Localized valence bond method

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

Quantum-chemical cluster models, 34 131-202 computer programs, 34 134 methods, 34 135-138 for chemisorption, 34 135 the local approach, 34 132 molecular orbital methods, 34 135 for surface structures, 34 135 valence bond method, 34 135 Quantum chemistry, heat of chemisorption determination, 37 151-154 Quantum conversion, in chloroplasts, 14 1 Quantum mechanical simulations bond activation, 42 2, 84—107 Quasi-elastic neutron scattering benzene... 

VALENCE BOND METHODS BASED ON LOCALIZED ORBITALS 247... 

If we prefer to describe the bonding of a polyatomic molecule using localized two-center, two-electron (2c-2e) bonds, we can turn to the hybridization theory, which is an integral part of the valence bond method. In this model, for AX systems, we linearly combine the atomic orbitals on atom A in such a way that the resultant combinations (called hybrid orbitals) point toward the X atoms. For our BeH2 molecule in hand, two equivalent, colinear hybrid orbitals are constructed from the 2s and 2pz orbitals on Be, which can overlap with the two Is hydrogen orbitals to form two Be-H single bonds. (The 2p and 2py... 

In order to gain both a more local and a more accurate description of the bonding in SF we introduced intra-pair correlations via the perfect pairing generalized valence bond method (GVB-PP) (35). The valence electrons are described by generalized Heitler-London pairs,... 

Calculations of the H., potential energy surface have been carried out by an open shell valence-bond method using a localized orbital basis of spherical Gaussians. Results are presented for both single Gaussians as the localized orbitals and for linear combinations of two spherical Gaussians for each localized orbital. 

Molecular orbital theory differs from valence bond theory in that it does not require the electrons involved in a bond to be localized between two of the atoms in a molecule. Instead, the electron occupies a molecular orbital, which may be spread out over the entire molecule. As in the valence bond approach, the molecular orbital is formed by adding up contributions from the atomic orbitals on the atoms that make up the molecule. This approach, which does not explicitly model bonds as existing between two atoms, is somewhat less appealing to the intuition than the valence bond approach. However, molecular orbital calculations typically yield better predictions of molecular structure and properties than valence bond methods. Accordingly, most commercially available quantum chemistry software packages rely on molecular orbital methods to perform calculations. 

The molecular orbital theory is more satisfying esthetically, perhaps, but its lack of emphasis on a localized chemical bond has led many chemists to prefer the valence bond method, which gives them a better pictorial grasp of the situation. The above distinction between the two methods is a primitive one. If all the refinements in the present day valence bond and molecular orbital theories are included, any distinction between them is probably more imagined than real. 

The first quantum-mechanical treatment of the hydrogen molecule was by Heitler and London in 1927. Their ideas have been extended to give a general theory of chemical bonding, known as the valence-bond (VB) theory. The valence-bond method is more closely related to the chemist s idea of molecules as consisting of atoms held together by localized bonds than is the molecular-orbital method. The VB method views molecules as composed of atomic cores (nuclei plus inner-shell electrons) and bonding valence electrons. For H2, both electrons are valence electrons. 

Localized Structures at the Hiickel Level, a Hiickel-Derived Valence Bond Method... 

Another method, by Cullen, uses the monomer s own basis set, which is a very localized valence bond description. This method is complicated in its implementation and also does not include the important charge transfer effects in its treatment. 

A description of covalent bond formation in terms of atomic orbital overlap is called the valence bond method. The creation of a covalent bond in the valence bond method is normally based on the overlap of half-filled orbitals, but sometimes such an overlap involves a filled orbital on one atom and an empty orbital on another. The valence bond method gives a localized electron model of bonding Core electrons and lone-pair valence electrons retain the same orbital locations as in the separated atoms, but the bonding electrons do not. Instead, they are described by an electron probability density that includes the region of orbital overlap and both nuclei. 

Electrostatic stabilization, 181, 195,225-228 Empirical valence bond model, see Valence bond model, empirical Energy minimization methods, 114-117 computer programs for, 128-132 convergence of, 115 local vr. overall minima, 116-117 use in protein structure determination,... 

Localized molecular orbital/generalized valence bond (LMO/GVB) method, direct molecular dynamics, ab initio multiple spawning (AIMS), 413-414 Longuet-Higgins phase-change rule conical intersections ... 

Many other methods, of course, take advantage of invariances with respect to orbital transformations to obtain alternative representations of wavefunctions, such as for example the commonly employed localization procedures for the doubly-occupied MOs from Hartree-Fock calculations [11-15]. We give here a brief account of procedures that particularly seek a valence bond representation of MO wavefunctions. 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

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