Fragment-Based Electronic Structure for Potential Energy Surfaces Using a Superposition of Fragmentation Topologies.

We present a new approach for adaptive molecular fragmentation. Here multiple fragmentation protocols, or fragmentation topologies, are combined to efficiently and accurately construct potential energy surfaces that are in agreement with post-Hartree-Fock levels of electronic structure theories at density functional theory (DFT) cost. We benchmark the method through evaluation of quantum nuclear effects in a set of protonated water clusters that are known to display significant quantum effects. In such systems, the straightforward use of molecular fragmentation is hindered by the fact that the most appropriate fragmentation strategy changes as a function of nuclear degrees of freedom. Our approach uses a multilayered hypergraph formalism to decompose the potential energy surface, where, at the very top layer, a tessellation of the potential surface yields a set of independent, but correlated, graphical nodes or vertices; each node represents a different protocol to fragment the molecular system. Correlation between the nodes appears as edges and faces in the graph at the top layer and allows the overall potential surface to be represented as a superposition of multiple fragmentation topologies with the coefficients for the superposition arising from a Hamiltonian formalism that is reminiscent of nonadiabatic dynamics. This allows for a natural interpretation of the individual molecular fragmentation topologies as diabatic or valence-bond-type states which we exploit in our formalism. As stated, the method is demonstrated for protonated water clusters where we are able to obtain potentials surfaces in agreement with post-Hartree-Fock methods at DFT cost.