HMWR3 - 2 Group Theory(30 pts Evaluate the products between...

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110B Physical Chemistry Homework #2: assigned 2/2/11; due 2/14/11 in class 1. Quantum Chemistry Calculations (40 pts) Within the context of quantum chemistry calculations, what does one mean by basis set? Describe at least three different choices of basis set for a quantum mechanical calculations. Show that the overlap integral of the two normalized Gaussian functions g1 = (2 α / π ) 3/4 exp [ - α (r- R A ) 2 ] centered at R A and g2 = (2 β / π ) 3/4 exp [ - β (r- R B ) 2 ] centered at R B is proportional to exp [- αβ ( R A - R B ) 2 /( α + β )]. Here A and B denote two atoms in a molecule and r denotes electronic coordinates. Discuss how this overlap varies as a function of the distance between the two atoms, and how large it is when the two atoms are at an infinite distance. What would the value of the overlap be if the A-B distance went to zero?
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Unformatted text preview: 2. Group Theory (30 pts) Evaluate the products between the symmetry operations of the point group C 2v . Give examples of molecules (at least 3) whose symmetry is represented by the C 2v group. Consider a water molecule and substitute one hydrogen atom with deuterium. Does the symmetry of the molecule change. If so, explain how. List the symmetry elements for the trigonal planar molecule SO 3 . 3. Hueckel approximation (30 pts) Compute the Hueckel π electron energy (the sum of all energies of orbitals occupied by p electrons, taking into account spin multiplicity) of trimethylenemetane (C 4 H 6 ) and compare it with that of two isolated ethane molecules....
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