A Guide to Molecular Mechanics and Quantum Chemical by Warren J Hehre

By Warren J Hehre

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Extra resources for A Guide to Molecular Mechanics and Quantum Chemical Calculations

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Thermodynamic vs. Kinetic Control of Chemical Reactions The fact that there are two different and independent mechanisms controlling product distributions - thermodynamic and kinetic - is why some chemical reactions yield one distribution of products under one set of conditions and an entirely different distribution of products under a different set of conditions. It also provides a rationale for why organic chemists allow some reactions to “cook” for hours while they rush to quench others seconds after they have begun.

Ia | jb) = ∫ ψi(r1)ψa(r1) r12 1 ψj(r2)ψb (r2)dr 1dr2 . (40) The two are related by a simple transformation, basis functions (ia | jb) = c ΣΣΣΣ µ ν λ σ µi c νj c λa cσb (µν | λσ) (41) where (µν | λσ) are given by equation 17. Møller-Plesset theory terminated to second-order, or MP2, is perhaps the simplest model based on electron promotion which offers improvement over Hartree-Fock theory. It is well-defined and leads to unique results. * Analytical first energy derivatives are available making geometry (and transition-state geometry) optimization routine.

Basis functions Jµv = Σ ΣP λ Kµv * 1 = 2 λσ (µν | λσ) (14) σ basis functions ΣΣP λ λσ (µλ | νσ) (15) σ Insisting that the basis functions be nuclear centered eliminates the problem of having to specify their locations. * occupied molecular orbitals Pλσ = 2 Σc c (16) λi σi i The product of an element of the density matrix and its associated atomic orbitals summed over all orbitals leads to the electron density. Further discussion is provided in Chapter 4. (µν | λσ) are two-electron integrals, the number of which increases as the fourth power of the number of basis functions.

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