino, phenoxy and 2-azabenzyl as well as 2- and 3-thenyl radicals. The present procedure differentiates between s-, p- and d-orbitals on an atom in estimating various integrals involving them, satisfies the rotational invariance requirements and employs an orthogonalized basis set of atomic orbitals for obtaining core-Hamiltonian matrix elements. The calculations based on using the exponents which depend only on the type of orbital and the nature of atom fail to provide correct relative order of ortho and para proton splittings in benzyl as well as anilino, phenoxy and 2-azabenzyl radicals. On the other hand, use of the exponents which are modified according to the charge densities in various orbitals leads to a high absolute value for para proton splitting compared to that for ortho proton splitting which in case of all these radicals is in agreement with experiment. A spin density calculation on benzyl, anilino and phenoxy radicals considering the variation of one-center one-electron and one-center two-electron integrals for different protons with their charges is found to yield further improvement in the relative order of ortho and para proton splittings in all these radicals. In 2- and 3-thenyl radicals the role of 3d-orbitals on sulfur has also been examined. To our knowledge, no unrestricted INDO calculations including 3d-orbitals on sulfur have been reported in the literature so far.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560080311
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  • 4
    Electronic Resource
    Electronic Resource
    A perturbed generalized eigenvalue equation for the helium atom. II (1971)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 387-394 
    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 Schrödinger equation for helium is written as a generalized eigenvalue equation which is solved for the ground state using perturbation theory. Two zero order equations are used and defined implicitly by specifying their eigenvalues and eigenfunctions. In both cases the eigenfunctions are taken to be the complete discrete set of products of eigenfunctions of the generalized eigenvalue equation for the hydrogen atom. To complete the definition the zero order eigenvalues are needed and two different intuitive choices are made. In the better of our two calculations an energy of -2.9014 a.u. is obtained for helium using the perturbation theory to second order.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560050404
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  • 5
    Electronic Resource
    Electronic Resource
    A comment on the super-secular-equation in a symmetry adapted basis (1971)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 699-702 
    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 super-secular-equation has been introduced by Löwdin to discuss the Schrödinger equation in terms of a linearly dependent basis. The method is shown to be particularly simple when the basis is a symmetry adapted one. By expanding the secular equation a formula giving a good estimate of the eigenvalue is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560050609
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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
    Solution of the Hartree-Fock problem by expansion onto nested basesAided by research grants to the Johns Hopkins University from the National Science Foundation (Grant No. GP-8702) and the National Institutes of Health (Grant No. 5 R01 GM14470). (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 245-255 
    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 method for solving the Hartree-Fock problem in a finite basis set is derived, which permits each orbital to be expanded in a different basis. If the basis set for each orbital φi contains the basis functions for the preceding orbitals, φi-1, φi-2,… φ1, then the φi form an orthonormal set. One advantage over the standard Hartree-Fock method is that a different long range behavior for each orbital, as for example is required in the Hartree-Fock-Slater method, can be forced. A calculation on the ground state of beryllium is performed using the nested procedure. Very little energy is lost because of nesting, and the node in the 1s orbital disappears.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040303
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  • 8
    Electronic Resource
    Electronic Resource
    On energy bounds derived from the conjugate eigenvalue problemThis work was supported by national science foundation grant GP-12832, National Aeronautics and Space Administration Grant NGL 50-002-001, and in part by the Mathematics Research Center, U.S. Army, under Contract DA-31-124-ARO-D-462. (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 453-463 
    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: An upper bound for E0, which has been derived from the conjugate eigenvalue problem by Hall, is discussed. It is emphasized that the bound is only guaranteed when V is negative-definite. An alternative bound is presented which is free from this restriction, and the underlying iterative procedure is given. Hall's result is generalized to admit internuclear distances, and the theory is illustrated by a one-dimensional system with delta-function potentials. Some disadvantages of the approach are mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040502
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  • 9
    Electronic Resource
    Electronic Resource
    Small, simultaneous adjustments of orbital exponents in LCAO-MO-SCF calculations using self-consistent perturbation theory (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 89-95 
    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: Self-consistent perturbation theory is introduced to facilitate making small, simultaneous variations in orbital exponents. This is accomplished by interpreting these variations as perturbations on the quantum mechanical system. The minimum-energy condition yields a set of linear equations for the desired exponential corrections.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040108
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  • 10
    Electronic Resource
    Electronic Resource
    A perturbed generalized eigenvalue equation for the helium atom (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 613-623 
    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 Schrödinger equation for helium is written as a generalized eigenvalue equation and this is solved perturbatively for the ground state. The zero order equation is taken to be that of a “six-dimensional hydrogen atom” since, in generalized eigenvalue form, this has a discrete spectrum. Although the zero-order wave function is very poor and gives only 86% of the energy the perturbation procedure is able to improve this to 99% through third-order.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040608
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