# Tag Info

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### Why do people care about reversibility in molecular dynamics simulations?

This is an excellent question! Reversibility in MD is useful because: Time-reversibility in a numerical integrator leads to a doubling of the accuracy order (see Propositions 5.2 and Theorem 6.2 ...
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### References for Molecular Dynamics?

Another extremely popular resource is Frenkel and Smit's textbook "Understanding Molecular Simulation". It covers all basics on molecular dynamics, Monte Carlo, some common enhanced sampling ...
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### References for Molecular Dynamics?

A good place to start is the classical Allen-Tildesley book, Computer Simulation of Liquids, which covers the basics of molecular dynamics that hasn't really changed in a long time. The book can be ...
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### Why do people care about reversibility in molecular dynamics simulations?

I would argue the main reason this is important is philosophical, linked to the history of science and determinism (as proposed by Laplace). Newtonian mechanics is mathematically reversable while any ...
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### How do you calculate the "true" chemical potential in classical density functional theory?

Seeing that this question has gathered attention but no replies, I will give it a stab. Note that I am not an expert on DFT or functional calculus, so take this with a grain of salt. As usual, ...
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### References for Molecular Dynamics?

Another good book that starts from the very beginning and it's very hands-on is "The art of molecular dynamics" by D. C. Rapaport. It is particularly useful if you want to code up a MD code ...
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### Which ensemble to use for a molecular dynamics simulation?

It's very hard to answer this definitively unless you are a bit more specific. However, to speak somewhat generally, it is the case that NVE and NVT ensembles become equivalent in certain ...
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### Why is specific heat not zero at absolute zero?

You are correct that this is due to not including quantum effects. Ref 1 in your figure is the paper cited below. In this paper, they explicitly mention that $C_v$ calculated using the cell-cluster ...
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### Flying ice cube effect in molecular dynamics?

High frequency in this case is 'particles move all independently, with different directions and speed', and low frequency means 'particles can be represented as gradually changing field of speed and ...
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### Derivation on correlation function and response functions in polymer physics

It looks Doi makes some extra simplifications (beyond expanding the exponential) that are valid when the external field is weak. Let's start with what you wrote and make one simplification,  \begin{...
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### For ergodicity, what is the significance of the R value and slope?

Short introduction to ergodicity Ergodicity is when the time-average equals the ensemble-average. A process is ergodic if the time-average "converges in the square mean" to the ensemble ...
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### Calculating diffusion coefficient from Mean Squared Displacement

As with all MD simulations, you have to assume (often wrongly) convergence with finite time. This is fairly easy to do with autocorrelation functions though, because you know that once they become ...
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### Are there any MD packages that do proper free energy sampling in the NPT ensemble?

It is straightforward to show that in a typical $NPT$ setting the Zwanzig equation still only depends on the energy difference and not on the volume (here I define $H$ to be the Hamiltonian of each ...
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### Flying ice cube effect in molecular dynamics?

The flying ice cube effect is when the kinetic energy leaks into the translations and rotations. In a constant energy simulation (NVE) this must come at the expense of vibrations, which has the effect ...
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### What contributes to the total enthalpy of a system?

Thermochemistry (for a single molecule, e.g., ideal gas) depends on the Temperature. At T=0K thermochemistry is kind to us. At T = 0K $U = G = H$. This is because H = U + PV, which for an ideal gas ...
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### Is there any reason not to sum the kinetic and potential energy from an NPT simulation to get internal energy?

Energy in an NPT simulation is not conserved, but (once equilibrated), it will fluctuate around an average value, and that average value has meaning. That is the ensemble average for your NPT and is a ...
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### How often does one have to run polymer Monte Carlo moves to effectively sample phase space?

This is a very good and tricky question, which I don't think has a clear and definite answer. I think I should also preface by saying that I can't answer it from the point of view of polymer physics, ...
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### Understanding the rigorous bridge between atomistic and coarse-grained simulations

Before working through the equations, I'll try to explain the logic behind what they are doing. It helps to think of think of their process backwards and assume they want an expression like equation ...
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### Which ensemble to use for a molecular dynamics simulation?

It definitely can matter. The best thing to do is to consider the experiment you are comparing to, even if that experiment hasn't actually been done yet. In many cases, that means you want to run ...
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### Solving for the deviation in the polymer volume fraction under the random phase approximation

Doi makes this slightly more confusing because just after these equations, he writes: Here for simplicity we have dropped the subscript q. So all of the pieces of your Eqs \eqref{7} and \eqref{8} ...
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### Should one consider the spatial degeneracies of the electronic state while calculating the Gibbs free energy?

First, let's look from the most fundamental point of view. For this part of the answer I'll be referencing McQuarrie's Statistical Mechanics [1]. As the Gibbs free energy, $G$, can be calculated from ...
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### Rigorous definition of electronic entropy

I'll try to summarize the argument mentioned in the comments from Daniel Schroeder's Introduction to Thermal Physics. Your derivation is correct within a certain approximation commonly made when ...
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### Derivation of probability density of isolated polymers

For context to future readers, Doi starts with a model of an $N$ unit polymer formed by a random walk along a uniform grid of lattice length $b$. It seems to be implicitly assumed in the described ...
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### Which ensemble to use for a molecular dynamics simulation?

Ensembles are essentially artificial constructs. In the thermodynamic limit (for an infinite system size) and as long as we avoid the neighborhood of phase transitions it is generally believed that ...
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### Selection of appropriate Langevin damping parameter for MD of solid metal

I know it's a boring thing to say, but: It depends on what you want to do. The way I use Langevin thermostats, is to ensure good equipartitioning in my setup, so that I don't have any local hotspots ...
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### Phonon density of states in statistical thermodynamics

There are two possible things tripping you up here: Phonons are collective oscillations: they involve the motion of all the atoms together. Therefore it only makes sense to talk about the phonons of ...
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### References for Molecular Dynamics?

Also worth mentioning Bill Hoover's excellent textbooks, Molecular Dynamics which provide an introduction and a slightly different perspective on molecular dynamics, along with Computational ...
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### Excited determinants, electronic partition function and thermochemistry calculation

"This works for organic molecules, but what happens when the excited states are closer in energy to the ground state, for example in open-shell molecules or in atoms?" If there's excited ...
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Based on your previous questions, I assume this equation was from Section 1.2.1 of Doi's Polymer Physics. While Doi doesn't explicitly state this anywhere that I can find, $\mathbf{q}$ is the label he ...
The work is a single integral over $|r_1-r_2|$, not a double integral over $r_1$ and $r_2$. As you are fixing particle 1, you shouldn't integrate over particle 1. Moreover, the work is \$w(r) = \int ...