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Aim of this work was the development, implementation and application of an energy decomposition analysis (EDA), which is capable of characterizing chemical bonds for extended systems. Here, the interaction energy, which is equal to the energy difference between separated fragments and a relaxed, extended system, is decomposed into well-defined terms for the Pauli repulsion, the Coulomb interaction, the orbital relaxation term and the dispersion interaction term. Hence, the new method mimics the EDA for molecules, developed by Ziegler and Rauk. Theirs scheme was extended by Mitoraj et al. by combining the natural orbitals of chemical valency (NOCV) method with the EDA. (EDANOCV) Thereby, the charge flow between fragments, due to the orbital relaxation, is decomposed into smaller parts, which allow for a detailed investigation of strength and character of covalent bonding contributions. Furthermore, Parafiniuk and Mitoraj developed the natural orbitals for the Pauli repulsion (NOPR) analysis, which allows for the decomposition of charge flow between fragments due to the Pauli repulsion. Within this work the scope of these three methods was enhanced to extended systems, approximated with periodic boundary conditions (PBC), and shall be referred to as periodic EDA (pEDA), periodic EDANOCV (pEDANOCV) and periodic EDANOPR (pEDANOPR). Hence, a detailed analysis of chemical bonding for surface and bulk structures is now possible. It shall be mentioned that the pEDA can be performed for calculations using an arbitrary number of sampling points in reciprocal space, while the pEDANOCV and pEDANOPR allow only for one k-point - the Gamma point.
The new methods were applied to various molecular and extended systems to verify that the results are reasonable. Thereby, shared electron bonding and donor acceptor interactions were investigated for molecular test systems. Here, main group element compounds and transition metal complexes were involved. As extended test systems the interaction of organic and inorganic molecular fragments adsorbed on metallic, semi-conducting and non-conducting surfaces were investigated. Whenever possible, the results of the PBC calculations were compared to cluster approach studies. Here, the results of the new methods are comparable to those of cluster studies. For systems, which need well described periodic potentials and electron densities, the new methods gave more reasonable results.
For compounds, described reasonably only by the Gamma point in reciprocal space, the pEDANOCV allows to decompose the orbital relaxation term into its contributions. Hence, the discussion of covalent bonding with respect to symmetric contributions like sigma- and pi-like bonding is enabled. Not only is the visualisation of charge density transfer between fragments possible, but the association with an energy value and a NOCV eigenvalue, too. The latter is describing the amount of transferred charge.
The pEDANOPR allows for the decomposition of a charge density flow induced by the Pauli repulsion. Hence, the visualisation of the charge transfer, the association with an energy value and a NOPR eigenvalue is possible.
In contrast to the EDA, EDANOCV and NOPR, the new methods can rely on spin-polarised and spin-unrestricted fragment wavefunctions. Thereby, the description of shared electron bonds does not involve the introduction of an additional approximation by depending on spin-restricted fragment wavefunctions.
For selected, extended system the transfer of chemical bonding concepts was presented. Hence, the Dewar-Chatt-Duncanson modell, hyperconjugation and spacer separated donor acceptor interaction can now be applied to bonding interactions between molecular fragments and infinite surfaces.