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We present a graph‐theoretic approach to adaptively compute many‐body approximations in an efficient manner to perform (a) accurate post‐Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium‐ to large‐sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed‐phase simulations at the cost of pure density functionals, (c) reduced‐cost on‐the‐fly basis extrapolation for gas‐phase AIMD and condensed phase studies, and (d) accurate post‐HF‐level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM‐like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many‐body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph‐theoretic methods. Specifically, a region of chemical interest is coarse‐grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many‐body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one‐dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two‐dimensional periodic boundary conditions.

 

We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites. To address the challenge of reactive rare events, we begin with an ab initio molecular dynamics adaptation of the Caldeira–Leggett system-bath Hamiltonian and apply this approach to the study of the hydrogen transfer rate-determining step in soybean lipoxygenase-1. Through direct application of this method to compute an ensemble of classical trajectories, we discuss the critical role of isoleucine-839 in modulating the primary hydrogen transfer event in SLO-1. Notably, the formation of the hydrogen bond between isoleucine-839 and the acceptor-OH group regulates the electronegativity of the donor and acceptor groups to affect the hydrogen transfer process. Curtailing the formation of this hydrogen bond adversely affects the probability of hydrogen transfer. The second part of this paper deals with complementing the rare event sampled reaction pathways obtained from the aforementioned development through quantum nuclear wavepacket dynamics. Essentially the idea is to construct quantum nuclear dynamics on the potential surfaces obtained along the biased trajectories created as noted above. Here, while we are able to obtain critical insights on the quantum nuclear effects from wavepacket dynamics, we primarily engage in providing an improved computational approach for efficient representation of quantum dynamics data such as potential surfaces and transmission probabilities using tensor networks. We find that utilizing tensor networks yields an accurate and efficient description of time-dependent wavepackets, reduced dimensional nuclear eigenstates and associated potential energy surfaces at much reduced cost.