Hartree-Fock molecular orbital theory

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

Ab Initio Implementations of Hartree-Fock Molecular Orbital Theory... 

One-electron picture of molecular electronic structure provides electronic wavefunction, electronic levels, and ionization potentials. The one-electron model gives a concept of chemical bonding and stimulates experimental tests and predictions. In this picture, orbital energies are equal to ionization potentials and electron affinities. The most systematic approach to calculate these quantities is based on the Hartree-Fock molecular orbital theory that includes many of necessary criteria but very often fails in qualitative and quantitative descriptions of experimental observations. 

As in the Hartree-Fock molecular orbital theory, which is based on the independent particle model, the above Hartree product method also lacks enough correlation among the orbitals, and thereby the resultant accuracy is limited. To overcome the drawback, one can take account of the interaction among possible configurations (or the Hartree products) as in the configuration interaction method and multiconfiguration SCF methods in electronic structure theory. The multiconfigulational time-dependent Hartree... 

Many chemical problems can be addressed easily and reliably using Hartree-Fock molecular orbital theory or Kohn-Sham density functional theory with modest-sized basis sets. Unfortunately, 7t interactions, and non-covalent interactions in general, are not among them. In this section we consider the electron correlation and basis set requirements for computations of n interactions. 

Finally, we should also briefly discuss the performance of semiempirical methods. These are methods that neglect some of the more expensive integrals in Hartree-Fock molecular orbital theory and replace others with empirical parameters. Because semiempirical methods are based on Hartree-Fock theory, and because Hartree-Fock theory does not capture dispersion effects, semiempirical methods are not suitable for computing dispersion-dominated noncovalent interactions. Semiempirical methods yield repulsive potentials for the sandwich benzene dimer, just as Hartree-Fock does. However, given that semiempirical methods already contain empirical parameters, there is no reason not to fix this deficiency by adding terms proportional to r, as is done in force-field methods and the empirical DFT-D methods. Such an approach has been tested for some base pairs and sulfur-7t model systems. 

Hartree-Fock energy 227 Hartree-Fock molecular orbitals 224 Hartree-Fock theory 229 helical domains 94 heroin 81... 

This initial guess may then be inserted on the right-hand sides of the equations and subsequently used to obtain new amplitudes. The process is continued until self-consistency is reached. For the special case in which canonical Hartree-Fock molecular orbitals are used, the Fock matrix is diagonal and the T2 amplitude approximation above is exactly the same as the first-order perturbed wave-function parameters derived from Moller-Plesset theory (cf. Eq. [212]). In that case, the Df and arrays contain the usual molecular orbital energies, and the initial guess for the T1 amplitudes vanishes. 

Until recently, almost all quantum chemical methods used for numerical calculations were formulated within the conceptual framework of Hartree-Fock molecular orbital (MO) theory. Its basic premise is that a many-electron wavefunction can be formulated in terms of a set of one-electron wavefunc-tions V / (MOs), which are in turn composed of a linear combination (LC) of basis functions ()), . The latter are usually centered on the nuclei and are therefore called atomic orbitals (AOs), even though the optimal (]), for a molecule may be very different from the optimal AOs for an isolated atom. Mathematically, the LCAO-MO approximation is expressed as... 

The use of a Hartree-Fock reference function is ubiquitous in molecular electronic structure theory because of the beneficial computational consequences of the orthogonality of the Hartree-Fock molecular orbitals. However, many quantum chemical studies require the use of a multi-reference formalism. For example, studies of systems involving bond breaking processes almost invariably require the use of a reference function constructed as a linear combination of a number of reference functions. For cases where electron correlation effects are large and, in particular, when the Hartree-Fock model gives qualitatively incorrect results, the system is said to be strongly correlated. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

Hartree-Fock (HF), molecular orbital theory satisfies most of the criteria, but qualitative failures and quantitative discrepancies with experiment often render it useless. Methods that systematically account for electron correlation, employed in pursuit of more accurate predictions, often lack a consistent, interpretive apparatus. Among these methods, electron propagator theory [1] is distinguished by its retention of many conceptual advantages that facilitate interpretation of molecular structure and spectra [2, 3, 4, 5, 6, 7, 8, 9]. 

When the Hartree-Fock method is applied to molecules, molecular orbitals are used instead of atomic orbitals. To construct the molecular orbitals, one widely used approximation is LCAO (linear combinations of atomic orbitals). According to molecular orbital theory, the total wave function of the system is written as a combination of molecular orbitals, spin functions describing electrons in terms of spin j(a) or — j p). 

Li, J. Cramer, and Truhlar, D. G. 1999. Application of a Universal Solvation Model to Nucleic Acid Bases. Comparison of Semiempirical Molecular Orbital Theory, Ab Initio, Hartree-Fock Theory, and Density Functional Theory , Biophys. Chem.. 78, 147. 

---