Questions tagged [statistical-thermodynamics]

Questions relating to the discipline of statistical thermodynamics.

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9
votes
1answer
113 views

Should one consider the spatial degeneracies of the electronic state while calculating the Gibbs free energy?

The Gibbs free energy of a molecule is generally expressed as a sum of translational, rotational, vibrational, electronic and nuclear contributions. The electronic contribution $G_{elec}$ is formally ...
8
votes
1answer
83 views

How often does one have to run polymer Monte Carlo moves to effectively sample phase space?

I have a polymer and solvent on a lattice, and I am performing an NVT Monte Carlo simulation. I am performing the following moves on it: My question is, how should these moves be conducted to ...
5
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0answers
65 views

What is the qualitative meaning of the Nosé thermostat?

The Nosé thermostat is explained in Chapter 6 of Understanding Molecular Simulation. Perhaps it's because I find it difficult to follow the derivation, but the physical meaning behind the $s$ ...
6
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0answers
40 views

How to use the HNC approximation to find the change in grand potential

I am reading Hansen and MacDonald's Theory of Simple Liquids, and I am going through Integral Equation theories. In section 4.3, they put forward the equation (4.3.14), $${\small \Omega _{\phi} = \...
8
votes
1answer
116 views

Functional derivatives in DFT

Crossposted from Physics SE. I am studying density functional theory and I am currently dealing with manipulating the intrinsic free energy, $\mathcal{F}$, which is defined as $$\mathcal{F} = F - \int ...
3
votes
1answer
98 views

Simplifying double integrals of isotropic functions

Cross-posted from physics SE. I am studying statistical mechanics, and I am studying ideas surrounding potential of mean force and n-body density functions. In a derivation, they mention that $$-\left\...
16
votes
2answers
858 views

Flying ice cube effect in molecular dynamics?

I am trying to understand what exactly the flying ice cube effect is, and how it manifests itself in MD simulation. From what I have read about it, I see that as we run certain forms of velocity-...
10
votes
1answer
133 views

What is the physical meaning of the q in Fourier transforms of correlation functions?

While studying polymer dynamics, one comes across a wide range of correlation functions. A lot of times, we are interested in the Fourier transforms of these functions, as the FT allows us to solve ...
6
votes
1answer
46 views

Solving for the deviation in the polymer volume fraction under the random phase approximation

I am reading through Introduction to Polymer Physics by Doi, and I am studying the concentration fluctuation in polymer solutions, specifically the random phase approximation. For the most part, I ...
9
votes
1answer
87 views

Rigorous definition of electronic entropy

Suppose we want to compute the exact standard molar electronic entropy of helium at a finite but not very high temperature, say $T = 298.15 \textrm{ K}$. By "standard" I mean the standard ...
9
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1answer
137 views

Is it possible to experimentally verify this collision rate formula?

Background Let's say I have the $i$'th gas molecule with velocity $\vec v_i(t)$ at time $t$. To find the net displacement $s_i$ we integrate with respect to $t$: $$ \vec s_i = \int_{0}^{t} \vec v_i(t')...
9
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1answer
130 views

Derivation on correlation function and response functions in polymer physics

I am reading Introduction to Polymer Physics by Doi and I am having trouble understanding a derivation by him on the concentration fluctuations in polymer solutions. I have outlined his method and ...
5
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1answer
68 views

Derivation of probability density of isolated polymers

(Crossposted on physics SE) I am reading Introduction to Polymer Physics by Doi, and in his proof for the probability distribution for ideal polymers of length $N$ and end-to-end vector $\mathbf{R}$, ...
4
votes
1answer
62 views

Has there been any work done on fluid dynamic or acoustic modeling of the human oral (or nasal) cavity?

The purpose is for me to develop a deeper understanding of speech production and how distinct features that identify a phenome are produced. ab initio models based on classical & statistical ...
4
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2answers
85 views

CASSCF and thermochemistry—effect of excited determinants on rotational and vibrational modes

So this question is linked to the other question I asked about the electronic patition function and CASSCF. When calculating thermochemical data (e.g. Gibbs Free energy) the partition functions are ...
4
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1answer
93 views

Excited determinants, electronic partition function and thermochemistry calculation

While studying statistical thermodynamics I came across the partition functions, which connect the quantum world to the macroscopic world. I understand that partition functions are used to calculate ...
10
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1answer
102 views

Understanding the rigorous bridge between atomistic and coarse-grained simulations

I am currently reading this paper by Noid et. al. on the rigorous bridge between atomistic and coarse-grained simulations. In the paper, he defined a linear map from the atomistic coordinates and ...
11
votes
3answers
638 views

Which ensemble to use for a molecular dynamics simulation?

