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The Advances in Chemical Physics sequence presents the chemical physics and actual chemistry fields with a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline. choked with state of the art learn stated in a cohesive demeanour no longer discovered in other places within the literature, each one quantity of the Advances in Chemical Physics sequence serves because the excellent complement to any complicated graduate type dedicated to the research of chemical physics.

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Then the generalized Hellmann-Feynman theorem states that (86) The proof of the generalized Hellmann-Feynman theorem is Differentiating the equation (YIHe- El") = O (87) with respect to y gives The integrals involving aY/ay vanish since (He - E)Y = 0 and He is Hermitian. Thus, Eq. (88) becomes the generalized Hellmann-Feynman theorem. Exactly what this theorem means depends to a large extent on what coordinates are used to describe the electronic configuration' 32 (see subsection D). '~'-'~~ Thus, for one parameter y, there can be a number of generalized Hellmann-Feynman theorems.

For energy calculations for the larger molecules, the Hartree-Fock and related methods are particularly useful. Also these self-consistent field potential energy curves need not agree with the exact curves to give useful information. ^^ of the potential curves for diatomic molecules and therefore can give good vibrational and rotational constants and may be useful in establishing good semiempirical estimates of the actual potential energy curves as well. V. ELECTROSTATIC PERTURBATION CALCULATIONS Whereas variational techniques are especially suited for the calculation of short- and intermediate-range intermolecular forces, perturbation techniques are suited for the calculation of long-range forces.

If (p)qqt= 0, but (Q;),,. # 0, then the lead term in the first-order perturbation energy is given by the matrix components of V , and the resonance energy varies as l/RS. This quadrupole-type resonance should be much weaker than the dipole but, nevertheless, it should be recognized and expected in S-D, P-F, etc. collisions between like atoms. d. The Second-Order Energy. The second-order energy for resonant interactions of two like atoms has the same form as for nonresonant interactions (since the cross terms vanish because of selection rules).

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