Over a series of publications we have introduced a graph-theoretic description of molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces and higher order simplexes, to represent a collection of locally interacting sub-systems. Each such sub-system is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of sub-systems and have been used for AIMD calculations (Born-Oppenheimer as well as Car-Parrinello-type), for computing multi-dimensional potential energy surfaces, where multiple graphical descriptions are simultaneously used. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at DFT cost. Thus, in a sense, the approach also allows, for the first time, Car-Parrinello-like calculatoins with CCSD accuracy. The approach has been demonstrated for gas-phase dynamics studies, for condensed phase electronic structure, and also for basis set extrapolation based AIMD. Recently, our approach has been used to derive new quantum computing algorithms that enormously reduce the quantum circuit depth in a circuit based computation of correlated electronic structure. We have also introduced a scheme by which an array of neural networks, that act in parallel, can be derived based on our graph-decomposition method and used to further improve the efficiency of the above algorithm. To achieve the latter, we use a unique multi-dimensional tessellation/clustering algorithm to determine our training data for all fragments obtained from the graph-theoretic decomposition. These are then used to extrapolate, through fully connect dense neural networks, the energies for an AIMD trajectory at one-tenth cost as compared to a regular fragmentation-based AIMD calculation, to further imporive efficiency and accuracy. While providing a brief overview of our graph-theoretic approach for potential surface and AIMD, a part of the talk will focus on these recent quantum computing and machine learning developments.

Graph theoretic molecular fragmentation methods for accurate and efficient post-Hartree Fock AIMD and potential energy surfaces: Machine learning and quantum computing enhancements

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