HMWR2 - r denotes electronic coordinates) is a Gaussian...

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110B Physical Chemistry Homework #2: assigned 1/26/11; due 2/2/11 in class 1. Quantum Chemistry Calculations (40 pts) Explain how one goes about performing a Hartree Fock self consistent field calculations of the electronic levels and total energy of a molecule. Explain each step in detail (including set up the many body wavefunction, choice of a basis set, solution of the Fock equations and evaluation of orbital and total energy). If one chooses a Gaussian basis set, then integrals involving Gaussian functions centered on different atoms will be involved. Explain why. Show that the product of a (not normalized) Gaussian g1 = exp [ - α (r- R A ) 2 ] centered at R A and one gaussian centered at R B : g2 = exp [ - β (r- R B ) 2 ] (where A and B denote two atoms in a molecule and
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Unformatted text preview: r denotes electronic coordinates) is a Gaussian centered at R p = ( α R A + β R B )/( α + β ). 2. Hybrid orbitals (30 pts) Show that the following sp 3 hybridized orbitals are normalized and orthogonal. Give an example of a molecule whose orbitals may be described by these hybrids. 3. Hueckel approximation (30 pts) Using the Hueckel approximation, show that the π molecular orbital corresponding of the energy E = α – β for the ethene molecule is Φπ = (2p zA – 2p zB )/sqrt(2). A and B denote Carbon atoms and 2p z denotes an orbital centered at the C atom. Explain all approximations involved in the so called Hueckel theory that you are using. Find the wavefunction in the case when the overlap S is different from zero....
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This note was uploaded on 02/13/2011 for the course CHE 110B taught by Professor Galli during the Winter '11 term at UC Davis.

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