Solving the Schrödinger Equation for the Hydrogen Molecular Ion in a Magnetic Field Using the Free-Complement Method

Abstract

AbstractThe hydrogen molecular ion (H +2 ) in a magnetic field is investigated theoretically using the free-complement (FC) method for solving the Schrödinger equation. H +2 was placed in magnetic fields of moderate strengths. Our results were shown to be highly accurate. Total energies, dissociation energies, quadrupole moments, and electron densities were calculated for parallel and perpendicular fields. The gauge-origin dependence of the wave function was examined in detail. It was shown that the results of the FC method are always gauge independent when the gauge-including function is employed as the initial function. Even when we start from the gauge-nonincluding functions, the FC method gives the gauge-independent result in some order, because the FC wave function becomes exact as the order of the FC calculations increases. We observed that properties such as total energy, potential energy curve, vibrational level, and electron density distribution became gauge-origin independent as the order of the FC wave function increased.KeywordsWave FunctionInitial FunctionStrong Magnetic FieldComplement FunctionParallel Magnetic FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.