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Diagonal Born-Oppenheimer Corrections within the Nuclear-Electronic Orbital Framework.

Patrick E Schneider¹, Fabijan Pavošević¹, Sharon Hammes-Schiffer¹

¹Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States.

The Journal of Physical Chemistry Letters

|July 27, 2019

Summary

The nuclear-electronic orbital (NEO) method treats nuclei and electrons quantum mechanically. Adding the diagonal Born-Oppenheimer correction (DBOC) minimally impacts molecular properties, validating the NEO approach.

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Area of Science:

Quantum chemistry
Theoretical chemistry
Computational chemistry

Background:

The nuclear-electronic orbital (NEO) method quantizes nuclei alongside electrons, departing from the Born-Oppenheimer approximation.
This approach requires understanding the validity of the adiabatic approximation introduced by treating nuclei and electrons on an equal quantum footing.

Purpose of the Study:

To derive, analyze, and numerically calculate the diagonal Born-Oppenheimer correction (DBOC) within the NEO framework.
To assess the impact of the NEO DBOC on molecular properties.

Main Methods:

Derivation of the NEO DBOC.
Numerical calculation of the NEO DBOC for eight molecules.
Analysis of the correction's effect on equilibrium bond lengths and vibrational frequencies.

Main Results:

The NEO DBOC was derived and calculated, showing minimal changes to molecular properties.
Equilibrium bond lengths were altered by approximately 10⁻⁴ Å.
Heavy atom vibrational stretching frequencies shifted by about 1-2 cm⁻¹ per quantum proton.

Conclusions:

The diagonal Born-Oppenheimer correction (DBOC) has a negligible impact on molecular properties calculated using the nuclear-electronic orbital (NEO) method.
The NEO approach is robust, with the DBOC offering a minor refinement when needed.
Findings have implications for multicomponent density functional theory and wave function methods.