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  • 1
    Digitale Medien
    Digitale Medien
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. II. Second-order Møller–Plesset (MP2-R12) calculations on closed-shell atoms (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2002-2019 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The MP2-R12 method in approximations A and B as outlined in part I of this series is applied to the ground states of the closed-shell atoms He, Be, Ne, Mg, Ar, Ca, Cu+, Zn2+, and Kr, in terms of both STO and GTO basis sets. For He, Be, and Ne the partial wave increments of the various pairs are documented and compared with their conventional counterparts. The fast convergence of the partial wave increments, that go as (l+ (1)/(2) )−8 in the MP2-R12/B scheme, is demonstrated. From the MP2-R12 calculations more accurate estimates of the exact MP2 energies are possible than from the conventional partial wave expansion. The actually calculated values differ generally by a fraction of a 1% from the estimated basis sets limits if STO basis sets with l≤5 (in some cases l≤6) are used, while errors of typically 1% are obtained with GTO basis sets and l≤3.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.459922
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  • 2
    Digitale Medien
    Digitale Medien
    Rates of convergence of the partial-wave expansions of atomic correlation energies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 4484-4508 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The coefficients of the leading terms of the partial-wave expansion of atomic correlation energies in powers of (l+1/2)−1 are derived for the second- and third-order perturbed energies in the 1/Z expansion for all possible states of two-electron atoms, and for second-order Møller–Plesset (many-body perturbation) theory for arbitrary n-electron atoms. The expressions for these coefficients given in Table I involve simple integrals over the zeroth-order wave functions (for the third order energies first-order wave functions are also involved). The leading term of E(2) goes as (l+1/2)−4 for natural parity singlet states, as (l+1/2)−6 for triplet states, and as (l+1/2)−8 for unnatural parity singlet states. There are no odd powers of (l+1/2)−1 present in E(2), and the coefficient of the (l+1/2)−6 term for natural parity singlet states of two-electron systems in the 1/Z expansion is generally −5/4 times the coefficient of the (l+1/2)−4 term. In E(3) there are terms that go as odd powers of (l+1/2)−1; the leading term is expressible in terms of the zeroth-order wave function and goes as (l+1/2)−5 for natural parity singlet states, as (l+1/2)−7 for triplet states, and as (l+1/2)−9 for unnatural parity singlet states. Numerical values of the coefficients for E(2) in two-electron atoms are given in Table II. The relation of our results to those obtained by Hill for variational calculations on the He ground state is discussed and generalizations of Hill's formulas are conjectured. The unexpected results for unnatural parity singlet states are traced back to the behavior of their wave functions at the point of coalescence of two electrons. In terms of the relative coordinate of the two electrons they represent d waves, in contrast to s waves for natural parity singlet states and p waves for triplet states of either parity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.462811
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  • 3
    Digitale Medien
    Digitale Medien
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1985-2001 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The matrix elements needed in a CI-SD, CEPA, MP2, or MP3 calculation with linear r12-dependent terms for closed-shell states are derived, both exactly and in a consistent approximate way. The standard approximation B guarantees that in the atomic case the error due to truncation of the basis at some angular momentum quantum number L goes as ∼L−7, at variance with L−3 in conventional calculations (without r12 terms). Another standard approximation A has errors ∼L−5, but is simpler and—for moderate basis sets—somewhat better balanced. The explicit expressions for Møller–Plesset perturbation theory of second and third order with linear r12 terms (MP2-R12 and MP3-R12, respectively) are explicitly given in the two standard approximations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.459921
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  • 4
    Digitale Medien
    Digitale Medien
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. III. Second-order Møller–Plesset (MP2-R12) calculations on molecules of first row atoms (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2020-2030 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The MP2-R12 method (Møller–Plesset second-order perturbation theory with terms linear in the interelectronic coordinate r12) in the approximations A and B as outlined in paper I of this series is applied to the ground states of the molecules H2, LiH, HF, H2O, NH3, CH4, Be2, N2, F2, C2H2, and CuH in their experimental equilibrium geometry, and to the van der Waals interaction between two He atoms. In all cases MP2 correlation energies are obtained that are supposed to differ by at most a few percent from the basis set limit. For CH4 the dependence of the energy on the symmetric stretching coordinate is studied, which together with other information leads to a recommended bond length of 1.086 A(ring) for the CH bond length. For He2 and F2 the canonical and localized descriptions are compared. The latter is superior for the K-shell contributions, otherwise there is a little difference. For He2 in the localized representation rather good results for the dispersion interaction are obtained. The potential curve of Be2 is significantly improved in MP2-R12 as compared to conventional MP2. The examples C2H2 and CuH show that the method is not limited to very small systems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.459923
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  • 5
    Digitale Medien
    Digitale Medien
