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Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

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Updated: May 17, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

A staging Monte Carlo algorithm for sampling off-diagonal density matrix elements via open-chain path integrals.

Alan Robledo1, Mark E Tuckerman1,2,3,4,5

  • 1Department of Chemistry, New York University, New York, New York 10003, USA.

The Journal of Chemical Physics
|May 15, 2026
PubMed
Summary
This summary is machine-generated.

We developed a simple staging open path integral Monte Carlo (OPIMC) algorithm for quantum systems. This method efficiently samples polymer-like chains to accurately calculate momentum distributions.

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Last Updated: May 17, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

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Published on: April 12, 2019

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Area of Science:

  • Computational physics
  • Quantum mechanics

Background:

  • Imaginary-time Feynman path integration is crucial for quantum system simulations.
  • Existing methods for sampling polymer-like chains can be computationally intensive.

Purpose of the Study:

  • To introduce a computationally simple algorithm for sampling open-chain distributions.
  • To enable efficient calculation of momentum-dependent quantities in quantum systems.

Main Methods:

  • The staging open path integral Monte Carlo (OPIMC) algorithm samples off-diagonal density matrix elements.
  • It utilizes a staging transformation to sample polymer-like chains from a free-particle distribution.
  • The method involves sampling Gaussian distributions and a Metropolis acceptance/rejection step.

Main Results:

  • The staging OPIMC method accurately reproduces end-to-end distributions.
  • It also accurately reproduces momentum distributions for various quantum systems.
  • The algorithm was validated on systems from coupled harmonic oscillators to liquid water.

Conclusions:

  • The staging OPIMC algorithm provides a computationally simple and efficient approach.
  • It is effective for simulating quantum systems and calculating key distributions.
  • The method is straightforward to implement for researchers in computational physics.