============= Direct results (without any inter/extrapolation) ================== For present temperature (in Kelvin): T= 495.050 The cold contribution (in eV/atom): U_0 = -944.384 The specific heat (in k_b/atom): C_v= 2.794 The vibrational entropy (in k_b/atom): S_vib = 4.217 The internal energy (in eV/atom): U_vib = 0.137 The vibrational contribution (in eV/atom): F_vib = U_vib -T.S_vib = -0.043 The harmonic free energy (in eV/atom) --> F_tot^HA = U_0 + F_vib = -944.426 Useful quantities for melting : The mean square displacement (in a.u.): sqrt() = 0.294 The factor (in THz^(-2)) = 0.108 The Wigner-Seitz radius (in a.u.) : d_at = 5.388 The average mass / proton-electron mass ratio (in a.u.) = 47.338 The Lindemann constant : sqrt()/d_at = 0.055 The integral of vDOS = 1.000 ============= Harmonic Approximation (HA) ================== Note that the following results come from an EXTRAPOLATION: 1/ F_vib^HA(T) is computed for each T using vDOS(T= 495) 2/ F_tot^HA(T) = F_vib^HA(T) + U_0 T F_vib^HA(T) F_tot^HA(T) C_v(T) S_vib(T) U_vib(T) MSD(T) 100 0.050 -944.333 1.266 0.742 0.057 0.157 200 0.039 -944.345 2.137 1.931 0.072 0.196 300 0.018 -944.366 2.516 2.878 0.092 0.233 400 -0.010 -944.394 2.700 3.630 0.115 0.266 500 -0.044 -944.428 2.798 4.244 0.139 0.296 600 -0.083 -944.467 2.856 4.760 0.163 0.323 700 -0.126 -944.510 2.892 5.203 0.188 0.348 800 -0.173 -944.556 2.917 5.591 0.213 0.372 900 -0.222 -944.606 2.934 5.936 0.238 0.394 1000 -0.275 -944.659 2.946 6.246 0.263 0.415 1100 -0.330 -944.714 2.955 6.527 0.289 0.435 1200 -0.387 -944.771 2.962 6.784 0.314 0.454 1300 -0.447 -944.831 2.968 7.021 0.340 0.472 1400 -0.508 -944.892 2.972 7.242 0.365 0.490 1500 -0.572 -944.955 2.976 7.447 0.391 0.507 1600 -0.637 -945.020 2.979 7.639 0.417 0.524 1700 -0.703 -945.087 2.981 7.820 0.442 0.540 1800 -0.771 -945.155 2.983 7.990 0.468 0.556 1900 -0.841 -945.225 2.985 8.151 0.494 0.571 2000 -0.912 -945.296 2.986 8.304 0.519 0.586 2100 -0.984 -945.368 2.987 8.450 0.545 0.600 2200 -1.057 -945.441 2.989 8.589 0.571 0.614 2300 -1.132 -945.516 2.990 8.722 0.597 0.628 2400 -1.208 -945.592 2.990 8.849 0.622 0.641 2500 -1.285 -945.668 2.991 8.971 0.648 0.654 2600 -1.362 -945.746 2.992 9.089 0.674 0.667 2700 -1.441 -945.825 2.992 9.202 0.700 0.680 2800 -1.521 -945.905 2.993 9.310 0.726 0.693 2900 -1.602 -945.985 2.993 9.416 0.751 0.705 3000 -1.683 -946.067 2.994 9.517 0.777 0.717 3100 -1.766 -946.149 2.994 9.615 0.803 0.729 3200 -1.849 -946.233 2.995 9.710 0.829 0.740 3300 -1.933 -946.317 2.995 9.802 0.855 0.752 3400 -2.018 -946.402 2.995 9.892 0.880 0.763 3500 -2.103 -946.487 2.995 9.979 0.906 0.774 3600 -2.190 -946.574 2.996 10.063 0.932 0.785 3700 -2.277 -946.661 2.996 10.145 0.958 0.796 3800 -2.365 -946.748 2.996 10.225 0.984 0.807 3900 -2.453 -946.837 2.996 10.303 1.009 0.817 