Density-functional method for very large systems with LCAO basis sets

TLDR

The authors develop a linear‑scaling, fully self‑consistent density‑functional method employing norm‑conserving pseudopotentials and LCAO basis sets to enable first‑principles calculations on very large systems. The method replaces conventional diagonalization with a minimization of a modified energy functional, projects basis functions and density onto a real‑space grid, enforces finite‑range wave functions for linear scaling, and computes forces and stresses efficiently for structural relaxation and molecular dynamics. Test calculations on molecules up to a DNA fragment show that geometries obtained with double‑z polarized bases deviate by less than 1 % from experimental values. © 1997 John Wiley & Sons, Inc., Int J Quant Chem 65:453–461.

Abstract

We have implemented a linear scaling, fully self-consistent density-functional method for performing first-principles calculations on systems with a large number of atoms, using standard norm-conserving pseudopotentials and flexible linear combinations of atomic orbitals (LCAO) basis sets. Exchange and correlation are treated within the local-spin-density or gradient-corrected approximations. The basis functions and the electron density are projected on a real-space grid in order to calculate the Hartree and exchange–correlation potentials and matrix elements. We substitute the customary diagonalization procedure by the minimization of a modified energy functional, which gives orthogonal wave functions and the same energy and density as the Kohn–Sham energy functional, without the need of an explicit orthogonalization. The additional restriction to a finite range for the electron wave functions allows the computational effort (time and memory) to increase only linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, allowing structural relaxation and molecular dynamics simulations. We present test calculations beginning with small molecules and ending with a piece of DNA. Using double-z, polarized bases, geometries within 1% of experiments are obtained. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 453–461, 1997