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Energy decomposition analysis

Advanced Review

Gernot Frenking, Diego M. Andrada, Moritz von Hopffgarten, Lili Zhao

Published Online: Nov 10 2017

DOI: 10.1002/wcms.1345

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The energy decomposition analysis (EDA) is a powerful method for a quantitative interpretation of chemical bonds in terms of three major components. The instantaneous interaction energy ΔEint between two fragments A and B in a molecule A–B is partitioned in three terms, namely (1) the quasiclassical electrostatic interaction ΔEelstat between the fragments; (2) the repulsive exchange (Pauli) interaction ΔEPauli between electrons of the two fragments having the same spin, and (3) the orbital (covalent) interaction ΔEorb which comes from the orbital relaxation and the orbital mixing between the fragments. The latter term can be decomposed into contributions of orbitals with different symmetry which makes it possible to distinguish between σ, π, and δ bonding. After a short introduction into the theoretical background of the EDA we present illustrative examples of main group and transition metal chemistry. The results show that the EDA terms can be interpreted in chemically meaningful way thus providing a bridge between quantum chemical calculations and heuristic bonding models of traditional chemistry. The extension to the EDA–Natural Orbitals for Chemical Valence (NOCV) method makes it possible to breakdown the orbital term ΔEorb into pairwise orbital contributions of the interacting fragments. The method provides a bridge between MO correlations diagrams and pairwise orbital interactions, which have been shown in the past to correlate with the structures and reactivities of molecules. There is a link between frontier orbital theory and orbital symmetry rules and the quantitative charge‐ and energy partitioning scheme that is provided by the EDA–NOCV terms. The strength of the pairwise orbital interactions can quantitatively be estimated and the associated change in the electronic structure can be visualized by plotting the deformation densities. This article is categorized under: Structure and Mechanism > Molecular Structures Electronic Structure Theory > Density Functional Theory Computer and Information Science > Visualization

Fragments which are used for the EDA (a) of benzene and (b) 1,3,5,7‐octatetraene. D, doublet; OS, open shell singlet.

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Breakdown of the actual donor orbital Ψ₂ and acceptor orbital Ψ₋₂ that are associated with the deformation density Δρ(2) in the transition state for H₂ addition to the amido digermyne 1Ge into the most important MOs of the fragments. The mixing coefficients that are given in parentheses show that the donor orbital Ψ₁ is mainly composed of the HOMO of 1Ge and the acceptor orbital Ψ₋₁ is mainly composed of the LUMO of H₂. The contributions of further three MOs of the fragments are much smaller.

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Breakdown of the actual donor orbital Ψ₁ and acceptor orbital Ψ₋₁ that are associated with the deformation density Δρ(1) in the transition state for H₂ addition to the amido digermyne 1Ge into the most important MOs of the fragments. The mixing coefficients that are given in parentheses show that the donor orbital Ψ₁ is mainly composed of the HOMO of H₂ and the acceptor orbital Ψ₋₁ is mainly composed of the LUMO of 1Ge. The contributions of further four MOs of the fragments are much smaller.

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Top: Calculated transition state for H₂ addition to the amido digermyne 1Ge. Middle row: Schematic representation of the orbital interaction between the σ(H₂) MO and the LUMO of 1Ge. Shape of the HOMO of H₂ and LUMO of 1Ge. Plot of the deformation density Δρ(1) which is associated with the strongest orbital interaction ΔE₁ between H₂ and 1Ge in the transition state. Bottom row: Schematic representation of the orbital interaction between the HOMO of 1Ge and the σ(H₂)* MO of H₂. Shape of the HOMO of HOMO of 1Ge and LUMO of H₂. Plot of the deformation density Δρ(2) which is associated with the second strongest orbital interaction ΔE₂ between H₂ and 1Ge in the transition state. The color code for the charge flow is red→blue. Figure taken from Ref 177.

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First column: Plot of the deformation densities Δρ_1–4 with associated stabilization energies ΔE_1–4 of the four most important orbital interactions in B₂(NHC^Me)₂. The color code for the charge flow is red→light blue. Third and fourth column: Plot of the interacting donor and acceptor orbitals and calculated eigenvalues ε of (NHC^Me)₂ and (¹Σ_g⁺) B₂. Second column: Resulting MOs of the complex B₂(NHC^Me)₂. Figure taken from Ref 172.

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(a) Calculated geometry at BP86/TZVPP of the complex B₂(NHC^Me)₂ with the most important bond lengths in Å. Experimental values of the analogous complex B₂(NHC^Dip)₂ are shown in parentheses. Schematic MO diagram of B₂ in (b) the X³Σ_g⁻ ground state; (c) (3)¹Σ_g⁺ excited state. (d) Schematic view of out‐of‐phase (+,−) and in‐phase (+,+) σ donation of the ligand orbitals into the vacant 1σ_u und 2σ_g MOs of B₂. (e) Calculated excitation energy ΔE for X³Σ_g⁻→(3)¹Σ_g⁺ of B₂ and bond dissociation energy D_e of B₂(NHC^Me)₂. Figure taken from Ref 172.

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Plot of the deformation densities Δρ of the most important orbital interactions in (a) C(PPh₃)₂ and (b) C(NHC^Me)₂ between C in the excited¹D electronic reference state and the ligands L₂ in the frozen geometry of the molecule. Associated stabilization energies ΔE₁ − ΔE₃ are given in kcal/mol (see also Table ). The eigenvalues |υ₁| − |υ₃| indicate the size of the charge deformation. The color code of the charge flow is red→blue. Figure taken from Ref 161.

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Sketch of the bonding situation in carbones CL₂. (a) Lewis structure. (b) Donation of the lone pair electrons of L into vacant orbitals of carbon. The in‐phase(+,+) combination of the lone‐pair electrons donates charge into the sp.‐hybridized σ‐AO of C while the out‐of‐phase (+,−) combination of the lone‐pairs donates charge into the 2p_π║ AO of carbon.

