58 research outputs found
The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics
This paper deals with the critical issue of approximating the pre-exponential
factor in semiclassical molecular dynamics. The pre-exponential factor is
important because it accounts for the quantum contribution to the semiclassical
propagator of the classical Feynman path fluctuations. Pre-exponential factor
approximations are necessary when chaotic or complex systems are simulated. We
introduced pre-exponential factor approximations based either on analytical
considerations or numerical regularization. The approximations are tested for
power spectrum calculations of more and more chaotic model systems and on
several molecules, for which exact quantum mechanical values are available. The
results show that the pre-exponential factor approximations introduced are
accurate enough to be safely employed for semiclassical simulations of complex
systems
Application of the Mixed Time-averaging Semiclassical Initial Value Representation method to Complex Molecular Spectra
The recently introduced mixed time-averaging semiclassical initial value
representation molecular dynamics method for spectroscopic calculations [M.
Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is
applied to systems with up to 61 dimensions, ruled by a condensed phase
Caldeira-Leggett model potential. By calculating the ground state as well as
the first few excited states of the system Morse oscillator, changes of both
the harmonic frequency and the anharmonicity are determined. The method
faithfully reproduces blueshift and redshift effects and the importance of the
counter term, as previously suggested by other methods. Differently from
previous methods, the present semiclassical method does not take advantage of
the specific form of the potential and it can represent a practical tool that
opens the route to direct ab initio semiclassical simulation of condensed phase
systems.Comment: 11 figure
Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems
A new semiclassical "divide-and-conquer" method is presented with the aim of
demonstrating that quantum dynamics simulations of high dimensional molecular
systems are doable. The method is first tested by calculating the quantum
vibrational power spectra of water, methane, and benzene - three molecules of
increasing dimensionality for which benchmark quantum results are available -
and then applied to C60, a system characterized by 174 vibrational degrees of
freedom. Results show that the approach can accurately account for quantum
anharmonicities, purely quantum features like overtones, and the removal of
degeneracy when the molecular symmetry is broken
"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems
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
Anharmonic Vibrational Eigenfunctions and Infrared Spectra from Semiclassical Molecular Dynamics
We describe a new approach based on semiclassical molecular dynamics that
allows to simulate infrared absorption or emission spectra of molecular systems
with inclusion of anharmonic intensities. This is achieved from semiclassical
power spectra by computing first the vibrational eigenfunctions as a linear
combination of harmonic states, and then the oscillator strengths associated to
the vibrational transitions. We test the approach against a 1D Morse potential
and apply it to the water molecule with results in excellent agreement with
discrete variable representation quantum benchmarks. The method does not
require any grid calculations and it is directly extendable to high dimensional
systems. The usual exponential scaling of the basis set size with the
dimensionality of the system can be avoided by means of an appropriate
truncation scheme. Furthermore, the approach has the advantage to provide IR
spectra beyond the harmonic approximation without losing the possibility of an
intuitive assignment of absorption peaks in terms of normal modes of vibration
An Effective Semiclassical Approach to IR Spectroscopy
We present a novel approach to calculate molecular IR spectra based on
semiclassical molecular dynamics. The main advance from a previous
semiclassical method [M. Micciarelli, R. Conte, J. Suarez, M. Ceotto J. Chem.
Phys. 149, 064115 (2018)] consists in the possibility to avoid state-to-state
calculations making applications to systems characterized by sizable densities
of vibrational states feasible. Furthermore, this new method accounts not only
for positions and intensities of the several absorption bands which make up the
IR spectrum, but also for their shapes. We show that accurate semiclassical IR
spectra including quantum effects and anharmonicities for both frequencies and
intensities can be obtained starting from semiclassical power spectra. The
approach is first tested against the water molecule, and then applied to the
10-atom glycine aminoacid
'Divide-and-conquer' semiclassical molecular dynamics: An application to water clusters
We present an investigation of vibrational features in water clusters
performed by means of our recently established divide-and-conquer semiclassical
approach [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401
(2017)]. This technique allows us to simulate quantum vibrational spectra of
high-dimensional systems starting from full-dimensional classical trajectories
and projection of the semiclassical propagator onto a set of lower dimensional
subspaces. The potential energy surface employed is a many-body representation
up to three-body terms, in which monomers and two-body interactions are
described by the high level Wang-Huang-Braams-Bowman (WHBB) water potential,
while, for three-body interactions, calculations adopt a fast permutationally
invariant ab initio surface at the same level of theory of the WHBB 3-body
potential. Applications range from the water dimer up to the water decamer, a
system made of 84 vibrational degrees of freedom. Results are generally in
agreement with previous variational estimates in the literature. This is
particularly true for the bending and the high-frequency stretching motions,
while estimates of modes strongly influenced by hydrogen bonding are red
shifted, in a few instances even substantially, as a consequence of the
dynamical and global picture provided by the semiclassical approach
Simplified Approach to the Mixed Time-averaging Semiclassical Initial Value Representation for the Calculation of Dense Vibrational Spectra
We present and test an approximate method for the semiclassical calculation
of vibrational spectra. The approach is based on the mixed time-averaging
semiclassical initial value representation method, which is simplified to a
form that contains a filter to remove contributions from approximately harmonic
environmental degrees of freedom. This filter comes at no additional numerical
cost, and it has no negative effect on the accuracy of peaks from the
anharmonic system of interest. The method is successfully tested for a model
Hamiltonian, and then applied to the study of the frequency shift of iodine in
a krypton matrix. Using a hierarchic model with up to 108 normal modes included
in the calculation, we show how the dynamical interaction between iodine and
krypton yields results for the lowest excited iodine peaks that reproduce
experimental findings to a high degree of accuracy
Herman-Kluk propagator is free from zero-point energy leakage
Semiclassical techniques constitute a promising route to approximate quantum
dynamics based on classical trajectories starting from a quantum-mechanically
correct distribution. One of their main drawbacks is the so-called zero-point
energy (ZPE) leakage, that is artificial redistribution of energy from the
modes with high frequency and thus high ZPE to that with low frequency and ZPE
due to classical equipartition. Here, we show that an elaborate semiclassical
formalism based on the Herman-Kluk propagator is free from the ZPE leakage
despite utilizing purely classical propagation. This finding opens the road to
correct dynamical simulations of systems with a multitude of degrees of freedom
that cannot be treated fully quantum-mechanically due to the exponential
increase of the numerical effort.Comment: 6 pages 2 figure
- …