The multireference constant denominator perturbation theory for one-particle systems and its application to the anharmonic oscillator

In this paper a multireference constant denominator perturbation theory (CDPT) is developed to reduce incomplete basis set errors arising when solving the Schrodinger equation with a finite basis set. The advantage of this method is that very few basis functions are needed, and all calculations if carried out to high enough order in the perturbation treatment effectively use a complete basis set. As a first step the theory has been restricted to one-particle Hamiltonians and applied to the anharmonic oscillator to study the convergence properties. For perturbation calculations carried out to fifth order, results from Pade approximates show an improvement in accuracy of between one and three orders of magnitude.