    Time-independent theory of one-particle Green's functions (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 5578-5594 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A new time-independent theory of Green's functions is presented, which is based on a Fock space Liouvillean and its resolvent. Unlike current time-independent approaches in this formalism there is no need to introduce a complete operator manifold like that of Manne and Dalgaard for inner projection, nor for invoking a "killer condition.'' A perturbative construction of the Green's functions involves a perturbation expansion of both the resolvent of the Liouvillean and of the wave function. The approach is very general and is by no means limited to a closed-shell reference function. For functions of the latter type a very compact approach is possible in a particle–hole formalism, which automatically leads to the Feynman–Dyson series. An essential point in its derivation is that the perturbation expansion of the resolvent and of the wave function lead to diagrams with the same topology but with different energy denominators but that such diagrams can be added up to a single one, which may contain both "Rayleigh–Schrödinger'' and "Brillouin–Wigner'' denominators. It is shown that a consistent theory can be based on "principal-value'' Green's functions. The one-particle Green's function is treated in some detail, the polarization propagator is only briefly discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.456411
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  • 6
    Digitale Medien
    Digitale Medien
    Configuration interaction calculations with terms linear in the interelectronic coordinate for the ground state of H+3. A benchmark study (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 8830-8839 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The CISD-R12 method is applied to the ground states of H2 and H+3 at their equilibrium configurations, with both bare nuclear Hamiltonian (BNH) and self-consistent field (SCF) references with eight basis sets that range from 10 s (i.e., ten contracted s-type Gaussians) to 30s20p12d9f. With the largest basis set, the energy of H2 is obtained with an error of 2μEh, while for H+3, the error is probably smaller and the best calculated energy of −1.343 835Eh is supposed to be accurate to all indicated figures. The BNH reference is always superior to the SCF reference. The relativistic corrections are evaluated at the SCF level by means of "direct perturbation theory'' both for H2 and H+3. The Hylleraas-SCF methods and related concepts for the construction of an optimum reference function are discussed in the Appendix.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.465551
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  • 7
    Digitale Medien
    Digitale Medien
    Calculation of nuclear magnetic resonance shieldings and magnetic susceptibilities using multiconfiguration Hartree–Fock wave functions and local gauge origins (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2330-2340 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A multiconfiguration generalization of the individual gauge for localized orbitals (IGLO) method for the calculation of magnetic properties such as susceptibilities and nuclear magnetic resonance chemical shifts is presented in detail. This includes a rederivation of the IGLO method by means of a nonlocal gauge transformation. The method is most successfully applied if strong (static) correlation effects have to be taken into account. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.470928
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  • 8
    Digitale Medien
    Digitale Medien
    Nature of the semipolar XO bond. Comparative ab initio study of H3NO, H2NOH, H3PO, H2POH, H2P(O)F, H2SO, HSOH, HClO, ArO, and related molecules (1979)
    s.l. : American Chemical Society
    Journal of the American Chemical Society 101 (1979), S. 2804-2814 
    Details
    ISSN: 1520-5126
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/ja00505a002
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  • 9
    Digitale Medien
    Digitale Medien
    Relativistic Hartree–Fock by means of stationary direct perturbation theory. I. General theory (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 1740-1751 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: Perturbation theory of relativistic effects (if done properly, i.e. avoiding spurious singularities as they arise, e.g. if one starts with the Foldy–Wouthuysen transformation) has many advantages and only few drawbacks compared to a nonperturbative relativistic theory. In this paper relativistic Hartree–Fock theory for closed-shell states is combined with the stationary direct perturbation theory of relativistic effects in powers of the inverse velocity of light c−1 (which in hartree units is equal to the fine structure constant α). After a formulation for an arbitrary electron interaction the explicit expressions for the Dirac–Coulomb Hamiltonian are presented. The first step is always a nonrelativistic Hartree–Fock calculation, followed by the construction of the perturbation adapted zeroth order bispinors in terms of their large and small components cursive-phi(0)i and χ(0)i, respectively. The leading relativistic correction to the energy c−2E(2) is obtained as an expectation value involving cursive-phi(0)i and χ(0)i. The higher-order corrections c−4E(4) and c−6E(6) require that first the lowest order relativistic corrections cursive-phi(2)i and χ(2)i to the Hartree–Fock MOs are constructed by means of a coupled-Hartree–Fock-type approach. A hierarchy of approximations to the full treatment up to O(c−6) is proposed, in three of which the lowest order relativistic correction c−2E(2) to the energy is calculated exactly, while two-electron contributions to c−4E(4) and c−6E(6) are neglected in part or entirely. Finally the use of the Breit interaction and related interactions is discussed. © 1995 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468701
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  • 10
    Digitale Medien
    Digitale Medien
    Relativistic Hartree–Fock by means of stationary direct perturbation theory. II. Ground states of rare gas atoms (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 1752-1757 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The combination of relativistic Hartree–Fock theory with stationary direct perturbation theory presented in paper I of this series is applied to the ground states of the rare gas atoms He, Ne, Ar, Kr, Xe, Rn, in STO basis sets with finite nuclei. The error of the truncation of the perturbation expansion at O(c−6)—with the nonrelativistic reference O(c0)—is only ≈1% for Rn and 〈0.1% for Xe. The corresponding error for truncation at O(c−2) is 〈1% for Ar. An approximation in which c−2E(2) is calculated exactly, but in which two electron contributions to c−4E(4) and c−6E(6) are neglected, performs almost as well as rigorous perturbation theory up to c−6E(6) but is computationally much cheaper. © 1995 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468702
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