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Hybridization and hypervalency in transition-metal and main-group bonding Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 2009.

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Presentation on theme: "Hybridization and hypervalency in transition-metal and main-group bonding Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 2009."— Presentation transcript:

1 Hybridization and hypervalency in transition-metal and main-group bonding Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec , 2009  (The Absence of) Radial Nodes of Atomic Orbitals, an Important Aspect in Bonding Throughout the Periodic Table  Consequences for p-Block Elements: Hybridization Defects, Hypervalency, Bond Polarity, etc….  Consequences für the Transition Metal Elements  Non-VSEPR Structures of d 0 Complexes

2 Analogy between Wave Functions and Classical Standing Waves Vibrations of a string fixed at both ends. Base tone and the first two harmonics are shown. base tone 1. harmonic 2. harmonic Note the nodes (zero crossings)!! They result from the necessary orthogonality of the modes. x=0 x=

3 The Nodes of the Radial Solutions R is the product of an exponential e -(1/2)  and of an associated Laguerre polynomial;  = 2Zr/na 0 1s, 2p, 3d, 4f: no „primogenic repulsion“ (Pekka Pyykkö)

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

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

6 Hybridization Defects and their Consequences in p-Block Chemistry

7 X-H Binding Energies of Monohydrides XH, and of „Saturated“ Hydrides MH n W. Kutzelnigg Angew. Chem. 1984, 96, 262.

8 AO-Energies from Moore Tables r-expectation values from Desclaux tables (DHF) 20-33%24-40% 26-55% 10% Radial Extent and Energies of Valence Orbitals

9 Reasons for Hybridization (1) better bonding overlap reduced antibonding overlap (angular) (radial)

10 W. Kutzelnigg, Einführung in die Theoretische Chemie, Vol. 2 Reasons for Hybridization (2)

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

12 Hybridization Defects (2) NPA/NLMO Hybridization * CH 4 sp 3.16 SiH 4 sp 2.10 GeH 4 sp 2.00 SnH 4 sp 1.81 PbH 4 sp 1.77 *A posteriori hybridization analyses from DFT calculations (BP86/TZVP) cos(180-  ) = a 2 /(1-a 2 ) (a 2 = s-character, 1-a 2 = p-character) Holds only for orthogonal hybrids!

13 Explanations of the 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 Why is Inorganic Lead Chemistry Dominated by Pb II, but Organolead Chemistry by Pb IV ? (J. Am. Chem. Soc. 1993, 115, 1061) Pb(IV)Pb(II) inorganic lead chemistry : PbCl 4 : decomposes at low temperatures PbCl 2, PbO, Pb(OAc) 2 : stable ionic compounds PbO 2 or Pb(OAc) 4 : strong oxidation agents organolead chemistry: PbMe 4, PbEt 4 : stable compounds, earlier appreciable commercial value PbMe 2, PbEt 2 unknown, possibly reactive intermediates decreasing stability: R 4 Pb > R 3 PbX > R 2 PbX 2 > RPbX 3 > PbX 4 (R = alkyl, aryl; X = halogen, OR, NR 2, OOCR, etc……)

15 PbF 4 PbMeF 3 PbMe 2 F 2 3 F 4 n F 4-n  n F 2-n +F 2 PbMe n F 4-n  n-1 F 3-n +MeF PbMe n F 4-n  n-2 F 4-n +C 2 H 6  E react. (kJ mol - 1 ) Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds J. Am. Chem. Soc. 1993,115, QCISD/DZ+P data

16 PbF 4 PbMeF 3 PbMe 2 F 2 PbMe 3 F PbMe 4 PbMe n F 4-n → PbMe n F 2-n +F 2 PbMe n F 4-n → PbMe n-1 F 3-n +MeF PbMe n F 4-n → PbMe n-2 F 4-n +C 2 H 6  E react. (kJ mol -1 ) Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds J. Am. Chem. Soc. 1993, 115, QCISD/DZ+P data

17 Hybridization Defects (3) EH 4 h(E)charge Q(E) EF 4 h(E)charge Q(E) CH 4 sp CF 4 sp SiH 4 sp SiF 4 sp GeH 4 sp GeF 4 sp SnH 4 sp SnF 4 sp PbH 4 sp PbF 4 sp h(E): NPA/NLMO Hybridization results from DFT calculations (BP86)

18

19 Bent‘s Rule: Basic Principles H. A. Bent Chem. Rev. 1961, 61, 275; H. C. Allen at al. J. Am. Chem. Soc. 1958, 80, 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) 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 e.g.:

20 Pb Bent‘s rule effects in organolead fluorides Quasirelativistic ab initio calculations, J. Am.Chem. Soc. 1993, 115,

21 Bent‘s Rule: Counteracting Effects negative hyperconjugation counteracts EN effects negative hyperconjugation „switched off“ negative hyperconjugation small for heavier elements

