Perturbation theoiy first-order

When E > Et, the only second-order perturbation theoiy contribution comes from the first term of Eq. (3.39), Thus,... 

A second theoretical approach to understanding E- V transfer is based on the notion that long-range attractive forces might couple the electronic and vibrational degrees of freedom. Ewing has developed a theory for such coupling that is similar to the theory for V- V transfer proposed earlier by Sharma and Brau. First order perturbation theoiy is used in this approach to calculate the probability for the E->V transition ... 

Let us recall that the electrostatic interaction energy Ee]st(.ABC) of the ground-state ha =0,riB = 0, nc = 0) molecules is defined as the first-order correction to the energy in the polarization approximation perturbation theoiy ... 

The expression for the three-bo(ty non-additivity of the valence repulsion [given by formula (f3.39), based on definition (13.37) of the first-order correction in symmetry-adapted perturbation theoiy and from definition (13.52) of the three-body contribution] is ... 

The omissions made in (3CISD theory relative to CCSD theoiY may be justified by the observation that the singles amplitudes are usually smaller than the doubles anplitudes. For further justification, we may invoke perturbation theory, noting that, in Mpller-Plesset theory, the doubles amplitudes appear to first order and the singles to second order in the fluctuation potential. Carrying out an... 

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