Prev. Article Next Article Table of Contents

Article

Quantum Chemistry without Wave Functions: Diffusion Monte Carlo Applied to H and H2+

Your current credentials do not allow retrieval of the full text.

Purchase the full-text

PDF/HTML,
figures/images,
references and tables,
(where available)

Heather L. Cuthbert and Stuart M. Rothstein

Brock University, Department of Chemistry, St. Catherines, Ontario L2S 3A1, Canada

J. Chem. Educ., 1999, 76 (10), p 1378

DOI: 10.1021/ed076p1378

Publication Date (Web): October 1, 1999

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.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Pedagogy):

Computer-Based Learning

Keywords (Subject):

Quantum Chemistry

View: Hi-Res PDF | PDF w/ Links

Citing Articles

Citation data is made available by participants in CrossRef's Cited-by Linking service. For a more comprehensive list of citations to this article, users are encouraged to perform a search in SciFinder.

This article has been cited by 1 ACS Journal articles (1 most recent appear below).

A Variational Monte Carlo Approach to Atomic Structure
Stephen L. Davis
Journal of Chemical Education2007 84 (4), 711
- A Variational Monte Carlo Approach to Atomic Structure
  Stephen L. Davis
  Journal of Chemical Education2007 84 (4), 711
  A simple version of the variational Monte Carlo method is applied to the electronic structure of atomic hydrogen, helium, lithium, and beryllium. For simplicity, the trial functions are taken as products of hydrogenic orbitals for which Z is treated as a ...
  Abstract | Hi-Res PDF | PDF w/ Links