Coupled electron-pair approximations

Coupled—Pair Functional (ACPF) and Coupled Electron Pair Approximation (CEPA). The simplest form of CEPA, CEPA-0, is also known as Linear Coupled Cluster Doubles (LCCD). 

Coupled Electron Pair Approximation Botschwina and Sebald, Ref. 98. 

The relationship between the coupled-electron pair approximation (c.e.p.a.) and the many-body perturbation theory has been discussed in detail by Ahl-richs.149 All of the methods denoted by c.e.p.a. (x) (x=0, 1, 2, 3) may be related to the summation of certain classes of diagrams in the many-body perturbation theory to infinite order. For example, c.e.p.a. (0), which is Cizek s linear approximation or Hurley s c.p.a. (0) ansatz150 is equivalent to the summation of all double-excitation linked diagrams in the perturbation series. This is also denoted d.e.m.b.p.t. (double excitation many-body perturbation theory) by some workers.151 168... 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

CEPA Coupled Electron Pair Approximation for including dynamic correlations. 

The multi-reference coupled electron pair approximation (MRCEPA) has a long pedigree as one of the more rigorous quantum chemical procedures. A recent development, the state specific version (SS-MRCEPA) has been... 

Computation of Excited State Potential Energy Surfaces via Linear Response Theories Based on State Specific Multi-Reference Coupled Electron-Pair Approximation Like Methods (S. Chattopadhyay, D. Pahari, U. Mahapatra D. Mukherjee)... 

C. Coupled Electron-pair Approximation and Related Methods... 

MO calculations have been reported for the BH and BH3 molecules, using the pair natural orbital configuration interaction (PNO—Cl) and coupled electron pair approximation with natural orbitals (CEPA—PNO) methods." The force constant and equilibrium distance of BH agreed very well with experimental values. 

Aluminium Hydrides.—PNO-CI (pair natural orbital/configuration interaction) and CEPA-PNO (coupled electron pair approximation with pair natural orbitals) MO calculations on AIH3 give a binding energy (referred to A1 + 3H) of ca. 205 kcal mor. °... 

Note that Eq. [40] is true regardless of the subset of CC excitations (Tp) included (CCD, CCSD, CCSDT, etc.). Similarly, it is true for such approximations as CCSD + T(CCSD)" and CCSDfT)" " (see below), where the initial contributions of triple excitations are computed noniteratively after a CCSD calculation, as well as essentially any other approximation based on CC and MBPT theory. [The CEPA (coupled electron-pair approximations) are approximations to CC theory but do not necessarily retain all the invariance properties required to ensure rigorous extensivity.]... 

It is now well established by numerous and extensive applications that the single reference (SR) based many-body methods, viz. many-body perturbation theory (PT) [1], coupled cluster (CC) theory [2], coupled electron-pair approximations (CEPA) [3], etc. provide rather accurate descriptions of the energy in and around the equilibrium geometry of the closed-shell states. In particular, the single reference coupled cluster (SRCC)... 

Two ab initio methods, which were well known and much discussed in the 1970s and 1980s, were the pair natural orbital Cl (PNO-CI) method and the coupled electron pair approximation (CEPA) method. They were proposed by Meyer [67] in 1973 and 2 years later improved by Ahlrichs et al. [68]. In 1983, Burton and Senff [69] applied the method of Ahlrichs et al. to an analysis of the anisotropy of (H2)2 interaction near the minimum in the van der Waals interaction energy. 

P.G. Szalay, Towards state-specihc formulation of multireference coupled-cluster theory Coupled electron pair approximations (CEPA) leading to multireference configuration interaction (MR-CI) type equations, in R.J. Bartlett (Ed.), Modem ideas in coupled-cluster methods, World Scientific, Singapore, 1997, pp. 81-123. 

In a study on the proton afrinity of diacetylene, Botschwina et al. reported more extended ab-initio calculations for C4H2 by allowing for effects of electron correlation, using the coupled-electron-pair approximation (CEPA) [207], Thor obtained C —C bond lengths of... 

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