Hartee-Fock

A calculation approach to this question is ongoing, but it has been noted that the conclusion depends on the level of approximation <1999JMT1>. According to Hartee-Fock calculations, the most stable structure of l,6,6aA-trithia-pentalene 175 has Cs symmetry, with the structure 8.7 or 10.7 kcal mol 1 higher in energy <1991JA6449>. 

With the rapid evolution of the ab initio MO technique involving complete geometry optimization, quantum chemists are now seeking analytical expressions of molecular force fields for their expensive results (215). It should be possible, in principle, to construct a complete artificial force field that faithfully describes the Hartee-Fock limit energy surface, but still reflects important properties of the real surface sufficiently to allow useful applications (149). 

Spectroscopic (MS, NMR, IR) studies of quinoxalines were conducted . The structure and vibrational spectra of 2,3-bis(2-pyridyl)quinoxaline (bpq) and 2(A -methylpyridyl)-3-pyridylquinoxaline (meppq) useful for building blocks for dendrimers were measured by crystal X-ray diffraction and IR spectral experiments, respectively <2002JMT(589/90)301>. Those results were compared with ones calculated from the ab initio Hartee-Fock and the hybrid density functional methods. 

Mukheijee et al [56] also used the half projected Hartee-Fock (HPHF) method due to Smeyers and co-workers [70-74], which is based on variational formulation with two DODS determinant for the representation of the wave function and is proved to be very effective in calculating singly excited states of molecules. Table 5 displays the energy values only in the cis and trans conformations of the two excited states. 

The spin orbitals can be separated into a spatial part, if/ (orbital or molecular orbital) and a spin eigenfunction, a (or for the opposite spin). In restricted Hartee-Fock theory (RHF), the spatial part is independent on the spin state, in contrast to unrestricted Hartree-Fock (UHF) where it is spin dependent. Consequently, the RHF spin orbitals can be written as %i= whereas in UHF the corresponding relation is Xi= even number of electrons (closed shell system), but can easily be extended to treat also UHF1. 

Current post-Hartee-Fock OEP methods were shown to handle successfully such cases for which other strategies to approximate the exchange-correlation potential fail.82 They are very promising although their efficient numerical implementations making it competitive with the corresponding parent correlated wavefunction-based methods have not been developed yet. 

Decomposition Scheme for Molecular Interactions within the Hartee-Fock Approximation. 

Rullman et al. (1989) studied the initial proton transfer of Cys to His with a Hartee-Fock SCF direct reaction field (DRF) method, based on the refined X-ray structure of papain (Kamphuis et al., 1984). Parts of the active site residues were represented quantum mechanically and the environment was represented by partial charges and polarizabilities. The "QM motif consisted of methanethiol (modeling Cys-25), imidazole (for His-159) and formamide (for Asn-175). All atoms at the vicinity of the active site were included, except for atoms that are too close to the active site atoms, which were deleted from the structure... 

M.J. Field, Constrained optimization of ab initio and semiemperical Hartee-Fock wave functions using direct minimization or simulated annealing. Journal of Physical Chemistry, 95 (1991) 5104. 

A b initio quantum chemical studies of hyperfine structures (hfs) were initiated some 25 years ago, with the pioneering work of Meyer and others [127]. However, results from the early Hartee-Fock-based methods deviated considerably from experimentally determined hf parameters. It was not until the configuration interaction (Cl) techniques were fully developed for hfs calculations, that theoretical predictions of high accuracy were possible for atomic and molecular radicals [20]. This is mainly associated with the importance of electron correlation and with the development of new and fax larger basis sets. In later years, hfs calculations have also been carried out with great success using various levels of multiconfiguration SCF (MCSCF) [21], multireference Cl (MRCI) [22] and coupled cluster (CC) theory [23]. 

Before closing this section, the extensions of the SAC/SAC-CI method to the quasi-degenerate and multi-reference cases are described. The first such proposal was made in 1985 as the MR-SAC method, in which the reference function was extended from the Hartee-Fock single-determinant to a general Cl type wave function [34]. Further, based on the consideration on the nature of electron correlations in quasidegenerate situations, a generalization of the exponential operator was made i.e. 

The Hartee-Fock (HF) theory [2], at its limit, may provide perhaps 98% of the energy of an atom or molecule. Still, we wish for better, not only in the search of testing quanmm mechanics, but also because the small 2% error has the magnitude of an ionization potential or an electronic transition. 

The perturbation series can be truncated to various orders and one indicates the accuracy of MP methods applied within the Restricted Hartee-Fock (RHF) scheme by referring to the highest-orderterm allowed in the energy expansion. Thus a truncation to second-order corresponds to an MP2 approach, to third-order to an MP3 approach and so forth [27]. MP theory may also be used in the spin-Unrestricted Hartree-Fock (UHF) model. In this case, second- and third-order approximations of MP theory are indicated as UMP2andUMP3. 

For bound states it is not possible to come up with a prescription which can reliably distinguish which eigenstates differ by two active electrons. A possible way is to appeal to perturbation theory and postulate that if a state had several active electrons in the IPM it will maintain this character when improved in the MBPT. This sometimes works, but can easily fail. For example the ground state Hartee-Fock potential of a neutral atom supports no bound excited particle-hole states. Yet such states are present in the real correlated spectrum. There are no states to track from the IPM to identify these states present only in the MBPT. This problem presents a severe difficulty in applying finite Hilbert basis state (FHBS) methods to theoretically describe two-electron processes all eigenstates are bound in this treatment and need interpretation. 

HF denotes Hartee Fock theory, LSD the local spin density with no correlation but exchange according to a free electron gas, and GC has exchange according to ref. [230] and correlation according to ref. [229]. Thus LSD refers to the simplest and GC to a more state-of-the-DFT theory. Data adapted from ref. [236]. 

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