Force-free identification of minimum-energy pathways and transition states for stochastic electronic structure theories
Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods, enable highly accurate total energy calculations which in principle can be used to construct highly accurate potential energy surfaces. However, their stochastic nature poses a challenge to the computation and use of forces...
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Zusammenfassung: | Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods,
enable highly accurate total energy calculations which in principle can be used
to construct highly accurate potential energy surfaces. However, their
stochastic nature poses a challenge to the computation and use of forces and
Hessians, which are typically required in algorithms for minimum-energy pathway
(MEP) and transition state (TS) identification, such as the nudged-elastic band
(NEB) algorithm and its climbing image formulation. Here, we present strategies
that utilize the surrogate Hessian line-search method - previously developed
for QMC structural optimization - to efficiently identify MEP and TS structures
without requiring force calculations at the level of the stochastic electronic
structure theory. By modifying the surrogate Hessian algorithm to operate in
path-orthogonal subspaces and on saddle points, we show that it is possible to
identify MEPs and TSs using a force-free QMC approach. We demonstrate these
strategies via two examples, the inversion of the ammonia molecule and an SN2
reaction. We validate our results using Density Functional Theory- and coupled
cluster-based NEB calculations. We then introduce a hybrid DFT-QMC approach to
compute thermodynamic and kinetic quantities - free energy differences, rate
constants, and equilibrium constants - that incorporates
stochastically-optimized structures and their energies, and show that this
scheme improves upon DFT accuracy. Our methods generalize straightforwardly to
other systems and other high-accuracy theories that similarly face challenges
computing energy gradients, paving the way for highly accurate PES mapping,
transition state determination, and thermodynamic and kinetic calculations, at
significantly reduced computational expense. |
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DOI: | 10.48550/arxiv.2402.13189 |