Integral transform functions. A new class of approximate wave functions

✍ Scribed by R.L. Somarjai

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 295 KB
• Volume: 2
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(68)80037-5

✦ Synopsis

The construction of a new class of approximate wave functions by integral transforms is described. Slater and Gaussian type functions correspond to special. limiting cases of the new class. Some of the conceptuai and practical advantages associated with the new functions are discussed.

Recently Parr and coworkers [l] have demonstrated that for two-, three-and four-electron atoms the replacement of 1s orbitals by 2-parameter Hulthen functions Fas (T):

produces total energies of essentially Hartree-Fock (H-F.) accuracy. For the He isoelectronic series F,B(Y) is also a good approximation to the exact H.F. orbital: it gives operator expectation values that are within a few percent of the corresponding H.F. values [2]. Even when J&p(r) is constrained to satisfy the orbital cusp condition the total energy deteriorates but slightly [lb]. The simplicity of F,,3(3m), combined with its overall success makes its extension and generalization attractive. The outlines of one such scheme are presented in the following.

Our starting point is the identity: Faa(3-) = 3' -1 -\e-"'-e -p'] c J' ewA7&y. (1) o! * Issued as NRC publication.