Posts
Qijing Zheng
Cancel

Molecular Dynamics at Constant Temperature

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 ...

Matplotlib: Plot within a hexagon

Problem Suppose we have a periodic function $f(x,y)$ defined within a hexagonal unit cell, how can we plot the function on the Wigner-Seitz cell? Codes #!/usr/bin/env python # -*- coding: utf-8 ...

Fourier Transform of Radial Functions

Description of the problem Suppose we have a function which can be expressed in terms of spherical harmonics [\begin{equation} \label{eq:radial_fun} f(r, \theta, \phi) = \sum_{l=1...

Numerov Algorithm

Numerov’s method Numerov’s method1 (also called Cowell’s method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is...

Plotly: Spherical Harmonics

Introduction In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. The spherical harmonics form a complete set of orthogonal functions...

Plotly: Tight-binding Model for Graphene

Honeycomb lattice of graphene The unit cell of graphene’s lattice consists of two different types of sites, which we will refer to as $A$ and $B$ sites (see Figure 1). ...

Plotly: 1D Diatomic Chain Dispersion

1D Diatomic Chain Dispersion Consider a 1D chain with two atoms in the unit cell 1D diatomic chain. two sublattices. Generated by TikZ/LaTeX. ...

Transforming Between Supercell and Primitive Cell

Primitive Cell to Supercell Suppose the transformation matrix between the primitive cell ($\mathbf{A}$) and the supercell ($\mathbf{a}$) is $M$, i.e. \[ \mathbf{A} = M\cdot \mathbf{a} \] For ...