Coupled pair functionals

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). 

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...

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. 

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). 

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... 

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. 

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... 

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. 

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). 

Bacskay et al. also concerned themselves with the possible effects of electron correlation on the aforementioned electronic properties. They consequently compared their SCF data with results obtained using an approximate coupled pair functional (ACPF) approach to correlation. As the authors had noted that geometries optimized at the SCF level typically... 

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. 

ACPF Approximate Coupled-Pair Functional approach to compute electron correlation... 

CPF Coupled Pair Functional procedure for including dynamic electron correlation. 

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