Quantized liquid density-functional theory for hydrogen adsorption in nanoporous materials

We develop a finite-temperature quantized version of density-functional theory of atomic and molecular liquids (QLDFT). Following the Kohn-Sham partitioning of the free energy, we introduce a noninteracting reference fluid of particles obeying the Maxwell-Boltzmann statistics. The kinetic and potential energy of the reference fluid are evaluated exactly. All remaining contributions, including interactions between fluid particles and corrections due to the appropriate quantum statistics are subsumed by an excess (in electronic DFT called exchange-correlation) functional. Two variants to approximate the excess functional are presented: the simplest local-interaction expression (LIE-0) avoids the direct calculation of interparticle interactions and includes them in the excess functional, which is parametrized to reproduce experimental equation of state of normal hydrogen. The more sophisticated LIE-1 approximation is based on the weighted local-density approximation and includes the explicit interparticle interaction potential as well as the local approximation of the excess functional, the latter being weighted by the average over a spherical environment to include nonlocal effects in an approximate way. We apply LIE-0 and LIE-1 to two benchmark systems, bulk fluid hydrogen and hydrogen in a slit pore, and compare it with classical molecular-dynamics simulations employing the same potential. Both functionals produce similar results for direct quantum effects in adsorption free energy. At the same time, LIE-1 also yields a reasonable description of the fluid structure and classical packing effects, which are not reproduced by LIE-0. The source code of our implementation of the LIE-QLDFT is distributed under the GNU public license and is included as a supporting material.