29 research outputs found
Anomalous quantum and isotope effects in water clusters: Physical phenomenon, model artifact, or bad approximation?
Free energy differences are computed for
several isomers of water hexamer relative to the "prism" isomer using the
self-consistent phonons method. % We consider the
isotope effect defined by the quantity , and the quantum effect, , and evaluate them using different flexible
water models. While both and are found
to be rather small for all of the potentials, they are especially small for two
of the empirical models, q-TIP4P/F and TTM3-F, compared to q-SPC/Fw and the two
{\it abinitio}-based models, WHBB and HBB2-pol. This qualitative difference in
the properties of different water models cannot be explained by one being "more
accurate" than the other. We speculate as to whether the observed anomalies are
caused by the special properties of water systems, or are an artifact of either
the potential energy surface form/parametrization or the numerical
approximation used.Comment: Submitted to Journal of Chemical Physic
Water hexamer: Self-consistent phonons versus reversible scaling versus replica exchange molecular dynamics
Classical free energies for the cage and prism isomers of water hexamer
computed by the self- consistent phonons (SCP) method and reversible scaling
(RS) method are presented for several flexible water potentials. Both methods
have been augmented with a rotational correction for improved accuracy when
working with clusters. Comparison of the SCP results with the RS results
suggests a fairly broad temperature range over which the SCP approximation can
be expected to give accurate results for systems of water clusters, and
complements a previously reported assessment of SCP. Discrepancies between the
SCP and RS results presented here, and recently published replica exchange
molecular dynamics (REMD) results bring into question the convergence of the
REMD and accompanying replica exchange path integral molecular dynamics
results. In addition to the ever-present specter of unconverged results,
several possible sources for the discrepancy are explored based on inherent
characteristics of the methods used.Comment: Submitted to Journal Chemical Physic
Assessing the Performance of the Diffusion Monte Carlo Method as Applied to the Water Monomer, Dimer, and Hexamer
The Diffusion Monte Carlo (DMC) method is applied to the water monomer,
dimer, and hexamer, using q-TIP4P/F, one of the most simple, empirical water
models with flexible monomers. The bias in the time step () and
population size () is investigated. For the binding energies, the bias in
cancels nearly completely, while a noticeable bias in still
remains. However, for the isotope shift, (e.g, in the dimer binding energies
between (HO) and (DO)) the systematic errors in do
cancel. Consequently, very accurate results for the latter (within
kcal/mol) are obtained with relatively moderate numerical effort (). For the water hexamer and its (DO) isotopomer the DMC results
as a function of are examined for the cage and prism isomers. For a given
isomer, the issue of the walker population leaking out of the corresponding
basin of attraction is addressed by using appropriate geometric constraints.
The population size bias for the hexamer is more severe, and in order to
maintain accuracy similar to that of the dimer, the population size must
be increased by about two orders of magnitude. Fortunately, when the energy
difference between cage and prism is taken, the biases cancel, thereby reducing
the systematic errors to within kcal/mol when using a population of
walkers. Consequently, a very accurate result for the
isotope shift is also obtained. Notably, both the quantum and the isotope
effects for the prism-cage energy difference are small.Comment: 11 pages, 5 figures, 36 references. Submitted to the Journal of
Physical Chemistr
Thermodynamics and equilibrium structure of Ne_38 cluster: Quantum Mechanics versus Classical
The equilibrium properties of classical LJ_38 versus quantum Ne_38
Lennard-Jones clusters are investigated. The quantum simulations use both the
Path-Integral Monte-Carlo (PIMC) and the recently developed
Variational-Gaussian-Wavepacket Monte-Carlo (VGW-MC) methods. The PIMC and the
classical MC simulations are implemented in the parallel tempering framework.
