# Martin Mistrík defended his master thesis, Congratulations!

Topic: Fractional Charge Modeling in Atoms

Abstract: The basic goal of this work is modeling of fractional charge and the associated study of the change in energy depending on the fractional charge and charge delocalization with using the DFT (B3LYP), DFT (PBE) and HF methods with

the basis 6-31++G(d,p), on specific low-spin models 8 H, 8 O and high-spin models 8 H, 8 O and 8 Fe composed of 8 atoms of the same element H, O, and, Fe, at least 1000 ̊A apart. The final results of the 8 H, 8 O and 8Fe models point to the failure of the DFT and HF methods in describing the fractional charge obtained from the convex or concave course of the function in a graph of total energy per atom versus number of electrons per atom. One of the parts of this work includes a demonstration of the fractional charge problem on the examples of the molecule FHand ion F−calculated separately in their own systems and together in one system,where they are 1000 ̊A apart. Calculations of the FH molecule and the F−ion by the DFT(B3LYP), DFT(PBE) and HF methods with a basis 6-31++G(d,p) separately and together led to results which indicate different energy values for individual methods. For the possible use of the results from this work, the possible applications of the obtained values from model 8H for the correction of the calculated energy on the model molecule H+2are presented. On the model molecule H+2it was possible to present way of correction by subtraction energy from the results of total energy calculated by DFT (B3LYP) and DFT (PBE), linear connection of boundary points of total energy function and exact solution. The results obtained thanks to this work can be further used for the development and correction of the DFT method when used in the calculations of many chemical reactions, which provide erroneous energy results depending on the fractional charge due to the error of charge delocalization.