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0Ψ0 = E(0)Ψ0 H (34a) (0) (1) ˆ Hˆ 0Ψ(1) + VΨ + E(1)Ψ0 0= E Ψ (34b) ˆ (1) = E(0) Ψ(2) + E(1) Ψ(1) + E(2) Ψ0 ˆ 0Ψ(2) + VΨ H (34c) Multiplying each of the equations 34 by Ψ0 and integrating over all space yields the following expression for the nth order (MPn) energy. E(0) = ∫ ... dτn Ψ0H (35a) E(1) = ∫ ... dτn Ψ0VΨ (35b) E(2) = ∫ ... dτn Ψ0VΨ (35c) In this framework, the Hartree-Fock energy is the sum of the zero and first-order Møller-Plesset energies. E(0) = ∫ ... dτn E(0) + E(1) Ψ0(Hˆ 0 + V) (36) The correlation energy can then be written.

Discussion is provided in Section II. An alternative approach to improve upon Hartree-Fock models involves including an explicit term to account for the way in which electron motions affect each other. In practice, this account is based on an “exact” solution for an idealized system, and is introduced using empirical parameters. As a class, the resulting models are referred to as density functional models. Density functional models have proven to be successful for determination of equilibrium geometries and conformations, and are (nearly) as successful as MP2 models for establishing the thermochemistry of reactions where bonds are broken or formed.

This is generally assumed to be constant for reactions involving a single set of reactants going to different products, or for reactions involving closely-related reactants. In general, the lower the activation energy the faster the reaction. ** Such limiting reactions have come to be known as “diffusion controlled” reactions. The product formed in greatest amount in a kinetically-controlled reaction (the kinetic product) is that proceeding via the lowest-energy transition state, irrespective of whatever or not this is lowest-energy product (the thermodynamic product).

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