Canonical Ensemble In a canonical ensemble, the particle number $N$, the volume $V$ and the temperature $T$ are fixed. The temperature of the system is connected to the averaged kinetic energy via...
Hefei-NAMD Training
In this training session, we will learn how to do an NAMD calculation using Hefei-NAMD. Outline of the session: A bit of theory Installation of Hefei-NAMD ...
Band Unfolding Tutorial
Introduction The supercell (SC) method is the ubiquitous approach for the study of solid-state periodic boundary condition systems. In the simplest case, one just construct an SC by repeating the ...
Bloch Oscillation in 1D Model Potential
Introduction Bloch oscillation is a phenomenon from solid state physics. It describes the oscillation, both in real- and momentum-space, of a particle (e.g. an electron) confined in a periodic po...
Time evolution of 1D Gaussian Wavepacket in Free Space
Introduction Consider a 1D free particle which is described at $\mathrm{t} = 0$ by the normalized Gaussian wavefunction [\begin{equation} \psi(x, t=0) = \left[ \frac{1}{\pi\sigma^2} \rig...
Origin of High Harmonic Peak in Fourier Transform of Time-dependent Kohn-Sham Energies
Introduction When performing ab initio molecular dynamics, one often can obtain the time evolution of Kohn-Sham energies $\epsilon_n(t)$, as is shown schematically in the figure below. ...
Ewald Summation
Introduction Let’s consider an ionic crystal with atomics charges $q_\alpha$ at $\boldsymbol\tau_\alpha$ and $\sum q_\alpha = 0$, where $\alpha$ runs from 1 to the number of atoms in a unit cell....
Angular Momentum in Solids
Conservation of Crystal Total Angular Momentum Einstein-De Haas Effect The Einstein–de Haas effect is a physical phenomenon in which a change in the magnetization causes mechanical rotation of t...
Light-Matter Interaction and Dipole Transition Matrix
Quantum theory of light-matter interaction Let us consider an atom in the presence of an external classical electromagnetic fields, the gauge invariant Schrödinger equation writes 1 [\begin{equa...
PAW All-Electron Wavefunction in VASP
Introduction In the PAW method, the all-electron (AE) wavefunction (AEWFC) $\psi_{n\mathbf{k}}$ is related to the pseudo-wavefucntion (PSWFC) $\tilde\psi_{n\mathbf{k}}$ by means of a linear trans...