Molecular Relativistic Corrections Determined in the Framework Where the Born–Oppenheimer Approximation is Not Assumed

Relativistic Correction from the Four-Body Nonadiabatic Exponential Wave Function

We present a method for calculating the relativistic correction in hydrogen molecules that significantly exceeds the accuracy of all the previous literature results. This method utilizes the explicitly correlated nonadiabatic exponential wave function, and thus treats electrons and nuclei equivalently. The proposed method can be applied to any rovibrational state, including highly excited ones. The numerical precision of the relativistic correction reaches several kHz (∼10-7 cm-1), which is below the best experimental accuracy.

Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD

The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.

Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+

Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+}  ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.