CEPA coupled electron pair

Parallel to these endeavors, work started in Germany on new concepts to account for electron correlation. The independent electron pair approach (lEPA) was developed by Ahlrichs and Kutzelnigg, followed a few years later by the CEPA (coupled electron pair approach).The relation of these methods to contemporary Moller-Plesset second order (MP2) and coupled cluster treatments is discussed in Ref. 60. Work on circular dichroism by Ruch and on the chemical shift by Voitlander showed the variety of ab initio problems treated. The special priority program of the DFG from 1966-1970 demonstrated the intended impact. 

CEPA Coupled Electron Pair Approximation for including dynamic correlations. 

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.]... 

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. 

CEPA Coupled electron pair approach N Slight underestimate of bonding... 

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]. 

CEPA, coupled electron-pair pseudopotential calculations ... 

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). 

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). 

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. °... 

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