Nuclear quantum effects play a crucial role in many chemical and biological systems involving hydrogen atoms yet are difficult to include in practical molecular simulations. In this paper, we combine our recently developed methods of constrained nuclear–electronic orbital density functional theory (cNEO-DFT) and constrained minimized energy surface molecular dynamics (CMES-MD) to create a new method for accurately and efficiently describing nuclear quantum effects in molecular simulations. By use of this new method, dubbed cNEO-MD, the vibrational spectra of a set of small molecules are calculated and compared with those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with significant hydrogen motion characters, demonstrating the promise of cNEO-MD for simulating chemical and biological systems with significant nuclear quantum effects.

Proton transfer is crucial in various chemical and biological processes. Because of significant nuclear quantum effects, accurate and efficient description of proton transfer remains a great challenge. In this Communication, we apply constrained nuclear–electronic orbital density functional theory (CNEO-DFT) and constrained nuclear–electronic orbital molecular dynamics (CNEO-MD) to three prototypical shared proton systems and investigate their proton transfer modes. We find that with a good description of nuclear quantum effects, CNEO-DFT and CNEO-MD can well describe the geometries and vibrational spectra of the shared proton systems. Such a good performance is in significant contrast to DFT and DFT-based ab initio molecular dynamics, which often fail for shared proton systems. As an efficient method based on classical simulations, CNEO-MD is promising for future investigations of larger and more complex proton transfer systems.

The modeling and interpretation of vibrational spectra are crucial for studying reaction dynamics using vibrational spectroscopy. Most prior theoretical developments focused on describing fundamental vibrational transitions while fewer developments focused on vibrational excited state absorptions. In this study, we present a new method that uses excited state constrained minimized energy surfaces (CMESs) to describe vibrational excited state absorptions. The excited state CMESs are obtained similarly to the previous ground state CMES development in our group but with additional wave function orthogonality constraints. Using a series of model systems, including the harmonic oscillator, Morse potential, double-well potential, quartic potential, and two-dimensional anharmonic potential, we demonstrate that this new procedure provides good estimations of the transition frequencies for vibrational excited state absorptions. These results are significantly better than those obtained from harmonic approximations using conventional potential energy surfaces, demonstrating the promise of excited state CMES-based methods for calculating vibrational excited state absorptions in real systems.