Coupled Hartree-Fock Method

The first two kinds of terms are called derivative integrals, they are the derivatives of integrals that are well known in molecular structure theory, and they are easy to evaluate. Terms of the third kind pose a problem, and we have to solve a set of equations called the coupled Hartree-Fock equations in order to find them. The coupled Hartree-Fock method is far from new one of the earliest papers is that of Gerratt and Mills. 

The Hartree-Fock equations have to be solved by the coupled Hartree-Fock method. The following article affords a typical example. 

The 13C chemical shift contour map for the Cp carbon of the L-alanine residue in peptides and polypeptides was made as a function of the dihedral angles(, W) by using the experimental data. Also, the corresponding calculated map was made by using the ab initio coupled Hartree-Fock method with the gauge included atomic orbitals(GIAO-CHF). From these results, it was found that the calculated map explains the chemical shift behavior of the a-helix and p-sheet forms in poly(L-alanine) and some proteins. This suggests that the calculated map is applicable to the structural analysis of proteins with complicated structure. 

Thomsen Kand Swanstr0m P 1973 Calculation of molecular one-electron properties using coupled Hartree-Fock methods I. Computational scheme Mol. Phys. 26 735-50 More recent contributions are summarized in ... 

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]. 

In the coupled Hartree-Fock method (CHF), which was probably derived the first time by Peng (1941) and rederived many times (Stevens et al, 1963 Gerratt and Mills, 1968), second- and higher-order static properties are obtained by solving the... 

Visser, F. and Wormer, P. E. S. (1984). The non-empirical calculation of second order molecular properties by means of effective states. I Application to time-dependent coupled Hartree-Fock method. Mol. Phys., 52, 923-937. 

Af-cyclohexylamino)ethanesulfonic acid coupled Hartree-Fock (method) chlorophyll choline... 

The coupled Hartree-Fock method (in one or other of the forms discussed in the last section) may be generalized in various important ways, three of which we now consider in turn. 

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