Highly Compact Wavefunctions for Two-Electron Systems

Two-electron systems, i.e. the He atom and its isoelectronic ions, are the simplest species exhibiting electron correlation, and ever since the earliest days of quantum mechanics there has been interest in finding simple, yet accurate descriptions of correlation effects in such systems. Independent-particle 

ADVANCES IN QUANTUM CHEMISTRY, VOLUME 48 ISSN 0065-3276 DOI I0.I0I6/S0065-3276(05)48021-1 

Much more recently, extremely accurate studies on He-like systems have been reported, including that of Frolov [4] on H and He, an even more precise study of He by Schwartz [5], and computations on the He-like positive ions with nuclear charges Z=3-10 by Frolov and Smith [6]. While these investigations quantitatively reproduced the energy and other properties of He-like systems, the wavefunctions which did so contained thousands of terms, making an understanding of their features less than apparent. The situation corresponds well to an observation made by Mulliken [7] (and resuscitated in a recent paper by Scully et al. [8])  

More recently, Kleinekathofer, Patil, Tang, and Toennies (KPTT) [10] proposed a far more compact wavefunction for He-like systems, based on the use of a functional form that is essentially completely determined by requiring proper behavior of the wavefunction at small and large-r limits. The KPTT wavefunction is more complicated to use than the functions entering the large-scale accurate computations and from the perspective of the present authors is comparable in utility to a moderate-length configuration expansion. Its virtue is its lack of arbitrary parameters. 

The present contribution investigates compact wavefunctions for the He isoelectronic series from a more pragmatic viewpoint, with the goal of finding functional forms that are easy both to use and to understand. 

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