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Hybridization and hypervalency in transition-metal and main-group bonding

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  1. Hybridization and hypervalency in transition-metal and main-group bonding • (The Absence of) Radial Nodes ofAtomic Orbitals, • an ImportantAspect in BondingThroughoutthePeriodic Table • Consequencesfor p-Block Elements: HybridizationDefects, • Hypervalency, Bond Polarity, etc…. • Consequencesfür the Transition Metal Elements • Non-VSEPR Structuresof d0Complexes Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 2009

  2. Analogybetween Wave Functionsand Classical Standing Waves Note thenodes (zerocrossings)!! Theyresultfromthenecessary orthogonalityofthemodes. x=l x=0 Vibrationsof a stringfixedatboth ends. Base tone andthefirsttwo harmonicsareshown. 2. harmonic 1. harmonic base tone

  3. The Nodes ofthe Radial Solutions R istheproductof an exponential e-(1/2)randof an associatedLaguerrepolynomial; r = 2Zr/na0 1s, 2p, 3d, 4f: no „primogenicrepulsion“ (Pekka Pyykkö)

  4. 1s 2p 2p 3d 4f See also: J. Comput. Chem.2007, 28, 320.

  5. 2p 2p P-Block Main-Group Elements See also: J. Comput. Chem.2007, 28, 320.

  6. HybridizationDefectsandtheirConsequencesin p-Block Chemistry

  7. X-H Binding Energiesof Monohydrides XH, andof „Saturated“ Hydrides MHn W. KutzelniggAngew. Chem.1984, 96, 262.

  8. Radial ExtentandEnergiesofValence Orbitals W. Kutzelnigg Angew. Chem.1984, 96, 262. AO-Energies from Moore Tables 26-55% 20-33% 24-40% 10% r-expectationvaluesfromDesclauxtables (DHF)

  9. ReasonsforHybridization (1) better bonding overlap (radial) reduced antibonding overlap (angular)

  10. ReasonsforHybridization (2) W. Kutzelnigg, Einführung in die Theoretische Chemie, Vol. 2

  11. HybridizationDefects (1) Mulliken gross populations for valence AOs in XHn hydrides without free electron pairs W. Kutzelnigg Angew. Chem.1984, 96, 262.

  12. HybridizationDefects (2) cos(180-) = a2/(1-a2) (a2 = s-character, 1-a2 = p-character) Holdsonlyfor orthogonal hybrids! *A posteriori hybridizationanalysesfromDFT calculations (BP86/TZVP)

  13. Explanationsofthe Inert-Pair Effect 1) Promotion energies increase down the group 2) Drago: Binding energies decrease down the group  promotion energies are not overcompensated anymore 3) Extension following Kutzelnigg: Promotion does not take place anymore  no good hybrids and weakened covalent bonds in higher oxidation state

  14. decreasing stability: R4Pb > R3PbX > R2PbX2 > RPbX3 > PbX4 (R = alkyl, aryl; X = halogen, OR, NR2, OOCR, etc……) Why is Inorganic Lead Chemistry Dominated by PbII, but Organolead Chemistry by PbIV? (J. Am. Chem. Soc.1993, 115, 1061)

  15. Substituent Effects on 1,1 - Elimination Reactions of Pb(IV) Compounds PbMe F  PbMe F +F 160 n 4 - n n 2 - n 2 140 ) 120 1 - 100 (kJ mol 80 60 40 react. PbMe F  PbMe F +MeF n 4 - n n - 1 3 - n 20 E D 0 PbMe F  PbMe F +C H - 20 n 4 - n n - 2 4 - n 2 6 - 40 - 60 PbMeF PbMe F PbF PbMe F PbMe 3 3 4 2 2 4 1993 J. Am. Chem. Soc. , 115 , 1061. QCISD/DZ+P data

  16. 160 140 120 100 80 60 40 20 0 -20 -40 -60 Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds PbMenF4-n→ PbMenF2-n +F2 DEreact. (kJ mol-1) PbMenF4-n→ PbMen-1F3-n +MeF PbMenF4-n→ PbMen-2F4-n +C2H6 PbMeF3 PbMe3F PbF4 PbMe2F2 PbMe4 J. Am. Chem. Soc.1993, 115, 1061. QCISD/DZ+P data