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(a)–(d). Plot of deformation densities Δρ₁−Δρ₄ (isocontour 0.003 a.u.) of the pairwise orbital interactions in [B(CO)₂]⁻ together with the associated interaction energies ΔE_n and charge eigenvalues |υ_n| (in e). The charge flow is red→blue. The charge eigenvalues υ give the amount of donated/accepted electronic charge. (e) Schematic representation of the orbitals involved in the OC→B⁽⁻⁾←CO σ donation and the OC←B⁽⁻⁾→CO π‐backdonation. Only one component of the latter is shown. Figure taken from Ref 142.

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Plot of deformation densities Δρ of the pairwise orbital interactions and the associated interaction energies ΔE_orb between CO and BeO moieties in OCBeO and OCBeCO₃. The direction of the charge flow is red→blue. (a) σ donation OC→BeO. (b) and (c) π backdonation OC←BeO. (d) σ donation OC→BeCO₃. (e) and (f) π backdonation OC←BeCO₃. Figure taken from Ref 98.

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Optimized geometries at M06‐2X/def2‐TZVPP, MP2/cc‐pVTZ (in parentheses) and CCSD(T)/cc‐pVTZ [in brackets]. The bond lengths and angles are in [Å] and [°], respectively. Calculated bond dissociation energies (D_e) for the C─Be and O─Be bond are given in kcal/mol. Theoretical CCSD(T)/cc‐pVTZ (and experimental) stretching frequencies ν(C─O) and their shift Δν(C─O) wrt free CO (cm⁻¹). Figure taken from Ref 98.

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Schematic representation of the six sd⁵ hybrid orbitals. Figure taken from Ref 87.

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MO correlation diagram between Mo and (ZnH)₁₂ in [Mo(ZnH)₁₂]. Each fragment in its septet state. Figure taken from Ref 11.

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X‐ray structure of [Mo(ZnCp*)₃(ZnMe)₁₂]. Mo red, Zn green, C gray. Figure taken from Ref 87.

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MO correlation diagram between a d⁸ transition metal with the electronic configuration (a_1g)²(e_2g)⁶(e_1g)⁰ and a cyclic 12π aromatic sandwich ligand. Shapes of the orbitals have been taken from the Bz₂ ligand. The orbitals of (Cp₂)²⁻ look very similar. Figure taken from Ref 78.

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(a) Schematic representation of the tautomers ‘normal’ N‐heterocyclic carbene (nNHC), ‘abnormal’ N‐heterocyclic carbene (aNHC) and imidazol (IMID). (b) Schematic representation of the complexes of the above ligands with W(CO)₅.

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Schematic representations of interactions according to the Dewar–Chatt–Duncanson model. (a) and (b): σ donation and π‐back donation in an interaction between a transition metal (TM) and a carbonyl (CO); (c) and (d): σ donation and π backdonation in an interaction between a TM and a C─C double‐ or triple bond; (e) and (f): additional possible contributions of π donation and δ backdonation in the interaction between a TM and a C─C‐triple bond; (g) and (h): σ donation and π backdonation in singlet carbene complexes.

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(a) Equilibrium geometries of benzene and cyclobutadiene and distorted geometries which were used in the EDA calculations in Ref 65. (b) Schematic representation of the two fragments (colored in red and blue) which were used for the EDA calculations in Ref 65.