22 EH 3 h(E-H)h(LP-E) NH 3 sp 3.14 sp 2.61 PH 3 sp 5.29 sp 0.76 AsH 3 sp 7.08 sp 0.51 Bent‘s Rule and Lone Pairs h: NPA/NLMO Hybridization results from DFT calculations (BP86)

23 Inversion Barriers and Hybridization 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. NH 3 << PH 3 < AsH 3 < SbH 3 < BiH 3 NLi 3 << NH 3 << NF 3 NH 3 << NH 2 F << NHF 2 << NF 3

24 Further Pecularities of 1st-Row (2. Period) Elements (p-Block) N-NP-P single double triple important: size, electronegativity, hybridization defects particularly weak bonds for F 2, H 2 O 2, N 2 H 4, e.g. BDE (kJ mol ‑ 1): F 2 155, Cl 2 240, Br 2 190, I (cf. also low EA of fluorine atom!) explanation: „lone-pair bond weakening effect“ (Sanderson), (less pronounced for heavier homologues) preference for  -  multiple bonding compared to chain-linked single bonds e.g.: O 2 vs S 8, CO 2 vs. SiO 2, ketones vs. silicones e.g. BDE (kJ mol ‑ 1):

25 Binding Energies

26 increments (  / , in kJ mol ‑ 1 ): C-CN-NO-O 322/295160/395145/350 Si-SiP-PS-S 195/120200/145270/155 Ge-GeAs-AsSe-Se 165/110175/120210/125 Preference for  -  multiple bonding compared to chain-linked single bonds also: bond ionicity cf. silicates, etc…! I Br Cl F Si-XC-XX BDEs (kJ mol ‑ 1 ):

27 Allred-Rochow Pauling

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

29 Summary: Hybridization Defects and Related Phenomena in p-Block Main-Group Chemistry 2p shell has no primogenic repulsion and is thus compact this favors isovalent hybridization in the 2nd period electronegative substituents enhance hybridization defects for the heavier p-block elements, hybridization defects are important for inert-pair effect, inversion barriers, Bent‘s rule effects, double-bond rule….. large electronegativity of 2p-elements also arises from compact 2p shell

30 Hypervalency? On Myth and Reality of d-Orbital-Participation in Main-Group Chemistry

31 On the Definition of Hyper-(co)-Valency MgF 6 4- SiF 6 2- SF 6 covalency increasesionicity increases certainly no hypervalency hypervalency ?

32 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

33 The Early History of Hypervalency, Part 1 electron pair theory, octet rule Lewis 1916; Kossel 1916; Langmuir 1919 directed valency, sp m d n hybrids, electroneutrality principle Pauling 1931, 1940, center-4-electron-bond Pimentel 1951; Hach, Rundle 1951

34 Limiting Bonding Situations: Example of Different Lewis Structures for XeF 2 covalent, hypervalent partially ionic, delocalized ionic F - Xe 2+ F - F Xe F F Xe + F - F - Xe + F

35 F Xe + F - F - Xe + F 3-Center-4-Electron MO Model aa bb nn aa bb nn

36 aa bb nn aa bb nn F Xe + F - F - Xe + F Modified 3-Center-4-Electron MO Model

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

38 + = The Role of d-Polarization-Functions p  +  d  polarized p  electric field

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

40 modified Roby/Davidson population analysis Ahlrichs et al. 1976, 1985; Wallmeier, Kutzelnigg 1979 „Natural Population Analysis“ (NPA), „Natural Bond Orbital Analysis“ (NBO) Reed, Weinhold 1986; Reed, Schleyer 1990 „Natural Resonance Theory“ (NRT) Weinhold et al., 1995 energy contributions from d-orbitals Magnusson 1986, 1990, 1993 topological analysis of electron density (QTAIM) Cioslowski, Mixon 1993 „Generalized Valence Bond“ (GVB) theory Hay 1977, Cooper et al (full-GVB) one-center expansion of one-particle density matrix Häser 1996 Since late 1990‘s QTAIM based on experimental densities (e.g. D. Stalke et al.) Improved Analyses of Accurate Wave Functions

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

42 O O 2- - O Cl 3+ O - O - O Cl O - O O Which NRT-Lewis Structure Describes the Perchlorate Ion Best? 0% NRT weight: 60.9% 12x2.0% = 24.0% 15% - O Cl 3+ O - further ionic structures: NRT at HF/6-31G* level Weinhold et al., 1995

43 C C C C C H H C C C C H H Hyperconjugation Exemplified by Cyclopentadiene C H+H+ C C C C-C- H uu 3*3* C C C C-C- C H+H+ H C

44 Negative Hyperconjugation Exemplified by Difluoromethane C H H F F  (F)  *(C-F) C H H F-F- F+F+ C H H F+F+ F-F- C H H F F

45 Negative Hyperconjugation in F 3 PO P+P+ F O-O- F F P+P+ F-F- O F F P+P+ F O F F-F-  (O) (to e-MO)  *(P-F) (to e*-MO) P F O F F

46  (M)  *(P-F) P F M F F …….and for  -backbonding in phosphane complexes…….

