Hellmann-Feynman Forces And Dipole Moments Using Multiple-Scattering Xa Wavefunctions for Diatomic Molecules.

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APPENDIX C HELLMANN-FEYNMAN THEOREM AND THE Xa WAVEFUNCTIONS* In Chapter II and Chapter III, we mentioned that the exact Xa wavef unctions, for the case where a is constant ev- erywhere, rigorously obey the Hellmann-Feynman theorem. We present a proof in this appendix.
Starting with the expression for the exact Xa total energy in equation (2.1): = T n i \^ 1 n-V 1 )n i ^ 1 yd 3 v 1 J fr I'l'RpI 1 X 2 ■>> r 12 1 + I [ "^\a^l )d \ + \ j U xa + (? l )d3r l + 5 ^ 2Z p Z q/ H pq (CD wher
...e the energy is in Eydbergs and the distances are in atomic units. Also, U ™ «

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