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References

Heitler, W, London, F. Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik 1927, 44:455–472.
Several essays and opinions on the role of chemical models in chemical science have been published recently, e.g.WHE, S. Chemical bonding: state of the art in conceptual quantum chemistry. An introduction. Theor Chem Acc 2001, 105:271–275.
Shaik, S. Is my chemical universe localized or delocalized? Is there a future for chemical concepts? New J Chem 2007, 31:2105–2028.
Frenking, G, Krapp, A. Unicorns in the world of chemical bonding models. J Comput Chem 2007, 28:15–24.
Lewis, GN. The atom and the molecule. J Am Chem Soc 1916, 38:762–785.
A discussion of the impact and importance of the work of G. N. Lewis to the theory of chemistry is presented in a special issue edited by Frenking, G, Shaik, S. 90 years of chemical bonding. J Comput Chem 2007, 28:1–3.
Pauling, L. The nature of the chemical bond and the structure of molecules and crystals. 3rd ed. Ithaca, NY: Cornell University Press; 1960.
Morokuma, K. Molecular orbital studies of hydrogen bonds. J Chem Phys 1971, 55:1236–1244.
Ziegler, T, Rauk, A. On the calculation of bonding energies by the Hartree Fock Slater method. Theor Chim Acta 1977, 46:1–10.
Bader, RFW. Atoms in Molecules. A Quantum Theory. Oxford, UK: Oxford University Press; 1990.
Frenking, G, von Hopffgarten, M. Calculation of bonding properties. In: Solomon, EI, Scott, RA, King, RB, eds. Computational Inorganic and Bioinorganic Chemistry. New York: John Wiley %26 Sons; 2009, 3–16.
Mitoraj, M, Michalak, A. Natural orbitals for chemical valence as descriptors of chemical bonding in transition metal complexes. J Mol Model 2007, 13:347–355.
Mitoraj, MP, Michalak, A, Ziegler, T. A combined change and energy decomposition scheme for bond analysis. J Chem Theory Comput 2009, 5:962–975.
Fukui, K. Theory of Orientation and Stereoselection. Berlin: Springer Verlag; 1975.
Woodward, RB, Hoffmann, R. The Conservation of Orbital Symmetry. Verlag Chemie: Weinheim; 1970.
Mo, YR, Peyerimhoff, SD. Theoretical analysis of electronic delocalization. J Chem Phys 1998, 109:1687–1697.
Mo, YR, Gao, JL, Peyerimhoff, SD. Energy decomposition analysis of intermolecular interactions using a block‐localized wave function approach. J Chem Phys 2000, 112:5530–5538.
Mo, YR. Geometrical optimization for strictly localized structures. J Chem Phys 2003, 119:1300–1306.
Mo, YR. Intramolecular electron transfer: computational study based on the orbital deletion procedure (ODP). Curr Org Chem 2006, 10:779–790.
Mo, Y. The block‐localized wavefunction (BLW) perspective of chemical bonding. In: Frenking, G, Shaik, S, eds. The Chemical Bond 1. Fundamental Ascpects of Chemical Bonding. Weinheim: Wiley‐VCH; 2014, 199–232.
Cardozo, TM, Chaer Nascimento, MA. Energy partitioning for generalized product functions: The interference contribution to the energy of generalized valence bond and spin coupled wave functions. J Chem Phys 2009, 130:104102.
Cardozo, TM, Nascimento, MAC. Chemical bonding in the N2 molecule and the role of the quantum mechanical interference effect. Journal of Physical Chemistry A 2009, 113:12541–12548.
de Sousa, DWO, Nascimento, MACI. There a quadruple bond in C₂? J Chem Theory Comput 2016, 12:2234–2241.
Mo, Y, Song, L, Lin, Y. Block‐localized wavefunction (BLW) method at the density functional theory (DFT) level. J Phys Chem A 2007, 111:8291–8301.
Blanco, MA, Martín Pendás, A, Francisco, E. Interacting quantum atoms: a correlated energy decomposition scheme based on the quantum theory of atoms in molecules. J Chem Theory Comput 2005, 1:1096–1109.
Pendás, AM, Blanco, MA, Francisco, E. Chemical fragments in real space: definitions, properties, and energetic decompositions. J Comput Chem 2007, 28:161–184.
Pendás, AM, Blanco, MA, Francisco, E. Steric repulsions, rotation barriers, and stereoelectronic effects: a real space perspective. J Comput Chem 2009, 30:98–109.
García‐Revilla, M, Francisco, E, Popelier, PLA, Martín Pendás, A. Domain‐averaged exchange‐correlation energies as a physical underpinning for chemical graphs. ChemPhysChem 2013, 14:1211–1218.
Maxwell, P, Martin Pendas, A, Popelier, PLA. Extension of the interacting quantum atoms (IQA) approach to B3LYP level density functional theory (DFT). Phys Chem Chem Phys 2016, 18:20986–21000.
Khaliullin, RZ, Head‐Gordon, M, Bell, AT. An efficient self‐consistent field method for large systems of weakly interacting components. J Chem Phys 2006, 124:204105‐1–204105‐11.
Khaliullin, RZ, Cobar, EA, Lochan, RC, Bell, AT, Head‐Gordon, M. Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals. J Phys Chem A 2007, 111:8753–8765.
Horn, PR, Mao, Y, Head‐Gordon, M. Probing non‐covalent interactions with a second generation energy decomposition analysis using absolutely localized molecular orbitals. Phys Chem Chem Phys 2016, 18:23067–23079.
Thirman, J, Head‐Gordon, M. Efficient implementation of energy decomposition analysis for second‐order Møller–Plesset perturbation theory and application to anion−π interactions. Chem A Eur J 2017, 121:717–728.
Horn, PR, Sundstrom, EJ, Baker, TA, Head‐Gordon, M. Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: theory and applications to intermolecular interactions involving radicals. J Chem Phys 2013, 138:134119.
