Gauge function optimization 2: An accurately solvable model

摘要

The gauge function is optimized by using the Kennedy–Kobe (KK) theory [Kennedy and Kobe, Phys Rev A, (1984) 30, 51] for the anisotropic harmonic oscillator model in a magnetic field. We extend the KK model to describe various electron density distributions, which resemble to those for the ground and excited states of a H_2~+ ion. The almost divergence-free current densities can be obtained by this method. The convergence is the fastest for the h2 model without the node of the wavefunction. When the wavefunction has nodal points, the first- and the second-order derivatives of the gauge function diverge at the nodes. We examine these singularities of the gauge function near the nodes both numerically and analytically. We also investigate the computed divergence-free current density in detail. Many new stagnation vortices appear after the gauge function optimization. The positions of the vortices are compared with those of the electron density maxima. When the maxima are separated from each other, some correlations are found between them. We also investigate the nuclear cusp condition of current density by inspecting the solutions of the KK equation when the electron density has a cusp. We find that the local mean velocity becomes a C~0 continuous function at the nucleus.