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  • 1
    Electronic Resource
    Electronic Resource
    Potential energy surface for interactions between N2 and He: Ab initio calculations, analytic fits, and second virial coefficients (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2541-2547 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An ab initio potential energy surface (PES) for the interaction of rigid N2 with He is calculated by supermolecular fourth-order Møller–Plesset perturbation theory. The computations involve full counterpoise corrections and large basis sets including bond functions. The 61 ab initio points on the PES are fitted to a 21-parameter algebraic form with an average absolute error of 0.39% and a maximum error less than 1.2%. The characteristics of the fitted PES are compared with those of previous surfaces. Unlike the older surfaces, our PES has the anisotropy thought to be required for a proper description of experimental data. Pressure second virial coefficients are calculated from our surface and compared with experimental values. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471002
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  • 2
    Electronic Resource
    Electronic Resource
    Multipole moments, polarizabilities, and hyperpolarizabilities for N2 from fourth-order many-body perturbation theory calculations (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 7623-7632 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: All multipole moment, polarizability, and hyperpolarizability tensors up to the fourth rank are calculated for the ground 1Σ+g state of N2 at its equilibrium bond length. These properties are obtained from fourth-order Møller–Plesset perturbation theory energies of N2 in the presence of various configurations of point charges. Electron correlation was found to affect the longitudinal components the most. Some of the anisotropies of these tensors change by as much as 105% upon inclusion of electron correlation. The results are in good agreement with all previous reliable theoretical and experimental values. The calculated values of the quadrupole–quadrupole (C) and dipole–octopole polarizabilities, and the dipole–dipole–quadrupole (B) and dipole–dipole–dipole–dipole (γ) hyperpolarizabilities are the most accurate ones available. Our best vibrationless estimates of the isotropic averages of these quantities are C¯=40.371 e2 a40 E−1h, B¯=−149 e3 a40 E−2h, and γ¯=830e4 a40 E−3h.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454327
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  • 3
    Electronic Resource
    Electronic Resource
    Relativistic kinetic energies and mass–velocity corrections in diatomic molecules (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 4509-4514 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Expectation values of various operators with respect to nonrelativistic, self-consistent-field wave functions of good quality for 46 diatomic molecules are computed to examine the differences between the relativistic kinetic energy 〈Hr〉 and the quasirelativistic kinetic energy 〈Tnr〉+〈Hmv〉 in which 〈Tnr〉 is the nonrelativistic kinetic energy and 〈Hmv〉 is the mass–velocity correction. Then 〈Hrc〉=〈Hr〉−〈Tnr〉=〈H mv〉+〈δE〉 is the full relativistic correction to the kinetic energy. 〈Hrc〉 can differ appreciably from 〈Hmv〉 for molecules containing at least one atom with a moderately large atomic number Z. These differences are greatly amplified when the relativistic corrections to dissociation energies are considered; the mass–velocity contribution to the binding energy is found to be inaccurate even for moderate values of Z. Great care is necessary to ensure that the molecular and atomic calculations are of comparable accuracy. A qualitative argument is provided to explain why 〈Hmv〉 can provide a reasonable approximation to 〈Hrc〉 for small enough Z despite the fact that the two operators are inequivalent for αp≥1 where α is the fine structure constant and p is the momentum. Finally the asymptotic behavior of the pertinent integrands is used to show why the numerical evaluation, in momentum space, of 〈Hrc〉 is easier than that of 〈Hmv〉.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451771
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  • 4
    Electronic Resource
    Electronic Resource
    Sum rules for atomic form factors and total x-ray scattering intensities (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 747-749 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Sum rules relating the position moments 〈xlymzn〉 and 〈rn〉 to the atomic form factor are derived. Exactly analogous sum rules relate the intracular moments 〈x12ly12mz12n〉 and 〈r12n〉 to the total x-ray scattering intensity in Waller–Hartree theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449487
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic expansions of the electron momentum densities of the atoms from hydrogen through lawrencium (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 1212-1215 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The first three coefficients in each of the small p Maclaurin and large p asymptotic expansions of the spherically averaged electron momentum densities of the ground states of the 103 neutral atoms from hydrogen through lawrencium, 73 atomic cations and 41 atomic anions are calculated from nonrelativistic self-consistent-field wave functions. These coefficients should be useful in the analysis of experimental Compton profiles. An analysis of the periodic behavior of these coefficients is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453301
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  • 6
    Electronic Resource
    Electronic Resource