Horn, PR, Head‐Gordon, M. Polarization contributions to intermolecular interactions revisited with fragment electric‐field response functions. J Chem Phys 2015, 143:114111.
Levine, DS, Horn, PR, Mao, Y, Head‐Gordon, M. Variational energy decomposition analysis of chemical bonding. 1. Spin‐pure analysis of single bonds. J Chem Theory Comput 2016, 12:4812–4820.
Azar, RJ, Horn, PR, Sundstrom, EJ, Head‐Gordon, M. Useful lower limits to polarization contributions to intermolecular interactions using a minimal basis of localized orthogonal orbitals: theory and analysis of the water dimer. J Chem Phys 2013, 138:084102.
Bitter, T, Ruedenberg, K, Schwarz, WHE. Toward a physical understanding of electron‐sharing two‐center bonds. I. General aspects. J Comput Chem 2007, 28:411–422.
Bitter, T, Wang, SG, Ruedenberg, K, Schwarz, WHE. Toward a physical understanding of electron‐sharing two‐center bonds. II. Pseudo‐potential based analysis of diatomic molecules. Theor Chem Acc 2010, 127:237–257.
Schmidt, MW, Ivanic, J, Ruedenberg, K. The physical origin of the chemical bond. In: Frenking, G, Shaik, S, eds. The Chemical Bond. 1. Fundamental Aspects of Chemical Bonding. Weinheim: Wiley‐VCH; 2014, 1–67.
Bickelhaupt, FM, Baerends, EJ. Kohn Sham density functional theory: predicting and understanding chemistry. In: Lipkowitz, KB, Boyd, BD, eds. Reviews in Computational Chemistry, vol. 15. New York: Wiley‐VCH; 2000, 1–86.
Wagner, JP, Schreiner, PR. London dispersion in molecular chemistry—reconsidering steric effects. Angew Chem Int Ed 2015, 54:12274–12296.
Grimme, S. Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem 2004, 25:1463–1473.
Grimme, S. Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction. J Comput Chem 2006, 27:1787–1799.
Esterhuysen, C, Frenking, G. The nature of the chemical bond revisited: An energy decomposition analysis of diatomic molecules E₂ (E=N‐Bi, F‐I), CO and BF. Theor Chem Acc 2004, 111:381–389.
Kovács, A, Esterhuysen, C, Frenking, G. The nature of the chemical bond revisited: an energy partitioning analysis of nonpolar bonds. Chem – A Eur J 2005, 11:1813–1823.
Krapp, A, Bickelhaupt, FM, Frenking, G. Orbital overlap and chemical bonding. Chem – A Eur J 2006, 12:9196–9216.
Spackman, MA, Maslen, EN. Chemical properties from the promolecule. J Phys Chem 1986, 90:2020–2027.
Loschen, C, Voigt, K, Frunzke, J, Diefenbach, A, Diedenhofen, M, Frenking, G. Quantum chemical investigations of the phosphane complexes X₃B‐PY₃ and X₃Al‐PY₃ (X = H, F, Cl; Y = F, Cl, Me, CN). Zeitschrift für anorganische und allgemeine Chemie 2002, 628:1294–1304.
Bessac, F, Frenking, G. Chemical bonding in phosphane and amine complexes of main group elements and transition metals. Inorg Chem 2003, 42:7990–7994.
Frenking, G, Wichmann, K, Fröhlich, N, Loschen, C, Lein, M, Frunzke, J, Rayón, VM. Towards a rigorously defined quantum chemical analysis of the chemical bond in donor‐acceptor complexes. Coord Chem Rev 2003, 238–239:55–82.
Cappel, D, Tüllmann, S, Krapp, A, Frenking, G. Direct estimate of the conjugative and hyperconjugative stabilization in diynes, dienes and related compounds. Angew Chem Int Ed 2005, 44:3617–3620 Angew Chem 117:3683–3686.
Fernández, I, Frenking, G. Direct estimate of the strength of conjugation and hyperconjugation by the energy decomposition analysis method. Chem A Eur J 2006, 12:3617–3629.
Fernández, I, Frenking, G. Direct estimate of conjugation and aromaticity in cyclic compounds with the EDA method. Faraday Discuss 2007, 135:403–421.
Hückel, E. Quantentheoretische Beiträge zum Benzolproblem. I. Die Elektronenkonfiguration des Benzols und verwandter Verbindungen. Zeitschrift für Physik 1931, 70:204–286.
Hückel, E. Quantentheoretische Beiträge zum Benzolproblem. II. Quantentheorie der induzierten Polaritäten. Zeitschrift für Physik 1931, 72:310–337.
Hückel, E. Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III. Zeitschrift für Physik 1932, 76:628–648.
Hückel, E. Die freien Radikale der organischen Chemie. Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. IV. Zeitschrift für Physik 1933, 83:632–668.
Doering, W v E, Detert, FL. Cycloheptatrienylium oxide. J Am Chem Soc 1951, 73:876–877.
von Ragué Schleyer, P. The theoretical treatment of aromaticity is topic of a special issue entitled “Aromaticity”. Chem Rev 2001, 101:1115–1118.
von Ragué Schleyer, P. for reviews on conjugation and delocalization see the special issue entitled “Delocalization – pi and sigma”. Chem Rev 2005, 105:3433–3435.
See Refs 60, 61 A detailed review on different ways to estimate aromaticity is given in: Mo, Y, von Ragué Schleyer, P. An energetic measure of aromaticity and antiaromaticity based on the Pauling‐Wheland resonance energies. Chem A Eur J 2006, 12:2009–2020.
Thorn, DL, Hoffmann, R. Delocalization in metallocycles. Nouveau J de Chimie 1979, 3:39–45.
Fernández, I, Frenking, G. Aromaticity in Metallabenzenes. Chem A Eur J 2007, 13:5873–5884.
Pierrefixe, SCAH, Bickelhaupt, FM. Aromaticity: molecular‐orbital picture of an intuitive concept. Chem A Eur J 2007, 13:6321–6328.
Pierrefixe, SCAH, Bickelhaupt, FM. Aromaticity and antiaromaticity In 4‐, 6‐, 8‐, and 10‐membered conjugated hydrocarbon rings. J Phys Chem A 2008, 12:12816–12822.
