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1answer
149 views

Understanding the mean square displacement in molecular dynamics

In a Molecular Dynamics (MD) simulation, the mean square displacement $\text{MSD}$ is given by $$\text{MSD}(\delta t) = \left\langle\left|\vec{r}(\delta t)-\vec{r}(0)\right|^2\right\rangle,$$ where ...
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0answers
44 views

Langevin equation

A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a harmonic spring, so that ...
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1answer
119 views

Deriving the change in the Helmholtz free energy in the context of the free energy perturbation method

I am reading Free Energy Calculations: Theory and Applications in Chemistry and Biology by Chipot and Pohorille. At the beginning of the text (page 19, for example), the authors define the Helmholtz ...
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1answer
134 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
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2answers
1k views

Molecular Dynamics (MD) Simulation: energy fluctuations in NVE ensemble

I'm writing my first MD simulation (ever) for liquid Argon. The code is up and running. I am supposed to do the calculations in the NVE ensemble. Having implemented a 4th order symplectic integrator ...
6
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4answers
3k views

Why is the canonical ($NVT$) ensemble often used for (classical) molecular dynamics (MD) simulations?

Molecular dynamics (MD) simulation is a common approach to the (classical) many-body problem. It relies on integration of Newton's equations of motion to simulate the trajectories of many (e.g., ...