Questions tagged [molecular-dynamics]
Molecular dynamics (MD) is an approach used for simulating dynamic processes through successive integration of Newton's equations of motion.
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Autocorrelation functions - haven ratio
I'm studying Haven coefficients (I created similar question but with MSD). Right now I have question referring to calculating haven ratio using velocity-velocity autocorrelation functions. What I have ...
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Calculating cross terms for Haven coefficient using windowed MSD
My problem is that from this site: MSD Module I'm taking an equation that expresses the windowed mean squared displacement (MSD):
$$MSD(m) = \frac{1}{N}\sum_{i=1}^{N}\frac{1}{N-m}\sum_{k=0}^{N-m-1}(\...
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Calculating charge diffusion coefficient from Green Kubo relation
I'm trying to calculate Haven coefficient in some crystal that I have assembled coordinates of N ions of oxygen in k time steps. I looked up equations in this article: Pressure-Dependent Diffusion ...
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How to calculate windowed mean squared displacement for multiple particles?
I'm new to molecular dynamics and I find this equation pretty confusing:
$MSD(\tau)=<r(t+\tau)-r(t)>$
For example take a structure with N mobile ions (e.g. oxygen particles). In different ...
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Molecular Dynamics | Calculating Haven coefficient
So i have following problem: I have some structure with 106 particles of oxygen in it, which is responsible for ionic conductivity in this structure: what I want to achieve is to calculate the Haven ...
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What are the $x$, $y$, and $z$ components of a force acting on $i$-th atom in a Lennard-Jones system of $N$ atoms?
What are the $x$, $y$, and $z$ components of a force acting on the i-th atom in a Lennard-Jones system of $N$ atoms?
According to my understanding:
The Lennard-Jones potential function is given by the ...
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Derivation of Pressure Correction Term in Lennard-Jones Fluid Simulation
Context
Hey everyone, I'm working on a molecular dynamics assignment where I'm simulating a Lennard-Jones fluid in the Gibbs ensemble. The potential is given by equation (1):
$$
U(r) = 4\epsilon \...
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Why fibers go to the liquid/liquid interface instead of staying in the bulk phase?
I have an ionic liquid solution phase and an organic phase. They are immiscible. When I place a small piece of nylon fibre in the liquid it always goes to the liquid/liquid interface instead of ...
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Visualize sound propagation in molecular dynamics?
I am simulating a simple Lennard-Jones fluid confined between two fixed walls and I am analyzing the autocorrelation function of the velocity along the direction of the confinement (normal to the ...
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Determination of Intermediate Scattering Function in numerical simulation
The Fourier transform of single particle density :
$$\rho(\textbf{k},t)=\int\rho(\textbf r,t)\exp(-i\textbf k.\textbf r)d\textbf r=\sum_j \exp(-i\textbf k.\textbf r(t))$$
The Intermediate Scattering ...
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Calculating shear amplitude for molecular dynamics
I’m working on a molecular dynamics simulator and want to find shear amplitude. How could do I so when particles are moving randomly? The simulation is 3d, I know some stuff about shear anplitude. I ...
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Normal Force - What if I stepped on a molecularly frozen object? [closed]
I’ve been trying to understand normal force on a molecular level, and I’ve come across the idea that atoms are connected to each other by forces that act like springs. You step on the floor; the floor ...
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Raman Rotational Effect for Diatomic Molecules
I have a doubt about Rotational Raman effect phenomena. As we know for Rotational effect the heavier of the two isotopes the band levels goes down between the two (which is most heavy).
So say for H2 ...
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Berry connection in condensed matter vs. molecular dynamics
In principle, a connection is totally arbitrary. Berry connection is not the connection, but rather it is simply a connection that is physically motivated. That is, mathematically, we could connect ...
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Conserved quantities in overdamped dynamics
I have an implementation of over-damped Brownian dynamics, with particles that follow the version of the Newtons law where the inertia is absent. This is a common thing to do at micrometer scale.
$m x'...
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Calculating Fourier spectra of particle current autocorrelation functions
The particle current density can be defined as :
$$\textbf j(\textbf r,t)=\sum_{i=1}^{N} \textbf v_i\delta(\textbf r-\textbf r_i(t))$$
Its spatial Fourier transform :
$$\textbf j(\textbf k,t)=\sum_{i=...
