8 Color codes

In this section we briefly summarize the color codes of some of the figures that can be obtained from thermo_pw.

• Total energy versus kinetic energy. This is a single figure of the total energy versus wave-functions kinetic energy cut-offs. When the test requires several charge density cut-offs there is a different curve for each charge density cut-off. The curve corresponding to the lowest charge density cut-off is red, the one corresponding to the highest is blue, all the others are green. Note that the total energy of the last configuration (highest wave function and charge density cut offs) is subtracted from all energies.

• Total energy versus size of the k-point mesh. This is a single figure of the total energy as a function of the size of the k-point mesh. When the test requires several values of degauss, there is a curve for each degauss. The curve corresponding to the first degauss is red, the one corresponding to the last is blue, all the others are green. Note that the total energy of the last configuration (highest number of points and lowest degauss) is subtracted from all energies.

• Total energy as a function of volume (lmurn=.TRUE.). This plot is composed by two figures. Total energy as a function of volume and pressure as a function of volume. Both curves are red. The points on the first curve are the energies calculated by pw.x, the continuous curve is the fit.

• Total energy as a function of one or two crystallographic parameters (lmurn=.FALSE.). When there is a single parameter the curve is red as in the case lmurn=.TRUE.. When there are two parameters a contour plot of the energy as a function of two parameters is shown. The contour levels, their number and their colors can be given in input. By default the code shows nine levels with three colors. From the lowest to the highest levels, the colors are red, green, and blue. The energy value of each level is written on output. When the user requests more levels without specifying their colors, the code continues with three yellow levels, then pink, cyan, orange, black, and when more than 24 levels are requested the sequence of colors is repeated. For crystal systems with more crystallographic parameters, this figure is not available.

• Energy bands. In this figure the bands have the color of their irreducible representation. Each line of the path can have a different point group and set of representations. See the point_groups.pdf file for the list of representations and their color code. When the symmetry analysis is not done all the bands are red.

• Electron density of states. This is a plot composed by two figures, the first contains the electron density of states, the second the integral of the density of states up to that energy. The dos is red. In the local spin density case, the dos for spin up is red the one for spin down is blue and with a negative sign. The integrated density of states is blue. In the spin polarized case, the curve shows the integral of the sum of the up and down density of states.

• Electronic energy, free energy, entropy, and isochoric heat capacity (metals only). This plot is composed by four pictures one for each quantity. There is a single blue curve per plot.

• Phonon dispersions. In this figure the phonon dispersions have the color of their irreducible representations. The same comments made for the plot of the band structure apply here.

• Phonon dos. There is one picture with a single red curve.

• Vibrational energy, free energy, entropy, and isochoric heat capacity. This plot is composed by four figures each one showing one quantity. In red the quantities obtained using the phonon density of states, in blue those obtained from three dimensional integrals over the Brillouin zone. In some cases the red curve is not visible because it is exactly below the blue one.

• Atomic B factors as a function of temperature. This plot is composed by one figure for each atom for cubic solids and by two figures for each atom in the other cases. One figure contains B_xx (red), B_yy (blue) and B_zz (green) as a function of temperature. If the three curves coincide only the last one (green) will be visible. The second figure, when plotted shows B_xy (red), B_xz (blue), and B_yz (green).

• Debye vibrational energy, free energy, entropy, and isochoric heat capacity. This plot is composed by four figures each one showing one quantity. The curves are in blue and the word Debye appears in the y axis label.

• Equilibrium volume, Helmhotz (or Gibbs at finite pressure) free energy, bulk modulus, pressure derivative of the bulk modulus, isochoric heat capacity, isobaric heat capacity, thermal expansion, isobaric-isochoric difference of the heat capacity, isoentropic-isothermal difference of the bulk modulus, and average Grüneisen parameter as a function of T (lmurn=.TRUE.). This is a plot composed by ten figures, each one containing a different quantity in the order given above. In red the quantities calculated using the phonon dos, in blue those obtained by a three dimensional integral over the Brillouin zone. Thermal expansion and average Grüneisen parameter can also be calculated using the mode Grüneisen parameters and the result is plotted in green.

• Crystallographic parameters, volume, Helmholtz (or Gibbs at finite pressure) free energy, thermal expansion tensor, and volume thermal expansion as a function of temperature (lmurn=.FALSE.). The number of pictures in this plot depends on the crystal system. It shows a , b/a (for orthorhombic solids) and c/a (for tetragonal, hexagonal, and orthorhombic solids) as a function of temperature. Then it shows the volume, the thermal expansion tensor, and the volume thermal expansion as a function of temperature. All quantities calculated using the phonon density of states are in red, those calculated from integration over the Brillouin zone are in blue with the exception of the thermal expansion tensor. This tensor is in red or blue as above, or it might be green if computed from Grüneisen parameters. For hexagonal and tetragonal solids $\alpha_{{xx}}^{}$ is red if computed from phonon dos, blue if computed from three-dimensional frequency integration and green if computed from Grüneisen parameters. $\alpha_{{zz}}^{}$ is pink, cyan, and orange in the same three cases. In the orthorhombic case $\alpha_{{xx}}^{}$ and $\alpha_{{zz}}^{}$ have the same colors, while $\alpha_{{yy}}^{}$ is gold, olive, and light-blue in the three cases described above. Only a , the volume, and the volume thermal expansion are shown for all the other crystal systems. When the working directory contains a file with the elastic constants and the flag lb0_t=.FALSE. the code uses the elastic constants to compute the bulk modulus and plots the difference between isobaric and isochoric heat capacities and the difference between isobaric and isothermal bulk modulus. In each plot there are three curves in red or blue that indicate quantities calculated from the phonon density of states or from direct integration over the Brillouin zone. The green curves use the mode Grüneisen parameters to calculate the thermal expansion and the elastic constants to calculate the bulk modulus. The volume instead is the same as in the blue curve if ltherm_freq=.TRUE. or as in the red curve if ltherm_freq=.FALSE.. When both ltherm_freq=.FALSE. and ltherm_dos=.FALSE. the volume is kept fixed at the equilibrium volume at T = 0 K. The difference C_$\sigma$ - C_$\epsilon$ of the heat capaticities computed at constant stress or constant strain is computed also using the anisotropic formula, without introducing the bulk modulus. In this case it is plotted in yellow (orange) when the crystallographic parameters are calculated from the minimization of the free energy obtained from phonon density of states (direct integration over the Brillouin zone).

• Mode Grüneisen parameters. In this plot the mode Grüneisen parameters have the color of the irreducible representation of the phonon dispersion curve of which they are the derivative. The same comments made for the band structure plot apply here.

• Phonon dispersions at the geometry that corresponds to a given temperature. The color are assigned on the basis of the irreducible representation of each mode. The same comments made for the band structure plot apply here.

• Temperature dependence of the elastic constants within the `Quasi-static Approximation'. There is a plot for each non-zero elastic constant and the number depends on the Laue class. Elastic constants interpolated at the geometry computed using the phonon density of states are in red, those calculated from integration over the Brillouin zone are in blue.