Localized molecular orbitals methods

Fukui et al. studied the bond interchange in the course of ammonia addition to formaldehyde by means of a localized molecular orbital method, based on the analysis of the semiempirical INDO molecular orbitals of the isolated molecules and of the reacting system [127], Here, the N... C = 0 angle was fixed at 107°, since preliminary calculations gave results in fairly good agreement with the experimental reaction path, i.e. the Biirgi-Dunitz trajectory. 

Magnetic susceptibility tensors were calculated by the ab initio IGLO (individual gauge for localized molecular orbitals) method with a large basis set. The calculations showed... 

In the MOVB method, we use one Slater determinant with block-localized molecular orbitals to define individual VB configuration, called diabatic state. For example, the reactant state of the Sn2 reaction between HS- and CH3CI is defined as the Lewis bond structure of the substrate CH3CI ... 

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 ... 

Numerical LMOs of this work are determined by the natural localized-molecular-orbital (NLMO) method A. E. Reed and F. Weinhold, J. Chem. Phys. 83 (1985), 1736. The LMOs determined by other methods (e.g., C. Edmiston and K. Ruedenberg, Rev. Mod. Phys. 34 [1963], 457 and J. M. Foster and S. F. Boys, Rev. Mod. Phys. 32 [1960], 300) are rather similar, and could be taken as equivalent for present purposes. 

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... 

Contrarily to conventional MP2 theory, the original formulation of MP2-R12 theory (3,4) did not provide the same results when canonical or localized molecular orbitals were used. Indeed, for calculations on extended molecular systems, unphysical results were obtained when the canonical Hartree-Fock orbitals were rather delocalized (5). In order to circumvent this problem, an orbital-invariant MP2-R12 formulation was introduced in 1991, which is the preferred method since then (6),... 

The truncation procedure for fiill-valence-space and N-electrons-in-N-orbitals SDTQ MCSCF waveflmctions is based on choosing split-localized molecular orbitals as configuration generators since they lead to the greatest number of deadwood configurations that can be deleted. A quite accurate estimation method of identifying the latter has been developed so that the truncation can be performed a priori. The method has been shown to be effective in applications to the molecules HNO, OCO and NCCN where, for instance, the energies of the full SDTQ[N/N] calculations are recovered to better than 1 mh by truncated expansions that require only 11.8%, 10.9% and 6.3%, respectively, of the number of determinants in the full calculations. Similar trends are observed for the FORS 1 model. 

It could thus be stated that a pair description analogous to the Lewis picture is quite conveniently yielded by localized molecular orbitals. In other words, to the extent that the one-electron (orbital) method is in principle capable of faithful description of molecular electronic stmcture, the orbital analysis may provide a useful rationale of some molecular characteristics. Having generated LMOs, using any localizability criteria, the degree of spatial localization obtained may also be inquired. 

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. 

In Peralta et a/. s18,82 method the NJC decomposition into localized molecular orbitals procedure is as follows. Given a perturbative Hamiltonian A, A being either the FC or PSO operators, the corresponding J coupling term can be obtained as... 

In more recent years, both in the Soviet Union and the Western Countries, less critical attempts have been made to replace such an empirical approach by a more mathematical one, often based on the molecular orbital methods, although the basic assumptions, e.g. those of non-localized bonds (the incompatibility of which with experimental observations has been the subject of my numerous criticisms), remained the same. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

In a quantum chemical calculation on a molecule we may wish to classify the symmetries spanned by our atomic orbitals, and perhaps to symmetry-adapt them. Since simple arguments can usually give us a qualitative MO description of the molecule, we will also be interested to classify the symmetries of the possible MOs. The formal methods required to accomplish these tasks were given in Chapters 1 and 2. That is, by determining the (generally reducible) representation spanned by the atomic basis functions and reducing it, we can identify which atomic basis functions contribute to which symmetries. A similar procedure can be followed for localized molecular orbitals, for example. Finally, if we wish to obtain explicit symmetry-adapted functions, we can apply projection and shift operators. 

The next step to reach to our aims is to determine the localized molecular orbitals of the anionic group. Of course, there are many methods available for the calculations of molecular orbitals in our theory, such as the various approximation methods and even the recently developed Dv-Xa method discussed in quantum chemistry. But, in view of the nature of the basic assumptions in our theory, the CNDO approximation seems to be suitable for calculations of SHG coefficients when the anionic groups consist of elements from the first, second and third families in the periodic table. EHMO type approximations are suitable for other elements, particularly if transition metal elements take part in the ionic groups or molecules. It is not necessary to use higher approximations. 

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