The VGW method is used to locate and characterize the low energy states of
Ne_38, which are then further refined by PIMC calculations. Unlike the
classical case, the ground state of Ne_38 is a liquid-like structure. Among the
several liquid-like states with energies below the two symmetric states (O_h
and C_5v), the lowest two exhibit strong delocalization over basins associated
with at least two classical local minima. Because the symmetric structures do
not play an essential role in the thermodynamics of Ne_38, the quantum heat
capacity is a featureless curve indicative of the absence of any structural
transformations. Good agreement between the two methods, VGW and PIMC, is
obtained.Comment: 13 pages, 9 figure
A fast Variational Gaussian Wave-packet method: Size-induced structural transitions in large neon clusters
The Variational Gaussian wavepacket (VGW) method is an alternative to Path
Integral Monte-Carlo (PIMC) for the computation of thermodynamic properties of
many-body systems at thermal equilibrium. It provides a direct access to the
thermal density matrix and is particularly efficient for Monte-Carlo
approaches, as for an N-body system it operates in a non-inflated 3N
dimensional configuration space. Here we greatly accelerate the VGW method by
retaining only the relevant short-range correlations in the (otherwise full)
Gaussian width matrix without sacrificing the accuracy of the
fully-coupled VGW method. This results in the reduction of the original
scaling to . The Fast-VGW method is then
applied to quantum Lennard-Jones clusters with sizes up to N=6500 atoms.
Following Doye and Calvo [JCP 116, 8307 (2002)] we study the competition
between the icosahedral and decahedral structural motifs in Ne_N clusters as a
function of N.Comment: submitted to JC
Pseudo-time Schroedinger equation with absorbing potential for quantum scattering calculations
The Schroedinger equation with an energy-dependent complex absorbing
potential, associated with a scattering system, can be reduced for a special
choice of the energy-dependence to a harmonic inversion problem of a discrete
pseudo-time correlation function. An efficient formula for Green's function
matrix elements is also derived. Since the exact propagation up to time 2t can
be done with only t real matrix-vector products, this gives an unprecedently
efficient scheme for accurate calculations of quantum spectra for possibly very
large systems.Comment: 9 page
Gaussian resolutions for equilibrium density matrices
A Gaussian resolution method for the computation of equilibrium density
matrices rho(T) for a general multidimensional quantum problem is presented.
The variational principle applied to the ``imaginary time'' Schroedinger
equation provides the equations of motion for Gaussians in a resolution of
rho(T) described by their width matrix, center and scale factor, all treated as
dynamical variables.
The method is computationally very inexpensive, has favorable scaling with
the system size and is surprisingly accurate in a wide temperature range, even
for cases involving quantum tunneling. Incorporation of symmetry constraints,
such as reflection or particle statistics, is also discussed.Comment: 4 page
Transport coefficients of O(N) scalar field theories close to the critical point
We investigate the critical dynamics of O(N)-symmetric scalar field theories
to determine the critical exponents of transport coefficients as a second-order
phase transition is approached from the symmetric phase. A set of stochastic
equations of motion for the slow modes is formulated, and the long wavelength
dynamics is examined for an arbitrary number of field components, , in the
framework of the dynamical renormalization group within the
expansion. We find that for a single component scalar field theory, N=1, the
system reduces to the model C of critical dynamics, whereas for the model
G is effectively restored owing to dominance of O(N)-symmetric charge
fluctuations. In both cases, the shear viscosity remains finite in the critical
region. On the other hand, we find that the bulk viscosity diverges as the
correlation length squared, for N=1, while it remains finite for .Comment: revised for publication in PR
Comment on "Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization"
In a recent paper [Int. J. Quant. Chem. (2016) DOI: 10.1002/qua.25144,
arXiv:1502.06579] Markovich, Blau, Sanders, and Aspuru-Guzik presented a
numerical evaluation and comparison of three methods, Compressed Sensing (CS),
Super-Resolution (SR), and Filter Diagonalization (FDM), on their ability of
"recovering information" from time signals, concluding that CS and RS
outperform FDM. We argue that this comparison is invalid for the following
reasons. FDM is a well established method designed for solving the harmonic
inversion problem or, similarly, for the problem of spectral estimation, and as
such should be applied only to problems of this kind. The authors incorrectly
assume that the problem of data fitting is equivalent to the spectral
estimation problem, regardless of what parametric form is used, and,
consequently, in all five numerical examples FDM is applied to the wrong
problem. Moreover, the authors' implementation of FDM turned out to be
incorrect, leading to extremely bad results, caused by numerical instabilities.
As we demonstrate here, if implemented correctly, FDM could still be used for
fitting the data, at least for the time signals composed of damped sinusoids,
resulting in superior performance. In addition, we show that the published
article is full of inaccuracies, mistakes and incorrect statements