Highly accurate potential energy curves for the hydrogen molecule ion

TL;DR

This paper uses the Riccati-Padé method to compute highly accurate potential energy curves for the hydrogen molecular ion, achieving unprecedented precision and providing valuable benchmarks for future research.

Contribution

The paper introduces the application of the Riccati-Padé method to compute potential energy surfaces of H₂⁺ with up to 100 digits of accuracy, surpassing previous results.

Findings

Equilibrium internuclear distance and energies computed to 40 digits.

Ground state energies computed with over 100 digits of accuracy.

Benchmark values provided for multiple states and internuclear distances.

Abstract

Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pad\'e method (RPM). The convergence properties of the method are analyzed for different states. The equilibrium internuclear distance, as well as the corresponding electronic plus nuclear energy, and the associated separation constants, are computed to 40 digits of accuracy for several bound states. For the ground state the same parameters are computed with more than 100 digits of accuracy. Additional benchmark values of the electronic energy at different internuclear distances are given for several additional states. The software implementation of the RPM is given under a free software license. The results obtained in the present work are the most accurate available so far, and further additional benchmarks are made available through the software provided.