Averaged coupled pair functionals ACPF

Another point worth making is that since the SD-CI method is exact within the chosen basis set for a two-electron system, it must be size-consistent in this particular case. Nevertheless, when Davidson s correction is applied to an SD-CI wave-function for a two-electron system it will give a non-zero contribution, which is thus an artefact of this correction. (The same error appears also when the functional (10.1) is used with g=0.) This artefact can be simply removed and this is done in the Averaged Coupled Pair Functional (ACPF) method. In this method the factor g is considered to be a function of the number of electrons N, g=g(N), and one considers the special case of n separated He atoms. If the denominator De in (10.1) for one He atom is... 

R.J. Gdanitz and R. Ahlrichs, The Averaged Coupled-Pair Functional (ACPF) A Size-Extensive Modification of MR CI(SD), Chem. Phys. Letters 143, 413 (1988). 

Gdanitz and Ahlrichs devised a simpler variant of CPF, the averaged coupled-pair functional (ACPF) approach [30]. This produces results very similar to CPF for well-behaved closed-shell cases and is completely invariant to a unitary transformation on the occupied MOs. Its big advantage is that it can be cast in a multireference form. Multireference ACPF is probably the most sophisticated treatment of the correlation problem currently available that can be applied fairly widely, although it can encounter difficulties with the selection of reference spaces, as discussed elsewhere. 

The properties of oligomers of thiophene at the ground and excited states have been investigated by semi-empirical and ab initio methods. Semi-empirical calculations for the ground state of thiophene involve the QCFF/PI -f CISD method, while ab initio calculations are carried out at the HF/6-31G and the CASSF/3-21G" levels and also at the SCF and the averaged coupled-pair functional (ACPF) levels, with (basis set I) and without (basis set II) the sulfur 3d-orbitals. 

Karpfen et al. turned their attention from (HF)2 to the analogous dimer of HCl in 1991, using an averaged coupled pair functional (ACPF) approach - to include correlation the two basis sets were of [6,5,2/4,21 and [6,5,3,174,2] quality. In addition to the minimum illustrated in Fig. 4.5a, several other stationary points were identified on the PES. 

One can further try to formulate a generalization of CEPA or rather CPF to a multiconfiguration reference function. On these lines the average coupled pair functional (ACPF) has been derived by Gdanitz and Ahlrichs [157]. A straightforward MC-CEPA method has been proposed by Fink and Staeramler [158]. This is extensive, while ACPF is only approximatively so. 

Gdanitz, R.J., Ahlrichs, R. The averaged coupled-pair functional (ACPF)—a size-extensive modification of MR-CISD, Chem. Phys. Lett. 1988,143,413-20. 

Systematic ab initio studies were carried out with two basis sets on the vibrational spectra of thiophene and its oligomers <92JST(259)l8l>. The first basis set was applied at the SCF level and the second at the averaged couple pair functional (ACPF) level. For thiophene, the latter showed an excellent agreement with the experimental values <65SA689,66JSP(19)188> with deviations of up to 10 cm for the in-plane frequencies (see Table 8). 

Austin Model 1 (AMI), 87 Autocorrelation function, in simulations, 380 Averaged Coupled-Pair Functional (ACPF), 139... 

Kofraneck and coworkers24 have used the geometries and harmonic force constants calculated for tram- and gauche-butadiene and for traws-hexatriene, using the ACPF (Average Coupled Pair Functional) method to include electron correlation, to compute scaled force fields and vibrational frequencies for trans-polyenes up to 18 carbon atoms and for the infinite chain. 

In such an approach, the correlation energy is partitioned into a complete active space self-consistent field (CASSCF) part which describes the static correlations and a MR configuration interaction part for the dynamic correlations. In the case of metals we select an active space for the CASSCF calculation including the important bands around the Fermi level. The dynamic correlations are treated on top of the CASSCF wavefunction with an approximately size-extensive MR correlation method, i.e. an MR averaged coupled pair functional (MR-ACPF). 

For the higher multipole moments of NH(X Z ), only theoretical data from ab initio Hartree-Fock calculations [5 to 7, 14] and an ACPF (averaged coupled-pair functional) calculation [7] are available. Values for the quadrupole, octopole, and hexadecapole moments , Q, and equilibrium Internuclear distance re are as follows (e= 1.60217733 x 10" C, ao = 5.29177249 x 10 m) ... 

A recent quantum-chemical ab initio ACPF (averaged coupled-pair functional) calculation gave the parallel and perpendicular components of the polarizability of NH(X Z"), 0C = 11.770 ao ( = 1.744 A ) and a = 9.016 ao ( = 1.336 A ) the average molecular polarizability thus is a= (oC + 2a )/3 = 9.934 Sq ( = 1.472 A ). Slightly higher values were obtained for the two lowest excited states, a and b of NH [1]. Using the time-dependent coupled Hartree-Fock method, the frequency-dependent polarizability a(co) was calculated for the isotropic static polarizability, a value of 9.3655 a was obtained [2]. 

Multireference averaged coupled-pair-functional (MR-ACPF) and multi-reference average quadratic coupled-duster (MR-AQCC) with size-extensivity corrections. 

ACPF = averaged CPF ANO = atomic natural orbital CCSD(T) = singles and doubles coupled-cluster approach with a perturbational estimate of the triples excitation Cl = configuration interaction CPF = coupled pair functional CPP = core polarization potential CVCI = core-valence Cl FCI = full configuration interaction ICACPF = internally contracted ACPF ICMRCI = internally contracted MRCI MCPF = modified CPF MRCI = multi-reference configuration interaction NHF = numeric Hartree-Fock SDCI = singles plus doubles Cl. 

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