Questions tagged [statistical-thermodynamics]

Questions relating to the discipline of statistical thermodynamics.

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4 votes
1 answer
69 views

Why does the 𝛿 (delta) term exist in the density-density correlation for simple liquids?

Cross-posted from the PhysicsSE. I am reading Theory of Simple Liquids by Hansen and McDonald, and they in chapter 3, they describe the density-density correlation for a simple liquid in the grand ...
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6 votes
0 answers
36 views

Is it possible to evaluate rotational and vibrational partition functions for diffusion in the Eyring Theory of Absolute Rates?

Let us consider the usual expression for Diffusion processes and diffusion coefficients in the Eyring's theory: $$D=\lambda^2k = \lambda^2 \frac{k_BT}{h}\frac{\Omega_\ddagger}{\Omega}e^{-\frac{\...
3 votes
0 answers
36 views

How to get started modeling liquid crystals?

I am an experimentalist who is interested in getting hands on experience with how simulations play into our understanding of liquid crystal formation. I have tried to read several reviews on the topic ...
4 votes
0 answers
107 views

How do I define the density of system?

Lets' say I have a solid nanomaterial made with N atoms in a simulation box with a volume of V as shown below. In this case, the number density of my material is simply $\frac{N}{Volume\; of \; ...
2 votes
0 answers
26 views

Relationship between grand potential and free energy?

What is the fundamental relationship between grand potential and free energy? In other words, what assumptions need to be made in order to obtain the free energy equation rather than the grand ...
3 votes
1 answer
85 views

Grand potential vs. Gibbs free energy of adsorption for ab initio thermodynamics

I have seen descriptions of ab initio thermodynamics where the phase energy diagram for the oxidation of metal surfaces can be constructed in terms of minimizing the grand potential or the Gibbs free ...
7 votes
1 answer
105 views

Water Dimer and Free Energy Perturbation (FEP)

I am trying to understand the FEP in the context of water dimer. Let's say I want to calculate $\Delta A$, the free energy change for the following reaction: $\ce{H_2O +H_2O\rightarrow H_2O-H_2O}$, ...
4 votes
1 answer
69 views

How to assign a "Boltzmann weight"?

I would like to assign a "Boltzmann weight" i.e. $\exp(-E/kT)$ to interactions between particles based on the relative energies. But wouldn't the largest particle-particle energies have the ...
  • 1,453
5 votes
1 answer
190 views

Selecting the time lag and time window in calculating an MSD

A mean square displacement (MSD) can be calculated as either a time or an ensemble average. In the former, it is: $${\rm msd}(\tau)=\langle\Delta r(\tau)^{2}\rangle=\langle[r(t+\tau)-r(t)]^{2}\rangle\...
  • 1,453
4 votes
0 answers
36 views

Statistical properties of semi-flexible polymers

I am reading Statistical Physics of Particles by Kardar. I am struggling with problem 12d, in chapter 2, about semi-flexible polymers in two dimensions. The problem is as follows: Configurations of a ...
  • 4,091
5 votes
1 answer
177 views

How to estimate chemical potential at a temperature?

Fermi level is electron chemical potential at 0K and we can obtain it from DFT calculation. However, the chemical potential is dependent on temperature. But I only find the equation for gas or simple ...
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7 votes
1 answer
138 views

Is it incorrect to use a NVT ensemble for Non-equilibrium MD simulation?

I am getting some conflicting results on this topic while searching for literature online, so I am asking this question here with respect to a simplified experimental setup. If we are trying to ...
  • 2,052
9 votes
1 answer
182 views

How do you calculate a radial distribution function on a lattice?

For the radial distribution function $$g(r)=\frac{N(r)}{4\pi r^{2}dr \rho}$$ how do you do the calculation of the volume of the spherical shell in the denominator, $4\pi r^{2} dr$, when the simulation ...
  • 1,453
6 votes
1 answer
69 views

End-to-end correlation of polymers not decorrelating

I am running Monte Carlo simulations of polymers with nearest neighbor interactions only. For benchmarking purposes, I decided to run some excluded volume simulations (no overlaps) allowed on a 3D ...
  • 4,091
9 votes
1 answer
117 views

Some questions about implementing Swendsen-Wang algorithm

I have a lattice system with two types of sites, namely A and B. Both A and B have a possible up or down spin orientation. There exists $J_\textrm{aa,align}/J_\textrm{aa,mis}$, $J_\textrm{bb,align}/...
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10 votes
1 answer
144 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 ...
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8 votes
1 answer
90 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 ...
  • 4,091
5 votes
0 answers
87 views

What is the qualitative meaning of the Nosé thermostat? [closed]

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 $s$ ...
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7 votes
0 answers
79 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} = \...
  • 4,091
8 votes
1 answer
176 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 ...
  • 4,091
3 votes
1 answer
110 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\...
  • 4,091
17 votes
2 answers
986 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-...
  • 4,091
10 votes
1 answer
147 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 ...
  • 4,091
6 votes
1 answer
51 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 ...
  • 4,091
9 votes
1 answer
130 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 ...
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10 votes
1 answer
160 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 votes
1 answer
144 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 ...
  • 4,091
5 votes
1 answer
72 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 $\mathbf{R}$, ...
  • 4,091
4 votes
1 answer
65 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 votes
2 answers
93 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 ...
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4 votes
1 answer
138 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 ...
  • 5,956
10 votes
1 answer
131 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 ...
  • 4,091
11 votes
3 answers
2k 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 ...
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11 votes
1 answer
925 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 ...
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3 votes
0 answers
54 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
1 answer
521 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 votes
1 answer
138 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 ...
  • 709
13 votes
1 answer
141 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 votes
0 answers
96 views

Deriving relations for a hard sphere phase diagram [closed]

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 ...
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6 votes
0 answers
52 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 ...
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25 votes
2 answers
1k 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 (...
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10 votes
2 answers
582 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 ...
  • 4,091
16 votes
1 answer
304 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 ...
  • 709
9 votes
0 answers
102 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 ...
21 votes
5 answers
2k 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
0 answers
753 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
2 answers
821 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
1 answer
303 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 ...
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25 votes
1 answer
454 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} \...
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8 votes
1 answer
135 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 ...