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

Abstract

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.

Hydrogen adsorption in metal-organic frameworks: The role of nuclear quantum effects

“…The members of the IRMOF series share the same connecting SBU, but different organic linkers provide a systematic variation of pore size. The series of isoreticular MOFs studied in this work are IRMOF-n with n=1, 4,6,8,9,10,12,14,16,18 is derived from linking the octahedral zinc acetate unit Zn 4 O(CO 2 ) 6 , with a variety of linear ditopic carboxylates 4,31 (see Figure 1). MOF-177 is constructed from the same connecting SBU and the tritopic BTB linker.…”

“…After validating our computational approach for IRMOF-1, we apply QLDFT within the same setup as for IRMOF-1 to assess hydrogen adsorption properties at T = 77 K on a series of IRMOFs (IRMOF-n with n = 1,4,6,8,9,10,12,14,16,18) and MOF-177. In Table I, we list the total gravimetric and volumetric adsorption capacities at 20, 40, 60, 80 and 100 bars, and the excess adsorption at saturation condition.…”

Grand-canonical quantized liquid density-functional theory in a Car-Parrinello implementation

“…Different suggestions for the choice of F xc have already been discussed in ref. [19]. There, the most sophisticated functional is the LIE1 (LIE=local interaction expression) excess functional which uses the weighted local density approximation (WLDA) [27].…”

“…It is straight-forward to obtain the free energy of the uniform fluid from experiment over a wide range of pressures and temperatures [19], and also the molar volume is available. This information is sufficient to relate the chemical potential, pressure and temperature using standard thermodynamic relations.…”

“…The non-physical absence of the density oscillations has already been discussed in detail earlier. [19] Here, we note that it is irrelevant if the local approximation is made to the classical or the quantum-mechanical system and state that it should only be applied if the potential variation and the associated density oscillations are expected to be very small.…”