Global and local properties of the S states of the dtμ molecular ion: A finite-element study

An accurate finite-element method (FEM) is applied to solve the three-dimensional Schrödinger equation for the S states of the dtμ molecular ion. Using an adaptive refinement of the grid and higher-order polynomials the energy eigenvalues are obtained with a relative precision better than 10^-11. The deviation from the virial theorem, the two-body cusp ratios, and the expectation values 〈1/r〉,〈r〉,〈r²〉,〈δ(r)〉 for the three interparticle distances are computed and discussed. The FEM values turn out to be comparable to results obtained with sophisticated global basis sets. Special local refinement techniques are applied to study the expectation values for the Dirac delta functions. New benchmark values for these local properties are presented.