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Radial distribution function in a plane
I have a three-dimensional system of N particles. The particle positions are described by three coordinates $x$, $y$, $z$. For this system, I can calculate the Radial Distribution Function (RDF) in 3D....
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What is wrong with my single Nose-Hoover thermostat?
I am trying to implement a single Nose-Hoover thermostat inside of my leapfrog velocity verlet algorithm in Python. This is what I have so far:
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Why am I wrong when calculating the atomic system's stress?
Assume a static non-periodic-bounday-condition $N$-atom system in a cuboid box only have potential energy $U$, which is merely the function of all atom positions, i.e.,
$$U=U(\{{r_i}\}) \tag{1},$$
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How to get temperature from the results of WHAM?
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 ...
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Verlet algorithm without initial conditions
I was working on a problem asking 'in an oscillation of a bond in a single O2 molecule with a pair-wise Lennard-Jones (LJ) potential how does the total energy $E$ vs $t$ change?' it goes on to provide ...
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Quantum simulation of molecular spectroscopy: why?
Molecular spectroscopy, e.g. through light-matter interaction, is a powerful tool to measure molecular properties such as bond lengths, energy levels, vibration frequencies, ... which give insights ...
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Energy of polyatomic molecular vibrations
I understand that the energies of a simple diatomic molecular vibration are equal to $E_n=(n+\frac12)\hbar\omega$, and I also know the accompanying eigenfunctions for these energies. I have also heard ...
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Energy of molecular vibrations
I have just read that the energy of a molecular vibration with frequency $\omega$ has eigenvalues of $(n+\frac12)\hbar\omega$, where $n$ is the quantum number. However, this equation really surprises ...
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Normalized units versus dimensionless units
In a molecular dynamics code, suppose, the distances are expressed in units of a characteristic length of the simulated system, $R_0$. In some papers it is written as, " distances are normalized ...
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Does free molecular flow have a newtonian force in between 2 chambers? [closed]
If a vacuum chamber is in free molecular flow pressure say $10^{-7}$ Pascal, and another container is added to it that is at $10^{-9}$ Pascal, will they reach pressure equilibrium eventually? At ...
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Elucidation needed in protein dynamics
I'm reading some papers about protein dynamic, stability and energy landscape. Switching from paper to paper I'm encountering different term used for talking about protein movements, for example: α- ...
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How are temperature changes implemented in a molecular dynamics simulations?
Molecular dynamics simulations are always associated with a temperature that represents the natural state of a system.
However, some techniques, like Simulated Annealing Molecular Dynamics, where ...
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How do I define the density of system?
Lets' say I have a solid system made with N atoms in a box with a volume of V as shown below. In this case, the number density of my system is simply $\frac{N}{Volume\; of \; occupied\;3D\; space}$.
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Born-Oppenheimer approximation: electronic wave function and nuclear kinetic energy term?
The Born-Oppenheimer approximation in a nutshell
Given a molecule's Schrödinger equation
$$
[\hat{T}_N + \hat{T}_e+\hat{V}_{NN}(\textbf{R})+\hat{V}_{eN}(\textbf{r}, \textbf{R})+\hat{V}_{ee}(\textbf{r})...
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Integrating Langevin Dynamics equations in computer simulation
In a Langevin Dynamics simulation the following equation is solved numerically :
$$
m_i\frac{d^2r_i}{dt^2}=F_{int}-\gamma\frac{dr_i}{dt}+R(t)$$
$$\langle R(t)\rangle=0 \quad \quad \langle R(t)R(t')\...
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Initial velocities in a Molecular Dynamics simulation
In classical Molecular Dynamics simulations Newton's equations of motion are solved to get the evolution of particle positions and velocities. To do the integration of the equation of motion, one ...
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What is the speed of the information transmission between water molecules?
What I would like to know is if for example I move a molecule in water how fast this information will reach the neighboring molecules
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Langevin Dynamics simulation at different values of friction coefficient
I am a beginner in the area of Langevin Dynamics simulation. The following equation is solved numerically:
$m_i\frac{d^2r_i}{dt^2}=F_{int}-\gamma\frac{dr_i}{dt}+R(t)$
In Langevin Dynamics simulation ...