Shaik, SS, Hiberty, PC. When does electronic delocalization become a driving force of molecular shape and stability? 1. The aromatic sextet. J Am Chem Soc 1985, 107:3089–3095.
Diefenbach, A, Bickelhaupt, FM, Frenking, G. The nature of the transition metal‐carbonyl bond and the question about valence orbitals of transition metals. a bond‐energy decomposition analyses of TM(CO)₆^q (TM^q = Hf²⁻, Ta⁻, W, Re⁺, Os²⁺, Ir³⁺). J Am Chem Soc 2000, 122:6449–6458.
Nechaev, MS, Rayòn, VM, Frenking, GF. Energy partitioning analysis of the bonding in ethylene and acetylene complexes of group 6, 8, and 11 metals: (CO)₅TM‐C₂H_x and Cl₄TM‐C₂H_x (TM=Cr, Mo, W), (CO)₄TM‐C₂H_x (TM = Fe, Ru, Os), and TM⁺‐C₂H_x (TM=Cu, Ag, Au). J Phys Chem A 2004, 108:3134–3142.
Tonner, R, Heydenrych, G, Frenking, G. Bonding analysis of N‐heterocyclic carbene tautomers and phosphine ligands in transition metal complexes: a theoretical study. Chem Asian J 2007, 2:1555–1567.
Frenking, G, Wichmann, K, Fröhlich, N, Grobe, J, Golla, W, Van, DL, Krebs, B, Läge, M. Nature of the metal‐ligand bond in M(CO)₅PX₃ complexes (M = Cr, Mo, W; X = H, Me, F, Cl): synthesis, molecular structure, and quantum‐chemical calculations. Organometallics 2002, 21:2921–2930.
Dewar, MJS. A review of the π‐complex‐theory. Bull Soc Chim France 1951, 18C:74–79.
Chatt, J, Duncanson, LA. Olefin co‐ordination compounds. Part III. Infra‐red spectra and structure: attempted preparation of acetylene complexes. J Chem Soc 1953:2939–2947.
Frenking, G. Understanding the nature of the bonding in transition metal complexes: from dewar`s molecular orbital model to an energy partitioning analysis of the metal‐ligand bond. J Organomet Chem 2001, 635:9–23.
Frenking, G. The Dewar‐Chatt‐Duncanson bonding model of transition metal‐olefin complexes examined by modern quantum chemical methods. In: Leigh, GJ, Winterton, N, eds. Modern Coordination Chemistry: The Legacy of Joseph Chatt. London: The Royal Society; 2002, 111.
Heydenrych, G, von Hopffgarten, M, Stander, E, Schuster, O, Raubenheimer, HG, Frenking, G. The nature of the metal‐carbene bond in normal and abnormal pyridylidene, quinolylidene and isoquinolylidene complexes. Eur J Inorg Chem 2009, 2009:1892–1904.
Nemcsok, D, Wichmann, K, Frenking, G. The significance of π interactions in group 11 complexes with N‐heterocyclic carbenes. Organometallics 2004, 23:3640–3646.
Rayón, VM, Frenking, G. Bis(benzene)chromium is a δ‐bonded molecule and ferrocene is a π‐bonded molecule. Organometallics 2003, 22:3304–3308.
Miller, SA, Tebboth, JA, Tremaine, JF. Dicyclopentadienyliron. J Chem Soc 1952:632–635.
Kealy, TJ, Pauson, PL. A new type of organo‐iron compound. Nature 1951, 168:1039–1040.
Fischer, EO, Pfab, W, Zur Kristallstruktur, D. Di‐cyclopentadienyl‐verbindungen des zweiwertigen eisens, kobalts und nickels. Zeitschrift für Naturforschung 1952, 7B:377–379.
Wilkinson, G, Rosenblum, M, Whiting, MC, Woodward, RB. The structure of iron bis‐cyclopentadienyl. J Am Chem Soc 1952, 74:2125–2126.
Elschenbroich, C, ed. Organometallics. 3rd ed. Weinheim: Wiley‐VCH; 2006.
Fischer, EO, Hafner, W. Di‐benzol‐chrom. Zeitschrift für Naturforschung 1955, 10B:665–668.
A historical review of the way to the synthesis of chromium bisbenzene and the subsequent development of organometallic chemistry is illustrated in two reviews:Seyferth, D. Bis(benzene)chromium. 1. Franz Hein at the University of Leipzig and Harold Zeiss and Minoru Tsutsui at Yale. Organometallics 2002, 21:1520–1530.
Seyferth, D. Bis(benzene)chromium. 2. Its Discovery by E. O. Fischer and W. Hafner and Subsequent Work by the Research Groups of E. O. Fischer, H‐ H. Zeiss, F. Hein, C. Elschenbroich, and Others. Organometallics 2002, 21:2800–2820.
Cadenbach, T, Bollermann, T, Gemel, C, Fernández, I, von Hopffgarten, M, Frenking, G, Fischer, RA. Twelve one‐electron ligands coordinating one metal center: structure and bonding of [Mo(ZnCH₃)₉(ZnCp*)₃]. Angew Chem Int Ed 2008, 47:9150–9154 Angew Chemie 2008, 120:9290–9295.
Lein, M, Frunzke, J, Timoshkin, A, Frenking, G. Iron bispentazole Fe(η⁵‐N₅)₂, a theoretically predicted high‐energy compound: structure, bonding analysis, metal‐ligand bond strength and a comparison with the isoelectronic ferrocene. Chem A Eur J 2001, 7:4155–4163.
Frunzke, J, Lein, M, Frenking, G. Structures, metal‐ligand bond strength, and bonding analysis of ferrocene derivatives with group‐15 heteroligands Fe(η⁵‐E₅)₂ and FeCp(η⁵‐E₅) (E = N, P, As, Sb). A theoretical study. Organometallics 2002, 21:3351–3359.
Lein, M, Frunzke, J, Frenking, G. Structures and bonding of the sandwich complexes [Ti(η⁵‐E₅)₂]²⁻ (E = CH, N, P, As, Sb): a theoretical study. Inorg Chem 2003, 42:2504–2511.
Rayón, VM, Frenking, G. Structures, bond energies, heats of formation, and quantitative bonding analysis of main group metallocenes [E(Cp)₂] (E = Be‐Ba, Zn, Si‐Pb) and [E(Cp)] (E = Li‐Cs, B‐Tl). Chem A Eur J 2002, 8:4693–4707.
Resa, I, Carmona, E, Gutierrez‐Puebla, E, Monge, A. Decamethyldizincocene, a stable compound of Zn(I) with a Zn‐Zn bond. Science 2004, 305:1136–1138.
Velazquez, A, Fernández, I, Frenking, G, Merino, G. Multimetallocenes. A theoretical study. Organometallics 2007, 26:4731–4736.
