The full configuration interaction (FCI) method produces the most accurate results possible using a given basis set. Unfortunately, FCI is so computationally expensive that it can only be used on very small molecules. Popular methods including Hartree-Fock, tensor product state methods, and coupled cluster methods can be thought of as truncations or parameterizations of FCI that reduce the computational cost at the expense of accuracy, with different methods being more accurate for different types of systems.

We have developed a new type of method: the determinant ratio method. As the name suggests, the determinant ratio method parameterizes the FCI coefficients as products/ratios of several determinants. The method theoretically works well even with a small number of determinants, which should lead to good results using a much smaller number of parameters compared to similar tensor-product or exponential based methods. Since it does not truncate FCI and therefore includes contributions from all possible electron configurations, the method is suitable for studying strongly correlated systems. We have completed some preliminary testing of the method on a sequence of geometries representing the dissociation of BeH\(_{2}\).