Anomalous quantum and isotope effects in water clusters: Physical phenomenon, model artifact, or bad approximation?

Free energy differences $\Delta F:=F-F_{\text{prism}}$ are computed for several isomers of water hexamer relative to the "prism" isomer using the self-consistent phonons method. %$\Delta F:=F-F({prism})$ We consider the isotope effect defined by the quantity $\delta F_{D_2O}:=\Delta F_{\rm D_2O}-\Delta F_{\rm H_2O}$, and the quantum effect, $\delta F_{\hbar=0}:=\Delta F_{\hbar=0}-\Delta F_{\rm H_2O}$, and evaluate them using different flexible water models. While both $\delta F_{D_2O}$ and $\delta F_{\hbar=0}$ 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 ($\Delta\tau$) and population size ($N_w$) is investigated. For the binding energies, the bias in $\Delta\tau$ cancels nearly completely, while a noticeable bias in $N_w$ still remains. However, for the isotope shift, (e.g, in the dimer binding energies between (H$_2$O)$_2$ and (D$_2$O)$_2$) the systematic errors in $N_w$ do cancel. Consequently, very accurate results for the latter (within $\sim 0.01$ kcal/mol) are obtained with relatively moderate numerical effort ($N_w\sim 10^3$). For the water hexamer and its (D$_2$O)$_6$ isotopomer the DMC results as a function of $N_w$ 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 $N_w$ 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 $\sim 0.01$ kcal/mol when using a population of $N_w=4.8\times 10^5$ 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) $3N\times 3N$ Gaussian width matrix without sacrificing the accuracy of the fully-coupled VGW method. This results in the reduction of the original $\mathcal{O}(N^3)$ scaling to $\mathcal{O}(N^2)$. 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, $N$, in the framework of the dynamical renormalization group within the $\epsilon$ 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 $N>1$ 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 $N>1$.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