Open-shell many-body perturbation theory

T. D. Crawford, Ph.D. Thesis, University of Georgia, 1996. Many-Body Perturbation Theory and Perturbational Triple Excitation Corrections to the Coupled-Cluster Singles and Doubles Method for High-Spin Open-Shell Systems. 

Many-Body Perturbation Theory with a Restricted Open-Shell Hartree-Fock Reference. 

H.P. Kelly, Many-body perturbation theory applied to open-shell atoms, Phys. Rev. 144 (1966) 39. 

Stategy (i) is the one followed by the school of Kelly [242] and his coworkers. It is known as many-body perturbation theory (MBPT) and has the advantage of being very flexible, as it can be applied to all atoms, including those with open shells, but the disadvantage that the calculi tions can only be taken to finite (and in practice rather low) orders of... 

W. J. Lauderdale, J. F. Stanton, J. Gauss, J. D. Watts, and R. J. Bartlett, J. Chem. Phys., 97, 6606 (1992). Restricted Open-Shell Hartree-Fock Based Many-Body Perturbation Theory. Theory and Application of Energy and Gradient Calculations. 

Coupled electron pair and cluster expansions. - The linked diagram theorem of many-body perturbation theory and the connected cluster structure of the exact wave function was first established by Hubbard211 in 1958 and exploited in the context of the nuclear correlation problem by Coester212 and by Coester and Kummel.213 Cizek214-216 described the first systematic application to molecular systems and Paldus et al.217 described the first ab initio application. The analysis of the coupled cluster equations in terms of the many-body perturbation theory for closed-shell molecular systems is well understood and has been described by a number of authors.9-11,67,69,218-221 In 1992, Paldus221 summarized the situtation for open-shell systems one must nonetheless admit... 

It is known that within the framework of the Roothaan coupling operator approach, there is no unique way of choosing a reference Hamiltonian, with respect to which a perturbation expansion for correlation effects can be developed. Several proposals have been made for open-shell many-body perturbation theory expansions based on a reference from the ROHE formalism [41, 42] or the umestricted Hartree-Fock formalism [43, 44]. We follow our papers [10, 45] where an alternative technique for the open-shell systems has been developed. In our method, the second-order correction to the ground state energy can be presented by [45] ... 

Lauderdale, W. J., Stanton, J. R, Gauss, J., D., W. J., 8c Bartlett, R. J. (1991). Many-body perturbation theory with a restricted open-shell Hartree-Fock reference. Chemical Physics Letters, 187, 21-28. 

MELD belongs to traditional Cl codes. It was developed primarily for the study of electronic excitation spectra and molecular properties. It is a conventional Cl program which makes no use of GUGA, direct Cl, or many-body perturbation theory. The advantage retained, over more modem methods, is the flexibility to describe a wide variety of open-shell states, and options for some molecular properties. Preparation of data and running a job may seem complicated for those who are not familiar with the program. 

Lindgren, A coupled-cluster approach to the many-body perturbation theory for open-shell systems, Int. J. Quantum Chem. Symp. 12 33 (1978). 

I. Hubac and P. Carsky, Phys. Rev., All, 2392 (1980). Correlation Energy of Open-Shell Systems. Application of the Many-Body Rayleigh-Schrodinger Perturbation Theory in the Restricted Roothaan-Hartree-Fock Formalism. 

The interaction energies of clusters of molecules can be decomposed into pair contributions and pairwise-nonadditive contributions. The emphasis of this chapter is on the latter components. Both the historical and current investigations are reviewed. The physical mechanisms responsible for the existence of the many-body forces are described using symmetry-adapted perturbation theory of intermolecular interactions. The role of nonadditive effects in several specific trimers, including some open-shell trimers, is discussed. These effects are also discussed for the condensed phases of argon and water. 

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