Questions tagged [statistical-thermodynamics]

Questions relating to the discipline of statistical thermodynamics.

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phase average uncertainty in molecular dynamics

I was wondering if I could find some scaling relation of the uncertainity of phase averages of thermodynamic quantities with the number of atoms $N_a$, the number of timesteps $N_t$ and size of the ...
n1ps's user avatar
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Why is potential energy used and not total energy when calculating free energy?

I have run a replica-exchange molecular dynamics simulation, using a number, $n$, of replicas initiated at the same number, $n$, of unique temperatures. I have calculated the free energy profile over ...
napadia's user avatar
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Thermal Properties Calculated with Phonopy

In Phonopy the thermal properties, free energy, heat capacity, and entropy, are calculated from their statistical thermodynamic expressions using phonon frequencies on a sampling mesh in the ...
Jaafar Mehrez's user avatar
6 votes
0 answers
122 views

Free energy calculation as a function of temperature over phase transition

I've run a molecular dynamics simulation (NVT) of a simple Lennard-Jones system of a few particles and I'm trying to calculate the Helmholtz free energy $\Delta F$ as a function of temperature over ...
napadia's user avatar
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Thermodynamics: System versus Ensemble

In the context of thermodynamics, an ensemble is a hypothetical collection of identical copies of a system, each in a different state, used to represent the statistical behavior of the system. That ...
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Are MD and MC both parts of statistical physics?

Are MD (Molecular Dynamics) and MC (Monte Carlo) both parts of statistical physics or is only one of them? If so, which branch (e.g., mechanics, thermodynamics, etc.) and why?
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9 votes
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Difference between Statistical Physics, Statistical Mechanics, and Molecular Modeling?

I am looking for relevant books to study the modeling and Monte Carlo simulation of protein chains. I see that books related to Statistical Physics, Statistical Mechanics, and Molecular Modeling have ...
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gyration radius of short freely jointed chain with excluded volume

The freely jointed chain model without excluded volume has the following gyration radius, $$ \langle R_g^2 \rangle=\frac{1}{6}\frac{N+2}{N+1}Na^2 $$ where $N$ is the number of bonds and $a$ their ...
Marco Mendívil Carboni's user avatar
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How to apply solvent-correction to Gaussian derived Gibbs energies?

I study reaction A + B → C + D in a water using DFT. I think I should apply some kind of correction over RRHO because it is not true in a solvent. I found the given work (https://doi.org/10.1021/...
farmaceut's user avatar
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5 votes
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How to get statistical temperature from WHAM? [closed]

I ran a series of replica exchange molecular dynmaics for the different temperatures. I used WHAM to sample metastable states. From the results of WHAM, we can get probabilties ($p $) from the energy ...
이영규's user avatar
4 votes
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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 ...
megamence's user avatar
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Is it possible to evaluate rotational and vibrational partition functions for diffusion in the Eyring Theory of Absolute Rates? [closed]

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{\...
Giuseppe Basile's user avatar
3 votes
0 answers
97 views

How to get started modeling liquid crystals? [closed]

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 ...
Yetinsyny's user avatar
4 votes
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119 views

How do I define the density of system? [closed]

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 \; ...
Magic_Number's user avatar
2 votes
1 answer
96 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 ...
Manasi Vyas's user avatar
3 votes
1 answer
238 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 ...
Manasi Vyas's user avatar
9 votes
1 answer
146 views

Water dimer and Free Energy Perturbation (FEP)

I am trying to understand FEP in the context of a 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},\tag{...
user3001408's user avatar
4 votes
1 answer
218 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 ...
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4 votes
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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 ...
megamence's user avatar
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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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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 ...
mykd's user avatar
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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 ...
user avatar
6 votes
1 answer
93 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 ...
megamence's user avatar
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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}/...
megamence's user avatar
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10 votes
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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
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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 ...
megamence's user avatar
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5 votes
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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 $s$ ...
Connor's user avatar
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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} = \...
megamence's user avatar
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8 votes
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250 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 ...
megamence's user avatar
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3 votes
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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\...
megamence's user avatar
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18 votes
2 answers
1k 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-...
megamence's user avatar
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10 votes
1 answer
221 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 ...
megamence's user avatar
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6 votes
1 answer
59 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 ...
megamence's user avatar
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9 votes
1 answer
172 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 ...
wzkchem5's user avatar
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10 votes
1 answer
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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')...
More Anonymous's user avatar
9 votes
1 answer
179 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 ...
megamence's user avatar
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5 votes
1 answer
83 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 $\mathbf{R}$, ...
megamence's user avatar
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4 votes
1 answer
68 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 ...
MarcelineH's user avatar
4 votes
2 answers
104 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 ...
S R Maiti's user avatar
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4 votes
1 answer
209 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 ...
S R Maiti's user avatar
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10 votes
1 answer
149 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 ...
megamence's user avatar
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11 votes
3 answers
3k 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 ...
Gnovice's user avatar
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12 votes
1 answer
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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 ...
anneb101's user avatar
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3 votes
0 answers
69 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 ...
user586228's user avatar
9 votes
1 answer
572 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 ...
Magic_Number's user avatar
7 votes
1 answer
181 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 ...
NTS's user avatar
  • 749
13 votes
1 answer
188 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 $\omega_i$ ...
Hitanshu Sachania's user avatar
7 votes
0 answers
116 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 ...
megamence's user avatar
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6 votes
0 answers
53 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 ...
megamence's user avatar
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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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