4000 -2.542 -946.926 2.997 10.379 1.035 0.828 4100 -2.632 -947.016 2.997 10.453 1.061 0.838 4200 -2.722 -947.106 2.997 10.525 1.087 0.848 4300 -2.813 -947.197 2.997 10.595 1.113 0.858 4400 -2.905 -947.289 2.997 10.664 1.139 0.868 4500 -2.997 -947.381 2.997 10.732 1.164 0.878 4600 -3.090 -947.474 2.997 10.798 1.190 0.888 4700 -3.183 -947.567 2.997 10.862 1.216 0.897 4800 -3.277 -947.661 2.998 10.925 1.242 0.907 4900 -3.372 -947.755 2.998 10.987 1.268 0.916 5000 -3.466 -947.850 2.998 11.048 1.294 0.925 5100 -3.562 -947.946 2.998 11.107 1.319 0.934 5200 -3.658 -948.042 2.998 11.165 1.345 0.944 5300 -3.754 -948.138 2.998 11.222 1.371 0.953 5400 -3.851 -948.235 2.998 11.278 1.397 0.962 5500 -3.949 -948.332 2.998 11.333 1.423 0.970 5600 -4.047 -948.430 2.998 11.387 1.449 0.979 5700 -4.145 -948.529 2.998 11.440 1.474 0.988 5800 -4.244 -948.628 2.998 11.493 1.500 0.997 5900 -4.343 -948.727 2.998 11.544 1.526 1.005 6000 -4.443 -948.826 2.998 11.594 1.552 1.014 6100 -4.543 -948.927 2.999 11.644 1.578 1.022 6200 -4.643 -949.027 2.999 11.692 1.604 1.030 6300 -4.744 -949.128 2.999 11.740 1.629 1.039 6400 -4.846 -949.230 2.999 11.788 1.655 1.047 6500 -4.948 -949.331 2.999 11.834 1.681 1.055 6600 -5.050 -949.433 2.999 11.880 1.707 1.063 6700 -5.152 -949.536 2.999 11.925 1.733 1.071 6800 -5.255 -949.639 2.999 11.969 1.759 1.079 6900 -5.359 -949.742 2.999 12.013 1.784 1.087 7000 -5.462 -949.846 2.999 12.056 1.810 1.095 7100 -5.566 -949.950 2.999 12.099 1.836 1.103 7200 -5.671 -950.055 2.999 12.141 1.862 1.110 7300 -5.776 -950.159 2.999 12.182 1.888 1.118 7400 -5.881 -950.265 2.999 12.223 1.914 1.126 7500 -5.986 -950.370 2.999 12.263 1.940 1.133 7600 -6.092 -950.476 2.999 12.303 1.965 1.141 7700 -6.198 -950.582 2.999 12.342 1.991 1.148 7800 -6.305 -950.689 2.999 12.381 2.017 1.156 7900 -6.412 -950.795 2.999 12.419 2.043 1.163 8000 -6.519 -950.903 2.999 12.457 2.069 1.170 8100 -6.626 -951.010 2.999 12.494 2.095 1.178 8200 -6.734 -951.118 2.999 12.531 2.120 1.185 8300 -6.842 -951.226 2.999 12.567 2.146 1.192 8400 -6.951 -951.335 2.999 12.603 2.172 1.199 8500 -7.060 -951.443 2.999 12.639 2.198 1.206 8600 -7.169 -951.552 2.999 12.674 2.224 1.213 8700 -7.278 -951.662 2.999 12.708 2.250 1.220 8800 -7.388 -951.771 2.999 12.743 2.276 1.227 8900 -7.498 -951.881 2.999 12.777 2.301 1.234 9000 -7.608 -951.992 2.999 12.810 2.327 1.241 9100 -7.718 -952.102 2.999 12.843 2.353 1.248 9200 -7.829 -952.213 2.999 12.876 2.379 1.255 9300 -7.940 -952.324 2.999 12.908 2.405 1.262 9400 -8.052 -952.435 2.999 12.941 2.431 1.269 9500 -8.163 -952.547 2.999 12.972 2.456 1.275 9600 -8.275 -952.659 2.999 13.004 2.482 1.282 9700 -8.387 -952.771 2.999 13.035 2.508 1.289 9800 -8.500 -952.884 2.999 13.066 2.534 1.295 9900 -8.613 -952.996 2.999 13.096 2.560 1.302 10000 -8.726 -953.109 2.999 13.126 2.586 1.308