Analytical investigations of an electron-water molecule pseudopotential. I. Exact calculations on a model system

Exact quantum mechanical calculations on the excess electronic states of th e electron-water molecule system have been performed in the static-exchange approximation. The computational model includes a steep, but smooth confin ing potential which keeps the excess electron in the vicinity of the neutra l molecule. Elimination of the core states of the water molecule by the app lication of the Phillips-Kleinman repulsion operator, and the removal of th e large core oscillations of the wave function of the excess electron by th e linear combination of the core states and the valence state result in a s mooth pseudo-wave function. The pseudo-wave function has proper asymptotic behavior with the correct eigenvalue, and, thus, can serve as a model for c omparisons to test the validity of various approximations employed in elect ron-molecule pseudopotential theory. From the comparisons we conclude that of the most commonly used approximations for the repulsion and the exchange operators only the combination of the local repulsion (LR) approximation a nd the semiclassical exchange (SCE) works partly satisfactorily. This parti cular combination reproduces the exact eigenvalue reasonably well, whereas the fit of the electron density is moderate. Although the calculated local potential, based on the LR-SCE approximation, is similar in its most charac teristic features to those employed earlier for hydrated electron calculati ons, we propose this potential to be considered as a reasonable starting po int for further work. Since the other examined approximations fail seriousl y, we find them inappropriate to use in the development of a new effective pair potential. (C) 2001 American Institute of Physics.