A Generalized Force-Modified Potential Energy Surface (G-FMPES) for Mechanochemical Simulations

We describe the modifications that a spatially varying external force produces on a Born-Oppenheimer potential energy surface (PES), and in this chapter, we present a formulation for describing a Generalized Force-Modified Potential Energy Surface (G-FMPES). Our formulation shows that the spatially varying force resembling hydrostatic pressure results in the G-FMPES having curvature different from that of the unmodified PES. Using electronic structure methods, the effect of pseudo-hydrostatic pressure on the PES is exemplified by calculating atomistic quantities (including transition states) for (i) conformational transitions in ethane ( \(\text {C}_{2}\text {H}_{6}\) ) and RDX (hexahydro-1,3,5-trinitro-s-triazine) molecules, (ii) the decomposition of RDX, and (iii) a Diels-Alder reaction between 1,3-butadiene and ethylene. The calculated transition states and Hessian matrices of stationary points of ethane and RDX molecules show that spatially varying external forces shift the stationary points and modify the curvature of the PES, thereby affecting the harmonic transition rates by altering both the energy barrier as well as the prefactor. The harmonic spectra of both molecules are blue-shifted with increasing compressive “pressure.” Some stationary points on the RDX-PES disappear under the application of the external force, indicating the merging of an energy minimum with a saddle point. This change in the topology of the PES demonstrates that new reaction pathways may be introduced by the application of mechanical forces. Part of this chapter is reproduced with permission from Refs. (J Chem Phys 143(13):134109 [1]) Copyright 2015 AIP Publishing, (J Chem Phys 145(7):074307 [2]) Copyright 2016 AIP Publishing, and  (Int J Quantum Chem 117(20):e25426 [3]) Copyright 2017 John Wiley & Sons.