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  • 1
    Electronic Resource
    Electronic Resource
    Electrostatic force theory for a molecule and interacting molecules. IV. Long-range forces between two atoms (1974)
    s.l. : American Chemical Society
    Journal of the American Chemical Society 96 (1974), S. 6000-6008 
    Details
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ja00826a008
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  • 2
    Electronic Resource
    Electronic Resource
    Electron densities in momentum and position spaces. II. Application of density mapping to the helium ground state (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4758-4762 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The recently proposed method of density mapping between momentum and position spaces is applied to the ground state of the helium atom. The Kellner densities and wave functions are used as reference, and the Eckart densities γ(p) and ρ(r) are employed as test densities keeping their parent wave functions in blind. From the momentum density γ(p), the corresponding position density ργ(r) and the position moments 〈rn〉γ (−2≤n≤4) are generated within a few percent error. The inverse procedure generates the momentum density γρ(p) and the momentum moments 〈pn〉ρ (−2≤n≤4) from the position density ρ(r) with a better accuracy. Density-functional calculations are performed in a simplified manner and the energies close to the Hartree–Fock limit value are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456764
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  • 3
    Electronic Resource
    Electronic Resource
    Schrödinger equation in terms of linearly averaged position moments (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4774-4778 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Linearly averaged position moment (LAPM) [Rk11Rk22⋅⋅⋅ Rk3N3N] is defined as the linear (not quadratic)average of the position moment operator Rk11Rk22⋅⋅⋅ Rk3N3N over the N-electron wave function Ψ({Rj}), where {Rj} are 3N Cartesian coordinates of electrons and {kj} are non-negative integers. When all the LAPM's are well defined, it is shown that the Schrödinger equation is equivalent to a set of an infinite number of equations between LAPM's involving the potential-energy operator. The kinetic energy operator does not appear. The spherical polar representation of the LAPM equation is also presented. Illustrations are given for simple one- and two-electron atoms, where the LAPM equation is applied to the determination of approximate wave functions and associated energies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456766
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Position moments linearly averaged over the wave function (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 5961-5962 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown that there exists a set of relations between position moments rk (with k being a nonnegative integer) linearly averaged over the wave function. The true wave function must satisfy all of these relations, and therefore they can be used as criteria to assess the accuracy of approximate wave functions. The zero momentum energy formula proposed previously is the simplest case of the present results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455527
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  • 5
    Electronic Resource
    Electronic Resource
    Nonvariational configuration interaction calculations by local scaling method (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3805-3807 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: To first order, the Hartree–Fock one-electron density of a given state of an N-electron system is identical to the exact density. For this reason, an accurate wave function must fulfill the necessary condition of yielding a one-electron density similar to the Hartree–Fock density. For a given configuration interaction (CI) wave function with arbitrary parameters, we have used the local scaling method in order to construct a modified CI wave function which associates a one-electron density exactly the same as the Hartree–Fock density. The resultant nonvariational CI wave function is shown to have an energy comparable to that from the variational CI calculation for the ground state of the helium atom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459752
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  • 6
    Electronic Resource
    Electronic Resource
    One-electron diatomics in momentum space. VI. Nonvariational approach to excited states (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 1092-1095 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based on the Fock transformation of momentum variable, we can reduce the momentum-space Schrödinger equation for one-electron diatomics to a homogeneous Fredholm-type integral equation with a degenerate kernel. A nonvariational LCAO solution to this integral equation is applied to various nontrivial excited states of the hydrogen molecular ion for the first time. The results show an excellent convergence and the exact electronic energy given in the literature is reproduced almost completely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457181
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  • 7
    Electronic Resource
    Electronic Resource
    Electron momentum redistribution during the van der Waals interaction between two hydrogen atoms (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3020-3026 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using a momentum-space method, we first determine the leading second-order perturbation wave function ψ(2)6(p1,p2) (proportional to R−6) of the van der Waals interaction between two ground-state hydrogen atoms. The resultant wave function is used to study the electron momentum redistribution γ6(p) which appears in the second order of the perturbation. The momentum density is shown to have the contractive nature as has been conjectured previously. The accuracy of the present ψ(2)6(p1,p2) is numerically verified through the calculation of the second-order kinetic energy T6, which should be equal to five times the dispersion energy E6 according to the virial theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456923
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  • 8
    Electronic Resource
    Electronic Resource
    Pathologic inversion of core orbitals in approximate Hartree–Fock calculations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 7313-7316 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The common sense in quantum chemistry that each bonding orbital is filled before the corresponding antibonding orbital is shown to be often violated for the core orbitals of diatomic systems in approximate Hartree–Fock calculations. Through theoretical analysis of the core orbital energies and numerical analysis of some specific diatomic systems, the origin of this pathologic ordering is suggested to be unusual mixing of valence orbitals into core orbitals induced by the use of basis sets with unbalanced core–valence quality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456210
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  • 9
    Electronic Resource
    Electronic Resource
    Sum rules for nuclear attraction integrals over hydrogenic orbitals (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4696-4699 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based on the property of two functions Snlmn'l'm'(R) and Wnlmn'l'm'(R) introduced in the Fock representation of the momentum-space Schrödinger equation for one-electron diatomics, we derive various relations and sum rules for the one-, two-, and three-center nuclear attraction integrals over (bound state) hydrogenic orbitals with a common exponent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452833
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  • 10
    Electronic Resource
    Electronic Resource
    Accurate third order energy of the H(1s)–H(1s) van der Waals interaction (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 1137-1141 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report an accurate coefficient of the leading third order energy (proportional to R−11) of the H(1s)–H(1s) van der Waals interaction based on the very accurate first order perturbation wave function obtained recently by using the momentum space technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453346
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