# Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

journal contribution

posted on 2021-10-08, 13:35 authored by Anup Kumar, Nicole DeGregorio, Srinivasan S. IyengarWe present a multitopology molecular
fragmentation approach, based
on graph theory, to calculate multidimensional potential energy surfaces
in agreement with post-Hartree–Fock levels of theory but at
the density functional theory cost. A molecular assembly is coarse-grained
into a set of graph-theoretic nodes that are then connected with edges
to represent a collection of locally interacting subsystems up to
an arbitrary order. Each of the subsystems is treated at two levels
of electronic structure theory, the result being used to construct
many-body expansions that are embedded within an ONIOM scheme. These
expansions converge rapidly with the many-body order (or graphical
rank) of subsystems and capture many-body interactions accurately
and efficiently. However, multiple graphs, and hence multiple fragmentation
topologies, may be defined in molecular configuration space that may
arise during conformational sampling or from reactive, bond breaking
and bond formation, events. Obtaining the resultant potential surfaces
is an exponential scaling proposition, given the number of electronic
structure computations needed. We utilize a family of graph-theoretic
representations within a variational scheme to obtain multidimensional
potential surfaces at a reduced cost. The fast convergence of the
graph-theoretic expansion with increasing order of many-body interactions
alleviates the exponential scaling cost for computing potential surfaces,
with the need to only use molecular fragments that contain a fewer
number of quantum nuclear degrees of freedom compared to the full
system. This is because the dimensionality of the conformational space
sampled by the fragment subsystems is much smaller than the full molecular
configurational space. Additionally, we also introduce a multidimensional
clustering algorithm, based on physically defined criteria, to reduce
the number of energy calculations by orders of magnitude. The molecular
systems benchmarked include coupled proton motion in protonated water
wires. The potential energy surfaces and multidimensional nuclear
eigenstates obtained are shown to be in very good agreement with those
from explicit post-Hartree–Fock calculations that become prohibitive
as the number of quantum nuclear dimensions grows. The developments
here provide a rigorous and efficient alternative to this important
chemical physics problem.

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resultant potential surfacesquantum nuclear degreesprotonated water wiresmultidimensional clustering algorithmexponential scaling propositioncomputing potential surfacesuse molecular fragmentsmolecular configuration spacepotential energy surfacesexponential scaling costexpansions converge rapidlyconformational space sampledbody interactions alleviatesbody interactions accuratelyphysically defined criterialocally interacting subsystemselectronic structure theorytheoretic representations withinbased molecular fragmentationbody expansionsmolecular assemblyreduced costenergy calculationsembedded withinconformational samplingbody ordertheoretic nodestheoretic expansionvariational schemetwo levelsoniom schememultiple graphsmultiple dimensionsmuch smallerincreasing ordergraphical rankfull systemfreedom comparedfragment subsystemsfast convergencebond formationbond breakingbecome prohibitivearbitrary orderalso introduce

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