Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme

124

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

Section: B Implementation Of Ab Initio Instanton Theorymentioning

confidence: 99%

Perspective: Ring-polymer instanton theory

Richardson

2018

124

“…It allows to perform on-the-fly semiclassical molecular dynamics simulations given a few input trajectories. [58][59][60][61][62][63][64][65] The approach is amenable to ab initio direct molecular dynamics, thus avoiding the effort to construct an accurate analytical potential energy surface which may be quite demanding especially for large systems, [66][67][68][69][70][71][72][73][74] and permits to faithfully reproduce quantum effects like quantum resonances, [60] intra-molecular and long-range dipole splittings, and the quantum resonant ammonia umbrella inversion. [62] Nevertheless, all SCIVR methods run out of steam when straightforwardly applied to problems involving large-sized systems.…”

Section: Introductionmentioning

confidence: 99%

“Divide and conquer” semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

Liberto

Conte

Ceotto

2018

Self Cite

100

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

“…36 This method is valid since the Hessians change rather smoothly along the trajectories. Comparison of the results of the Hessian update scheme with the numerically exact Hessians along a single trajectory shows that the update scheme leads to a typical error of 5%, which we believe is acceptable.…”

Section: A the Semiclassical Implementationmentioning

confidence: 98%

On-the-fly semiclassical study of internal conversion rates of formaldehyde

Ianconescu

Tatchen

Pollak

2013

Internal conversion is an inherently quantum mechanical process. To date, "ab initio" computation of internal conversion rates was limited to harmonic based approximations. These are questionable since the typical transition to the ground electronic state occurs at energies which are far from the harmonic limit. It is thus of interest to study the applicability of the Semiclassical Initial Value Representation (SCIVR) approach which is in principle amenable to "on the fly" studies even with "many" degrees of freedom. In this work we apply the Herman-Kluk-SCIVR methodology to compute the internal conversion rates for formaldehyde for a variety of initial vibronic states. The SCIVR computation gives reasonable agreement with experiment, while the harmonic approximation typically gives rates that are too high.