  17. HybridizationDefects (3) h(E): NPA/NLMO Hybridization results from DFT calculations (BP86)

  18. Bent‘sRule: Basic Principles e.g.: larger angles between more electropositive substituents more s-character of central atom is directed towards less electronegative substituent, more p-character to more electronegative substituent H. A. Bent Chem. Rev.1961, 61, 275; H. C. Allen at al. J. Am. Chem. Soc.1958, 80, 2673. exceptions: a) large steric effects, b) very different sizes of substituent orbitals (e.g. H vs. Hg), c) counteracting effects for very light central atoms d) transition metal systems (cf. also Huheey text book)

  19. Bent‘sruleeffects in organoleadfluorides 101.10 Pb 115.50 Pb 116.40 102.80 101.40 104.10 Pb 134.80 Quasirelativistic ab initio calculations, J. Am.Chem. Soc.1993, 115, 1061.

  20. Bent‘sRule: CounteractingEffects negative hyperconjugation „switched off“ negative hyperconjugation counteracts EN effects negative hyperconjugation small for heavier elements

  21. Bent‘sRuleand Lone Pairs h: NPA/NLMO Hybridization results from DFT calculations (BP86)

  22. Inversion BarriersandHybridization † TS pure p-character of LP high s-character in bonds high s-character of LP high p-character in bonds • everything that enhances hybridization defects increases inversion barrier and decreases angles! • e.g. NH3 << PH3 < AsH3 < SbH3 < BiH3 • NLi3 << NH3 << NF3 • NH3 << NH2F << NHF2 << NF3

  23. Further Pecularitiesof 1st-Row (2. Period) Elements (p-Block) important: size, electronegativity, hybridizationdefects particularlyweakbondsfor F2, H2O2, N2H4, .......... e.g. BDE (kJ mol‑1): F2 155, Cl2 240, Br2 190, I2 149. (cf. also low EA offluorineatom!) explanation: „lone-pair bondweakeningeffect“ (Sanderson), (lesspronouncedforheavierhomologues) preferencefor- multiple bondingcomparedtochain-linkedsinglebonds e.g.: O2vs S8, CO2 vs. SiO2, ketones vs. silicones e.g. BDE (kJ mol‑1):

  24. Binding Energies

  25. BDEs (kJ mol‑1): also: bond ionicity cf. silicates, etc…! X C-X Si-X F 485 565 Cl 327 381 Br 285 310 I 213 234 Preference for- multiple bondingcomparedtochain-linkedsinglebonds increments (/, in kJ mol‑1):

  26. Pauling Allred-Rochow

  27. Silicon-Oxygen Bonds Electronegativity Si: 1.74 O: 3.50 154o 111o Electron-Localisation-Function Electron-Localisation-Function The Si-O Bond has a Strong Ionic Character

  28. Summary: HybridizationDefectsandRelatedPhenomena in p-Block Main-Group Chemistry • 2p shellhasnoprimogenicrepulsionandisthuscompact • thisfavorsisovalenthybridization in the 2nd period • electronegativesubstituentsenhancehybridizationdefects • fortheheavier p-block elements, hybridizationdefectsareimportantfor inert-pair effect, inversionbarriers, Bent‘sruleeffects, double-bondrule….. • large electronegativityof 2p-elements also arisesfromcompact 2p shell

  29. Hypervalency?On Mythand Reality ofd-Orbital-Participationin Main-Group Chemistry

  30. covalency increases ionicity increases certainly no hypervalency hypervalency ? On the Definition of Hyper-(co)-Valency MgF64-SiF62-SF6

  31. A Working Definition of Hypervalency We regard a molecule as hypervalent if at least for one atom the bonding situation requires more valence orbitals than available for the free atom

  32. The Early History of Hypervalency, Part 1 electron pair theory, octet rule Lewis 1916; Kossel 1916; Langmuir 1919 directed valency, spmdn hybrids, electroneutrality principle Pauling 1931, 1940, 1948 3-center-4-electron-bond Pimentel 1951; Hach, Rundle 1951

