Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory

TL;DR

This paper develops an analytic Hessian for constrained nuclear-electronic orbital DFT (cNEO-DFT) to accurately compute vibrational frequencies, highlighting its advantages over traditional DFT methods especially for systems with proton transfer.

Contribution

The paper introduces the analytic Hessian for cNEO-DFT, enabling efficient vibrational frequency calculations that incorporate nuclear quantum effects.

Findings

cNEO-DFT outperforms conventional DFT in vibrational frequency accuracy

cNEO-DFT is comparable to DFT-VPT2 for polyatomic molecules

cNEO-DFT effectively describes proton transfer modes in shared proton systems

Abstract

Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear-electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein we develop the analytic Hessian for cNEO-DFT energy with respect to the change of nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicomponent cNEO coupled-perturbed Kohn-Sham (cNEO-CPKS) equations, which describe the response of electronic and nuclear orbitals to the displacement of nuclear (expectation) positions. With the analytic Hessian, the vibrational frequencies of a series of small molecules are calculated and compared to those from conventional DFT Hessian calculations as well as those from the vibrational second-order perturbation theory (VPT2). It is found that even with a harmonic treatment, cNEO-DFT significantly outperforms DFT and is comparable to DFT-VPT2 in the description of vibrational frequencies in regular polyatomic molecules. Furthermore, cNEO-DFT can reasonably describe the proton transfer modes in systems with a shared proton, whereas DFT-VPT2 often faces great challenges. Our results suggest the importance of nuclear quantum effects in molecular vibrations, and cNEO-DFT is an accurate and inexpensive method to describe molecular vibrations.