A first solution, for LiH, of a molecular transcorrelated wave equation by means of restricted numerical integration

Abstract

The first calculation of a molecular wavefunction and energy by the solution of the appropriate transcorrelated wave equation ( C -1 HC – W )ϕ = 0 has been made for LiH. The results are in accord with the high accuracy found for the Ne atom by Handy & Boys (1968 c ). The spherical symmetry of the Ne problem gave such advantages that the integrals could virtually be evaluated exactly. The new problem of evaluating these integrals for functions about the many nuclei has now been overcome by a particular numerical integration procedure which gives a much higher accuracy in the energy than corresponds to the accuracy of integration for an ordinary integral. Hence a set of points which is much more restricted in number than otherwise can be used. The error per electron is nearly as small as 1 % of a bond energy, and it is reasonable to expect that later applications of this method will easily surpass this accuracy for a wide range of molecules, and for reacting systems. The method depends on the direct introduction of functions of r ij into the correlation factor in a way applicable to any molecule and the successful implementation of this for the first molecule may provide a turning point in methods of theoretical chemical prediction. The preparation of the whole set of programs requires less than one man year and the general characteristics are those of a method which is much simpler than the previous methods which do not appear capable of this level of accuracy.