  33. F Xe F F - Xe+ F F Xe + F - F - Xe2+ F - LimitingBondingSituations: Exampleof Different Lewis Structuresfor XeF2 covalent, hypervalent partially ionic, delocalized ionic

  34. 3-Center-4-Electron MO Model F - Xe+ F F Xe + F - pa pn pb sa sn sb

  35. F - Xe+ F F Xe + F - pa pn pb sa sn sb Modified 3-Center-4-Electron MO Model

  36. The Early History of Hypervalency, Part 2 discovery of noble-gas compounds Chernik et al.; Claasen et al.; Bartlett, Hoppe; since 1962: first ab initio calculations since ca. 1970 first improved wave functions, Mulliken population analyses since ca. 1975:

  37. + l = electric field The Roleof d-Polarization-Functions pp + l dp = polarized pp

  38. weak points of Mulliken population analysis: strong basis-set dependence unphysical (partly negative) populations failure for transition to ionic bonding

  39. ImprovedAnalysesofAccurate Wave Functions modifiedRoby/Davidson populationanalysis Ahlrichs et al. 1976, 1985; Wallmeier, Kutzelnigg1979 „Natural Population Analysis“ (NPA), „Natural Bond Orbital Analysis“ (NBO) Reed, Weinhold 1986; Reed, Schleyer 1990 „Natural ResonanceTheory“ (NRT) Weinhold et al., 1995 energycontributionsfrom d-orbitals Magnusson 1986, 1990, 1993 topologicalanalysisofelectrondensity (QTAIM) Cioslowski, Mixon 1993 „GeneralizedValence Bond“ (GVB) theory • Hay 1977, Cooper et al. 1994 (full-GVB) one-centerexpansionofone-particledensitymatrix • Häser 1996 • Sincelate 1990‘s • QTAIM based on experimental densities • (e.g. D. Stalke et al.)

  40. “Natural Population Analysis” “Natural Bond Orbital Analysis” Weinhold et al. 1984, 1988 AO basis NAO basis NHO basis NBO basis original basis set occupancy-weighted Löwdin orthogonalization “natural atomic orbitals” “natural minimal basis set” (strongly occupied) “natural Rydberg basis set” (sparsely occupied) “natural hybrid orbitals” “natural bond orbitals” NBO-Lewis-structure “natural resonance theory” (NRT) superposition of NBO-Lewis structures Weinhold et al. 1995 NLMO basis “natürliche lokalisierte Orbitale”

  41. NRT-Analysis of Sulfate Ion NRT weight: O 0% - O S O - O O - - O S2+O - 66.2% O - O 12x1.9% = 22.8% - O S2+ O - O 2- 11% NRT at HF/6-31G* level Weinhold et al., 1995 further ionic structures:

  42. Which NRT-Lewis StructureDescribesthe Perchlorate Ion Best? NRT weight: O 0% O Cl O - O O - 60.9% - O Cl3+O - O - O - O Cl3+O - 12x2.0% = 24.0% O 2- further ionic structures: 15% NRT at HF/6-31G* level Weinhold et al., 1995

  43. NRT Weights (w) forVarious Lewis Structures in Oxo Anions and Sulfur Oxides species NRT at HF/6-31G* (MP2/6-31G*) level Weinhold et al., 1995

  44. C C C C C C H+ H H+ C C C- C C C C- C C H H H HyperconjugationExemplifiedbyCyclopentadiene ...... H C C p3* su C C C H

  45. F F F+ F- F- F+ C C C H H H H H H Negative HyperconjugationExemplifiedbyDifluoromethane ...... p(F) F F s*(C-F) C H H

  46. F P O F F Negative Hyperconjugation in F3PO F F- F P+ O- P+ O P+ O F F F ...... F- F F p(O) (to e-MO) s*(P-F) (to e*-MO)

  47. F P M s*(P-F) p(M) F F …….andforp-backbonding in phosphanecomplexes…….

  48. Musher’sClassificationof „Hypervalent“ Compounds (Musher 1969)

  49. MO-Diagram of SF6