[1] Kubillus, M.; Kubar, T.; Gaus, M.; Rezac, J.; Elstner, M. J. Chem. Theory Comput. 2015, 10.1021/ct5009137

To avoid computing integrals on runtime Density Functional Tight Binding (DFTB) uses optimized wave function and electron densities for each atom and tabulates neccessary integrals pair-wise for several distances. Energy functional terms that cannot be obtained by solving Kohn-Sham equations are described by a set of repulsive splines. Modern models of DFTB (DFTB2 [1] or DFTB3 [2]) make use of the Self-Consistent Charge (SCC) concept that modifies the reference density in hindsight. Here we use the so-called monopole approximation which describes transferred charge between to atoms through spheres around the nucleus. In DFTB3 the DFT energy is approximated via a taylor expansion to the third order, in DFTB2 only to the second order. On that basis it is possible to simulatie and predict molecular structures and energies. Generally these properties are calculated with sufficient accuracy which makes it an important tool in biological research with a broad field of applications [3].

Still, there is need for further extension of the DFTB formalism. Intermolecular interactions of closed shell molecules is one of the most important phenomena in biological processes. The weak bond between two DNA base pairs or the formation of tertiary and quaternary structures in proteins as well as the molecular recognition of receptors and enzymes are only the most prominent features. Sadly, DFTB underestimates every single one of the attractive interactions. In extreme cases such as DNA base pairs it even shows repulsive behaviour [4], similar to many Generalised Gradient Approximation (GGA) DFT functionals. Therefore Elstner et. al. suggested a correction for London-Dispersion interactions on the basis of polarizabilities of atoms [4]. Still, this is not enough to describe the influence of fractional charges and steric effects between molecules. On the other hand it has been shown by the example of water that hydrogen bonds are overestimated which then again leads to the overcoordination of water in simulations, even leading to the formation of voids [5, 6]. Specifically for water there are empirical corrections currently in development, although the search for an general extension of the formalism continues that can improve upon both the water model and the descriptions of dispersion interactions in DFTB.

Another shortcoming in DFTB is the gross underestimation of intramolecular rotational barriers. Those are critical in the description of protein folding and similar conformational changes in biomolecules like DNA or membranes. The non-empirical functional, found by Perdew, Burke and Ernzerhof [7], that serves as the basis for all calculation of Hamiltonian matrix elements in DFTB, shows a distinct overestimation of rotational barriers. Also, the use of minimal basis sets used for the better part of atoms in DFTB leads to even more severe errors since the correct description of Pauli-Repulsion in DFTB requires virtual orbitals. But the inclusion of polarization functions is an undesired solution of the problem since the computational efficiency suffers with increasing size of the Hamiltonian. Hence my work as a PhD candidate focuses on the research of corrections for those shortcomings of DFTB, especially in biochemical systems.

Special areas of DFTB that can benefit from those new corrections are:

  - Van-der-Waals complexes: A better description of sterical interaction as well as the influence of atomic charges on the structure and energetics of these biologically very important, weakly bound complexes is expected and one main goal of this research project.

  - Charged supramolecular complexes: Coordination of (de-)protonated water or solvated ions is a challenge for DFTB. At the same time the satisfying description of structures and binding energies compromise each other. Implementation of a extension to DFTB hamilton matrix elements (the so-called on-site integrals) from the research group of Prof. Dr. Thomas Niehaus (website: link below) shows that these complexes can be reproduced with comparable accuracy without the empirical "Gamma H" function. The charge correction can further improve upon those findings.

  - Water model: The already mentioned correction to the long-range Pauli repulsion should be able to prevent the overcoordination of water and stop the appearance of voids. That way not only the biomolecules will be represented correctly in DFTB but their  enironment, too.

  - Rotational barriers: Protein folding and similar conformational changes during a simulation should me described correctly. A basis set correction for missing polarisation functions will add the missing Pauli repulsion and improve upon rotational barriers.

  - Angle-dependend potential surfaces: Alkaline metal complexes are not reproduced with sufficient accuracy in DFTB. This is another failure which originates in the usage of a minimal basis sets. This will be compensated by the the correct spatial charge representation and dipole interaction via the multipole extension.

  - Reactions: Some classes of reactions, e.g. proton transfer barriers, are not sufficiently described in DFTB. The on-site integrals are very promising candidates to solve these problems.

After implementation as well as thorough testing and parameterising of these extensions in popular DFTB codes a completely new parameterisation of all these elements with new methods, developed by the research group of Prof. Dr. Henryk Witek (website: below), will be performed. These methods solves an old problem in DFTB that leads to a conflict between reproducing energies or vibrational frequencies. A first goal here will be the elements hydrogen, carbon, nitrogen, oxygen, fluorine, phosphorous, sulfur and chlorine.

Prof. Dr. Thomas Niehaus, electron dynamics in complex systems:

http://www.physik.uni-regensburg.de/forschung/niehaus/index.html

Prof. Dr. Henryk Witek, Quantum and Computational Chemistry, Applied Linear Algebra,

Perturbation Theory: http://imols.nctu.edu.tw/people/bio.php?PID=44

[1] M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai, and G. Seifert Phys. Rev. B 58 (1998) 7260.

[2] M. Gaus, Q. Cui, and M. Elstner J. Chem. Theory Comput. 7 no. 4, (2011) 931.

[3] M. Elstner Theor. Chem. Acc. 116 (2006) 316.

[4] M. Elstner, P. Hobza, T. Frauenheim, S. Suhai, and E. Kaxiras J. Chem. Phys. 114 (2001) 5149.

[5] T. H. Choi, R. Liang, C. M. Maupin, and G. A. Voth J. Phys. Chem. B 117 (2013) 5165.

[6] P. Goyal, M. Elstner, and Q. Cui J. Phys. Chem. B 115 (2011) 6790.

[7] J. P. Perdew, K. Burke, and M. Ernzerhof Phys. Rev. Lett. 77 (1996) 3865.