High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion

Abstract

The Dirac equation for H${}_2^{+}$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic balance, which provides the fastest convergence, or without imposing any kinetic balance condition. Application to heavy molecular ions is also illustrated. Calculation of relativistic sum rules shows that this method gives an accurate representation of the complete Dirac spectrum, making it a promising tool for calculations of QED corrections in molecular systems.

References in corpus (11)

• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Electron Self Energy for the K and L Shell at Low Nuclear Charge
• How to observe the vacuum decay in low-energy heavy-ion collisions
• Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states
• Self-consistent extraction of spectroscopic bounds on light new physics
• Calculations of QED effects with the Dirac Green function
• Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
• Ab initio QED calculations in diatomic quasimolecules

Cited by in corpus (3)

• One-particle operator representation over two-particle basis sets for relativistic QED computations
• Light one-electron quasi-molecular ions within the finite-basis-set method for the two-center Dirac equation
• High-precision minmax solution of the two-center Dirac equation