# Vibrational temperature-dependent properties (e.g. thermodynamical properties)

### This page gives hints on how to compute vibrational free energy, entropy, specific heat, thermal expansion, as well as atomic temperature factors with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (XG)

Mentioned in topic_PhononBands, help_features#6.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

When the phonon band structure and corresponding eigenvectors are known over the whole Brillouin Zone, thanks fo Fourier interpolation (see PhononBands), integrals can be performed, allowing to obtain a wealth of properties, like free energy, entropy, specific heat, as well as atomic temperature factors. For applications of this technique, see [Lee1995].

Moreover, knowing such information for different volumes allows one to compute the thermal expansion, see gruns_ddbs.

The input variables needed to perform the interpolation over the Brillouin Zone are described in PhononBands and are not listed again in the present topic.
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### 2. Related lesson(s) of the tutorial.

- The lesson Response-Function 2 (RF2) presents the analysis of the DDBs that have been introduced in the preceeding lesson RF1. The computation of the interatomic forces and the computation of thermodynamical properties is an outcome of this lesson.
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### 3. Related input variables.

Compulsory input variables:

... thmflag@anaddb [THerMal FLAG]

Basic input variables:

... gruns_nddbs@anaddb [GRUNeiSen Number of DDB files]
... ntemper@anaddb [Number of TEMPERatures]
... temperinc@anaddb [TEMPERature INCrease]
... tempermin@anaddb [TEMPERature MINimum]

Useful input variables:

... gruns_ddbs@anaddb [GRUNeiSen DDBS]
... prtvol@anaddb [PRinT VOLume]
... thmtol@anaddb [THerModynamic TOLerance]

Input variables for experts:

... atftol@anaddb [ATomic Temperature Factor TOLerance]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v2/Input: t15.in t16.in
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### 5. References.

[Lee1995] C. Lee and X. Gonze, "Ab-initio calculation of the thermodynamic properties and atomic temperature factors of SiO2 α-quartz and stishovite", Phys. Rev. B 51, 8610 (1995).

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