Potential energy curves of the hydrogen molecular ion in the Born-Oppenheimer approximation are computed by means of the Riccati-Padé method (RPM). The convergence properties of the method are analysed 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.

中文翻译：

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氢分子离子的高精度势能曲线

Born-Oppenheimer 近似中氢分子离子的势能曲线是通过 Riccati-Padé 方法 (RPM) 计算的。分析了该方法在不同状态下的收敛特性。平衡核间距离，以及相应的电子加核能，以及相关的分离常数，对于几个束缚态，计算精度为 40 位。对于基态，相同参数的计算精度超过 100 位。对于几个附加状态，给出了不同核间距离处电子能量的附加基准值。RPM 的软件实现是在免费软件许可下提供的。目前工作中获得的结果是迄今为止最准确的，