## New computational methods for dynamics of nuclei and electrons

Potential energy surfaces are critical to determine dynamical properties, including reactivity as well as ensemble averages. However, the accurate determination of potential surfaces is compounded by (a) the (steeply algebraic) computational complexity of quantum mechanical calculations, and (b) the number of such calculations, which generally grows exponentially with system size. We tackle both problems using information theoretic measures and graph theoretic methods. These methods facilitate the study of complex phenomena in biological and atmospheric processes.

We have introduced methods that accurately compute quantum dynamical effects in a subsystem while simultaneously handling the motion of the surrounding atoms and changes in electronic structure, on-the-fly. The approach is quantum-classical, that is combines quantum mechanics and classical mechanics, and involves the synergy between a time-dependent quantum wave-packet description and ab initio molecule dynamics. As a result, the approach is called quantum-wave-packet {\em ab initio} molecular dynamics and abbreviated as QWAIMD. The approach allows a massively parallel implementation; computational treatment of simultaneous dynamics of electrons and nuclei in medium sized chemical systems can now be treated over 100s of computer processors leading to an efficient computational methodology. Furthermore, our approach allows the flexibility to treat a subset of the nuclei in a quantum mechanical fashion while simultaneously studying the dynamical evolution of the electrons with the majority of nuclei treated in a classical fashion. The links at the end of this page provide a list of publications with further details on this formalism. Also click a powerpoint presentation that describes QWAIMD may be found here.

More recently, we have begun to generalize this process by introducing an approach to reduce the computational complexity and storage pertaining to quantum nuclear wave functions and potential energy surfaces. The method utilizes tensor networks. A tensor network may be thought of as a graph, but where the elements of the graphs such as nodes and edges are also thermselves matrices and higher order tensors. Using these methods drastically reduces the overall storage and computational cost and this is illustrated in the parallax graphic shown here with more details in the publitcaions below.

Why would one want to treat “some nuclei using quantum mechanics”? It turns out that this problem is of relevance in many biological enzyme problems and also in atmospheric chemical problems, the study of which we are now actively pursuing. As an example, of our current study, the figure on the left represents the active site of the enzyme “lipoxygenase” where the quantum dynamical nature of a transferring hydrogen atom dictates the kinetics. Such interesting chemistry is also found in many atmospheric chemical problems as a result we are currently applying this methodology to problems in biological chemistry and atmospheric chemistry. The specific studies conducted on biological systems may be found here.