Ab initio modeling of volatility of ionic liquids with the help of computational crystallography

Ctirad CERVINKA¹, Petr TOUS^1
1UCT Prague, Prague, Czechia

Aprotic ionic liquids are known for their low vapor pressures at ambient conditions. This valuable property of ionic liquids, however, makes experimental determination of their vapor-liquid equilibrium extremely difficult. Still, vapor pressures even in the sub-Pascal region can be important for atmospheric spread of pollutants in the environment. Reliable computational approaches that would be competitive with state-of-the-art experiments would be thus most welcome for such low-volatile materials.
Numerous ionic liquids have been crystallized into structures, resembling molecular crystals with explicitly charged molecules. Computational chemistry offers various models to describe electronic, structural, and dynamical properties of molecular crystals [1]. A key idea of this work is to adapt the existing first-principles approaches for modeling of sublimation of molecular crystals to be applicable to crystals of ionic liquids [2]. Ab initio predictions of sublimation pressure at the triple-point temperature then essentially contribute also the knowledge of the vapor-liquid equilibrium of ionic liquids.
Current computational models initiate from experimental crystal structures. Density functional calculations with periodic boundary conditions serve as the primary method, being reliable enough to model unit-cell geometries, cohesion energies and phonon properties of the crystals. Following the quasi-harmonic approximation, all these crystal characteristics need to investigated as functions of unit-cell volume [3]. Only then, Helmholtz energy of the crystal can be constructed as a function of both temperature and volume, carving a path to all other thermodynamic properties of the crystal at finite temperatures.
Crucial contribution towards the sublimation enthalpy as well as to the sublimation pressure of a crystal comes from its cohesive energy. In the context of crystalline ionic liquids, this term represents an energy difference of an isolated ion pair, mimicking the vapor phase, and an ion pair in the geometry from the crystal structure. Since DFT exhibits various flaws impeding its quantitative accuracy in the field of modeling non-covalent interactions, an ab initio refinement of the cohesive energy is due.
Fragment-based models, summing monomer contributions and pair interactions of proximate molecules in the crystal lattice, all calculated using advanced wave-function methods, up to the coupled clusters theory, serve as an elegant tool for reaching better than the chemical accuracy. Long-range electrostatic interactions, as well as many-body interactions due to atomic polarizability or charge transfer contribute significantly to the cohesion of crystals of ionic liquids. Ab initio pair interactions are then coupled with a long-range many-body correction, extracted usually from a cheaper periodic DFT embedding model.
A proper combination of high-tier and low-tier quantum-chemical methods in this treatment enables to lower the computational error to the chemical accuracy level, representing roughly 3% of the sublimation enthalpy [4]. Sublimation pressures can be then captured within the same order of magnitude over broad temperature intervals [5]. Such a computational accuracy is definitely competitive with contemporary experiments.
[1] ?ervinka, Beran: Chem. Sci. 2018, 9, 4622-4629.
[2] ?ervinka, Klajmon, Štejfa: J. Chem. Theory Comput. 2019, 15, 5563-5578
[3] ?ervinka: J. Comput. Chem. 2022, 43, 448-456.
[4] Touš, ?ervinka: In preparation.
[5] ?ervinka, Beran: Phys. Chem. Chem. Phys. 2019, 21, 14799-14810