    What do kinetic energy anisotropies tell us about chemical bonding? II. First-row A2, AO, and AF diatomics (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 2845-2849 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The kinetic energy anisotropy is examined for 18 different diatomic molecules of the type A2, AO, and AF with A=Li, Be, B, C, N, O, and F. The dimensionless measure α=(Tz−Tx)/T, where Tz and Tx, respectively, are the bond-parallel and bond-perpendicular components of the total electronic kinetic energy T, is confirmed to be useful for interpretative studies. It is shown that the orbital values of α in free atoms depend only on the angular momentum quantum numbers, and can be expressed in terms of a Condon–Shortley coefficient. Comparison of α values for individual molecular orbitals with their free atom counterparts enables one to classify molecular orbitals in terms of their parent atomic orbitals. In favorable cases, α values can also be used to estimate the extent and nature of reorganization of each orbital upon bond formation. The total molecular value of α correlates roughly with the difference between the numbers of pσ and pπ electrons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451043
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  • 7
    Electronic Resource
    Electronic Resource
    The higher order electron–electron coalescence condition for the intracule function for states of maximum spin multiplicity (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 6830-6832 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The parallel spin components (hσσ) of the exact intracule function (h) are shown to satisfy the electron–electron coalescence condition (d3hσσ/du3)u=0 =(3/2)(d2hσσ/du2)u=0 for σ=α or β. This implies that the higher order coalescence condition (d3h/du3)u=0 =(3/2)(d2h/du2)u=0 (for S=||MS||=N/2) can be used as a nontrivial test of approximate wave functions for states of maximum spin multiplicity. This is particularly useful since the usual cusp condition h'(0)=h(0) is trivially satisfied with both sides equal to zero for such states. The higher order condition is used to test some explicitly correlated wave functions for the lowest triplet S and P states of the helium-like ions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450686
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  • 8
    Electronic Resource
    Electronic Resource
    Asymptotic behavior of atomic momentals (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 5060-5062 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Knowledge of the large and small momentum transfer behavior of the electron momentum distribution is an important ingredient in the analysis of experimental isotropic Compton profiles. This behavior ultimately rests upon the asymptotic behavior of atomic momentals (momentum space orbitals). The small momentum Maclaurin expansion and the large momentum asymptotic expansion of atomic momentals with arbitrary angular momentum quantum number are derived in this paper. Their implications for momentum densities and Compton profiles are derived and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452648
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  • 9
    Electronic Resource
    Electronic Resource
    Approximate relationships between density power integrals, moments of the momentum density, and interelectronic repulsions in diatomic molecules (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 958-962 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Moments, 〈pk〉, of the momentum distribution and density power integrals, Ik=∫ρ1+k/3dτ in which ρ is the charge density, with −2≤k≤4 are computed for 35 ground state diatomic molecules at equilibrium using self-consistent-field wave functions of nearly Hartree–Fock quality. These data are then used to test various relationships between 〈pk〉, Ik, and the interelectronic repulsion Vee. Empirical bounds to 〈pk〉 in terms of Ik are found. Moreover, empirical approximations to 〈pk〉 in terms of Ik for −1≤k≤4 are given; these have median errors not exceeding 2% for the 35 diatomics under consideration. Gradient-free density functional approximations, in both position and momentum space, to Vee with median errors of less than 5% are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451252
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  • 10
    Electronic Resource
    Electronic Resource
    Correlation energy generating potentials for molecular hydrogen (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 3577-3583 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A variety of local correlation energy functionals are currently in use. All of them depend, to some extent, on modeling the correlation energy of a homogeneous electron fluid. Since atomic and molecular charge densities are neither uniform nor slowly varying, it is important to attempt to use known high accuracy wave functions to learn about correlation energy functionals appropriate to such systems. We have extended the definition of the correlation energy generating potentials Vc introduced by Ros. A charge density response to correlation has been allowed for by inclusion of an electron–nuclear component Venc in addition to the electron–electron component Veec. Two different definitions of Venc are given. We present the first calculations of Vc for a molecular system—H2. The results show that Venc, in either definition, is by no means negligible. Moreover, Veec and both forms of Venc show significant nonlocal dependence on the charge density. Calculations with ten different model correlation energy functionals show that none of them is particularly sensitive to the charge density. However, they are quite sensitive to the parametrization of the electron fluid correlation energy. The schemes which include self-interaction corrections (SIC) are found to be superior to those of Kohn–Sham type. The correlation energy generating potentials implied by the SIC type and empirical correlation energy functionals are found to correspond roughly to averages of one of the accurate potentials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449163
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