Esenturk, EN, Fettinger, J, Lam, Y‐F, Eichhorn, B. [Pt@Pb₁₂]²⁻. Angew Chem Int Ed 2004, 43:2132–2134 Angew Chem 116:2184–2186.
Esenturk, EN, Fettinger, J, Eichhorn, B. The Pb₁₂²⁻ and Pb₁₀²⁻ zintl ions and the M@Pb₁₂²⁻ and M@ Pb₁₀²⁻ cluster series where M=Ni, Pd, Pt. J Am Chem Soc 2006, 128:9178–9186.
Wade, K. Structural and bonding patterns in cluster chemistry. Adv Inorg Chem Radiochem 1976, 18:1–66.
Mingos, DMP. Polyhedral skeletal electron pair approach. Acc Chem Res 1984, 17:311–319.
Chen, M, Zhang, Q, Zhou, M, Andrada, DM, Frenking, G. Carbon monoxide bonding with BeO and BeCO₃: surprisingly high CO stretching frequency of OCBeCO₃. Angew Chem Int Ed 2015, 54:124–128.
Zhan, C‐G, Liu, F, Hu, Z‐M. Bond strength and bond angles for hybrid orbitals composed of arbitrary sets of orbital angular momentum quantum number. Int J Quant Chem 1987, 32:13–18.
Firman, TK, Landis, CR. Structure and electron counting in ternary transition metal hydrides. J Am Chem Soc 1998, 120:12650–12656.
Fukui, K. The path of chemical reactions—The IRC approach. Acc Chem Res 1981, 14:363–372.
Bickelhaupt, FM, Baerends, EJ, Nibbering, NMM, Ziegler, T. Theoretical investigation on base‐induced 1,2‐eliminations in the model system F‐ + CH3CH2F. The role of the base as a catalyst. J Am Chem Soc 1993, 115:9160–9173.
Fernández, I, Frenking, G, Uggerud, E. The interplay of steric and electronic effects in S_N2 reactions. Chem A Eur J 2009, 15:2166–2175.
Bento, AP, Bickelhaupt, FM. Nucleophilicity and leaving‐group ability in frontside and backside S_N2 reactions. J Org Chem 2008, 73:7290–7299.
de Jong, GT, Bickelhaupt, FM. Transition state energy and position along the reaction coordinate in an extended activation strain model. ChemPhysChem 2007, 8:1170–1181.
van Zeist, W‐J, Visser, R, Bickelhaupt, FM. The steric nature of the bite angle. Chem A Eur J 2009, 15:6112–6115.
Bickelhaupt, FM, Ziegler, T, von Ragué Schleyer, P. Oxidative insertion as frontside S_N2 substitution: a theoretical study of the model reaction system Pd + CH₃Cl. Organometallics 1995, 14:2288–2296.
Diefenbach, A, Bickelhaupt, FM. Oxidative addition of Pd to C‐H, C‐C and C‐Cl bonds: importance of relativistic effects in DFT calculations. J Chem Phys 2001, 115:4030–4040.
Diefenbach, A, Bickelhaupt, FM. Activation of H‐H, C‐H, C‐C, and C‐Cl bonds by Pd(0). Insight from the activation strain model. J Phys Chem A 2004, 108:8460–8466.
Diefenbach, A, de Jong, GT, Bickelhaupt, FM. Activation of H‐H, C‐H, C‐C and C‐Cl bonds by Pd and PdCl⁻. understanding anion assistance in C‐X bond activation. J Chem Theory Comput 2005, 1:286–298.
Diefenbach, A, Bickelhaupt, FM. Activation of C‐H, C‐C and C‐I bonds by Pd and cis‐Pd(CO)₂I₂. Catalyst‐substrate adaption. J Organomet Chem 2005, 690:2191–2199.
de Jong, GT, Bickelhaupt, FM. Catalytic carbon‐halogen activation: trends in reactivity, selectivity, and solvation. J Chem Theory Comput 2007, 3:514–529.
de Jong, GT, Visser, R, Bickelhaupt, FM. Oxidative addition to main group versus transition metals: insight from the activation strain model. J Organomet Chem 2006, 691:4341–4349.
van Stralen, JNP, Bickelhaupt, FM. Oxidative addition versus dehydrogenation of methane, silane, and heavier AH₄ congeners reacting with palladium. Organometallics 2006, 25:4260–4268.
Fernández, I, Bickelhaupt, FM, Cossío, FP. Double group transfer reactions: role of activation strain and aromaticity in reaction barriers. Chem A Eur J 2009, 15:13022–13032.
Bickelhaupt, FM. Understanding reactivity with Kohn‐Sham molecular orbital theory: E2‐S_N2 mechanistic spectrum and other concepts. J Comput Chem 1999, 20:114–128.
van Zeist, W‐J, Bickelhaupt, FM. The activation strain model of chemical reactivity. Org Biomol Chem 2010, 8:3118–3127.
Fernandez, I, Bickelhaupt, FM. Deeper insight into the Diels‐Alder reaction through the activation strain model. Chem Asian J 2016, 11:3297–3304.
Lein, M, Krapp, A, Frenking, G. Why do the heavy‐atom analogues of acetylene E₂H₂ (E = Si – Pb) exhibit unusual structures? J Am Chem Soc 2005, 127:6290–6299.
Pu, L, Twamley, B, Power, PP. Synthesis and characterization of 2,6‐Trip₂H₃C₆PbPbC₆H₃‐2,6‐Trip₂ (Trip = C₆H₂‐2,4,6‐i‐Pr₃): a stable heavier group 14 element analogue of an alkyne. J Am Chem Soc 2000, 122:3524–3525.
Phillips, AD, Wright, RJ, Olmstead, MM, Power, PP. Synthesis and characterization of 2,6‐Dipp₂‐H₃C₆SnSnC₆H₃‐2,6‐Dipp₂ (Dipp = C₆H₃‐2,6‐Prⁱ₂): a tin analogue of an alkyne. J Am Chem Soc 2002, 124:5930–5931.
Stender, M, Phillips, AD, Wright, RJ, Power, PP. Synthesis and characterization of a digermanium analogue of an alkyne. Angew Chem Int Ed 2002, 41:1785–1787 Angew Chem 2002, 114:1863–1865.
Sekiguchi, A, Kinjo, R, Ichinohe, MA. Stable compound containing a silicon‐silicon triple bond. Science 2007, 305:1755–1757.
Jacobsen, H, Ziegler, T. Nonclassical double bonds in ethylene analogues: influence of pauli repulsion on trans bending and π bond strength. A density functional study. J Am Chem Soc 1994, 116:3667–3679.
Ziegler, T. Theoretical study of the triple metal bond in d³‐d³ binuclear complexes of chromium, molybdenum, and tungsten by the Hartree‐Fock‐Slater transition state method. J Am Chem Soc 1983, 105:7543–7549.
