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

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.