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Qijing Zheng
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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 ...

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...

NAC Calculation for 1D Model Hamiltonian

Introduction Let’s start with a parametric 1D Hamiltonian $H(r)$ [\begin{equation} H(r) = \begin{pmatrix} \varepsilon_1^d(r) & \lambda(r) \[6pt] \lambda(r) & \varepsilon_2^d(r) \end{pmat...

Evaluating Overlap Integral in Momentum Space

Introduction Suppose $\chi_{l,m}(\mathbf{r})$ is a atomic orbital of the form: [\begin{equation} \chi_{l,m}(\mathbf{r}) = f_{l}(r)\cdot Y_l^m(\hat{\mathbf{r}}) \end{equation}] where $f_l(...

General Wigner Crystal in Moiré Superlattice

Ratio of Potential and Kinetic Energy The dimensionless ratio of the potential energy ($U$) and the kinetic energy $K$, known as $\gamma_s$, can be written as 1 [\begin{align} \gamma_s &= \f...

Numerical Solutions to the Time-dependent Schrödinger Equation

Time-dependent Schrödinger Equation The single-particle time-dependent Schrödinger equation of an electron under an external potential read [\begin{align} i\hbar \frac{\partial}{\partial t} \psi...

Bravais Lattice

Bravais Lattices in 3D Figure 1. Primitive (red), conventional (blue if any) and Wigner-seitz cell (green) of 14 three-dimensional (3D) Bravais lattices. G...