# Canonical mean-field molecular dynamics derived from quantum mechanics

@article{Huang2021CanonicalMM, title={Canonical mean-field molecular dynamics derived from quantum mechanics}, author={Xin Huang and Petr Plech{\'a}{\vc} and Mattias Sandberg and Anders Szepessy}, journal={ArXiv}, year={2021}, volume={abs/2111.11478} }

Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature the ab initio molecular dynamics potential energy is based on the ground state electron eigenvalue problem and the accuracy has been proven to be [[EQUATION]] provided the first electron eigenvalue gap is sufficiently large compared to the given temperature and [[EQUATION]] is the ratio of nuclei and electron masses. For higher temperature eigenvalues corresponding to…

## References

SHOWING 1-10 OF 24 REFERENCES

### Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics

- PhysicsAnnales Henri Poincaré
- 2018

It is known that ab initio molecular dynamics based on the electron ground-state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low…

### Classical Langevin dynamics derived from quantum mechanics

- PhysicsDiscrete & Continuous Dynamical Systems - B
- 2020

The classical work by Zwanzig [J. Stat. Phys. 9 (1973) 215-220] derived Langevin dynamics from a Hamiltonian system of a heavy particle coupled to a heat bath. This work extends Zwanzig's model to a…

### Path integral Monte Carlo simulation of degenerate electrons: Permutation-cycle properties.

- PhysicsThe Journal of chemical physics
- 2019

A detailed analysis of the permutation-cycle properties of path integral Monte Carlo (PIMC) simulations of degenerate electrons is presented, which finds that finite-size effects predominate the observed behavior.

### On the Quantum Correction for Thermodynamic Equilibrium

- Physics
- 1947

The behavior of any system at high enough temperatures approaches that of its classical counterpart. The probability of any configurational position is then proportional to exp—U/kT, with U the…

### A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals.

- PhysicsThe Journal of chemical physics
- 2009

Improved sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations, and results indicate that CMD shows very similar performance to RPMD.

### Uniform semiclassical estimates for the propagation of quantum observables

- Mathematics, Physics
- 2002

We prove here that the semiclassical asymptotic expansion for the propagation of quantum observables, for C -Hamiltonians growing at most quadratically at infinity, is uniformly dominated at any…

### Semiclassical limit for mixed states with singular and rough potentials

- Mathematics
- 2010

We consider the semiclassical limit for the Heisenberg-von Neumann equation with a potential which consists of the sum of a repulsive Coulomb potential, plus a Lipschitz potential whose gradient…

### On the quantum langevin equation

- MathematicsPhysical review. A, General physics
- 1988

It is shown that the most general quantum Langevin equation can be realized by this simple model and a critical comparison is made with a number of other models that have appeared in the literature.

### Statistical Mechanics: An Intermediate Course

- Physics
- 1996

Discussing the foundations of both classical and quantum statistical mechanics, this book aims to bridge a gap that exists between standard textbooks on the subject and more advanced books. It is…

### Molecular Dynamics: With Deterministic and Stochastic Numerical Methods

- Mathematics
- 2015

1.Introduction.- 2.Numerical Integrators.- 3.Analyzing Geometric Integrators.- 4.The Stability Threshold.- 5.Phase Space Distributions and Microcanonical Averages.- 6. The Canonical Distribution and…