Jiri Klimes
(Faculty of Mathematics and Physics, Charles University)
The course of many industrial or natural processes is given by interactions
between molecules or between molecules and solids, let us mention the catalytic
formation of ammonia or the formation of snowflakes to name but a few.
If we want to model and understand such processes we need methods that describe
the interactions reliably. This is a difficult task as we often need to use description
on the level of quantum mechanics. However, solving the equations of quantum mechanics
for extended systems is not possible exactly and we need to use approximations.
Methods based on perturbation theory, such as the random phase approximation (RPA)
or the second order perturbation theory (MP2) are promising for the treatment of extended systems.
However, when applying such methods to extended systems one faces an issue that
there are several numerical parameters that affect the results, such as the real space grid density.
Converging with these parameters increases substantially the overall cost of the calculations.
However, converged properties are needed if we want to understand the accuracy of a given theoretical scheme.
We have calculated such highly converged binding energies of molecular solids using the RPA approach.
We were able to show that it provides much better and more consistent accuracy compared to the state-of-the-art
DFT methods [1,2]. As it is difficult to assess when a convergence has been reached,
we have used an alternative scheme to obtain the binding energies of molecular solids.
This is called the many-body expansion (MBE) and it assembles the binding energy from contributions
of individual dimers, trimers, etc. of molecules in the crystal. However, this doesn't
come without issues either, again there are several numerical parameters that need
to be controlled and that make the convergence difficult. By calculating binding
energies of four molecular crystals of small molecules within periodic boundary conditions
and with the MBE we were able to identify some of the issues related to both approaches.
Moreover, we were able to identify general guidelines to follow when performing
calculations of binding energies of molecular solids [3].
References
[1] Klimes, J. Chem. Phys. 145, 094506 (2016)
[2] Zen, Brandenburg, Klimes, Tkatchenko, Alfe, Michaelides, PNAS 115, 1724 (2018)
[3] Hofierka, Klimes, in preparation.
Summary
Molecular solids are important materials both in nature and industries. From methane clathrates
at the bottom of the sea, over pharmaceuticals in pills, to carbon dioxide ice caps on Mars.
Reliable theoretical prediction of their properties requires methods which are accurate,
that is, they faithfully describe the physics of the particles and their interactions.
Moreover, the calculations need to be precise, that is, converged well enough with
the parameters of the numerical implementation. I will give an overview of the methods
that we have been using for the calculation of properties of molecular solids
and will show the accuracy of different approaches. Moreover, I will discuss
ways how to further improve the accuracy of the calculations and how to make
precise calculations more affordable.
Jiri Klimes
(Faculty of Mathematics and Physics, Charles University)
Jaroslav Hofierka
(Faculty of Mathematics and Physics, Charles University)
