By Warren J Hehre
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Extra info for A Guide to Molecular Mechanics and Quantum Chemical Calculations
24) Fc = εSc Here the elements of the Fock matrix are given by. core XC Fµv = Hµv + Jµv – Fµv (25) core Hµv and Jµv are defined analogously to equations 13 and 14, respectively and FXC µv is the exchange/correlation part, the form of which depends on the particular exchange/correlation functional employed. Note, that substitution of the Hartree-Fock exchange, Kµv , for FXC µv yields the Roothaan-Hall equations. Three types of exchange/correlation functionals are presently in use: (i) functionals based on the local spin density approximation, (ii) functionals based on the generalized gradient approximation, and (iii) functionals which employ the “exact” Hartree-Fock exchange as a component.
Transition state transition state energy intermediate reactants rate limiting step products reaction coordinate The thermodynamics of reaction is exactly as before, that is, related to the difference in energies between reactants and products. The intermediates play no role whatsoever. However, proper account of the kinetics of reaction does require consideration of all steps (and all transition states). Where one transition state is much higher in energy than any of the others (as in the diagram above) the overall kinetics may safely be assumed to depend only on this “rate limiting step”.
May be addressed by providing two sets of valence basis functions (“inner” and “outer” functions). For example, proper linear combinations determined in the solution of the Roothaan-Hall equations allow for the fact that the p orbitals which make up a “tight” σ bond need to be more contracted than the p orbitals which make up a “looser” π bond. * Note that, while 2p functions are not occupied in the lithium and beryllium atoms, they are required to provide proper descriptions where these are bonded to atoms with lone pairs.
A Guide to Molecular Mechanics and Quantum Chemical Calculations by Warren J Hehre