Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: Implementation blending ONIOM and empirical valence bond theory.

We discuss hybrid quantum-mechanics/molecular-mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) generalizations to our recently developed quantum wavepacket ab initio molecular dynamics methodology for simultaneous dynamics of electrons and nuclei. The approach is a synergy between a quantum wavepacket dynamics, ab initio molecular dynamics, and the ONIOM scheme. We utilize this method to include nuclear quantum effects arising from a portion of the system along with a simultaneous description of the electronic structure. The generalizations provided here make the approach a potentially viable alternative for large systems. The quantum wavepacket dynamics is performed on a grid using a banded, sparse, and Toeplitz representation of the discrete free propagator, known as the "distributed approximating functional." Grid-based potential surfaces for wavepacket dynamics are constructed using an empirical valence bond generalization of ONIOM and further computational gains are achieved through the use of our recently introduced time-dependent deterministic sampling technique. The ab initio molecular dynamics is achieved using Born-Oppenheimer dynamics. All components of the methodology, namely, quantum dynamics and ONIOM molecular dynamics, are harnessed together using a time-dependent Hartree-like procedure. We benchmark the approach through the study of structural and vibrational properties of molecular, hydrogen bonded clusters inclusive of electronic, dynamical, temperature, and critical quantum nuclear effects. The vibrational properties are constructed through a velocity/flux correlation function formalism introduced by us in an earlier publication.