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The development and first applications of a new periodic energy decomposition analysis (pEDA) scheme for extended systems based on the Kohn-Sham approach to density functional theory are described. The pEDA decomposes the bonding energy between two fragments (e.g., the adsorption energy of a molecule on a surface) into several well-defined terms: preparation, electrostatic, Pauli repulsion, and orbital relaxation energies. This is complemented by consideration of dispersion interactions via a pairwise scheme. One major extension toward a previous implementation [Philipsen and Baerends, J. Phys. Chem. B , 12470 (2006)] lies in the separate discussion of electrostatic and Pauli and the addition of a dispersion term. The pEDA presented here for an implementation based on atomic orbitals can handle restricted and unrestricted fragments for 0D to 3D systems considering periodic boundary conditions with and without the determination of fragment occupations. For the latter case, reciprocal space sampling is enabled. The new method gives comparable results to established schemes for molecular systems and shows good convergence with respect to the basis set (TZ2P), the integration accuracy, and k-space sampling. Four typical bonding scenarios for surface-adsorbate complexes were chosen to highlight the performance of the method representing insulating (CO on MgO(001)), metallic (H on M(001), M = Pd, Cu), and semiconducting (CO and CH on Si(001)) substrates. These examples cover diverse substrates as well as bonding scenarios ranging from weakly interacting to covalent (shared electron and donor acceptor) bonding. The results presented lend confidence that the pEDA will be a powerful tool for the analysis of surface-adsorbate bonding in the future, enabling the transfer of concepts like ionic and covalent bonding, donor-acceptor interaction, steric repulsion, and others to extended systems.


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