Rare gases under ambient conditions
Melting simulations for all rare gases from Neon to super-heavy Oganesson have been performed.
For the studies we use a many-body expansion for the interaction energies
of the N-body system in which the total energy is split into two-, three- and higher-body
contributions. Fast convergence allows to restrict the expansion to the two- and three-body
parts. The two- and three-body potentials are obtained from fits to highly accurate ab initio data.
The phase space is then explored via the parallel-tempering Monte Carlo method in the canonical ensemble.
In a bottom-up approach the melting of small (magic number) clusters is studied (with spherical boundary conditions)
and the results are extrapolated to the infinite system. Since the nano-clusters have surfaces, the obtained
bulk melting temperatures can be compared directly with experimental data. This is in contrast to
direct melting simulations of extended system in the framework of periodic boundary conditions where missing
surface effects lead to superheating. We developed a method to correct for the superheating effects
so that both complementary approaches are in good agreement with each other and experimental values.
. Read more here:
Rare gases under ultra-high pressure
In order to treat systems at constant pressures, the parallel-tempering Monte Carlo method was extended from the canonical
to the isobaric-isothermal ensemble. We performed (periodic boundary) melting simulations up to pressures of
1 Million times the atmospheric pressure, 100 GPa and corrected for super-heating effects.
Applications to Argon showed that agreement with experimental data up to pressures of 50 GPa is very good.
Deviations between experimental and theoretical data for larger pressures are still debated -
interestingly, they are also observed for many other systems.
Rare gases in strong magnetic fields
This is a very recent collaborative project as a result of being a fellow at the
Centre for Advanced Studies in Oslo, Norway within the project
"Atoms and Molecules in Extreme Environments". The interaction of the rare gases
with a strong, homogeneous magnetic field are described via a many-body expansion
starting with the two-body contributions. MP2 and CCSD data are computed for rare-gas
dimers in varying magnetic fields in dependence of the interatomic distance and the
orientation of the dimer with respect to the direction of the magnetic field.
Why is mercury liquid at room temperature?
Mercury, Hg, is the only elemental metal liquid at room temperature -
the reasons for this phenomenon posed a long-standing puzzle in chemistry.
We were able to prove that relativistic effects are providing the answer!
Melting simulations including and excluding relativistic effects showed that
relativity (in combination with complicated many-body effects) lowers the melting
temperature by more than 100 degrees! Scalar-relativistic effects stabilize the 6s
valence electrons, making the mercury atoms more rare-gas like which results in the
observed lowering of the melting temperature. Read more:
Molecular Systems - Water
We recently extended our atomic parallel-tempering Monte Carlo (MC) code
to molecular systems allowing to include the needed additional degrees of freedom.
First applications were started for nitrogen and very recently to water.
Melting results for very small water clusters were reproduced for a crude
interaction model, the widely used Transferable Interaction Potentials TIP-n.
Currently we are working on interfacing our MC code to an ab initio water potential,
which is again based on a many-body decompostion of the total interaction.
Cohesive Energy of Solids
Rare Gases
Rare-gas crystals are seemingly simple systems, still, there exist many open
fundamental questions like: Why is nature preferring the close-packed cubic (fcc) structures
over the hexagonal densest (hcp) packing, although the energy difference between the
fcc and hcp structures is so tiny that very high-level computational methods and
effects of zero-point vibrational motion are needed to resolve it at all?
At what pressures is the transition from the expected transition from the fcc to
the hcp structure happening?
An enormous effort is needed in order to achieve the desired accuracies
in the binding energy and other crystal properties to allow a distinction
between the fcc and hcp lattices. Contributions from 700,000 atom pairs had to be
considered for the leading two-body energy term, as well as 70,000 trimer an 7,000
four-body contributions.
Evaluation via lattice sums
The main contribution to the cohesive (binding) energy of a solid comes from the interaction
energies between all possible atom pairs in the extended system. Using an extended Lennard
Jones functional form to describe the dimer interaction one arrives at an analytical
expression for the (two-body) cohesive energy per atom. The beauty
of this formula is that it only depends on the underlying dimer potential parameters,
the next-nearest neighbour distance
and the so-called Lennard-Jones-Ingham, LJI, coefficients.
Analytical expressions for other solid-state properties like pressure,
bulk moduli and zero-point energy follow directly.
The LJI coefficients only depend on the underlying symmetry of the lattice and thus,
have only be computed once for every lattice structure,
but they present very slowly converging sums.
For cubic lattices, several expressions for the LJI have already been derived
and mathematical techniques for a fast evaluation developed.
A visual interpretation of these cubic lattice sums was developped
which allowed us to find alternative representation for the cubic LJI coefficients
and most importantly, a new formula for the hexagonal closed packed, hcp, structure.
This formula allows us to use the same techniques as in the cubic cases.
Therefore an efficient and accurate evaluation of the LJI coefficients is now possible
also for the hcp lattice.
Copernicium
Full Configuration Interaction Quantum Monte Carlo for Bosonic Systems
The aim of this project is the study of bosonic quantum phase transitions
using a novel method, the Full Configuration Interaction Quantum Monte Carlo (FCIQMC),
that was originally developed for quantum chemical computations.
FCIQMC offers a stochastic approach to an exact diagonalisation procedure
extending to much larger Hilbert spaces than possible with deterministic approaches,
i.e. when the exact Hamiltonian matrix, or even a single eigenvector,
is too large to be fully stored in a computer.
A bosonic FCIQMC code was recently developed from scratch in the programming language Julia.
First applications to a one-dimensional Bose-Hubbard model are currently underway.
This project is a collaboration with Prof. Joachim Brand, CTCP and Prof. Ali Alavi, MPI Stuttgart.