Coupled pair functional method

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. 

Theoretical chemistry at UBC was further strengthened with the arrival of Delano Chong and Keith Mitchell in 1965 and 1966, respectively. Chong s interests in quantum chemistry have spanned the full range from semiempirical to ab initio molecular orbital methods. His long-standing interests in perturbation methods and constrained variations have figured prominently in his publications. He is probably best known for his attempts to calculate the X-ray and UV photoelectron spectra of molecules, often by means of perturbation corrections to Koopmans theorem.40 More recently he has shifted his focus to coupled pair functional methods and density functional methods, with a special interest in polarizabilities and hyperpolarizabilities.41... 

Sagarik, K. R, Ahlrichs, R., and Erode, S., Intermolecular potentials for ammonia based on the test particle model and the coupled pair functional method. Mol. Phys. 57, 1247-1264 (1986). 

Table 4 shows the results for the best LSD potential of Vosco, Wilk and Nusair [12] (DFT/L) compared with experiment [21] as well as with other theoretical extensive configuration interaction and coupled-pair functional method [23], where available. Four quintets, one doublet and two sextet states are included in the table. The overall impression which arises from inspection of numbers is that the LCGTO-LSD method works for vanadium oxide even better than could be expected for such a difficult example. Equilibrium bond distances approach the experimental values very closely, similarly to other spectroscopic constatnts even though they have been obtained from a very simple polynomial fit to an approximate, few-point curve. As a rule, the... 

K. P. Sagarik, R. Ahlrichs, and S. Brode, Mol. Phys., 57, 1247 (1986). Intermolecular Potentials for Ammonia Based on the Test Particle Model and the Coupled Pair Functional Method. 

To see the overall picture of the benchmark test, the mean absolute deviations A are given for several methods and basis sets in Table II. These methods include the previously mentioned ACPF and CCSD methods, but also the MCPF (modified coupled pair functional) method [11], the MP2 (Mpller-Plesset second-order perturbation theory) method and the CCSD(T) method [12], where a perturbational estimate of the triple excitations has been added. The basis sets include the DZP basis discussed above and the nearly equivalent VDZ basis set, a DZ basis set... 

Figure4.7 Relativistic bond contractions A re for Au2 calculated in the years from 1989 to 2001 using different quantum chemical methods. Electron correlation effects Acte = te(corn) — /"e(HF) at the relativistic level are shown on the right hand side of each bar if available. From the left to the right in chronological order Hartree-Fock-Slater results from Ziegler et al. [147] AIMP coupled pair functional results from Stbmberg and Wahlgren [148] EC-ARPP results from Schwerdtfeger [5] EDA results from Haberlen and Rdsch [149] Dirac-Fock-Slater...

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... 

Very similar in spirit to CEPA, but formulated as a functional to be made stationary, is the coupled-pair functional (CPF) approach of Ahlrichs and co-workers [28]. CPF can be viewed as modifying the CISD energy functional to obtain size-extensivity for the special case of noninteracting two-electron systems. One disadvantage of some of the CEPA methods is that, unlike CISD or CCSD, the results are not invariant to a unitary transformation that mixes occupied orbitals with one another. CPF... 

Modular FORTRAN programs for performing general ab initio multireference single- and double-excitation configuration interaction, averaged coupled-pair functional and linearized couple-cluster method calculations. Cray and other versions. 

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. 

Two recent ab-initio studies are devoted to the determination of the ground-state structure of Cg. Parasuk and AlmlOf concluded that the cyclic polyacetylenic structure ( Ag) and the linear cumulenic g state are essentially isoenergetic [260]. However, the choice of basis sets and methods (MRCI modified coupled-pair functional, MCPF) heavily affects the difference in energy between the linear and cyclic forms of Cg, and so the results are quite uncertain. On the other hand, Slanina et al. proposed a nonplanar Z)2d symmetrical cyclic structure as the minimum-energy structure of Cg [261]. According to their MP2/6-31G calculations, this form is 13 kcal/mol lower in energy than the planar Qa structure. Unexpectedly, all the C-C bond lengths in the species are equivalent (1.339 A). DFT calculations favor the linear structure as compared with a planar cyclic one, but nonplanar species seem to have not been considered in this study [236]. 

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