Coupled Electron Pair Approximation method

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... 

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. 

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. 

One of us [1] reviewed the situation of electron correlation a quarter of a century ago in a paper with the title electron correlation in the seventies [2]. At that time most quantum chemists did not care about electron correlation, and standard methods for the large scale treatment of electron correlation, like Mpller-Plesset (MP) perturbation theory or coupled-cluster (CC) theory were not yet available. However precursors of these methods such as lEPA (independent electron pair approximation) and CEPA (coupled-electron-pair approximation) had already been developped and were being used, mainly in research groups in Germany [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. 

Closely related to CC theory (and also to MP-theory) are the lEPA [3, 10, 12] and CEPA [11, 12, 13, 132, 133, 134] methods, that were used in molecular calculations prior even to the large scale studies in terms of MP2. lEPA (independent electron pair approximation) has in common with MP2 that the various electron pairs are decoupled, and MP2 has, in fact, been a first step on the way to lEPA [3,10,12]. Unlike in MP2 the various decoupled pairs are treated exactly (in the limitations due to the use of a finite basis) in lEPA. In CEPA (coupled electron pair approximation) the coupling of the pairs is taken into account, but unlike in CCSD, to which CEPA is closely related, some (generally small) indirect couplings are ignored. Although CEPA can be formulated as an approximation to CCSD [11, 12], in practical applications it has turned out that CEPA performs even better than CCSD (although it is cheaper), because apparently effects of triple substitutions are, to some extent simulated in CEPA [135, 136]. lEPA and CEPA share with MP and CC that they are extensive and not variational. 

Recently W. Meyer has proposed two rather straightforward extensions of the lEPA method that proved to be very useful in practical calculations. The first one termed PNO—Cl (Pseudo-Natural-Orbital Configuration Interaction) eliminates the first drawback of lEPA mentioned in the beginning of this section, the second one, called CEPA (for Coupled-Electron-Pair Approximation) improves lEPA with respect to the second drawback. The relation between the lEPA, PNO—Cl and CEPA methods is most easily explained in the following way. 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0)<-(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

PNO-CI (Pair Natural Orbital Configuration Interaction) and CEPA-PNO (Coupled Electron Pair Approximation with Pair Natural Orbitals) Calculations of Molecular Systems. I. Outline of the Method for Closed-Shell States. 

Electric moments, polarizabilities, and hyperpolarizabilities for BH were calculated for the first time [23], as were field and field gradient polarizabilities [24]. Spectroscopic properties were calculated for BH using the coupled electron pair approximation. The potential curve for BH was calculated at 22 points and Rq was found to be 1.23115 A and p to be 1.244 D [21]. The radiative lifetime of the A state of BH was calculated from second-order polarization propagator calculations [25], and the singlet-triplet separation in BH was calculated using ab initio MO methods. The latter, described as the singlet-triplet separation, was found to be 31.9 kcal/mol [26]. Finally, the possible dynamical pathways in the system BH + H+ were probed [27]. 

---