Coupled-perturbed many-electron theory

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

Bartlett R J and Purvis G D 1978 Many-body perturbation theory coupled-pair many-electron theory and the importance of quadruple excitations for the correlation problem int. J. Quantum Chem. 14 561-81... 

R. J. Bartlett and G. D. Purvis, Int. ]. Quantum Chetn., 14,561 (1978). Many-Body Perturbation Theory, Coupled-Pair Many-Electron Theory, and the Importance of Quadruple Excitations for the Correlation Problem. 

The success of this rather abrupt truncation for closed-shell molecular systems is not too surprising when one considers that the dominant terms of a perturbation expansion have been included.2 616 The next more complete approximation to attain recognition is the extended coupled-pair many-electron theory (ECPMET) of Paldus, Cizek, and Shavitt,6,17,18 which includes connected single and triple excitations,... 

Bartlett, R. J., Purvis, G. D. (1978). Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitation for the correlation problem. International Journal of Quantum Chemistry, 14, 561-581. 

Robinson and Frosch<84,133> have developed a theory in which the molecular environment is considered to provide many energy levels which can be in near resonance with the excited molecules. The environment can also serve as a perturbation, coupling with the electronic system of the excited molecule and providing a means of energy dissipation. This perturbation can mix the excited states through spin-orbit interaction. Their expression for the intercombinational radiationless transition probability is... 

To account for the interchannel coupling, or, which is the same, electron correlation in calculations of photoionization parameters, various many-body theories exist. In this paper, following Refs. [20,29,30,33], the focus is on results obtained in the framework of both the nonrelativistic random phase approximation with exchange (RPAE) [55] and its relativistic analogy the relativistic random phase approximation (RRPA) [56]. RPAE makes use of a nonrelativistic HF approximation as the zero-order approximation. RRPA is based upon the relativistic Dirac HF approximation as the zero-order basis, so that relativistic effects are included not as perturbations but explicitly. Both RPAE and RRPA implicitly sum up certain electron-electron perturbations, including the interelectron interaction between electrons from... 

Jiri Cizek s research program centers on the quantum theory of molecular electronic structure and related developments in quantum chemical methodology, coupled-cluster approaches to many-electron correlation problems,105 large-order perturbation theory,106 dynamical groups and exactly solvable models, lower bounds, and the use of symbolic computation language in physics and in chemistry. 

Since the Dirac equation is written for one electron, the real problem of ah initio methods for a many-electron system is an accurate treatment of the instantaneous electron-electron interaction, called electron correlation. The latter is of the order of magnitude of relativistic effects and may contribute to a very large extent to the binding energy and other properties. The DCB Hamiltonian (Equation 3) accounts for the correlation effects in the first order via the Vy term. Some higher order of magnitude correlation effects are taken into account by the configuration interaction (Cl), the many-body perturbation theory (MBPT) and by the presently most accurate coupled cluster (CC) technique. 

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