Compact wavefunctions

Therefore, it appears that the overall agreement obtained for a variety of spectroseopie eonstants is comparable for the two methods while the present method allows us to use a more compact wavefunction. It should also be noted that a good Cl description of a triple bonded system involving a third period atom is much harder to achieve. It can be concluded that the shape of the theoretical potential energy curve reflects its experimental counterpart with acceptable accuracy in the interatomic region of interest. 

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. 

One of the desirable features of compact wavefunctions is the ability to use them to examine additional features of the electron distribution without the necessity of repeating extensive computations to recreate complicated wavefunctions. We illustrate this point, and also exhibit the similarity of our wavefunctions with those of the 66-configuration study of Thakkar and Smith [15] by looking at the pair distribution functions. It is most instructive to present these as Z-scaled quantities Figure 3 contains the electron-nuclear distributions D r ) and p(ri) for clarity we only plot data for H, He, Li, and Ne. Even after Z scaling, a small but systematic narrowing of the distributions with increasing Z is still in process at Z-10. 

The ab initio spin-coupled valence bond (SCVB) approach continues to provide accurate ground and excited state potential energy surfaces for use in a variety of subsequent applications, with particular emphasis on intermolecular forces and reactive systems. The compactness of the various wavefunctions allows direct and clear interpretation of the correlated electronic structure of molecular systems. Recent developments, in the form of SCVB and MR-SCVB, involve the optimization of virtual orbitals via an approximate energy expression. These improved virtuals lead to still higher accuracy for the final variational wavefunctions, but with even more compact wavefunctions. 

Answer The ratio of probabilities is 55 a more compact wavefunction on account of the higher nuclear charge. 

---