Perturbation theory correcting bond orbitals

Combined Quantum Mechanical and Molecular Mechanical Potentials Hyperconjugation M0ller-Plesset Perturbation Theory Ifatural Bond Orbital Methods Rotational Barriers and Molecular Mechanics Corrections Rotational Barriers Ab Initio Computations Spectroscopy Computational Methods Structural Similarity Measures for Database Searching. 

For the non-bonding 2 fli orbital the corresponding perturbation theory correction is ... 

The theoretical interpretation of the results was made (334) in terms of the molecular orbital perturbation theory, in particular, of the FMO theory (CNDO-2 method), using the model of the concerted formation of both new bonds through the cyclic transition state. In this study, the authors provided an explanation for the regioselectivity of the process and obtained a series of comparative reactivities of dipolarophiles (methyl acrylate > styrene), which is in agreement with the experimental data. However, in spite of similar tendencies, the experimental series of comparative reactivities of nitronates (249) toward methyl acrylate (250a) and styrene (250b) are not consistent with the calculated series (see Chart 3.17). This is attributed to the fact that calculation methods are insufficiently correct and the... 

Bond orbitals are constructed ft om s/r hybrids for the simple covalent tetrahedral structure energies are written in terms of a eovalent energy V2 and a polar energy K3. There are matrix elements between bond orbitals that broaden the electron levels into bands. In a preliminary study of the bands for perfect crystals, the energies for all bands at k = 0 arc written in terms of matrix elements from the Solid State Tabic. For calculation of other properties, a Bond Orbital Approximation eliminates the need to find the bands themselves and permits the description of bonds in imperfect and noncrystalline solids. Errors in the Bond Orbital Approximation can be corrected by using perturbation theory to construct extended bond orbitals. Two major trends in covalent bonds over the periodic table, polarity and metallicity, arc both defined in terms of parameters from the Solid State Table. This representation of the electronic structure extends to covalent planar and filamentary structures. 

We define extended bond orbitals to be bond orbitals corrected in perturbation theory for those matrix elements that couple bonding and antibonding orbitals. This is done directly by using Eq. (1-16). Then corrections are added to every bond orbital 6> these arise from the interaction, 14, with neighboring antibond orbitals la),... 

Using standard Rayleigh-SchrOdinger perturbation theory, the first-order correction to the orbital energies of the unperturbed [4m] carbocycle caused by insertion of the new bonds can be shown to be... 

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