FBSD Simulation of Liquid para-Hydrogen

Molecular hydrogen is a system dominated by quantum effects at temperatures below 25K. Quantum effects are very large here, as seen in the pair distribution functions Classical treatments fail entirely in this case. In particular, the system freezes at 14K if treated by a classical molecular dynamics simulation. Even at 25K, the kinetic energy obtained by static path integral Monte Carlo (PIMC) calculations exceeds the classical estimate 1.5 kT by over 60%.

Pair distribution functions for liquid para-hydrogen under nearly zero external pressure. Red line: result by the pair-product approximation for the coherent state density. Black line: path integral Monte Carlo calculation. Blue line: classical result. (a) 25 K. (b) 14 K.

The calculations were performed using the single-bead PP-PI-FBSD method at several thermodynamic state points (between 14 K and 25 K) under nearly zero external pressure. The calculations employ the Silvera-Goldman potential, where a para-hydrogen molecule is treated as a spherical particle. The large quantum mechanical effects in this system are also witnessed by the large magnitude of the imaginary part of the correlation function.

The normalized velocity autocorrelation function of liquid para-hydrogen at (a) T = 25 K and (b) T = 14 K calculated by the PP-PI-FBSD method. The red and blue lines are the real and imaginary parts of the correlation function, respectively.

The diffusion constant is calculated from the time integral of the real part of the correlation function. The results were in excellent agreement with experimental values at temperatures higher than 20K.

The diffusion constant as a function of temperature for liquid para-hydrogen from T = 14 K to T = 25 K. Red circles: PP-PI-FBSD results. Black squares: experimental results.