Hylleraas’ variational method with orthogonality restrictions

Abstract

In this paper, we suggest a new computational technique for the minimization of Hylleraas’ functional with additional orthogonality restrictions imposed on the desired vectors. It is shown how Hylleraas’ constrained problem can be reduced to an unconstrained one by minimal computational efforts. The asymptotic projection (AP) method proposed earlier to minimize Rayleigh’s quotient subject to some orthogonality restrictions is applied to construct a modified Hylleraas’ functional whose solution fulfills the required constraints automatically. Specifically, equivalence between the original problem and the one for the modified Hamilton operator is derived. It is shown that the AP methodology allows additional restrictions to be treated in a unified approach for both Rayleigh’s quotient and Hylleraas’ functional. Specific features of the method are demonstrated on the electronic parallel polarizability of H₂⁺. Some emphasis is put on the choice of specific distributed basis set adapted for polarizability computation. A comparison with other methods, considered exact or extremely accurate, is also given.