Accurate adiabatic correction in the hydrogen molecule.

Area of Science:

• Quantum Chemistry
• Molecular Physics
• Spectroscopy

Background:

• Accurate theoretical predictions of molecular properties are crucial for understanding chemical phenomena.
• Adiabatic effects, corrections to the Born-Oppenheimer approximation, play a significant role in molecular spectroscopy.
• Previous methods for calculating adiabatic corrections had limitations in precision and scope.

Purpose of the Study:

• To develop a new, highly accurate formalism for treating adiabatic effects in hydrogen molecules.
• To calculate the adiabatic correction to the Born-Oppenheimer interaction energy with unprecedented precision.
• To determine the adiabatic correction to dissociation energies for various hydrogen isotopologues.

Main Methods:

• Expansion of the electronic wave function in James-Coolidge basis functions.
• Systematic variation of the basis set size to estimate accuracy.
• Numerical calculations for 88 internuclear distances to construct the adiabatic correction potential.
• Solving the nuclear Schrödinger equation.

Main Results:

• Achieved a relative precision of 10(-12) for the adiabatic correction to the Born-Oppenheimer interaction energy.
• Determined adiabatic corrections to dissociation energies for H2, HD, HT, D2, DT, and T2.
• Obtained a precision of 3 × 10(-7) cm(-1) for the ground state of H2, an improvement of three orders of magnitude.
• The achieved accuracy effectively removes the adiabatic contribution from the error budget of theoretical predictions.

Conclusions:

• The new formalism provides a highly accurate treatment of adiabatic effects in hydrogen molecules.
• This advancement significantly enhances the precision of theoretical predictions for rovibrational levels.
• The methodology can be extended to other diatomic molecules, advancing molecular physics and quantum chemistry.