Energy landscapes on multi-scale

Energy landscapes investigations and multi-scale modeling

A major task in computational material science is the prediction of stable crystalline compounds in a chemical system: At which composition does a system form a kinetically and/or thermodynamically stable compound, what is its structure and chemical/physical properties, to what degree is this compound stable and what will happen, if such a metastable compound undergoes a phase transition?

To answer these questions, one investigates the energy landscape of the system, i.e. the (potential) energy as a function of the atomic positions in the system. At low temperatures local minima of the potential energy surrounded by sufficiently high energy barriers correspond to kinetically stable structures, while at higher temperatures, entropic barriers become increasingly important for the kinetic stability, and a “minimization” of the free energy should replace the simpler search for minima of the potential energy.


Due to the fact that the solution of the full Schrödinger equation for solid systems is very expensive computationally, we usually employ a sequence of approximations, in order to simplify the energy calculation: Born-Oppenheimer approximation, periodic boundary conditions, and effective potentials mostly based on empirical data. This simplified energy landscape is then analyzed using simulated annealing for the determination of the local minima. During the global optimization, the positions of the atoms, the vectors of the repeated simulations cell, the distribution of electrons on the atoms and the composition of the atoms in the cell are varied, depending on the specific problem under investigation. For the computation of energy barriers and local densities of states, the threshold algorithm has been developed. In addition, algorithms have been developed to calculate structural and physical properties.

Closely related to the question of structure prediction of not-yet- synthesized compounds is the issue of determining the structures of already synthesized compounds, where only powder diffraction data are available but no successful structural model has been found. Here, a combined optimization of the potential energy and the difference between calculated and observed powder diffractograms (Pareto-optimization) can serve to identify good structure candidates. This research includes multi-scale modeling; from the atomic and molecular level to nano-particles and single crystals, applying the empirical, semi-empirical and pseudopotentials, and in the final phase, the experimental synthesis of the calculated models.

Recommended literature:

  1. D. Zagorac, J. C. Schön, K. Doll, M. Jansen, Structure prediction for PbS and ZnO at different pressures and visualization of the energy landscapes, Acta Physica Polonica A 120 (2) (2011). DOI:
  2. D. Zagorac, K. Doll, J.C. Schön, M. Jansen, Sterically Active Electron Pairs in Lead Sulfide? An Investigation of the Electronic and Vibrational Properties of PbS in the Transition Region Between the Rock Salt and the alpha-GeTe-Type Modifications, Chemistry. A European Journal, 18, 35 (2012) 10929-10936, IF=5.831, ISSN: 0947-6539,
  3. D. Zagorac, J. C. Schön, M. Jansen, Energy landscape investigations using the prescribed path method in the ZnO system, Journal of Physical Chemistry C 116(31) (2012) 16726-16739.DOI:
  4. D. Zagorac, J. C. Schön, M. Rosić, J. Zagorac, D. Jordanov, J. Luković, B. Matović, Theoretical and Experimental Study of Structural Phases in CoMoO4, Crystal Research and Technology 52(10) (2017) 1700069. DOI: