46 research outputs found

### Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral

The Feynman path integral approach for computing equilibrium isotope effects
and isotope fractionation corrects the approximations made in standard methods,
although at significantly increased computational cost. We describe an
accelerated path integral approach based on three ingredients: the fourth-
order Takahashi-Imada factorization of the path integral, thermodynamic
integration with respect to mass, and centroid virial estimators for relevant
free energy derivatives. While the frst ingredient speeds up convergence to the
quantum limit, the second and third improve statistical convergence. The
combined method is applied to compute the equilibrium constants for isotope
exchange reactions H2+D=H+HD and H2+D2=2HD

### Evaluation of the nondiabaticity of quantum molecular dynamics with the dephasing representation of quantum fidelity

We propose an approximate method for evaluating the importance of
non-Born-Oppenheimer effects on the quantum dynamics of nuclei. The method uses
a generalization of the dephasing representation (DR) of quantum fidelity to
several diabatic potential energy surfaces and its computational cost is the
cost of dynamics of a classical phase space distribution. It can be implemented
easily into any molecular dynamics program and also can utilize on-the-fly ab
initio electronic structure information. We test the methodology on three model
problems introduced by Tully and on the photodissociation of NaI. The results
show that for dynamics close to the diabatic limit the decay of fidelity due to
nondiabatic effects is described accurately by the DR. In this regime, unlike
the mixed quantum-classical methods such as surface hopping or Ehrenfest
dynamics, the DR can capture more subtle quantum effects than the population
transfer between potential energy surfaces. Hence we propose using the DR to
estimate the dynamical importance of diabatic, spin-orbit, or other couplings
between potential energy surfaces. The acquired information can help reduce the
complexity of a studied system without affecting the accuracy of the quantum
simulation.Comment: 5 pages, 3 figures, section Theory extended(v2), small textual
improvements(v2), added reference(v2 & v3), added acknowledgement(v3),
submitted to J. Chem. Phy

### Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass

Accurate path integral Monte Carlo or molecular dynamics calculations of
isotope effects have until recently been expensive because of the necessity to
reduce three types of errors present in such calculations: statistical errors
due to sampling, path integral discretization errors, and thermodynamic
integration errors. While the statistical errors can be reduced with virial
estimators and path integral discretization errors with high-order
factorization of the Boltzmann operator, here we propose a method for
accelerating isotope effect calculations by eliminating the integration error.
We show that the integration error can be removed entirely by changing particle
masses stochastically during the calculation and by using a piecewise linear
umbrella biasing potential. Moreover, we demonstrate numerically that this
approach does not increase the statistical error. The resulting acceleration of
isotope effect calculations is demonstrated on a model harmonic system and on
deuterated species of methane

### Role of the sampling weight in evaluating classical time autocorrelation functions

We analyze how the choice of the sampling weight affects the efficiency of
the Monte Carlo evaluation of classical time autocorrelation functions.
Assuming uncorrelated sampling or sampling with constant correlation length, we
propose a sampling weight for which the number of trajectories needed for
convergence is independent of the correlated quantity, dimensionality,
dynamics, and phase-space density. In contrast, it is shown that the
computational cost of the "standard" intuitive algorithm which samples directly
from the phase-space density may scale exponentially with the number of degrees
of freedom. Yet, for the stationary Gaussian distribution of harmonic systems
and for the autocorrelation function of a linear function of phase-space
coordinates, the computational cost of this standard algorithm is also
independent of dimensionality.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

### Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The
method uses the quantum-instanton approximation and is based on the
thermodynamic integration with respect to the mass of the isotopes and on the
path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The
central ingredients of the method are the Monte-Carlo estimators for the
logarithmic derivatives of the partition function and the delta-delta
correlation function. Several alternative estimators for these quantities are
described here and their merits are compared on the benchmark hydrogen-exchange
reaction, H+H_2->H_2+H on the Truhlar-Kuppermann potential energy surface.
Finally, a qualitative discussion of issues arising in many-dimensional systems
is provided.Comment: 11 pages, 2 figures, proceeding

### On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes

Vibrationally resolved spectra provide a stringent test of the accuracy of
theoretical calculations. We combine the thawed Gaussian approximation (TGA)
with an on-the-fly ab initio (OTF-AI) scheme to calculate the vibrationally
resolved emission spectra of oligothiophenes with up to five rings. The
efficiency of the OTF-AI-TGA permits treating all vibrational degrees of
freedom on an equal footing even in pentathiophene with 105 vibrational degrees
of freedom, thus obviating the need for the global harmonic approximation,
popular for large systems. Besides reproducing almost perfectly the
experimental emission spectra, in order to provide a deeper insight into the
associated physical and chemical processes, we also develop a novel systematic
approach to assess the importance and coupling between individual vibrational
degrees of freedom during the dynamics. This allows us to explain how the
vibrational line shapes of the oligothiophenes change with increasing number of
rings. Furthermore, we observe the dynamical interplay between the quinoid and
aromatic characters of individual rings in the oligothiophene chain during the
dynamics and confirm that the quinoid character prevails in the center of the
chain

### Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor

Time-resolved electronic spectra can be obtained as the Fourier transform of
a special type of time correlation function known as fidelity amplitude, which,
in turn, can be evaluated approximately and efficiently with the dephasing
representation. Here we improve both the accuracy of this approximation---with
an amplitude correction derived from the phase-space propagator---and its
efficiency---with an improved cellular scheme employing inverse Weierstrass
transform and optimal scaling of the cell size. We demonstrate the advantages
of the new methodology by computing dispersed time-resolved stimulated emission
spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast,
we show that in strongly chaotic systems such as the quartic oscillator the
original dephasing representation is more appropriate than either the cellular
or prefactor-corrected methods.Comment: submitte

### Beating the efficiency of both quantum and classical simulations with semiclassics

While rigorous quantum dynamical simulations of many-body systems are
extremely difficult (or impossible) due to the exponential scaling with
dimensionality, corresponding classical simulations completely ignore quantum
effects. Semiclassical methods are generally more efficient but less accurate
than quantum methods, and more accurate but less efficient than classical
methods. We find a remarkable exception to this rule by showing that a
semiclassical method can be both more accurate and faster than a classical
simulation. Specifically, we prove that for the semiclassical dephasing
representation the number of trajectories needed to simulate quantum fidelity
is independent of dimensionality and also that this semiclassical method is
even faster than the most efficient corresponding classical algorithm.
Analytical results are confirmed with simulations of quantum fidelity in up to
100 dimensions with 2^1700-dimensional Hilbert space.Comment: 5 pages, 4 figure