Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients

Mahapatra, Uttam Sinha; Datta, B. P.; Mukherjee, Debashis

doi:10.1016/s0009-2614(98)01227-5

Cited by 98 publications

(100 citation statements)

References 29 publications

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“…The perturbative realizations of the formalism are quite worthwhile to explore, since any possible low order perturbation expansion -which captures such essence of the parent SS-MRCC as size-consistency and avoidance of intruders without sacrificing its accuracy significantly -will turn out to be potentially attractive in terms of the applicability to bigger systems. We have in fact recently suggested a specific way to generate such state-specific multireference perturbation theories (SS-MRPT) [12] and demonstrated their usefulness with some preliminary applications [11,13]. This mode of formulation has the limitation that only a very specific partitioning of the hamiltonian H could be supported for a consistent development.…”

Section: Introductionmentioning

confidence: 99%

“…In one, to be hereafter called the frozen coefficients variety, the coefficients of the model functions forming the initial reference function are fixed by a prior diagonalization in the model space, and they are not revised or updated as a consequence of mixing with the virtual functions [14,15,[25][26][27][28][29]. In another approach, the combining coefficients are iteratively updated, which lends an intrinsic accuracy to the perturbed functions [12,13,[19][20][21]30]. We will henceforth call them as belonging to the relaxed coefficients variety.…”

Section: Introductionmentioning

confidence: 99%

“…There have been three formalisms [9,10,30,36], based on this idea. One of them is our SS-MRCC formalism [9,10] on which the present SS-MRPT [12,13] are based. There are two other SS formalisms [30,36] which bear kinship with our SS-MRCC formulation.…”

Section: Introductionmentioning

confidence: 99%

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State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Ghosh

Chattopadhyay

Jana

et al. 2002

IJMS

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We present in this paper two new versions of Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SS-MRPT) which stem from our state-specific multi-reference coupled-cluster formalism (SS-MRCC), developed with a complete active space (CAS). They are manifestly sizeextensive and are designed to avoid intruders. The combining coefficients c µ for the model functions φ µ are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of interest. By invoking suitable partitioning of the hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second order energy. The unperturbed hamiltonians for these theories can be chosen to be of both Mφller-Plesset (MP) and Epstein-Nesbet (EN) type. However, we choose the corresponding Fock operator f µ for each model function φ µ , whose diagonal elements are used to define the unperturbed hamiltonian in the MP partition. In the EN partition, we additionally include all the diagonal direct and exchange ladders. Our SS-MRPT thus utilizes a multi-partitioning strategy. Illustrative numerical applications are presented for potential energy surfaces (PES) of the ground ( 1 Σ + ) and the first delta ( 1 ∆) states of CH + which possess pronounced multi-reference character. Comparison of the results with the corresponding full CI values indicates the efficacy of our formalisms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Ghosh

Chattopadhyay

Jana

et al. 2002

IJMS

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“…Contracted perturbative expansions, which perturb the multideterminant zero-order wave function under the effect of linear combinations of outer-space determinants have also been proposed. One may quote the CASPT2 method 19,20 , which uses a monoelectronic zero-order Hamiltonian, faces intruder state problems and is not size consistent, the NEVPT2 method [21][22][23] which uses a bi-electronic zeroorder Hamiltonian (the Dyall's one 24 ) and is size consistent and intruder-state free, and the method from Werner 25 , as well as the perturbation derived by Mukherjee et al [26][27][28] from their MRCC formalism.…”

Section: Introductionmentioning

confidence: 99%

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

Giner

David

Scemama

et al. 2016

The Journal of Chemical Physics

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The multi-reference Coupled Cluster method first proposed by Meller et al (J. Chem. Phys. 1996) 1 has been implemented and tested. Guess values of the amplitudes of the single and double excitations (thê T operator) on the top of the references are extracted from the knowledge of the coefficients of the Multi Reference Singles and Doubles Configuration Interaction (MRSDCI) matrix. The multiple parentage problem is solved by scaling these amplitudes on the interaction between the references and the Singles and Doubles. Then one proceeds to a dressing of the MRSDCI matrix under the effect of the Triples and Quadruples, the coefficients of which are estimated from the action ofT 2 . This dressing follows the logics of the intermediate effective Hamiltonian formalism. The dressed MRSDCI matrix is diagonalized and the process is iterated to convergence. The method is tested on a series of benchmark systems from Complete Active Spaces (CAS) involving 2 or 4 active electrons up to bond breakings. The comparison with Full Configuration Interaction (FCI) results shows that the errors are of the order of a few milli-hartree, five times smaller than those of the CASSDCI. The method is totally uncontracted, parallelizable, and extremely flexible since it may be applied to selected MR and/or selected SDCI. Some potential generalizations are briefly discussed.

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“…The pioneering work in this direction by Dyall [155] was followed in Malrieu's [76,156] and Mukherjee's [157,158] laboratories. In our group, we have developed [159][160][161][162][163] a specific PT to perturb the antisymmetrized product of strongly orthogonal geminal [164] (APSG) wave function, where the geminals are eigenfunctions of an effective two-body Hamiltonian.…”

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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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Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients

Cited by 98 publications

References 29 publications

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

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

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