# Reference Manual

## Overview

Gibbs2 is a program for the calculation of thermodynamic properties in periodic solids under arbitrary conditions of pressure and temperature, within the quasiharmonic approximation. Gibbs2 is designed to work with data obtained from periodic solid-state quantum-mechanical calculations. At the most basic level, the only required information about a given solid is the number of atoms in the unit cell, the molar mass, and the energy-volume curve.

In a typical calculation the user selects a grid of volumes encompassing the equilibrium geometry of the system. At those volumes, the rest of the structural parameters are relaxed and an E(V) curve is obtained, called the static equation of state (static because no vibrations are involved). In the simplest possible use of gibbs2, the static equation of state is all that is needed to estimate thermodynamic properties via the Debye model. In more complex cases, vibrational information is also read, and the full quasiharmonic approximation is used. In general, better (more accurate) results are obtained if more information is passed to gibbs2.

The effect of pressure in gibbs2 is accounted for by simply adding a pV term to the energy. The effect of temperature, however, requires a thermal model: an approximate way of including the contribution to the free energy from the crystal degrees of freedom. In general, these contributions are dominated by the vibrational free energy, so thermal models are actually approximate methods to incorporate this contribution. Several thermal models with increasing complexity are available:

• Static: no vibrational effects (i.e. no temperature).

• Debye and Debye-Gruneisen: these thermal models treat all the phonons in the solid as long-wavelength stationary vibrations. They required require only the static energy-volume curve. Optionally, the Poisson ratio and the Grüneisen gamma can also be input.

• Debye-Einstein: this model treats the acoustic modes using the Debye model and the optical modes with the Einstein model (i.e. a single frequency for a whole optical band). In addition to the E(V) curve, it requires vibrational frequencies at the Brillouin zone center.

• Full quasiharmonic approximation (QHA): together with the static energy curve, either the phonon density of states or the vibrational frequencies on a grid sampling the 1BZ are required at each volume.

Once the thermal model is chosen, the vibrational Helmholtz free energy (Fvib) is calculated as a function of temperature at every volume in the grid. The equilibrium volume at a given T and p ($$V(p,T)$$) is calculated by minimizing:

$$$G(V;p,T) = E(V) + pV + F_{\rm vib}(V;T)$$$

The value of V(p,T) is then used to compute the rest of the thermodynamic properties. Note that, in this formulation, the internal degrees of freedom (i.e. those that determine the geometry besides the volume) are assumed to be unchanged by the vibrational effects.

In order to calculate the volume derivatives of the energy and the free energy, which are necessary for the thermodynamic calculations, an analytical expression for the E(V) and F(V;T) curves is required, called the equation of state (EOS). Using a least-squares fit, the EOS parameters for E(V) or F(V;T) at a given T are determined, and analytical differentiation used to compute the required derivatives. Gibbs2 implements a few methods for robust EOS fitting. The recommended (and default) procedure involves performing successive linear least-squares fits of polynomials in a chosen strain (Birch-Murnaghan, Poirier-Tarantola,…) with increasing degree. Then, an average polynomial is obtained. This averaging procedure provides a statistical measure of the goodness of the fit in the form of calculated error bars of the calculated thermodynamic properties. Gibbs2 is also to use traditional EOS like the Vinet or Murnaghan expressions using a non-linear minimization algorithm.

The temperature and pressure ranges accessible with a given data set is determined by the input E(V) grid. In general, the first (most compressed) volume in the grid determines the maximum pressure achievable while the last (most expanded) volume determines the maximum temperature.

Gibbs2 can be used to calculate the thermodynamic properties of multiple phases for the same system. When more than one phase is input, gibbs2 will determine the thermodynamically stable phase at each temperature and pressure, i.e. the phase diagram. In addition, temperature-dependent transition pressures are also calculated.

Finally, the gibbs2 code is the successor of the gibbs program by M. A. Blanco, E. Francisco and V. Luaña.

## Command-line options

The following command line options can be passed to gibbs2. Some of them correspond to options that can also be passed in the input file with a SET keyword (this is indicated in parentheses).

• -n, --noplot: Inhibits the creation auxiliary files. The only output written by gibbs2 goes to the standard output and error. (SET WRITELEVEL 0)

• -q, --quiet: Do not print timing information to the output.

• -e, --eos: Same as -n, but the .eos (thermal equation of state) and .eos_static (static equation of state) files are also written. (SET WRITELEVEL 1)

• -b, --errorbar: Calculate and output the error bars for each thermodynamic property. The error values are marked by an ‘‘e’’ at the beginning of the line in the .eos file. (SET ERRORBAR)

• -t, --notrans: Do not compute transition pressures. (SET NOTRANS)

• -d, --noplotdh: Do not write enthalpy difference plots. (SET NOPLOTDH)

• -f, --noefit: Do not write static energy plots. (SET NOEFIT)

• -h, --help, -?: Command-line help.