Does it matter which ensemble you use for a molecular dynamics simulation? Shouldn't they in principle give the same results? Why, historically, was it hard (and desirable) to develop simulations in ...
11
votes
1answer
421 views

Selection of appropriate Langevin damping parameter for MD of solid metal

I am performing an MD simulation involving solid metal. The system is in the NVT ensemble, and I am using the Langevin thermostat (fix Langevin in LAMMPS) to enforce this. I have previously used the ...
3
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0answers
41 views

Doubt in Raoultian and Henrian Standard State [closed]

$Si(liq)=Si_\text{(1 wt% Fe)}$ Can you describe what is going on here?All that they ask for is change in Gibbs free energy for the process.I am completely unable to figure why this particular model is ...
9
votes
1answer
473 views

Why is specific heat not zero at absolute zero?

In this old paper on Monte Carlo simulations of Lennard-Jones solid, specific heat behaviour (both $c_p$ and $c_v$) have been reported. As you can see from the picture below, both $c_p$ and $c_v$ goes ...
7
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1answer
94 views

For ergodicity, what is the significance of the R value and slope?

I am calculating MSDs for the first time and have been struggling to find newbie-level resources on understanding them. If anyone could please suggest any resources or provide guidance on how to ...
12
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1answer
86 views

Phonon density of states in statistical thermodynamics

Phonon density of states (DoS), $g_{(\omega_i)}$, help understand the distribution of states across frequencies of vibration. $\int g_{(\omega_i)}d\omega_i =$ the number of states between $\omega_i$ ...
7
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0answers
78 views

Deriving relations for a hard sphere phase diagram

In Torquato's book "Random Heterogeneous Materials", he has written: $$\frac{p}{\rho kT} = 1+2^{d-1}\eta g_2 (D^{+})\tag{1}$$ where $g_2(D^+)$ is the contact value from the right-side of the ...
6
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0answers
48 views

Evaluating $C_v$ for one mole $H_2$ molecules in a quantum simulation [closed]

Given an ensemble of $N$ diatomic molecules, we know that the rotational partition function is given by $$Z_r = z_r^N$$ where $$z_r = \sum_{l} (2l+1)e^{-Kl(l+1)}$$ where $K = \beta \hbar ^2 /2I$. I ...
23
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2answers
913 views

Why do people care about reversibility in molecular dynamics simulations?

When carrying out a molecular dynamics simulation, one has to choose an ensemble. Depending on the problem, one usually works in the microcanonical (NVE), canonical (NVT), or grand canonical ensemble (...
10
votes
2answers
317 views

Algorithm for calculating dielectric constant of water TIP3P

I am running a NVT TIP3P simulation of water with 125 molecules of water in a 16-by-16-16 angstrom box with periodic boundary conditions on LAMMPS, with a time-step of 1 fs for 10 ps. Once the ...
16
votes
1answer
222 views

Is there any reason not to sum the kinetic and potential energy from an NPT simulation to get internal energy?

I would be very grateful for some newbie-level advice from a thermodynamics guru. I ran NPT simulations on a particular system (in CP2K software) to get fluid densities for use in fluid dynamics ...
9
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0answers
100 views

Coupling between 1st and 2nd order phase transitions? [closed]

I am seeking some models or references on how to couple, or what to take into consideration, while coupling first-order phase transitions (for magnetic systems) and second-order phase transitions, in ...
20
votes
5answers
1k views

References for Molecular Dynamics?

I am new to the world of Molecular Dynamics (zero practical experience), and I know that a starting point to really go into the back-bone of MD is Statistical Mechanics (took a semester course in ...
9
votes
0answers
390 views

I wrote a Python code to do MD for a Lennard-Jones fluid but the VACF is wrong: What might be the problem? [closed]

I am trying to write a molecular dynamics simulation for a Lennard-Jones fluid in a box with periodic boundary conditions. The box has no net momentum. I am writing this in python. I have written a ...
11
votes
2answers
349 views

Calculating diffusion coefficient from Mean Squared Displacement

I am performing a molecular dynamics simulation and I have calculated the velocity autocorrelation function (VACF), $\psi (t)$ and mean square displacement, $\langle (\Delta r)^2 \rangle$. In my ...
11
votes
1answer
212 views

Are there any MD packages that do proper free energy sampling in the NPT ensemble?

Statistical Mechanics is the basis of molecular level calculations of properties and averages. Nowadays free energy calculations are fairly "turn-the-crank", which is not necessarily a good ...
24
votes
1answer
255 views

How do you calculate the "true" chemical potential in classical density functional theory?

In classical density functional theory, one traditionally calculates the chemical potential by taking the variational derivative, \begin{equation} \mu_{i} = \frac{\delta F}{\delta \rho_{i}}\tag{1} \...
8
votes
1answer
93 views

What contributes to the total enthalpy of a system?

This answer refers to a paper that calculates $\Delta H$ as $\Delta E_{\textrm{electronic}} + \Delta E_{\textrm{vibrational}}$. However, what if I had enough computing power, and I wanted to get the ...