Comment on Tuning of the CDW in MX Chains

TL;DR

This paper critiques a previous study's fitting method for modeling lattice energies in MX chains, demonstrating that the harmonic approximation is sufficient and that the earlier conclusion about anharmonic effects was based on an incorrect fit.

Contribution

It clarifies the validity of the harmonic approximation in modeling lattice energies and corrects previous misconceptions about anharmonic effects in MX chains.

Findings

Harmonic approximation accurately models lattice energy.

Small quartic correction aligns with LDA total energy.

Previous conclusions on anharmonic effects were based on incorrect fitting.

Abstract

In M. Alouani et al., Phys. Rev. Lett. 71, 1415 (1993), the authors performed local-density-approximation (LDA) calculations and fit to the two-band model [J.T. Gammel et al., Phys. Rev. B 45, 6408 (1992)] we proposed for halogen-bridged transition-metal linear-chain compounds ($M$$X$ chains). Based on that fit, the authors argue a hard-core repulsive term must be added to the lattice potential in our model. However, the authors fit only to the variation in total energy as a function of percent dimerization for a fixed $M$$M$ distance and did not fit the variation in total energy with $M$$M$ distance. Thus the fit was incorrectly calculated, the LDA total energy surface is {\it not} reproduced by the parameters listed in this paper, and the conclusion as to the importance of anharmonic corrections must be reexamined. In contradiction to their conclusion based on this erroneous fit, I show here that the harmonic approximation (linear $M$$X$ springs to model the lattice energy) is in fact very good, and a small quartic correction yields quantitative agreement with the LDA total energy, though to this order more realistic electron-phonon interactions should be included in the model, as discussed in I. Batistic et al., Phys. Rev. B 48, 6065 (1993). 1992 PACS: 71.38.+i, 71.25.Tn, 71.20.Hk