# hw6 - Chem 110A Homework 6: Due Friday, November 13...

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Chem 110A 1 Homework 6: Due Friday, November 13 Chemistry 110A — 2009 Professor McCurdy 1. Mathematica Problem: Using the trial function 2 = C i exp( 1 3 i r 2 ) i = 1 5 4 with the exponents in Table I below. Calculate the variational estimate of the ground state energy of the H atom. i 1 i 1 33.865 2 5.09479 3 1.15879 4 0.32584 5 0.1027410 You will have to build the Hamiltonian and overlap matrices, using atomic units in which the 1 = 1, e / 4 21 0 = 1, m e = 1 . Atomic units are also explained in the text in section 8-1. The Hamiltonian and overlap matrices are 5 by 5 matrices that you can name anything you want. If they were named H and S, for example, their elements would be given by H[[i,j]] and S[[i,j]]. To find the eigenvalues of the generalized eigenvalue problem HC = SCE , use the command Eigenvalues[{H, S}] If you have done this correctly, you will get the energy (to five significant figures) that appears in Table I of the attached paper by John Pople’s group on optimizing Gaussian basis sets for quantum chemistry calculations. John Pople won the Nobel prize in chemistry in 1998 (not for this paper though!).

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## This note was uploaded on 12/02/2009 for the course CHE 110A taught by Professor Mccurdy during the Spring '09 term at UC Davis.

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hw6 - Chem 110A Homework 6: Due Friday, November 13...

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