Monte-Carlo optimization of correlated helium wave function

A new type of correlated wave function for the normal helium is proposed in the form:ψ(r₁, r₂)=Σc _mφ_m withφ _m=exp]−α(r ₁+r ₂)]/(br ₁₂+a) ^m wherea, b, α are non-linear variational parameters. Optimizing these parameters by the Monte-Carlo technique, an energy eigen-value of −2.903645(a.u.) is obtained withonly three terms in the basis expansion alongwith satisfactory cusp condition, compared to the essentially exact non-relativistic value of −2.903724 as given by Freundet al (Phys. Rev. A29, 980 (1984)).