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  • AIP Publishing  (8)
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  • AIP Publishing  (8)
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  • 1
    Online Resource
    Online Resource
    AIP Publishing ; 1967
    In:  The Journal of Chemical Physics Vol. 46, No. 5 ( 1967-03-01), p. 1717-1726
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 46, No. 5 ( 1967-03-01), p. 1717-1726
    Abstract: The perturbation treatment of electron correlation is generalized to include an initial orbital approximation Ψ0 in which the orbitals are arbitrary within a unitary transformation which leaves Ψ0 unchanged. Various methods are considered for the partitioning of the total Hamiltonian into zeroth- and first-order parts consistent with a given zeroth-order Ψ0. One particular partitioning is discussed in detail which leads to simple and physically significant expressions for the second- and third-order energies, and for which the second-order energy gives a good estimate of the correlation energy when the orbitals are well localized and when no near-degeneracies are present. A calculation of the angular correlation in the ground state of the beryllium atom serves to investigate the validity of a number of concepts.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1967
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 2
    Online Resource
    Online Resource
    AIP Publishing ; 1962
    In:  The Journal of Chemical Physics Vol. 37, No. 2 ( 1962-07-15), p. 461-462
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 37, No. 2 ( 1962-07-15), p. 461-462
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1962
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 3
    Online Resource
    Online Resource
    AIP Publishing ; 1963
    In:  The Journal of Chemical Physics Vol. 39, No. 9 ( 1963-11-01), p. 2365-2366
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 39, No. 9 ( 1963-11-01), p. 2365-2366
    Abstract: A corollary to a theorem by Kato is derived which relates the charge density and its derivative at the nucleus of an atom. For nuclear charge Z it is (∂ρ/∂r)r=0=−2Zρ(0).
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1963
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 4
    Online Resource
    Online Resource
    AIP Publishing ; 1973
    In:  The Journal of Chemical Physics Vol. 59, No. 5 ( 1973-09-01), p. 2427-2429
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 59, No. 5 ( 1973-09-01), p. 2427-2429
    Abstract: The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1973
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 5
    Online Resource
    Online Resource
    AIP Publishing ; 1966
    In:  The Journal of Chemical Physics Vol. 45, No. 1 ( 1966-07-01), p. 328-337
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 45, No. 1 ( 1966-07-01), p. 328-337
    Abstract: The conditions under which a correlated wavefunction for an atomic system can be an eigenfunction of angular momentum are investigated. It is shown how symmetry-adapted pair-correlated wavefunctions may be set up in which the pair functions satisfy the condition of strong orthogonality to the orbitals in the initial orbital approximation, and in terms of which the variational equivalent of the first-order perturbation equation reduces to a set of uncoupled two-body equations, one for each pair. The approach is illustrated by application to the lowest 3P, 1D, and 1S states of carbon and to the ground state of neon, the latter case being of particular interest as it shows how the separation of the orbitals into unique pairs is unsatisfactory when the orbital approximation contains a number of equivalent orbitals.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1966
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 6
    Online Resource
    Online Resource
    AIP Publishing ; 1971
    In:  The Journal of Chemical Physics Vol. 54, No. 3 ( 1971-02-01), p. 1114-1119
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 54, No. 3 ( 1971-02-01), p. 1114-1119
    Abstract: The proposition that localized orbitals are the orbitals most suitable for extending the wavefunction to take into account electron correlation is examined in the light of recent calculations of correlation energies. It is found, in agreement with the results of other authors, that the total interorbital correlation energy may be expected to be larger than the intraorbital energy in many systems of chemical interest, and that the ratio of these contributions is probably rather insensitive to a transformation of orbitals. It is also found that the correlation between electrons with like spins can make a considerable contribution to the correlation energy, and that this contribution is invariant with respect to a transformation of orbitals. The concept of nearest-neighbor orbitals is used to propose a new localization criterion which minimizes the interaction between electrons in orbitals localized on different atoms in a molecule. The dependence on the orbitals of the two-particle density function is examined. Orbital correlation factors are introduced which provide information as to the dependence of electron correlation on the distribution of electrons in the orbital approximation.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1971
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
    Location Call Number Limitation Availability
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  • 7
    Online Resource
    Online Resource
    AIP Publishing ; 1967
    In:  The Journal of Chemical Physics Vol. 46, No. 5 ( 1967-03-01), p. 1727-1735
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 46, No. 5 ( 1967-03-01), p. 1727-1735
    Abstract: The perturbation—variation treatment of electron correlation is generalized to include a many-configuration initial approximation Ψ0 which is a linear combination of all those configurations consistent with a chosen basis set of orbitals. Such a generalization enables all configurations that make a large contribution to the wavefunction to be included in Ψ0, so that the problem of degeneracies and near-degeneracies is removed, and the correction to Ψ0, being essentially small, may then be determined by first-order perturbation theory. The initial approximation may be determined using configuration-interaction methods, which gives upper bounds to a number of states. Excited states may be treated as easily as, and together with, the ground state. It is shown that when Ψ0 is the optimum combination of configurations consistent with a chosen orbital basis, for any state, then it is invariant under a unitary transformation of the orbitals of the basis. This allows a transformation to orbitals which optimize the contribution of the first-order wavefunction.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1967
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
    Location Call Number Limitation Availability
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  • 8
    Online Resource
    Online Resource
    AIP Publishing ; 1966
    In:  The Journal of Chemical Physics Vol. 44, No. 10 ( 1966-05-15), p. 3934-3940
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 44, No. 10 ( 1966-05-15), p. 3934-3940
    Abstract: The behavior of the electronic energy for the ground state of a one-electron heteronuclear diatomic molecule in the vicinity of the united atom is obtained through terms of order R5 in the internuclear distance R. The presence of a term in R5logR reveals that the electronic energy is not an analytic function of R at the united atom. The expansion is checked by means of the Hellmann—Feynman theorem and the work of Dalgarno and Lynn.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 1966
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
    Location Call Number Limitation Availability
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