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 of 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 orthorhombic solids the code produces many postscript figures, one for each value of c/a on the grid. In each figure there is a contour plot of the energy as a function of a and b/a . The colors of the levels follow the same conventions of the previous case. When the levels are chosen by the code the entire energy range (for all c/a ) is divided into nine levels so each figure might have less that nine curves. 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.

• Energy bands with enhance_plot=.TRUE.. In this case the background color of the panels with lines at the zone border are gray, yellow, or pink. Gray means that the point group (or double point group) representations are used, yellow or pink means that a gauge transformation was applied and projective representations might have been used. A yellow background indicates that no switch from the point group to the double point group or viceversa was made, while a pink background means that such a switch was necessary.

• Electron density of states. This is a plot composed of 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 of four pictures one for each quantity. There is a single blue curve per plot.

• Dielectric constant as a function of frequency ( $\bf q$ = $\bf0$ ). There are two plots, one for the real part and one for the imaginary part. Other two plots contain the real and imaginary part of the complex index of refraction. For cubic solids other two plots show the reflectivity for normal incidence and the absorption coefficient. All curves are in red. For hexagonal, trigonal, and tetragonal systems the xx component is in red, while the zz component is in green. For orthorombic systems the xx component is in red, the yy component in green and the zz component in blue. For monoclinic and triclinic systems the plot is not done.

• Inverse of the dielectric constant as a function of frequency ( $\bf q$ $\neq$ $\bf0$ ). There are four plots: the real and imaginary part of $\varepsilon$($\bf q$,$\omega$) and the real and imaginary part of 1/$\varepsilon$($\bf q$,$\omega$) . They are all in red. Note that the latter is really calculated, while the first is just its inverse.

• 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 of four figures each one showing one quantity. In red the quantities obtained using the phonon density of states, in blue those obtained from integration 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 of one figure for each atom for cubic solids and of two figures for each atom in the other cases. One figure contains B_xx (red, pink), B_yy (blue, light_blue) and B_zz (dark_green, green) as a function of temperature. The first color refers to quantities calculated from generalized phonon density of states while the second refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted shows B_xy (red, pink), B_xz (blue, light_blue), and B_yz (dark_green, green).

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

• Equilibrium volume, Helmholtz (or Gibbs at finite pressure) free energy, bulk modulus, pressure derivative of the bulk modulus, volume thermal expansion, isochoric heat capacity, isobaric heat capacity, isobaric-isochoric difference of the heat capacity, isoentropic-isothermal difference of the bulk modulus, and average Grüneisen parameter as a function of temperature (lmurn=.TRUE.). This plot is composed of ten figures, one for each quantity in the order given above. The quantities calculated using the phonon dos are in red, those obtained by an integral over the Brillouin zone are in blue. The volume thermal expansion can be calculated using the mode Grüneisen parameters and is plotted in green. The isobaric-isochoric difference of the heat capacity, the isoentropic-isothermal difference of the bulk modulus, and average Grüneisen parameter calculated with this volume thermal expansion are plotted in green. The volume and the bulk modulus used to compute the volume thermal expansion via the mode Grüneisen parameters are the blue ones if ltherm_freq=.TRUE. or the red ones if ltherm_freq=.FALSE. and ltherm_dos=.TRUE.. When both ltherm_freq=.FALSE. and ltherm_ dos=.FALSE. the equilibrium values of the volume and of the bulk modulus calculated at T = 0 K are used at all temperatures. The equilibrium volume at T = 0 K is used at all temperatures also when lv0_t=.FALSE.. The equilibrium bulk modulus at T = 0 K is used all temperatures also when lb0_t=.FALSE.

