One of the most important issues in the modelling of materials is
the choice of an appropriate density functional. Many researchers
employ functionals commonly used in their field or they have some
sort of chemical intuition, why one density functional should be
preferred over another one. This is an ill-advised strategy. In this
paper, we present a concise approach to select the best functional
for structure prediction of a particular materials system. We use the
random phase approximation (RPA), which is placed one step above
hybrid functionals on the metaphorical Jacob's Ladder towards the
exact total energy. A new implementation of RPA-forces in VASP
(by Ramberger and Kresse, 2016) allows us to perform molecular
dynamics at the RPA level, something that seemed impossible just
a few years ago. A finite temperature ensemble of realistic crystal
structures and the associated energies are calculated. Comparing
these energies to the ones obtained with commonly used density
functionals allows to rank them based on their accuracy.
To verify this new approach, we study an exciting novel solar cell
material: MAPbI_{3}. Its structure is a particularly hard nut to crack
for DFT. This is due to the large dynamical degree of freedom of
the Methylammonium molecules and the interplay of van der Waals
forces and cage instabilities in the perovskite structure.
We have calculated the band structure and exciton binding energies
of the most studied ABX_{3} hybrid perovskites. We have incorporated
many body effects on the DFT calculated electronic structure in
the GW_{0} approximation and consecutively solved the Bethe-Salpeter
equation (BSE). Convergence of the red-shift of the optical band
gap requires the use of very dense k-point grids. We have therefore
implemented a modelBSE routine in VASP, where a model screening
function, fitted to W_{0}, is used.
A model that accurately describes the doping
level in graphene on a h-BN covered metal surface is presented. The model is
based on the electrostatical description of a simple planar capacitor.
Interface bonding effects are included as localized potential steps and
are obtained independently by first principles calculations. The doping
level can be tuned by an external electric field and the metal contact
results in a non-trivial intrinsic doping.
We have solved an open issue in this field, whether ionic movement
can screen an e-h pair and thereby effectively lower the exciton binding
energy. For this purpose we have calculated the room temperature
dielectric function from molecular dynamics. By following the
fluctuations of the total dipole moment in time, the polarizability
can be calculated in linear response.
Early DFT calculations of commensurate graphene on h-BN showed a
small induced band gap of approximately 40 meV. Low temperature STM images
later showed that the graphene|h-BN is in reality incommensurate as
indicated by the formation of large moir ́e patterns. We have shown
that this does not have to mean that the induced band gap disappears
and that a band gap of similar order can form. Since the required
super cells are so large, Kohn-Sham DFT is not a viable option.
We have therefore constructed a tight-binding model based on GW
calculations for commensurate structures.
At metal-insulator interfaces large potential steps (1 eV) can be
formed even though the interaction is of a weak van der Waals
type. We have used the interface between a metal and h-BN
(M|BN) as a archetypical example to study the underlying physical
mechanisms. As shown in the top figure, DFT is unable to predict
the equilibrium binding distance. However, the induced potential
step as a function of distance does not depend on the XC-functional.
We have approximated the M|BN wavefunction by constructing an
anti-symmetric product of the individual M and BN wavefunctions
in a self-adapted version of VASP. The resulting system is a good
description of the self-consistently calculated M|BN system. This
proofs directly that the interface dipole is formed by Pauli exchange
repulsion.
Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.