Monte Carlo optimisation of correlated wave functions for normal two-electron systems

Abstract

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ( r 1 , r 2 ) = Σc m Φ m ( r 1 , r 2 ) with Φ m ( r 1 , r 2 ) = exp [−α(r 1 + r 2 )] (br 12 + a) m , where α, a , b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.