Explicitly correlated Gaussian functions with r factors for calculations of the ground state of the helium atom

✍ Scribed by Zhenghong Zhang; Ludwik Adamowicz

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 400 KB
• Volume: 15
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540150810

✦ Synopsis

Explicitly correlated Gaussian functions with $ ; exp( -P62) factors have been used in variational calculations of the ground state of the helium atom. Additional correlation factors in the form of even powers of rii were introduced to the Gaussian functions with exponential correlation components by differentiating these functions with respect to the correlation exponent p. The algorithm of this method and its computational implementation is described. A number of calculations were performed for the ground state of helium atom to test the performance of the basis sets comprising different numbers of the Gaussians with the exp( -p6,) and 62 exp( -PI&) correlation factors. The numerical results indicate that including functions with rf2 factors does not lead to improved results, contrary to what was anticipated initially. 0 1994 by John Wiley & Sons, Inc.

utilizing the explicitly correlated functions has been slow because for most types of these functions the resulting many-electron integrals are very difficult to evaluate.2 There are, however, some exceptions. Boys3 and Singer" introduced the explicitly correlated Gaussian functions which contain correlation factors in the exponential form, exp( -PI$). A number of numerical examples, which have been presented in the literature by several workers, have indicated that these types of functions can effectively create the Coulomb holes (i.e., reduce the amplitude of the wave function when two electrons approach one another). All types of molecular in-*Author to whom all correspondence should be addressed.