# Sampling dependent systematic errors in effective harmonic models

## TL;DR

This paper investigates the systematic errors in effective harmonic models used for calculating temperature-dependent phonon frequencies, comparing sampling techniques and quantifying errors through DFT simulations.

## Contribution

It provides a theoretical explanation and numerical quantification of sampling-dependent systematic errors in effective harmonic methods.

## Key findings

- Sampling techniques significantly influence error magnitude.
- Errors can surpass those from zero-temperature harmonic analysis.
- Two sampling methods are compared and analyzed.

## Abstract

Effective harmonic methods allow for calculating temperature dependent phonon frequencies by incorporating the anharmonic contributions into an effective harmonic Hamiltonian. The systematic errors arising from such an approximation are explained theoretically and quantified by density functional theory based numerical simulations. Two techniques with different approaches for sampling the finite temperature phase space in order to generate the force-displacement data are compared. It is shown that the error in free energy obtained by using either can exceed that obtained from 0 K harmonic lattice dynamics analysis which neglects the anharmonic effects.