Atomic and Molecular Calculations Using Quasirandom Numbers

✍ Scribed by S.A. Alexander; R.L. Coldwell

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 56 KB
• Volume: 172
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.2001.6865

✦ Synopsis

We have calculated the total ground-state energy, kinetic energy, and potential energy of He, H 2 , Li, and Be using explicitly correlated wavefunctions and two numerical integration procedures. The first integration procedure uses pseudorandom numbers and converges as N -0.5 . The second uses a set of quasirandom numbers generated by Halton's algorithm. Under some circumstances the convergence of this integration procedure can be as fast as N -1 . When a small to intermediate number of quasirandom numbers are used, most of our expectation values converge faster than those computed using pseudorandom numbers. When a large number of quasirandom numbers are used, however, we find that most of the expectation values converge at roughly the same rate as those computed using pseudorandom numbers.