Finite-volume variational method: First application to direct molecular photoionization

A new finite-volume variational method (FVVM) devised for ab initio calculation of molecular continuum wave functions is presented. It is a generalization of Kohn's FVVM which appeared in the same paper [W. Kohn, Phys. Rev. 74, 1763 (1948)] as the well-known principle for phase shifts. In FVVM, the inner-region continuum wave functions are expanded onto a finite basis set. A symmetrization of the Hamiltonian matrix is realized by introducing a set of unknown logarithmic derivatives $b$ at the surface boundary. This leads to a generalized system of eigenequations in terms of the unknowns, namely, the expansion coefficients and eigenvalues $b$. The proposed method combines the respective advantages of $R$-matrix and eigenchannel theories in the sense that the system of eigenequations is solved only once and that the eigenfunctions so obtained are uniformly convergent at the surface boundary, where collision information may be extracted by matching. As a model calculation, we use FVVM to calculate eigenphases and cross sections for the photoionization of ${{\mathrm{H}}_2}^{+}(1\mathrm{}{\sigma }_g\to E{\sigma }_u)$. Very encouraging results are obtained that demonstrate the numerical feasibility of the method.