Orbital-invariant formulation and second-order gradient evaluation in M�ller-Plesset perturbation theory

Pulay, Péter; Sæbø, Svein

doi:10.1007/bf00526697

Cited by 521 publications

(327 citation statements)

References 37 publications

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“…Following the approach adopted in PAO methods, [8][9][10] we eliminate the redundant vectors by canonical orthogonalization of the overlap matrix S, and truncate small eigenvalues using a threshold of 10 −6 . Although the active virtual-orbital space is doubled in size by addition of the cross excitation, it is comparable in accuracy to the case where the number of active virtual orbitals is doubled in the direct excitation ansatz.…”

Section: B Full Excitation Ansatzmentioning

confidence: 99%

“…each (localized) occupied orbital. [8][9][10] The disadvantages of using a non-orthogonal representation of the virtual space is greatly outweighed by increased locality, and the predetermination of fixed domains has made possible extremely efficient implementations in the groups of Werner and Schütz. [11][12][13][14][15] In particular, linear scaling local implementations of key methods (LMP2, 12,16,17 LCCSD, 15,18 and LCCSD(T) (Refs.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Kurashige

Yang

Chan

et al. 2012

The Journal of Chemical Physics

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We present an orbital-optimized version of our orbital-specific-virtuals second-order Møller-Plesset perturbation theory (OSV-MP2). The OSV model is a local correlation ansatz with a small basis of virtual functions for each occupied orbital. It is related to the Pulay-Saebø approach, in which domains of virtual orbitals are drawn from a single set of projected atomic orbitals; but here the virtual functions associated with a particular occupied orbital are specifically tailored to the correlation effects in which that orbital participates. In this study, the shapes of the OSVs are optimized simultaneously with the OSV-MP2 amplitudes by minimizing the Hylleraas functional or approximations to it. It is found that optimized OSVs are considerably more accurate than the OSVs obtained through singular value decomposition of diagonal blocks of MP2 amplitudes, as used in our earlier work. Orbital-optimized OSV-MP2 recovers smooth potential energy surfaces regardless of the number of virtuals. Full optimization is still computationally demanding, but orbital optimization in a diagonal or Kapuy-type MP2 approximation provides an attractive scheme for determining accurate OSVs.

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Section: B Full Excitation Ansatzmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Kurashige

Yang

Chan

et al. 2012

The Journal of Chemical Physics

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“…The actual expressions for the energy and wave function corrections will therefore be changed. This is not a conceptual but merely a technical problem, and efficient formulations have been reported to evaluate second and higher order results with non-diagonal zero order [85][86][87]. Evaluation of the correlation energy in terms of lo-calized molecular orbitals is a typical example when such a formulation is needed.…”

Section: Møller-plesset Partitioningmentioning

confidence: 99%

“…This is an especially appealing feature as this makes it possible to perform the calculations, e.g., in terms of localized orbitals without affecting the PT formulae. This property markedly discerns the optimized partitioning from EN or MP, since the former is not orbital invariant at all, while the orbital invariant formulation of the latter [85,86] requires the use of non-diagonal resolvents. In the optimized partitioning the same second order formula (1.17) gives the same result whatever orbitals (canonical or localized) are used.…”

mentioning

confidence: 99%

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Śurján

Szabados

2004

Fundamental World of Quantum Chemistry

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The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Plesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.

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“…For example, it has sometimes proved more computationally efficient to use a variety of definitions of MOs in order to improve the convergence of the self-consistent field ͑SCF͒ procedure [1][2][3] ͑particularly for open-shell systems͒, though at convergence each set of MOs gives the same energy. Also, localized orbitals ͑as opposed to SCF canonical orbitals͒ have been used [4][5][6] to reduce the magnitude of components contributing to certain types of correlated wave functions, such as configuration interaction ͑CI͒, coupled electron-pair approximation ͑CEPA͒, 7 and second-order Mo "ller-Plesset perturbation theory ͑MP2͒ 8 wave functions, among others. Additionally, it is well known that energy invariance can be used to simplify the construction of analytic energy gradients.…”

Section: Introductionmentioning

confidence: 99%

On the energy invariance of open-shell perturbation theory with respect to unitary transformations of molecular orbitals

Crawford

Schaefer

Lee

1996

The Journal of Chemical Physics

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Restricted openshell Hartree-Fockbased manybody perturbation theory: Theory and application of energy and gradient calculations J. Chem. Phys. 97, 6606 (1992) A number of recently proposed single-reference open-shell perturbation theories based on a spin-restricted open-shell Hartree-Fock reference function are examined, with an emphasis on a consistent formalism within which the theories may be compared. In particular, the effect of unitary transformations among the molecular orbitals on the energy is discussed. Of the seven different perturbation theories examined here, the restricted Mo "ller-Plesset theory, open-shell perturbation theory method 1, the method of Hubač and Č ársky, Z-averaged perturbation theory, and invariant open-shell perturbation theory methods are found to be invariant to all types of rotations for which the reference wave function is unaffected, though all are invariant to transformations of a more limited nature. Explicit equations for the generalized invariant forms of each perturbation theory are presented, in order to provide working equations for extension of the theories to local correlation schemes or coupled-cluster perturbational corrections, among others.

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Orbital-invariant formulation and second-order gradient evaluation in M�ller-Plesset perturbation theory

Cited by 521 publications

References 37 publications

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

On the energy invariance of open-shell perturbation theory with respect to unitary transformations of molecular orbitals

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