• Crystallographic parameters, volume, Helmholtz (or Gibbs at finite pressure) free energy, thermal expansion tensor, volume thermal expansion, constant strain heat capacity ( C_$\epsilon$ ), isobaric heat capacity (C_P ), difference C_P - C_V of isobaric and isochoric heat capacities, difference C_$\sigma$ - C_$\epsilon$ of constant stress and constant strain heat capacities (note that C_$\sigma$ = C_P ), difference C_V - C_$\epsilon$ of isochoric and constant strain heat capacities, difference B_S - B_T of the isoentropic and isothermal bulk modulus, and average Grüneisen parameter as a function of temperature (lmurn=.FALSE.). The number of figures in this plot depends on the crystal system and on the presence of one or more files with the elastic constants. It shows a as a function of temperature for cubic solids, a , c/a , and c for tetragonal and hexagonal solids. For orthorhombic solids it shows also b/a and b while for trigonal solids it shows a and cos$\alpha$ . For monoclinic solids it shows a , b/a , b , c/a , c , and cos$\alpha$ (c-unique) or cos$\beta$ (b-unique). All the six crystallographic parameters as a function of temperature are shown for triclinic solids. All quantities calculated using the phonon density of states are in red, those calculated integrating over the Brillouin zone are in blue with the exception of the thermal expansion tensor. When this tensor is diagonal with all identical components it follows the above rules while the tensor computed from mode Grüneisen parameters is in green. For hexagonal, tetragonal and trigonal solids $\alpha_{{xx}}^{}$ follows the above rules while $\alpha_{{zz}}^{}$ is pink, cyan, and orange when computed from phonon density of states, Brillouin zone integration, or mode Grüneisen parameters, respectively. 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, respectively. For the other crystal systems the thermal expansion tensor is not given. The thermal expansion tensor from the mode Grüneisen parameters is calculated only when the elastic_constants directory contains at least one file with the elastic constants. In this case also C_P - C_V , C_$\sigma$ - C_$\epsilon$ , C_V - C_$\epsilon$ , and the average Grüneisen parameters are calculated using this thermal expansion tensor and plotted in green. The volume used in these calculations is the blue curve if ltherm_freq=.TRUE. or as in the red curve if ltherm_freq=.FALSE. and ltherm_dos=.TRUE.. When both ltherm_freq=.FALSE. and ltherm_dos=.FALSE. the volume is kept fixed at the equilibrium volume at T = 0 K. The same applies for the bulk modulus calculated from a single elastic constant file when the flag lb0_t=.FALSE. or computed within the ``quasi-static'' approximation when lb0_t=.TRUE.. The C_P , C_$\sigma$ - C_$\epsilon$ , C_V - C_$\epsilon$ , and the average Grüneisen parameter are plotted only in presence of one or more elastic constants file.

• Thermal stresses as a function of temperature. This plot is composed of one figure in cubic solids and of two figures in the other cases. One figure contains b_xx (red, pink), b_yy (blue, light_blue) and b_zz (dark_green, green) as a function of temperature. The first color refers to quantities calculated from phonon density of states while the second refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted, shows b_xy (red, pink), b_xz (blue, light_blue), and b_yz (dark_green, green).

• 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.

• Generalized average Grüneisen parameters as a function of temperature. This plot is composed of one figure in cubic solids and of two figures in the other cases. One figure contains $\gamma_{{xx}}^{}$ (red, pink), $\gamma_{{yy}}^{}$ (blue, light_blue) and $\gamma_{{zz}}^{}$ (dark_green, green) as a function of temperature. The first color refers to quantities calculated from phonon density of states while the second color refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted shows $\gamma_{{xy}}^{}$ (red, pink), $\gamma_{{xz}}^{}$ (blue, light_blue), and $\gamma_{{yz}}^{}$ (dark_green, green).

• Phonon dispersions at the geometry that corresponds to a given temperature. The colors 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 isothermal and isoentropic elastic constants within the `Quasi-static', `Fixed geometry quasi-harmonic' or 'Quasi-harmonic approximation'. There is a plot for each non-zero elastic constant and a plot of the bulk modulus. The number of plots depends on the Laue class. Elastic constants interpolated at the geometry computed using the phonon density of states are in red (isothermal) and green (isoentropic), those calculated from integration over the Brillouin zone are in blue (isothermal) and orange (isoentropic).

• Temperature dependence of the isothermal and isoentropic elastic compliances within the `Quasi-static', `Fixed geometry quasi-harmonic' or 'Quasi-harmonic approximation'. There is a plot for each non-zero elastic compliance and a plot of the compressibility. The number of plots depends on the Laue class. Elastic compliances interpolated at the geometry computed using the phonon density of states are in red (isothermal) and green (isoentropic), those calculated from integration over the Brillouin zone are in blue (isothermal) and orange (isoentropic).

• Temperature dependence of the isothermal elastic constants within the `Fixed geometry quasi-harmonic approximation' for all the geometries of the mesh. There is a plot for each non-zero elastic constant and a plot of the bulk modulus. The number of plots depends on the Laue class. Elastic constants of the different geometries are in the sequence red, green, blue, yellow, pink, cyan, orange, black. When there are more than eight geometries the sequence is repeated. The same colors are used for the elastic constants obtained with the phonon density of states or from the integration over the Brillouin zone.

• Temperature dependence of the isothermal elastic compliances within the `Fixed geometry quasi-harmonic approximation' for all the geometries of the mesh. There is a plot for each non-zero elastic compliance and a plot of the compressibility. The number of plots depends on the Laue class. Elastic compliances of the different geometries are in the sequence red, green, blue, yellow, pink, cyan, orange, black. When there are more than eight geometries the sequence is repeated. The same colors are used for the elastic compliances obtained with the phonon density of states or from the integration over the Brillouin zone.