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How to understand molecular speed derived from average KE?
Mean kinetic energy is related to temperature:
$$\langle K_E\rangle=\frac{3}{2}kT=\frac{1}{2}mv^2$$
where $k$ is the Boltzmann constant and $T$ the temperature in Kelvin.
For example, the average ...
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How do you Determine the Fastest Vibrational Mode of a Crystal?
I understand that a crystal's vibrational modes are Phonons and have a minimum wavelength that is limited by twice the equilibrium separation between neighbouring atoms. But I don't understand how you ...
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What is the mechanism behind the spectral property change in voltage sensitive dyes?
As far as I understand the change in spectral properties of voltage sensitive dyes is partially derived from the Stark Effect. However, even if this is the underlying physical phenomena, it is still ...
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Calculating average of a function of molecule's orientation (Euler angles)
In this paper, orientational average of a function of Euler angles, $f(\phi,\theta,\psi)$, is defined as: $$\langle f\rangle=\frac{1}{8 \pi^2} \int_0^\pi \int_0^{2 \pi} \int_0^{2 \pi} f(\theta, \phi, \...
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String vibration under periodic boundry conditions
I wish to known which are the vibration modes (in case that they exist) of an string vibrating under periodical boundary conditions (PBC).
The question is related to molecular dynamics simulations of ...
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How to deal with the force of the form $\delta (\mathbf{r}) u(\mathbf{r})$, $u(\mathbf{r})$is the interaction potential
Now I have such an expression for potential energy:
$$
U_j(\mathbf{r}_j) = \int_{\mathbf{r}_j-\frac{\mathbf{L}^b}{2}}^{\mathbf{r}_j+\frac{\mathbf{L}^b}{2}} d\mathbf{r} \sum_{\mathbf{n}} \sum_{i\ne j}^{...
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What's the difference in the quality of time evolution of MD vs QM?
In my research group, we're using molecular dynamics to estimate time evolution of molecules. Of course, the analogous calculations are unobtainable using time dependent Schrödinger equation using our ...
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Why are time-reversible integration algorithms in molecular dynamics simulations favorable?
I read that integration algorithms that are not time-reversible tend to be less "stable". Where stable means that the total energy stays constant (is conserved). I'd like to know what it ...
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How could we estimate the number of molecules below which a fluid cannot be adequately modeled by the Navier-Stokes equations?
As is known, the Navier-Stokes equations are an approximation in the continuum mechanics to model an aggregate of independent molecules, which, although they can move freely, interact strongly with ...
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Metropolis-Hastings and underlying Markov process
I tried to understand the workings of the Metropolis-Hasting algorithm.
As far as I can understand, it allows to draw samples from an unknown distribution $T(x)$ as long as a function proportional to ...
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Why aren't Runge-Kutta methods used for molecular dynamics simulations?
One of the most used schemes for solving ordinary differential equations numerically
is the fourth-order Runge-Kutta method. Why isn't it used to integrate the equation of motion of particles in ...
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What forces act on an element taken in a body which is subjected to no external forces?
Consider a block (rigid) which is lying on a table. If we take a differential element in the block and try to draw its Free-body diagram, will there be any forces other than gravitational force acting ...
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Why do two molecules of an element attract each other?
I was thinking about molecular attraction and a question suddenly struck in my mind which is 'Why do two molecule of an element attract each other?'
The answer is easy when we discuss about compound ...
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How does the wringing of gauge blocks make them stick together?
I was surprised to learn about gauge blocks and how you stick them together. The blocks have very smooth surfaces and still they stick by wringing (
https://youtu.be/2lOOl3VxOtE ).
One speaks of ...
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Uniform radial distribution function
I am attempting to properly account for excluded volume effects on the radial distribution function for a fluid. A correction for these effects has been proposed back in 2000 in this paper by Hartnig ...
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Unable to recreate plot for anisotropic Gay-Berne potentials from paper
I am trying to make a plot of the Gay-Berne potential using Mathematica. I am following this paper and I am trying to recreate Fig. 2. This is figure 2:
To save time, the equations from the paper are ...
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