Ziegler, T. Theoretical study of multiple metal‐metal bonds in binuclear complexes of group 6D and group 7D transition elements with the general formula M₂Cl₄(PH₃)₄ⁿ⁺ (n = 0, 1, 2) by the Hartree‐Fock‐Slater transition state method. J Am Chem Soc 1984, 106:5901–5908.
Krapp, A, Lein, M, Frenking, G. The strength of the σ‐, π‐ and δ‐bonds in ²⁻Re₂Cl₈. Theor Chem Acc 2008, 120:313–320.
Koch, W, Collins, JR, Frenking, G. Are there neutral helium compounds which are stable in their ground state? A theoretical investigation of HeBCH and HeBeO. Chem Phys Lett 1986, 132:330–333.
Koch, W, Frenking, G, Gauss, J, Cremer, D, Collins, JB. Helium chemistry: theoretical predictions and experimental challenge. J Am Chem Soc 1987, 109:5917–5931.
Frenking, G, Koch, W, Gauss, J, Cremer, D. Stabilities and nature of the attractive interactions in HeBeO, NeBeO, ArBeO and a comparison with analogues NGLiF, NGBN and NGLiH (NG = He, Ar). A theoretical investigation. J Am Chem Soc 1988, 110:8007–8016.
Andrews, L, Tague, TJ. Reactions of pulsed‐laser evaporated be atoms with CO₂‐infrared spectra of OCBeO and COBeO in solid argon. J Am Chem Soc 1994, 116:6856–6859.
Frenking, G, Koch, W, Collins, JR. Fixation of nitrogen and carbon monoxide by beryllium oxide: theoretical investigation of the structures and stabilities of NNBeO, OCBeO and COBeO. J Chem Soc Chem Commun 1988:1147–1148.
When CO is bonded via a σ‐bond to a Lewis acid A at the carbon end A←CO the bond becomes shorter and stronger, but σ‐bonding at oxygen A←OC weakens the bond. This can be explained with the change in the polarization of the orbitals:Lupinetti, AJ, Fau, S, Frenking, G, Strauss, SH. Theoretical analysis of the bonding between CO and positively charged atoms. J Phys Chem A 1997, 101:9551–9559.
Lupinetti, AJ, Frenking, G, Strauss, SH. Nonclassical metal carbonyls: appropriate definitions with a theoretical justification. Angew Chem Int Ed 1998, 37:2113–2116.
Lupinetti, AJ, Strauss, SH, Frenking, G. Nonclassical metal carbonyls. Prog Inorg Chem 2001, 49:1–112.
Diels, O, Wolf, B. Über das Kohlensuboxyd. Berichte der Deutschen Chemischen Gesellschaft 1906, 39:689–697.
Zhang, Q, Li, WL, Xu, C, Chen, M, Zhou, M, Li, J, Andrada, DM, Frenking, G. Formation and characterization of the boron dicarbonyl complex [B(CO)₂]⁻. Angew Chem 2015, 127:11230–11235 Angew Chem Int Ed 2015, 54: 11078–11083.
Jensen, P, Johns, JWC. The infrared spectrum of carbon suboxide in the ν₆ fundamental region: experimental observation and semirigid bender analysis. J Mol Spectr 1986, 118:248–266.
Koput, J. An ab initio study on the equilibrium structure and CCC bending energy levels of carbon suboxide. Chem Phys Lett 2000, 320:237–244.
Carbon suboxide has a very flat bending potential and becomes linear in the solid state, which is due to intermolecular interactions:Ellern, A, Drews, T, Seppelt, K. The structure of carbon suboxide, C₃O₂, in the solid state. Zeitung für Anorganische und Allgemeine Chemie 2001, 627:73–76.
Bernhardi, I, Drews, T, Seppelt, K. Isolation and structure of the OCNCO⁺ ion. Angew Chem 1999, 111:2370–2372 Angew Chem Int Ed 1999, 38: 2232–2233.
Zhang, Q, Li, WL, Xu, C, Chen, M, Zhou, M, Li, J, Andrada, DM, Frenking, G. Formation and characterization of the boron dicarbonyl complex [B(CO)₂]⁻. Angew Chem 2015, 127:11230–11235 Angew Chem Int Ed 2015, 54: 11078–11083.
Celik, MA, Frenking, G, Neumüller, B, Petz, W. Exploiting the twofold donor ability of carbodiphosphoranes. Theoretical studies of [(PPh₃)₂C→EH₂]^q (E^q = Be, B⁺, C²⁺, N³⁺, O⁴⁺) and synthesis of the dication [(Ph₃P)₂C=CH₂]²⁺. ChemPlusChem 2013, 78:1024–1032.
Andrada, DM, Frenking, G. Stabilization of heterodiatomic SiC through ligand donation. Theoretical investigation of SiC(L)₂ (L = NHC^Me, CAAC^Me, PMe₃). Angew Chem Int Ed 2015, 54:12319–12324 Angew Chem 2015, 127: 12494–12500.
Mohapatra, C, Kundu, S, Paesch, AN, Herbst‐Irmer, R, Stalke, D, Andrada, DM, Frenking, G, Roesky, HW. The structure of the carbene stabilized Si₂H₂ may be equally well described with coordinate bonds as with classical double bond. J Am Chem Soc 2016, 138:10429–10432.
Georgiou, DC, Zhao, L, Wilson, DJD, Frenking, G, Dutton, JL. NHC stabilized acetylene – how far can the analogy be pushed? Chem A Eur J 2017, 23:2926–2934.
Li, Z, Chen, X, Andrada, DM, Frenking, G, Benkö, Z, Li, Y, Harmer, J, Su, CY, Grützmacher, H. (L)₂C₂P₂, dicarbondiphosphide stabilized by N‐heterocyclic carbenes or cyclic diamido carbenes. Angew Chem 2017, 129:5838–5843 Angew Chem Int Ed 2017, 56: 5744–5749.
Tonner, R, Öxler, F, Neumüller, B, Petz, W, Frenking, G. Carbodiphosphoranes: the chemistry of divalent carbon(0). Angew Chem 2006, 118:8206–8211 Angew Chem Int Ed 2006, 45: 8038–8042.
For reviews see:Frenking, G, Tonner, R, Klein, S, Takagi, N, Shimizu, T, Krapp, A, Pandey, KK, Parameswaran, P. New bonding modes of carbon and heavier group 14 atoms Si – Pb. Chem Soc Rev 2014, 43:5106–5139.
Zhao, L, Hermann, M, Holzmann, N, Frenking, G. Dative bonding in main group compounds. Coord Chem Rev 2017, 344:163–204. https://doi.org/10.1016/j.ccr.2017.03.026.
Frenking, G, Tonner, R. Divalent carbon(0) compounds. Pure Appl Chem 2009, 81:597–614.
Ramirez, F, Desai, NB, Hansen, B, McKelvie, N. Hexaphenylcarbodiphosphorane (C₆H₅)₃PCP(C₆H₅)₃. J Am Chem Soc 1961, 83:3539–3540.
