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Unformatted text preview: Chemistry 120A Problem Set 8 (due April 12, 2010) 1. A configuration interaction calculation of the H 2 molecule . In lecture, we have spent much time discussing the various common approximations to the theory of molecu- lar electronic structure. Accurate implementation of these approximations generally requires significant computational effort. While results acquired from such efforts are often useful, underlying physical principles can be obscured. The purpose of this exercise is to illustrate what the computer is doing, but in a context where the mathematics is simple enough that principles are in clear sight. In particular, we will consider a minimal basis of spatial functions, and approximate various integrals with functional forms that can be treated analytically. Parameters are chosen so that orders-of-magnitude are consistent with nature. Let A ( ~ r ) and B ( ~ r ) represent normalized orbitals localized on hydrogen nuclei A and B , respectively, and let R be the separation of these two nuclei. We will consider the hydrogen molecule as if these two orbitals are a complete set of single electron spatial states. The hamiltonian for two electrons in the field of the two nuclei is H = T (1) + T (2) + V (1) + V (2) + V (1 , 2) , where 1 and 2 are abbreviations for the electron positions ~ r 1 and ~ r 2 , T ( i ) is the kinetic energy for electron i , V ( i ) is the electron-nuclei interaction for electron i , and V (1 , 2) = e 2 / | ~ r 1- ~ r 2 | is the electron-electron repulsion. Exact evaluations of one- and two-electron integrals are complicated tasks. For the purposes of this exercise, assume the relevant integrals are given by h A | B i = e- R/a , a = 2 A...
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