Coupled pair many electron theory

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... 

J. Paldus, J. Cizek, and 1. Shavitt, Correlation problems in atomic and molecular systems. IV. Extended coupled-pair many-electron theory and its application to the BHs molecule. Phys. Rev. A 5, 50 (1972). 

Paldus, J., Cfzek, J., Takahashi, M. Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory. Phys. Rev. A 1984, 30, 2193-209. 

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. 

G. Method of Coupled-Pair Many-Electron Theory and Its Results. . 148... 

Cfiek J, Paldus J (1971) Correlation problems in atomic and molecular systems III Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methods. Int J Quantum Chem 5 359-379. 

H. Coupled-Pair Many-Electron Theory (CPMET)... 

J. Cizek and J. Paldus, Int. J. Quantum Chem., 5, 359 (1971). Correlation Problems in Atomic and Molecular Systems. III. Rederivation of the Coupled-Pair Many-Electron Theory Using the Traditional Quantum Chemical Methods. 

Various approximations of Eq. (6), the exact wave function in the coupled-cluster formalism, have been discussed in the chemical literature. In particular, Cizek s coupled-pair many-electron theory (CPMET),5 also referred to as coupled-cluster doubles (CCD) by Bartlett,8 has re-... 

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,... 

Following the pair correlation approach of Sinanoglu,4 Cizek2 introduced the coupled-pair many-electron theory (CPMET) method, which takes into account only double excitation clusters T2. In the present paper we prefer our more systematic nomenclature for different versions of the CC method, consistently used in our previous papers. Thus the original Cizek approach will be denoted CCD (CC doubles), while its linearized version will be denoted as LCCD. By including in the CC equations single excitation clusters T, we arrive at the CCSD method, exploited in a series of papers by Bartlett and co-workers.9-11 We will also consider the linearized version of the CCSD method, LCCSD,15 the full CCSDT model that includes effects of triple excitation clusters T3, and the CCSDTQ model that also considers T. ... 

Another possibility is to increase the order of PT while restricting the excitation level of the intervening intermediate states. This is most easily done when the excitations are limited to doubles, yielding the rath order MBPT with doubles, or DMBPT(n). In fact, in this case, the summation can be carried out to infinite order, yielding the DMBPT(oo) method [27]. However, this result can be easily seen to be equivalent to the linear version of coupled-cluster (CC) theory that is restricted to two-body amplitudes, namely, to the L-CPMET (linear coupled-pair many-electron theory) or, more succinctly, to L-CCD (linear CC with doubles) in current terminology. 

Cizek s 1966 paper [73] and the subsequent paper from the Frascati Volume [48], both resulting from his Ph.D. thesis, are often portrayed as a formulation of what is today characterized as the CCD (CC with doubles), which he referred to as the CPMET (coupled-pair many-electron theory) method. It is tme that the actual explicit equations that are given in his paper are the CCD equations. It must be emphasized, however, that the essence of the paper is an entirely general formulation of the CC method, and the CCD... 

Coupled Cluster (cc) expansions Approximations based on CC expansions [3, 91,92] include ccd, ccsd, ccsdt, etc., and their multireference variants mr-CCD, MR-ccsD, MR-ccsDT, etc. The CCSD approximation is also known as the coupled pair approximation (cpa) [59] or the coupled pair many electron theory (CPMET) [20,21,93]. 

Using all the above, Cizek presents the explicit, spin orbital and spin-adapted CC doubles equations (CCD) i.e., T = T2 (then called coupled-pair many-electron theory) in terms of one- and two-electron integrals over an orthogonal basis set. Assisted by Joe Paldus with some computations, he also reports some CCD results for N2, which though limited to only ti to Ug excitations, uses ab initio integrals in an Slater-type-orbital basis. He also does the full Cl calculation to assess convergence, a tool widely used in Cizek s and Paldus work and by most of us, today. He also reports results for the minimum-basis TT-electron approximation to benzene. 

A rather drastic remedy for this shortcoming is to put Ay = 0. This leads to the linear version of Cizek s (coupled pair-many electron theory) CP-MET, " also called CEPA-0, which is size-extensive. 

In Section 5.2 we consider how to go beyond the lEPA by incorporating coupling between different pairs of electrons. We will discuss the coupled pair many-electron theory (CPMET) which is also called the coupled-cluster approximation (CCA). We then describe a number of simplifications to this rather sophisticated approach in particular, we consider the coupled electron pair approximation (CEPA). Finally, in Subsection 5.2.4 we present some numerical applications of coupled-pair theories. 

This equation, along with the definition of the symbol idS, c > given in Eq. (5.53), and the expression for the correlation energy in Eq. (5.48a) are the equations of Coupled-Pair Many-Electron Theory (CPMET), which is... 

As the next step in handling the correlation problem in larger molecules, the coupled-cluster doubles (CCD), also called coupled-pair many-electron theory (CPMET), introduced into the electronic correlation problem by Cizek, was first applied to smaller molecules and then to the nucleotide bases using localized orbitals. 

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. 

One of the possible ways of realizing the wave operator f2o is to use the exponential ansatz introduced into atomic and molecular electronic structure theory by Cf ek [76] in coupled pair many-electron theory and coupled cluster theory. Here the wave operator is written as... 

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