Centre for Theoretical Chemistry and Physics
at Massey University (Albany Campus), New Zealand

Pahl group - Computational Physics and Chemistry

Research topics in the group span a wide range of topics from Solid State Physics to Computational Chemistry, going from nano-clusters to solid-state properties, from atomic to molecular systems. A particular focus is the study of melting under ambient and extreme conditions (ultra high pressures and magnetic fields) using Monte-Carlo or molecular-dynamic simulations. Further topics are highly accurate calculations of cohesive energies of solids, computation of cohesive energies via lattice sums and the extension and implementation of the Full Configuration Interaction Monte Carlo method of bosonic systems, a stochastic approach to finding ground states of quantum systems.

Principal Investigator: Dr. Elke Pahl


Centre for Theoretical Chemistry and Physics
New Zealand Institute for Advanced Study
Bldg. 44, Massey University (Albany Campus)
Private Bag 102 904
North Shore Mail Centre
Auckland, New Zealand
Phone (64) 09 414 0800 ext 41432
Fax (64) 09 443 9779
Email: e.pahl@massey.ac.nz

Research topics

Melting Simulations

Nano-clusters are wonderful models to study the emergence of condensed matter phenomena like melting with increasing number of atoms, so to say in a bottom-up approach. Aggregates of 10s to 1000s of particles exhibit very complex potential energy surfaces describing the energy in dependence of the positions of the atoms, with many close-lying minima. In order to simulate the melting process, we need very accurate interaction potentials and have to explore the resulting potential landscapes extensively at a range of temperatures spanning the melting transition. While we use highly accurate quantum-chemical methods for the atomic interactions, so-called parallel-tempering Monte Carlo simulations or alternatively ‘interface-pinning’ molecular dynamics methods allow for an efficient sampling of the potential hyper-surfaces.
Research questions comprise: Can concepts of statistical physics, derived for a very large number of particles, still be applied to the description of clusters with only a few atoms? Is an extrapolation of cluster results to the bulk behavior possible? How does ultra-high pressure or high magnetic fields influence melting? Why is mercury the only liquid atomic metal at room temperature?

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:

Magic Clusters of Rare Gases - Mackay Icosahedra

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.
Melting of Argon under extreme pressures

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:
Mercury Melting

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.
Many-body decomposition of bulk Argon

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.


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.
Maintained by Peter Schwerdtfeger | Last updated: February, 2018 | Copyright 2014 | Massey University