Research

Constrained Nuclear-Electronic Orbital (CNEO) Framework

A major focus of our research group is the development of the Constrained Nuclear-Electronic Orbital (CNEO) framework, which incorporates nuclear quantum effects, particularly quantum nuclear delocalization effects, into an effective potential energy surface (PES).

This framework can be seen as a Born-Oppenheimer framework with direct incorporation of quantum nuclear delocalization, and the resulting effective PES can be referred to as either a quantum-corrected PES or zero-point-corrected PES.

Figure 1. Past and ongoing developments of CNEO framework

Existing functionalities

Within the CNEO framework, our group has developed and made available a broad range of computational tools, including:

• Energy calculations [Xu2020JCP1]
• Analytic gradient calculations [Xu2020JCP2], along with geometry optimization and transition state search
• Analytic Hessian calculations and harmonic analysis [Xu2021JCP]
• Molecular dynamics simulations (CNEO-MD) [Xu2022JACS] with theoretical justifications provided [Chen2023JPCL, Wang2023JPCA]
• Vibrational spectra calculations [Xu2022JACS, Zhang2023JCP, Zhang2023JCTC]
• Hybrid QM/MM calculations and QM/MM molecular dynamics simulations [Zhao2024CPR]
• Reaction rate predictions using Transition State Theory (CNEO-TST) [Chen2024]

We are particularly proud of CNEO-MD, which has significantly improved the accuracy of vibrational spectrum calculations for hydrogen-bonded systems while maintaining computational efficiency.

Additionally, we are very proud of the combination of CNEO with Transition State Theory (TST), which shows great potential for accurately predicting proton, hydrogen atom, and hydride transfer reaction rates.

Applications

The key applications of our methodologies include, but are not limited to:

• Characterizing gas-phase species through vibrational spectra, such as water clusters and amino acids
• Investigating structure and dynamics of low-barrier hydrogen bonds in biological systems
• Exploring proton, hydrogen atom, and hydride transfer reaction rates

Ongoing Developments

Our current research is centered around advancing the CNEO framework through the following key developments:

1. Periodic CNEO-DFT: Implementing periodic boundary conditions for CNEO-DFT to study condensed-phase systems, including hydrogen adsorption on noble metals and hydrogen evolution reactions on electrodes
2. Excited-State CNEO Methods: Expanding CNEO to excited states and investigating excited state problems with nuclear quantum effects by developing CNEO-CIS and CNEO-TDDFT.
3. CNEO Nonadiabatic Methods: Incorporating quantum nuclear delocalization effects into widely-used nonadiabatic dynamics methods, such as Ehrenfest dynamics and surface hopping.