liquid sodium MD, r_c = 1.986 bohr (temperature derivatives from r_c = 1.971), N = 2000, 30 ps per run after 6 ps equilibration
  left out (still crystalline, never melted): na_1.971_1.0_346_1.pkl
  density x0.98, target 371 K: mean T  373.8 K  P = -0.0894 +- 0.0001 GPa  E = -219.7125 mHa
  density x1.00, target 371 K: mean T  367.6 K  P = +0.0272 +- 0.0002 GPa  E = -219.8757 mHa
  density x1.02, target 371 K: mean T  374.7 K  P = +0.1667 +- 0.0001 GPa  E = -219.8478 mHa
  cut-off (impulsive) pressure added at density x0.98: +0.0351 GPa
  cut-off (impulsive) pressure added at density x1.00: +0.0419 GPa
  cut-off (impulsive) pressure added at density x1.00: +0.0400 GPa
  cut-off (impulsive) pressure added at density x1.02: +0.0488 GPa
  temperatures used: 373.0, 397.1 K;  (dP/dT)_V = 1.0925 +- 0.0275 MPa/K;  c_v = 3.498 +- 0.083 k_B per ion (measured, Fink & Leibowitz: 3.49)
  isothermal B_T = 6.381 +- 0.009 GPa;  adiabatic B_S = 6.755 GPa;  Cp/Cv = 1.0586
  thermodynamic route: speed of sound c = 2699.5 m/s at T = 367.6 K, pressure +0.027 GPa
  structural route: S(k) at k = 0.076, 0.108, 0.132, 0.153 bohr^-1: 0.0117, 0.0123, 0.0111, 0.0112; S(0) = 0.0123
    -> isothermal B from the structure alone = 10.02 GPa (thermodynamic 6.38); a pulse carried by the pair forces alone would run at about 3383 m/s
  measured: S(0) = n kT beta_T = 0.0235 (beta_T from Fink & Leibowitz-type data, 1.886e-10 /Pa)
BEST: c = 2699.5 +- 4.2 m/s
