Seite - 21 - in Charge Transport in DNA - Insights from Simulations

2.3QuantumChemistry of the kinetic energy canmakeDFT basedmethods very slow. Therefore, in the following section an approximative DFT method is introduced, which is able to describe systemsof relevant sizesonaquantummechanical levelmore efficiently. 2.3.2 ApproximativeDFT–Density-FunctionalTight-Binding Nowadays, DFT iswidely used for the calculation of properties ofmolecular sys- temsofup tohundredsof atoms. OnedisadvantageofDFT is the largeamountof computational time needed for the evaluation of integrals during runtime. Espe- ciallywhen calculating electronic structures alongMD trajectories, DFT becomes too expensive in computational cost. To avoid this issue, there are many semi- empiricalapproaches,whichachievehighercomputationalefficiencybyneglecting contributions deemed insignificant or parameterizing integrals in advance. One way toachieve this ispresented in the following [65]. Density-functional tight-binding (DFTB) is based on aminimal basis set, thus de- scribingonlythevalenceelectronsofatoms,while the innerelectronsare treatedby two-center potentials. Thereby, crystal-field and three-center terms are neglected. The two-center Hamiltonian and overlap matrix elements are tabulated for dis- tances of up to a reasonable threshold. Thisway, none of the integrals have to be computed at runtime. Rather, they are interpolated for the current distance be- tween the atoms. Finally, the DFT double-counting terms are included into the repulsive energy term. This term is pre-calculated and tabulated aswell. In the parametrization, thevalues for the repulsive energyare calculated fromthediffer- enceof theenergycalculatedwithDFTandthetight-bindingelectronicatomization energy for chosen representativemolecules. With these parametrizationsDFTB is up to3ordersofmagnitude faster thanDFT. The startingpoint forDFTB is to construct a referencedensity ρ0 froma superpo- sitionofdensities calculatedon isolatedatoms. ρ0=∑ α ρα (2.19) 21