Non-Born-Oppenheimer potential energy curve: Hydrogen molecular ion with highly accurate free complement method

Abstract

Although the concept of a potential energy curve (PEC) originates from the outgrowth of the Born-Oppenheimer (BO) approximation, we propose the application of analysis methods for the physical PEC with non-Born-Oppenheimer (non-BO) wave functions. A numerical examination was performed with the highly accurate non-BO vibronic wave functions of hydrogen molecular ion, which were obtained in our previous studies with the free complement method. The reduced density function integrated over the electron coordinates plays an important role in understanding nuclear motion dynamics, since it corresponds to the wave function density of the vibrational and rotational motions. The maximum positions of this density indicate the high existence probability of nuclei and can be considered as a discrete representation of the PEC. Whereas an ordinary PEC with the BO approximation is obtained as a numeric curve after multiple electronic state calculations at fixed nuclear coordinates, we propose a new analytical expression of the PEC from a non-BO wave function.

Elastic, charge transfer, and related transport cross sections for proton impact of atomic hydrogen for astrophysical and laboratory plasma modeling

“…Seeking to further improve this foundation, new calculations performed in Mathematica using 32-digit accuracy via the two-center Coulomb Sturmian method of Ovchinnikov and Macek [32] for short to intermediate to long range (2×10 −5 R 200 a.u.). Results of this new calculation agree well with other recent work, for example, use of the 'free complement method' of Nakashima and Nakatsuji [33], who find the value of the s 1s g potential near its minimum at R=2 a.u. to the first 18 digits of −0.102 634 214 494 946 237 compared to our result of −0.102 634 214 494 946 462, both results given in the Born-Oppenheimer approximation.…”

The minimum parameterization of the wave function for the many-body electronic Schrödinger equation. Theory and ansatz

“…8 is used to iteratively obtain an exact solution to the MBSE [48][49][50][51][52][53]. Nakatsuji has successfully used this on very small systems and obtained solutions with unprecedented accuracy [54][55][56].…”