Related Experiment Video
Updated: Jun 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Energy derivatives in quantum Monte Carlo involving the zero-variance property
A Badinski1, J R Trail, R J Needs
1Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
Abstract:
We give an exact expression for the nth derivative of the expectation value of the energy that satisfies the zero-variance (ZV) principle when the wave function and its first n derivatives are exact. The ZV principle was previously applied to the first energy derivative ("force") within the variational Monte Carlo and mixed-estimator diffusion Monte Carlo methods. We present a new expression for the force in pure-estimator diffusion Monte Carlo that satisfies the ZV principle and can be evaluated much more efficiently than previous expressions while maintaining comparable accuracy. This expression is the sum of a pure expectation value and a variational expectation value, which separately satisfy the ZV principle. The bias in this force estimator is second order in the deviation of the trial wave function from the diffusion Monte Carlo wave function. Results for small molecules demonstrate the accuracy of the method and its statistical efficiency.
Related Concept Videos
Potential-Energy Criterion for Equilibrium
One-Degree-of-Freedom System
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Calculation of First-Law Quantities II
Derivatives of Vector Functions
Partial Derivatives and Gas Laws
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...