Uncoupled Hartree-Fock Method

The Uncoupled-Hartree-Fock method (UCHF) [31, 32, 50, 54, 85, 88, 100, 110] is also referred to as the sum-over-orbitals (SOO) method. In tliis technique, one takes the unperturbed Hamiltonian H° as a sum of one-particle Hamiltonians ... 

While the uncoupled Hartree-Fock method and the single transition approximation have the merit of computational simplicity, they suffer, however, in particular from the usually unsatisfactory description of electronically excited states with a single-determinant wavefunction. 

Polarizability will be dealt with first because it is the easiest of the three properties to calculate and has certainly received the most attention. Many of the conclusions also apply to x and a, which are dealt with in much less detail. In each section we have tried to pick out the most important methods and consider them in detail at the expense of the less useful methods. Thus, for example, although the variational technique of Karplus and Kolker is simpler than the other uncoupled Hartree-Fock perturbation methods, it is not a very useful technique for calculating polarizabilities. It is very useful for calculations of magnetic susceptibility, however, where many other techniques are inappropriate. 

In practice, calculations of xHF are based on the uncoupled Hartree-Fock, the finite field, and the self-consistent perturbation methods. Some workers use gauge-invariant atomic orbitals (GIAOs). A full review of the gauge invariance of SCF wavefunctions has been given by Epstein. 6... 

In early years of quantum chemistry, several theoretical papers were devoted to calculations of linear and nonlinear responses of molecules to the electric field perturbations using the Uncoupled Hartree-Fock (UCHF) method. In comparison with the CI ansatz, the UCHF is less accurate in the description of electronic structure of molecules. Since this method was of some interest in computations of NLO properties we present this method in Section 5. 

We saw earlier that a very simple form of the dispersion energy is obtained from frequency-dependent polarizabilities at the so-called uncoupled Hartree-Fock level. The sum over states appearing in second order RS perturbation theory is simply a sum over (occupied and virtual) orbitals. A first improvement of this simple model is obtained by including apparent correlation [140], i.e. by using frequency-dependent polarizabilities obtained from the TDCHF method [36,141]. This method was initially proposed in the context of the multipole expansion, but could be generalized [142-146] to charge density susceptibility functions (or polarization propagators), which avoids the use... 

There exist two main methods for implementing nonlinear optical calculations into a given computational technique coupled methods and uncoupled methods. Coupled methods [sometimes called finite field (FF) or coupled-perturbed Hartree-Fock (CPHF) methods] include the effect of the perturbing field into the Hamiltonian. The energy (e) of the system in the field E... 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

COSY, NOESY and HETCOR NMR spectroscopies. The H and NMR chemical shifts of 3-PPA (C9H13N) were calculated by means of the Hartree-Fock (EIF), Becke-Lee-Yang-Parr (BLYP) and Becke-3-Lee-Yang-Parr (B3LYP) density functional methods with 6-311 -I- -I- G(d, p) basis set, respectively. The Fl, proton coupled and uncoupled N, DEPT, COSY, HETCOR, INADEQUATE NMR spectroscopies for 1,7-diamino-heptane and its magnitude of one bond coupling constants of... 

Unlike the true propagator, the UCHF approximation is given by a simple closed formula and reqnires only minimum computational effort to evalnate on the fly if the orbitals are available. The nnconpled Hartree-Fock/Kohn-Sham approximation has almost completely vanished from the chemistry literature about 40 years ago when modem derivative techniques became available because of the poor results it produced for second-order properties. Some systematic expositions of analytical derivative methods still use it as a starting point, but it is in our opinion pedagogi-cally inappropriate, as it requires considerable effort to recover the coupled-perturbed Hartree-Fock results which can be derived in a simpler way. UCHF/UCKS is still used in some approximate theories, but we suspect that its only merit is easy computability. According to Geerlings et al. [29], the polarizabilities derived from the uncoupled density response function correlate well with accurate results but can be off by up to a factor of 2, and thus they are only qualitatively useful. Our results in Table 1 confirm this. 

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