Classical Dynamics Methods for High Energy Vibrational Spectroscopy

Llorente, J. M. Gomez; Pollak, Eli

doi:10.1146/annurev.pc.43.100192.000515

Cited by 88 publications

(37 citation statements)

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“…70 The close correspondence between quantum mechanical states and POs is further illustrated in Figure 8 by showing for HCP 81,82 is quite convenient for getting an overview of the structure of the phase space and the different families of periodic orbits and how they behave as a function of energy. In the quantum mechanical part of the figure, the energy separations between the neighboring states of a given progression are depicted.…”

Section: Classical Mechanics Point Of View: Periodic Orbits and mentioning

confidence: 96%

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Joyeux

Farantos

Schinke³

2002

J. Phys. Chem. A

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The vibrational motion of highly excited molecules is discussed in terms of exact quantum and classical mechanics calculations, employing global potential energy surfaces, as well as in terms of a spectroscopic Hamiltonian and its semiclassical limit. The main focus is saddle-node bifurcations and their influence on the spectrum. The general features are illustrated by three examples, which despite their quite different intramolecular motions have several aspects in common: HCP, HOCl, and HOBr. In all three cases a 1:2 Fermi resonance is the ultimate cause of the complications observed in the spectra.

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Section: Classical Mechanics Point Of View: Periodic Orbits and mentioning

confidence: 96%

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

Joyeux

Farantos

Schinke³

2002

J. Phys. Chem. A

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“…[1][2][3][4][5] Alternatively, perturbative quantum methods have also been successfully applied to many systems, but they are intrinsically limited to a single reference geometry. [6][7][8][9][10][11] High dimensional systems, such as peptides, are instead usually simulated through ad-hoc scaled harmonic approaches or by means of classical mechanics, either using force fields [12][13][14] or employing ab initio molecular dynamics (AIMD) [15][16][17][18][19][20][21] approaches in which the nuclear forces are calculated using electronic structure codes. In classical simulations the curse of dimensionality is significantly tamed with respect to quantum mechanical counterparts.…”

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

The Journal of Chemical Physics

100

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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.

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“…1 . The dynamical approximation of assuming that nuclear motion can be treated classically allows us to find approximations to quantum solutions which are numerically relatively easy to calculate from information obtained along classical trajectories.…”

Section: Classical Approachmentioning

confidence: 99%