Quantum Chemistry without Wave Functions: Diffusion Monte Carlo Applied to H and H2+
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Abstract
Although it is an exactly solvable problem, in a standard quantum chemistry course the quantum mechanical treatment of H2+ is usually done within the LCAO-MO approximation. Even allowing for variable orbital exponents in the wave function, the variational energy has a substantial error at the equilibrium bond distance.As a computer project associated with our basic third-year-level quantum chemistry course, students solve the hydrogen atom and H2+ problems by using the so-called diffusion Monte Carlo method, a computer simulation technique. In this paper we present the theory of diffusion Monte Carlo in an intuitive manner. For these simple systems, we describe the algorithm and show it to be sufficiently straightforward to make an attractive exercise. Prior knowledge of the form of the wave function is not required. The results will be in agreement with the exact energies. Programming skills needed to perform the simulation are minimal. For possible use by the instructor, we posted a copy of our computer codes (written in Fortran) on the Web.
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