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MARTIN-LUTHER UNIVERSITÄT

HALLE-WITTENBERG

Methods

Density functional theory


In our investigations we combine classical and quantum-mechanical simulations. In the latter case, we mostly use density functional theory (DFT), which makes quantum-mechanical calculations possible for relatively large systems showing a very good cost to accuracy ratio.

In the Kohn-Sham formalism of DFT,[1] it is assumed that each electron feels an effective potential created by all the electrons plus another term which incorporated the quantum effects. With this assumption, one can then solve N one-electron Schrödinger (Kohn-Sham) equations for which the ground electronic state density matches that of the real many-body system of N electrons. The inherent mean-field assumption works quite well for a wide variety of chemical systems, but not for all.

Most of quantum chemistry code have a DFT module. During the past two decades there have been big strides towards solving the Kohn-Sham equations more and more efficiently. Thanks to the developed mathematical and computational methods, nowadays DFT calculations for systems with thousands of electrons are possible.

As mentioned above, DFT is a ground-state theory, and therefore, cannot be expected to give reliable results for excited-state properties and/or for processes triggered by an electronic excitation. To study such processes, we usually use time-dependent DFT[2] which makes the electronic excited-state properties accessible at a moderate computational cost. Higher-level quantum chemical methods, such as couple-cluster equation of motion, are also used in our research mostly as reference calculations.

In our studies, we use different DFT codes including (but not limited to) CP2K[3,4], ORCA[5], NWChem[6], and SIESTA[7].

Molecular dynamics simulations


The main idea behind molecular dynamics simulations is to study the evolution of the atoms in time, that is how they change their positions with time as they interact with each other. This practically translates to time-integration of Newton’s equation of motion. For this, one needs to know the forces acting on each atom. In classical simulations, these forces are obtained from parametric interatomic potentials. Such simulations are quite fast and therefore, investigation of systems with millions of atoms is possible. However, the electronic structure of the system is generally neglected in classical simulations. To include the electronic structure of a systems in molecular dynamics simulations, one can calculate contribution of the electrons to the forces acting on an atom using an electronic structure method, such as DFT. The combination of DFT with molecular dynamics techniques (often called ab initio molecular dynamics) enables the direct observation of microscopic processes through the calculation of atomistic trajectories. These simulations are much more accurate than classical molecular dynamics simulation but also much more costly.


We use both classical and ab initio molecular dynamics simulations to study the chemical processes in energy-storage systems, which, in combination with spectroscopy simulations provide a machinery to directly validate our theoretically predicted findings with experiments.


Spectroscopy simulations


Generally, spectroscopy is the study of interaction of electromagnetic radiation with matter. Depending on the energy of the incident electromagnetic radiation, various information about the system under study can be gathered. For example, vibrational spectroscopy (infrared, Raman, etc.) can reveal the atomic structure of the systems by exciting its vibrational modes, whereas, for instance, ultraviolet-visible spectroscopy can be used to study the optical properties of the system where the electromagnetic field is strong enough to excite the electrons.


During the past decades there have been promising strides towards simulation of spectroscopic parameters based on first-principles calculations and the theoretical foundations for spectroscopy simulations, such as infrared, Raman, nuclear magnetic resonance, ultraviolet-visible, are well established. Direct comparison of the theoretically predicted results with the spectroscopy measurements could not only validate the theoretical results but could also help with deciphering the experimentally observed spectra at an atomistic level.


For theoretical simulations to be more comparable to experiments, electronic structure of the system as well as the finite-temperature effects should be taken into account. In our studies, we commonly simulate vibrational and nuclear magnetic resonance spectra, in which the finite temperature effects are included via performing molecular dynamics simulations and the forces are calculated at DFT level. In particular, for Raman spectroscopy simulations, we use our newly developed method called Wannier polarizability,[8,9] in which the polarizability of the system during an AIMD simulation is computed as a function of total Wannier volume of the system. As such, polarizability of the system and hence the (non-resonance polarized) Raman spectra could be computed considerably faster compared to other methods, for example finite-differences or perturbation theory.

References

[1] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

[2] Erich Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).

[3] J. VandeVondele, M. Krack, F. Mohamed, et al., Comput. Phys. Commun. 167, 103 (2005).

[4] J. VandeVondele and J. Hutter, J. Chem. Phys. 127, 114105 (2007).

[5] F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2, 73 (2012).

[6] F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1327 (2018).

[7] M. Valiev, E.J. Bylaska, N. Govind, et al., Comput. Phys. Commun. 181, 1477 (2010).

[8] P. Partovi-Azar and T.D. Kühne, J. Comput. Chem. 36, 2188 (2015).

[9] P. Partovi-Azar, T.D. Kühne, and P. Kaghazchi, Phys. Chem. Chem. Phys. 17, 22009 (2015).

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Updated: Nov. 2020