47 Musher’s Classification of „Hypervalent“ Compounds 1. order2. order e.g. XeF 2, XeF 4, XeF 6, SF 4, ClF 3, etc…. lone pair present s-character concentrates in LP e.g. PF 5, SF 6, JF 7 highest possible oxidation state s-character in bonds (Musher 1969)

48 MO-Diagram of SF 6

49 Summary: Hypervalency, d-Orbital-Participation in p-Block Main-Group Chemistry in normal valent and „hypervalent“ p-block main-group systems, d-functions serve as „polarization functions“ but not as true valence orbitals hypervalent Lewis structures usually obtain small or no weight! ionic bonding contributions dominate, assisted by delocalization (3-c-4-el.-bonding, negative hyperconjugation) in PF 5, SF 6, etc., delocalization is more complex due to s- orbital participation  significant hypervalent populations

50 3d Transition Metal Systems

51 r f(r) in a.u. r in a.u. J. Comput. Chem. 2007, 28, 320 Radial Orbital Densities of the Manganese Atom

52 M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, M L (n-1)s,p outermost core shell Pauli repulsion  stretched bond (n-1)d The problem of the outermost core shells in transition-metal atoms The problem is most pronounced for the 3d elements (nodelessness of the 3d shell)  weak bonds, low-lying excited states, strong (nondynamical) correlation effects The 4d shell is already better suited for bonding overlap. The 5d shell even more so due to its relativistic expansion.

53 M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, The problem is most pronounced for the 3d elements (nodelessness of the 3d shell)  weak bonds, low-lying excited states, strong (nondynamical) correlation effects The 4d shell is already better suited for bonding overlap. The 5d shell even more so due to its relativistic expansion. M M (n-1)s,p outermost core shell Pauli repulsion  stretched bond (n-1)d The problem of the outermost core shells in transition-metal atoms

54 M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, M L (n-1)s,p outermost core shell Pauli repulsion  stretched bond (n-1)d The problem of the outermost core shells in transition-metal atoms The problem is most pronounced for the 3d elements (nodelessness of the 3d shell)  weak bonds, low-lying excited states, strong (nondynamical) correlation effects The 4d shell is already better suited for bonding overlap. The 5d shell even more so due to its relativistic expansion.

55 Non-VSEPR Structures and Bonding for d 0 -Systems

56 Non-VSEPR Structures of d 0 -Systems VSEPR = valence-shell electron-pair-repulsion model

57

58 e.g. catalysis Practical Relevance of d 0 -Systems e.g. bioinorganic chemistry Mo-Cofactor (after Rajagopalan, Johnson) ZrO 2, ferroelectric perovskites e.g. materials

59 123 0 Ba F F Mg F F linearization energies in kJ/mol from SDCI calculations (J. Am. Chem. Soc. 1991, 113, 6012) The Question of Bending of the Alkaline Earth Dihalides

60 regular, „VSEPR“ structuresdistorted, „non-VSEPR“ structures polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation maximization of d-orbital participation in  -bonding mutual repulsion and polarization of the ligands maximization of  -bonding M X X (??) Factors Controlling the Structures of d 0 Systems Review: Angew. Chemie 2001, 113, 642.

61 d-Orbital-Contributions to HOMO in d 0 MX 2 -Complexes

62

63 BaH 2 : Electron Localization Function (ELF, color scale) projected on electron density (cloud of points)

64 Bending Force Constants (at Linear Structure) for Molecular Alkaline Earth Dihalides J. Am. Chem. Soc. 1991, 113, 6017 force constants from polarized ion model too low for Be and Mg complexes but too high for Ca, Sr, and Ba complexes

65 r f (r) (a.u.) r (Å) 5p 5d 6s 6p Radial Distribution of (Pseudo)-Valence Orbitals of Barium outer-core polarization and d-orbital participation cannot be separated completely!

66 regular, „VSEPR“ structuresdistorted, „non-VSEPR“ structures polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation maximization of d-orbital participation in  -bonding mutual repulsion and polarization of the ligands maximization of  -bonding M X X (??) Factors Controlling the Structures of d 0 Systems Review: Angew. Chemie 2001, 113, 642.

