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Constrained nuclear-electronic orbital second-order Møller-Plesset perturbation theory.

Gabrielle B Tucker¹, Kurt R Brorsen¹

¹Department of Chemistry, University of Missouri, Columbia, Missouri 65211, USA.

The Journal of Chemical Physics

|May 14, 2026

Summary

A new computational method, constrained nuclear-electronic orbital MP2 (CNEO-MP2), accurately calculates molecular properties considering nuclear quantum effects. This approach simplifies and enhances the study of molecular vibrations and isotopic variations.

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Area of Science:

Quantum Chemistry
Computational Chemistry
Molecular Physics

Background:

Accurate calculation of molecular properties requires accounting for nuclear quantum effects.
Existing methods for incorporating nuclear vibrations are often computationally expensive and require multiple steps.

Purpose of the Study:

To develop and implement a novel multicomponent second-order Møller-Plesset perturbation theory (MP2) method within the constrained nuclear-electronic orbital (CNEO) framework.
To enable the simultaneous calculation of electronic-nuclear and nuclear correlation for vibrationally averaged molecular properties.
To provide a more efficient approach for capturing nuclear quantum effects like vibrational averaging, isotopic effects, and zero-point energy.

Main Methods:

Derivation and implementation of the multicomponent CNEO-MP2 method based on a generalized Hylleraas functional.
Inclusion of electronic-nuclear and nuclear correlation effects.
Benchmarking the CNEO-MP2 method on diatomic and small polyatomic molecules and ions.

Main Results:

The CNEO-MP2 method successfully incorporates nuclear quantum effects into a single calculation or geometry optimization.
Calculated internuclear distances, bond angles, potential energy surfaces, and vibrational frequencies demonstrate the method's accuracy.
The method eliminates the need for costly post-calculation steps to determine vibrational effects on molecular properties.

Conclusions:

The developed CNEO-MP2 method accurately captures the influence of nuclear vibrational motion on molecular properties.
This new approach offers a significant computational advantage for studying nuclear quantum effects in molecules.
CNEO-MP2 provides a robust framework for future investigations in computational and molecular physics.