The hydrogen molecule H2\rm{H}_{2} in inclined configuration in a weak magnetic field

Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect to the direction of a uniform constant magnetic field ${\bf B}$, for $B=0,\, 0.1,\, 0.175$ and $0.2\,$a.u. Three inclinations $\theta=0^\circ,\,45^\circ,\,90^\circ$ are studied in detail with emphasis to the ground state $1_g$. Diamagnetic and paramagnetic susceptibilities are calculated (for $\theta=45^\circ$ for the first time), they are in agreement with the experimental data and with other calculations. For $B=0,\, 0.1$ and $0.2\,$a.u. potential energy curves $E$ vs $R$ are built for each inclination, they are interpolated by simple, two-point Pad\'e approximant $Pade[2/6](R)$ with accuracy of not less than 4 significant digits. Spectra of rovibrational states are calculated for the first time. It was found that the optimal configuration of the ground state for $B \leq B_{cr}=0.178\,$a.u. corresponds always to the parallel configuration, $\theta=0$, thus, it is a $^1\Sigma_g$ state. The state $1_g$ remains bound for any magnetic field, becoming metastable for $B > B_{cr}$, while for $B_{cr} < B < 12$\,a.u. the ground state corresponds to two isolated hydrogen atoms with parallel spins.Comment: 31 pages, 11 Tables, 7 Figures (2 new), following referee's suggestions parts 4,5,6 essentially rewritten, to be published at Journal of Quantitative Spectroscopy and Radiative Transfe

A note about the ground state of the H3+{\rm H}_3^+ hydrogen molecular ion

Three simple $7-, (7+3)-, 10-$parametric trial functions for the ${\rm H}_3^+$ molecular ion are presented. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer ground state energy among several-parametric trial functions. These trial functions are chosen following a criterion of physical adequacy and includes the electronic correlation in the exponential form $\sim\exp{(\gamma r_{12})}$, where $\gamma$ is a variational parameter. The Born-Oppenheimer energy is found to be $E=-1.340 34, -1.340 73, -1.341 59$\,a.u., respectively, for optimal equilateral triangular configuration of protons with the equilibrium interproton distance $R=1.65$\,a.u. The variational energy agrees in three significant digits (s.d.) with most accurate results available at present as well as for major expectation values.Comment: 12 pages, 1 figure, 3 table