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Unformatted text preview: 0 Solution to 10.675 Assignment #1 1. Derive an expression for the total ground state energy of a twoelectron system using HartreeFock theory. This should be done in terms of spin orbitals. Identify the coulomb and exchange integrals, and explain their physical significance. Solution: Twoelectron system is fairly easy to deal with. Since we are doing the general derivation for Nelectron system in the next problem, we will omit the repeated work here. Please refer to chapter 2.3.1 in Szabo and Ostlunds Modern Quantum Chemistry (pages 6466) for the detailed derivation of twoelectron system. 2. Make yourself comfortable with the general derivation of this expression for N electrons. Solution: For Nelectron system, the Hamiltonian is: N N N 1 ( H = i h ) + r ij (1) i = 1 i = 1 j > i Where, i h ) = 1 i 2 Z A ( 2 A r iA In HartreeFock theory, we choose the form of the wave function to be that of single determinant, formed from spin orbitals: N !  >=  (1) (2) ( N ) >= 1 ( 1) P n P { (1) (2) ( N )} (2) m n k N !...
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
 Spring '03
 RogerD.Kamm
 Electron, pH

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