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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 97 (1997), S. 331-340 
    ISSN: 1432-2234
    Schlagwort(e): Key words: Gradients ; Perturbation theory of electronic structure ; MP2 ; Electron correlation ; Coulomb interaction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract. The evaluation of RI-MP2 first derivatives with respect to nuclear coordinates or with respect to an external electric field is described. The prefix RI indicates the use of an approximate resolution of identity in the Hilbert space of interacting charge distributions (Coulomb metric), i.e., the use of an auxiliary basis set to approximate charge distributions. The RI technique is applied to first derivatives of the MP2 correlation energy expression while the (restricted) Hartree-Fock reference is treated in the usual way. Computational savings by a factor of 10 over conventional approaches are demonstrated in an application to porphyrin. It is shown that the RI approximation to MP2 derivatives does not entail any significant loss in accuracy. Finally, the relative energetic stabilities of a representative sample of closed-shell molecules built from first and second row elements have been investigated by the RI-MP2 approach, and thus it is tested whether such properties that refer to potential energy hypersurfaces in a more global way can be described with similar consistency to the more locally defined derivatives.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 87 (1993), S. 147-173 
    ISSN: 1432-2234
    Schlagwort(e): Correlation ; MP2 ; AO ; Laplace transform ; Bounds ; Parallel computer ; Gradient ; Crystal ; Solid
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary A novel formulation of MP2 theory is presented which starts from the Laplace transform MP2 ansatz, and subsequently moves from a molecular orbital (MO) representation to an atomic orbital (AO) representation. Consequently, the new formulation is denoted AO-MP2. As in traditional MP2 approaches electron repulsion integrals still need to be transformed. Strict bounds on the individual MP2 energy contribution of each intermediate four-index quantity allow to screen off numerically insignificant integrals with a single threshold parameter. Implicit in our formulation is a bound to two-particle density matrix elements. For small molecules the computational cost for AO-MP2 calculations is about a factor of 100 higher than for traditional MO-based approaches, but due to screening the computational effort in larger systems will only grow with the fourth power of the size of the system (or less) as is demonstrated both in theory and in application. MP2 calculations on (non-metallic) crystalline systems seem to be a feasible extension of the Laplace transform approach. In large molecules the AO-MP2 ansatz allows massively parallel MP2 calculations without input/output of four-index quantities provided that each processor has in-core memory for a limited number of two-index quantities. Energy gradient formulas for the AO-MP2 approach are derived.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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