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WIREs Comput Mol Sci
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Deriving bonding concepts for molecules, surfaces, and solids with energy decomposition analysis for extended systems

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Chemical bonding concepts like covalency, ionicity, Pauli repulsion, shared‐electron, or donor–acceptor bonding are important tools to sort our vast knowledge in chemistry and predict new reactivity. Electronic structure analysis provides the basis for a detailed understanding of the origins of these concepts. Energy decomposition analysis (EDA) is an established method for molecules and has recently been implemented for application in extended systems, that is, surfaces and solids, where it is termed periodic EDA (pEDA). The foundations and applications of this method which enables the derivation of bonding concepts are outlined in this review. Embedded in key examples from molecular and solid‐state chemistry, the major part covers the adsorption and reactivity of molecules with surfaces with a focus on organic molecules interacting with semiconductor surfaces. Based on electronic structure analysis and supported by a quantitative methodology, we show that analogous bonding concepts can be applied in diverse chemical environments.

This article is categorized under:

  • Electronic Structure Theory > Ab Initio Electronic Structure Methods
  • Structure and Mechanism > Computational Materials Science
Schematic description of the steps in the energy decomposition analysis of a chemical bond between two fragments A and B forming an entity AB. (Reprinted with permission from Reference . Copyright 2015 AIP Publishing)
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(a,b) Projected crystal orbital Hamilton population (pCOHP) for the M‐Bi bonds and integrated value (IpCOHP) in (a) [CuBi2I12]4− and (b) [AgBi2I12]4−. (c,d) Corresponding density of states (DOS) with partial DOS (pDOS) for Cu or Ag and Bi with and without (nr‐pDOS) spin–orbit coupling. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Optimized (PBE‐D3) structures of (a) a reference slab with an ethylene precoverage of θ = 3/4 and (b) an additional molecule in the datively bonded mode (see also Scheme c). (Reprinted with permission from Reference . Copyright 2017 John Wiley and Sons)
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Schematic depiction of the bonding situation (a), optimized (PBE‐D3) structure (b) and periodic energy decomposition analysis (pEDA) deformation densities (c–e) of the CO/TiO2(110) system in a (2 × 2) super cell. Red: Depletion of electron density, blue: accumulation of electron density. Energies ΔE i in kJ/mol, eigenvalues v i in q e. (Reprinted with permission from Reference . Copyright 2015 Philipps‐Universität Marburg)
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(a) Schematic representation of the H2/M(001) (M = Cu, Pd) system and the reaction coordinates used in this study. (b–d) Change of periodic energy decomposition analysis (pEDA) terms along d(M‐H2): absolute values (c,d) and differences (b). (Reprinted with permission from Reference . Copyright 2015 AIP Publishing)
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Optimized (PBE‐D3) structures of the sublayer mode in the systems acetylene/Si(001) (a) and ethylene/Si(001) (b). Interatomic distances given in Å, Ebond values in kJ/mol. (Reprinted with permission from Reference . Copyright 2018 MDPI)
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Lewis (top) and optimized (PBE‐D3) structures (bottom) of the on‐top (a), datively bonded (b) and combined (c) modes of 5‐ethoxymethyl‐5‐methyl‐cyclooctyne (EMC) on Si(001). Ebond values given in kJ/mol. (Reprinted with permission from Reference . Copyright 2018 Springer Nature)
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Optimized (PBE‐D3) structures of the on‐top (a) and pedestal (b) modes of cyclooctyne on Si(001). Bond lengths given in Å, Ebond values in kJ/mol. (Reprinted with permission from Reference . Copyright 2017 John Wiley and Sons)
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Selected periodic energy decomposition analysis (pEDA) deformation densities Δρ i showing dative bonding (DB) in the systems THF/Si(001) (a) and ethylene/Si(001) (b) and the nucleophilic attack of a surface atom in the system THF/Si(001) at a transition state (TS) structure. (c) Red: Depletion of electron density, blue: accumulation of electron density. Energies ΔE i in kJ/mol, eigenvalues v i in q e. (Reprinted with permission from References (a,c) and (b). Copyright 2017 John Wiley and Sons)
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Dative bonding (a–c) and [2 + 2] cycloadducts (d,e) of molecules on Si(001): ammonia (a), THF (b), ethylene (c,d), acetylene (e)
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(a) Schematic depiction of the Si(001) surface reconstruction process. Dots indicate unpaired electrons. (b) Structure of Si(001) in the most stable reconstruction, c(4 × 2), with nomenclature used subsequently. (c) Crystal orbitals (at the Γ point in k space) of a Si(001) slab corresponding to the dimer states, calculated at PBE‐D3/TZ2P. (Reprinted with permission from Reference . Copyright 2018 MDPI)
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Restricted potential energy (rPES) curves for pitching (red) and yawing (blue) of IBioxMe4 in cis‐[M(IBioxMe4)(CO)2Cl] with M = Rh, Ir. Solid lines represent polynomial fits. (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Chronology of the reaction steps in β‐H elimination reactions for E(t‐(C4H9)H2) with (a) E = P–Bi and (b) E = Ga. Electron shifts (bent arrows) and bond length elongations (straight arrows) before (1.) and after (2.) the transition state (TS) are highlighted. (c) Δρ1β − α for the TS shown in (a) by energy decomposition analysis‐natural orbitals for chemical valence (EDA‐NOCV) analysis with neutral fragments. Red: Depletion of electron density, blue: accumulation of electron density. (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Structure and Mechanism > Computational Materials Science
Electronic Structure Theory > Ab Initio Electronic Structure Methods

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