Phonons and related crystal properties from density-functional perturbation theory

Stefano Baroni, Stefano de Gironcoli, and Andrea Dal Corso
SISSA–Scuola Internazionale Superiore di Studi Avanzati and INFM–Istituto Nazionale di Fisica della Materia, I-34014 Trieste, Italy

Paolo Giannozzi^*
Chemistry Department and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544

^*On leave of absence from Scuola Normale Superiore, Pisa, Italy.

By universal it is meant here that the functional is independent of the external potential acting on the electrons, though it obviously depends on the form of the electron-electron interaction.

The exchange-correlation energy is the name we give to the part of the energy functional that we do not know how to calculate otherwise. For this reason, it has been named the stupidity energy by Feynmann (1972). Whether or not this is a useful concept depends on the magnitude of the energy with respect to the total functional and on the quality of the approximations one can find for it.

In this case the broadening function is the derivative of the Fermi-Dirac distribution function: δ̃(x)=1/2[1+cosh(x)]^-1.

This is a fact occasionally overlooked in the literature. See, for example, Parlinski et al. (1997) and the comment by Detraux et al. (1998).

Note that the Berry’s phase approach cannot be used to calculate the dielectric constant.

The agreement is possibly fortuitous, since LDA does not correctly treat van der Waals interactions and materials held together by them.

Calculations have been performed for GaAs(110) (Fritsch et al., 1993), InP(110) (Fritsch, Pavone, and Schröder 1995), GaP(110) and InAs(110) (Eckl, Fritsch et al., 1997), InSb(110) (Buongiorno Nardelli, Cvetko et al., 1995); for Si(111) (Ancilotto et al. 1991) for Si(001) (Fritsch and Pavone, 1995) and Ge (001) (Stigler et al., 1997); for H-covered (110) surfaces of GaAs, InP (Fritsch, Eckert et al., 1995), and of GaP, InAs (Eckl, Honke et al., 1997), for H- and As-covered Si(111) (1×1) surfaces (Eckl, Honke et al., 1997; Honke, Pavone, and Schröder, 1996), for Ga- and B-covered Si(111) (√3×√3) R30 (Eckl, Honke et al., 1997); for Ge on GaAs(110) (Honke, Fritsch et al., 1996); and for As-covered (110) surfaces of GaAs, GaP, InAs, InP (Fritsch et al., 2000).

An open source computer code for performing DFT-DFPT pseudopotential calculation has been made available by the present authors on the net, at URL http://www.pwscf.org