arXiv subjects

Vladimir A. Mandelshtam

Publications and source records attributed to Vladimir A. Mandelshtam.

8 recordsLinked to original sources

arXiv2025

A computationally efficient subspace harmonic relaxation algorithm for coarse-graining of molecular systems with nearly exact thermodynamic consistency

In a recent paper, J. Chem. Phys. 162, 214101 (2025), a novel approach for the rigidification of a molecular cluster was proposed, in which starting with an all-atom (AA) potential, a coarse-grained (CG) potential for the associated cluster of rigid monomers was constructed directly. The method is based on using the harmonic approximation for the fast intramolecular degrees of freedom. While conceptually primitive, the resulting CG model turned out to be surprisingly accurate for selected water and ammonia clusters. However, as originally formulated, a single evaluation of the CG potential turned out to be much more expensive than the evaluation of the AA potential, since the former required a subspace minimization followed by a subspace normal mode calculation. In this communication, we formulate the approach more broadly, making it applicable, e.g., to coarse-graining a large protein. We also introduce key algorithmic improvements, reducing the cost of the subspace minimization and normal mode calculation. Combined with the fact that the CG simulation requires roughly an order of magnitude fewer Monte Carlo steps to reach similar statistical accuracy for selected observables compared to the AA model, the overall computational cost becomes comparable. These improvements are demonstrated on a water cluster.

physics.chem-ph↗

arXiv2021

Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

We revisit the collocation method of Manzhos and Carrington (J. Chem. Phys. 145, 224110, 2016) in which a distributed localized (e.g., Gaussian) basis is used to set up a generalized eigenvalue problem to compute the eigenenergies and eigenfunctions of a molecular vibrational Hamiltonian. Although the resulting linear algebra problem involves full matrices, the method provides a number of important advantages. Namely: (i) it is very simple both conceptually and numerically, (ii) it can be formulated using any set of internal molecular coordinates, (iii) it is flexible with respect to the choice of the basis, and (iv) it has the potential to significantly reduce the basis size through optimizing the placement and the shapes of the basis functions. In the present paper we explore the latter aspect of the method using the recently introduced, and here further improved, quasi-regular grids (QRGs). By computing the eigenenergies of the four-atom molecule of formaldehyde, we demonstrate that a QRG-based distributed Gaussian basis is superior to the previously used choices.

physics.chem-ph↗

arXiv2016

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.

physics.data-an↗

arXiv2015

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 ($Δτ$) and population size ($N_w$) is investigated. For the binding energies, the bias in $Δτ$ 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.

physics.chem-ph↗

arXiv2014

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

Free energy differences $ΔF:=F-F_{\text{prism}}$ are computed for several isomers of water hexamer relative to the "prism" isomer using the self-consistent phonons method. %$ΔF:=F-F({prism})$ We consider the isotope effect defined by the quantity $δF_{D_2O}:=ΔF_{\rm D_2O}-ΔF_{\rm H_2O}$, and the quantum effect, $δF_{\hbar=0}:=ΔF_{\hbar=0}-ΔF_{\rm H_2O}$, and evaluate them using different flexible water models. While both $δF_{D_2O}$ and $δF_{\hbar=0}$ 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.

physics.atm-clus↗

arXiv2014

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.

physics.atm-clus↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2005

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.

physics.chem-ph↗