npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Phys.: Sae Mulli 2020; 70: 646-651

Published online August 31, 2020

Copyright © New Physics: Sae Mulli.

A Self-Consistent Crank-Nicolson Method for Solving Time-Dependent Kohn-Sham Equation in a Localized Atomic Orbital Basis Set

Junhyeok BANG*1,2

1Department of Physics, Chungbuk National University, Cheongju 28644, Korea

2Research Institute for Nanoscale Science and Technology, Cheongju 28644, Korea


Received: July 7, 2020; Revised: July 21, 2020; Accepted: July 21, 2020


The excited state dynamics of electrons in materials is crucial for understanding various phenomena in nature and applications. However, time-dependent density functional theory, which is a first-principles method for studying electronic dynamics, requires extensive computational power, which makes theoretical study difficult. In this work, we studied how to improve the computational speed of TDDFT. A Crank-Nicolson approximation for a time evolution operator of the time-dependent Kohn-Sham equation preserves unitarity and preforms a high-speed calculation in a localized atomic orbital basis. By including a self-consistent loop in the Crank-Nicolson approximation, we were able to increase the calculational speed by more than tenfold while maintaining the calculational accuracy and stability. In this way, we made possible the application of the first-principles method to the study of excited state dynamics on a long time scale.

Keywords: TDDFT, Excited state dynamics, Method

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