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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - APES (Accuracy and precision for molecular solids)

Teaser

Summary

The problem that we want to solve in this project is the highly accurate calculation
of binding energies of molecular solids.
Molecular solids are materials important both in nature and in industries.
Examples of molecular solids occurring naturally are water ice on the Earth,
ice made of carbon dioxide (dry ice) on Mars, and solid methane on Pluto.
Interestingly, while solid methane is not stable on the Earth, as it melts at around -183
degree Celsius, its mixture with water ice can be stable.
Such mixtures are called methane hydrates or clathrates, as they consist of water
cage-like framework with each of the cages usually occupied by a single methane molecule.
Methane clathrates have been found at the bottom of the oceans on the Earth
and are though of as a possible source of natural gas.
Clathrates containing carbon dioxide are thought to be stable on Mars or moons of gas giants.
The reason why the crystals of these different molecules are stable at different conditions
while at different conditions their mixtures are preferred is their energy.
Given sufficient time, the lowest energy structure will be the one that is formed.

One of the goals of this project is to be able to calculate reliably the energy
of molecular solids, so that we could make reliable predictions about the stability of the
different forms.
The challenge of this goal lies in the fact that to obtain the internal energy, which is the main
component of the total energy, we need to solve the equations of quantum mechanics,
either Schroedinger\'s or Dirac\'s.
Unfortunately, this is only possible exactly for small molecules, and to obtain energies
for molecular solids and other large systems, we need to introduce approximations that reduce
the accuracy of the predicted energies.
In the project we want to combine two approximations to obtain a scheme capable of providing
very accurate binding energies of molecular solids.
The first one is currently the most accurate scheme for calculating the properties of the solids,
the second is a rather mature approach used to obtain reference quality binding energies of molecules.
Apart from that, we also want to develop and implement methods that would allow us to understand
the precision of our predicted binding energies.
That is, we would like to be able to say how much one can trust the result.

Another field where molecular solids play an important role is pharmaceutical industry
as many active ingredients are administered in crystalline form.
However, the molecules tend to contain tens of atoms and such molecules can have different
crystalline forms, which are called polymorphs.
These polymorphs can have different physico-chemical properties such as solubility
meaning possibly different activity in body.
One of the goals in the field is to be able to reliably predict the different polymorphs
and their stability.
We want to contribute to this goal, for example, by providing reliable energy differences
between different polymorphs.

Computational modelling plays an important role in our daily lives and in solving our current
and future problems, such as energy production or development of novel drugs.
In any area, modelling is the more useful the more reliable predictions it can make.
In this project we want to increase the reliability of methods used to predict properties
of molecular solids and other solid materials.
Having more reliable methods at hand would reduce the cost and time needed for the development
of materials useful for solving our current and future problems.

Work performed

The main approximation that we are using is the so-called random-phase approximation (RPA)
which is currently the most accurate scheme for obtaining binding energies of molecular solids.
The work so-far can be divided into three main parts: i) accuracy, ii) precision, and iii) reference data.
In the accuracy part we focused on understanding the accuracy of RPA for binding energies
of molecular dimers, trimers, and tetramers.
To this end, we used simple systems of noble gas trimers, a standard test set of molecular trimers,
and a methane clathrate model.
This range of structures and compounds allowed us to improve the accuracy of RPA in a simple way.
This work will continue as we try to understand the limits of RPA more.
Concerning precision, the main achievement was the development of an efficient and scalable computer code
for calculating RPA binding energies of molecular clusters with a tunable precision.
For the last part, we are working on the first set of molecular solids which are crystals of simple
hydrocarbons.

Final results

We have been able to improve the accuracy of the RPA approach and we understand what is the physical
origin of this improvement.
This was one of our initial goals required for the full success of the project.
Moreover, we have tested several posibilities how to improve the accuracy further
and we are following some of the promising paths.
This will provide a scheme which we believe will achieve very good accuracy not only for molecular
solids but also for obtaining very good adsorption energies and various properties of solids.
In fact, we have started to use this approach in a different project to exactly this purpose.
We have performed initial applications of the correction scheme for clathrate with very good
results and we are currently obtaining the data to use the correction scheme on the crystals
of hydrocarbons.
The initial data give us some confidence that we will be able to obtain the reference quality binding
energies of molecular solids.