Channel-coupling theory of molecular structure. Finite-element method solution forH2+

The problems encountered in the channel-coupling array (CCA) calculations of the preceding paper, viz., the failure to achieve convergence and the persistence of unphysical potential-energy curves, are resolved herein with the use of the ${\mathrm{H}}_2^{+}$ ion as a test case. Convergence is obtained by the use of local interpolates and the finite-element method in place of the globally defined, LCAO-type (linear combination of atomic orbitals) functions previously used. Physically correct, ungerade potential-energy curves result from calculations in which the ungerade CCA channel component wave functions are each required to vanish on the midplane normal to the symmetry axis, just like the solution to the Schrödinger equation. A proof of the foregoing property plus detailed discussions of the finite-element method and its CCA and Schrödinger-equation solutions, of spurious solutions, of convergence, and of implications of the calculations are presented.