Path integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators

Abstract

We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat capacity calculation of the (H_2)_22 and Ne_13 clusters at low temperature using the fourth-order Takahashi-Imada and Suzuki propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.

12 pages, 5 figures (to appear in J. Chem. Phys.)

References in corpus (16)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Simulated Tempering: A New Monte Carlo Scheme
• Parallel Tempering Algorithm for Conformational Studies of Biological Molecules
• Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium
• Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo
• Thermodynamics and equilibrium structure of Ne_38 cluster: Quantum Mechanics versus Classical
• Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schrödinger Equation
• Heat capacity estimators for random series path-integral methods by finite-difference schemes
• Quantum Statistical Calculations and Symplectic Corrector Algorithms
• An ab initio path integral Monte Carlo simulation method for molecules and clusters: application to Li_4 and Li_5^+
• Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
• Systematically Accelerated Convergence of Path Integrals
• Energy estimators for random series path-integral methods
• Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods
• Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
• Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data

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