Tonner, R, Frenking, G. Divalent carbon(0) chemistry, part 1: parent compounds. Chem A Eur J 2008, 14:3260–3272.
Tonner, R, Frenking, G. Divalent carbon(0) chemistry, part 2: protonation and complexes with main group and transition metal lewis acids. Chem A Eur J 2008, 14:3273–3289.
Tonner, R, Frenking, G. C(NHC)₂: divalent carbon(0) compounds with N‐heterocyclic carbene ligands – theoretical evidence for a class of molecules with promising chemical properties. Angew Chem 2007, 119:8850–8853 Angew Chem Int Ed 2007, 46: 8695–8698.
For a detailed description of carbodicarbenes see:Frenking, G, Tonner, R. Carbodicarbenes — divalent carbon(0) compounds exhibiting carbon–carbon donor–acceptor bonds. Wiley Interdiscip Rev Comput Mol Sci 2011, 1:869–878.
Herrmann, WA. N‐Heterocyclic carbenes: a new concept in organometallic catalysis. Angew Chem 2002, 114:1342–1351 Angew Chem Int Ed 2002, 41: 1290–1309.
Dyker, CA, Lavallo, V, Donnadieu, B, Bertrand, G. Synthesis of an extremely bent acyclic allene (a “carbodicarbene”): a strong donor ligand. Angew Chem Int Ed 2008, 47:3206–3209.
Alcarazo, M, Lehmann, W, Anoop, A, Thiel, W, Fürstner, A. Coordination chemistry at carbon. Nat Chem 2009, 1:295–301.
Fürstner, A, Alcarazo, M, Goddard, R, Lehmann, CW. Coordination chemistry of ene‐1, 1‐diamines and a prototype carbodicarbene. Angew Chem 2008, 120:3254–3258 Angew Chem Int Ed 2008, 47: 3210–3214.
Andrada, DM, Holzmann, N, Frenking, G. Bonding analysis of ylidone complexes EL₂ (E = C – Pb) with phosphine and carbene ligands L. Can J Chem 2016, 94:1006–1014.
Holzmann, N, Stasch, A, Jones, C, Frenking, G. Structures and stabilities of group 13 adducts [(NHC)(EX₃)] and [(NHC)₂(E₂X_n)] (E = B to In; X = H, Cl; n = 4, 2, 0; NHC = N‐heterocyclic carbene) and the search for hydrogen storage systems: a theoretical study. Chem A Eur J 2011, 17:13517–13525.
Pyykkö, P, Atsumi, M. Molecular double‐bond covalent radii for elements Li‐E112. Chem A Eur J 2009, 15:12770–12779.
Braunschweig, H, Dewhurst, RD, Hammond, K, Mies, J, Radacki, K, Vargas, A. Ambient‐temperature isolation of a compound with aboron‐boron triple bond. Science 2012, 336:1420–1422.
See also:Frenking, G, Holzmann, N. A boron‐boron triple bond. Science 2012, 336:1394–1395.
Two related complexes with saturated NHC^R ligands and cAAC (cylic Alkyl Amino Carbene) groups have in the meantime been isolated:Böhnke, J, Braunschweig, H, Ewing, WC, Hörl, C, Kramer, T, Krummenacher, I, Mies, J, Vargas, A. Diburabutatriene: an electron‐deficient cumulene. Angew Chem Int Ed 2014, 53:9082–9085.
Böhnke, J, Braunschweig, H, Dellermann, T, Ewing, WC, Hammond, K, Jimenez‐Halla, JOC, Kramer, T, Mies, J. The synthesis of B₂(SIDip)₂ and its reactivity between the diboracumulenic and diborynic extremes. Angew Chem Int Ed 2015, 54:13801–13805.
Zhou, M, Tsumori, N, Li, Z, Fan, K, Andrews, L. OCBBCO: A neutral molecule with some boron‐boron triple bond character. J Am Chem Soc 2002, 124:12936–12937.
Papakondylis, A, Miliordos, E, Mavridis, A. Carbonyl boron and related systems: an ab initio study of B−X and YB⋮BY (¹Σ_g⁺), where X = He, Ne, Ar, Kr, CO, CS, N₂ and Y = Ar, Kr, CO, CS, N₂. J Phys Chem A 2004, 108:4335–4340.
Ducati, LC, Takagi, N, Frenking, G. Molecules with all triple bonds: OCBBCO, N₂BBN₂ and [OBBBBO²]⁻. J Phys Chem A 2009, 113:11693–11698.
Koppe, R, Schnöckel, H. The boron–boron triple bond? A thermodynamic and force field based interpretation of the N‐heterocyclic carbene (NHC) stabilization procedure. Chem Sci 2015, 6:1199–1205.
Holzmann, N, Hermann, M, Frenking, G. The boron‐boron triple bond in NHC→B≡B←NHC. Chem Sci 2015, 6:4089–4094. The EDA‐NOCV results in this work slightly differ from the data in Table 13, because a different basis set was used.
Böhnke, J, Braunschweig, H, Constantinidis, P, Dellermann, T, Ewing, WC, Fischer, I, Hammond, K, Hupp, F, Mies, J, Schmitt, HC, Vargas, A. Experimental assessment of the strengths of B‐B triple bonds. J Am Chem Soc 2015, 137:1766–1769.
Perras, FA, Ewing, WC, Dellermann, T, Bohnke, J, Ullrich, S, Schafer, T, Braunschweig, H, Bryce, DL. Spying on the boron‐boron triple bond using spin‐spin coupling measured from ¹¹B solid‐state NMR spectroscopy. Chem Sci 2015, 6:3378–3382.
The unpaired electrons in the X³Σ_g⁻ state of B₂ are in the 1π_u and 1π_u’ MOs which are orthogonal to each other (Figure 11). The planes of the two NHC^Me ligands in B₂(NHC^Me)₂ are also nearly perpendicular and therefore they can easily form π MOs. The dihedral angle between the ligand planes deviates from 90^o and therefore, the π bonding contributions have different values.
Fleming, I. Frontier Orbitals and Organic Chemical Reactions. New York: John Wiley %26 Sons; 1976. A new edition has been published with the slightly altered title: Molecular Orbitals and Organic Chemical Reactions. New York: John Wiley & Sons; 2010.
Hermann, M, Goedecke, C, Jones, C, Frenking, G. Reaction pathways for addition of H₂ to amido‐ditetrylynes R₂N‐EE‐NR₂ (E = Si, Ge, Sn). A theoretical study. Organometallics 2013, 32:6666–6673.

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Energy decomposition analysis
Moritz von Hopffgarten,Gernot Frenking
Published Online: June 28 2011
DOI: 10.1002/wcms.71

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