67 Low Ligand-Ligand Repulsion for Neutral Ligands J. Phys. Chem. 1992, 96,  E(MP2) Lin = 0.6 kJ/Mol Ba 2+ (H 2 O) 2 Ba O O 98 0  E(HF) Plan = 0.4 kJ/Mol Ba 2+ (H 2 O) 3 Ba O O O

68 122 0 Cs O O  E(MP2) Lin = 0.2 kJ/Mol Cs + (H 2 O) 2

69 regular, „VSEPR“ structuresdistorted, „non-VSEPR“ structures polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation maximization of d-orbital participation in  -bonding mutual repulsion and polarization of the ligands maximization of  -bonding M X X (??) Factors Controlling the Structures of d 0 Systems Review: Angew. Chemie 2001, 113, 642.

70 X: Li BeH BH 2 CH 3 NH 2 OH F C 2v (in-plane) C 2v (out-of-plane) CsCs  E lin / kJ mol -1 Ba N N N N C 2v (in-plane)  E(HF) = 0.0 kJ mol -1 C 2v (out-of-plane)  E(HF) = kJ mol º 128.8º Effects of  -Bonding

71 MR 2 (M = Ca, Yb, Eu; R = C[Si(CH 3 ) 3 ] 3 ) Eaborn et al. Organomet. 1996, 15, J. Chem. Soc., Chem. Commun. 1997, 1961.

72 Sc H H H F F F Structural Preferences of d 0 MX 3 Complexes C. A. Jolly, D. S. Marynick Inorg. Chem. 1989, 28, 2893.

73 X X M X X X X ‘  ip ’, ‘b 2 ’ ‘  op ’, ‘a 2 ’ ‘  op ’, a 2 ‘  op ’, b 1 ‘  ip ’, a 1  -Acceptor-Type d-Orbitals for Linear and Bent MX 2 d 0 Complexes

74  -Bonding Favors Bent Structure in some Cases!

75

76 Inversion of Bent’s rule for d 0 -Systems (CH 3 ) 2 TiCl 2 GED data, Haaland et al., Explanation via  -contributions: Chem. Eur. J. 1999, 5, Si C C Cl (CH 3 ) 2 SiCl 2 Ti C C Cl

77

78 S-S- S-S- H2H2 H2H2 S-S- S-S- HH SS HH typical ligand types: Examples for Nonoctahedral Complexes with Sulfur Ligands See, e.g.: Can. J. Chem. 1989, 67, 1914 Inorg. Chem. 1993, 32, 2085 Inorg. Chem. 1989, 28, 773, etc.....

79

80 The Structure of W(CH 3 ) 6 C3C3 D3D3 minimum transition state +17 kJ/mol CCSD(T) 2.15 Å 2.21 Å Å W W M. Kaupp J. Am. Chem. Soc. 1996, 118, 3018.

81

82 MO Rationalization of Nonoctahedral d 0 Structures S. K. Kang, H. Tang, T. A. Albright J. Am. Chem. Soc. 1993, 115, 1971.

83 Landis’ sd-Hybridization Model (1) (J. Am. Chem. Soc. 1998, 120, 1842)

84 Landis’ sd-Hybridization Model (2) (J. Am. Chem. Soc. 1998, 120, 1842) Preferred coordination arrangements for sd 5 hybrids.

85 Relative energies (kJ mol —1 ) between D 3h and O h structures of group 6 hexahalide complexes CrMoW F Cl Br-a-a I-a-a -a-a 66.4 a DFT-BP86 results, Angew. Chem., Int. Ed. Engl. 2001, 40, No convergence for CrBr 6, CrI 6, MoI 6. minimum transition stateM M D 3h OhOh Energetics of Baylar Twist for MX 6 d 0 Complexes

86 2.414 Å 88.7º Å 83.5º Mo S S S S S S dihedral d = 26º d / deg E rel / kJ mol -1 Mo(SH) 6 : intermediate between octahedral and trigonal prismatic

87 Importance of trigonal prismatic intermediates and transition structures of certain molybdenum enzymes Review: M. Kaupp Angew. Chemie, Int. Ed. Engl. 2004, 43, 546.

88 minimum transition state +19 kJ/mol BP86/A 2.34 Å W The Structure of WCl 5 CH Å 2.35 Å C Cl1 C s oct. C s trig. prism Cl4 Cl3 Cl2 Cl Å W C Cl1 Cl4 Cl3 Cl2 Cl Å 2.19 Å 2.39 Å 2.35 Å 2.32 Å

89 The Structure of WCl 4 (CH 3 ) 2 trans oct. C 2 (min. 0.0) “intermediate” C 2 (min. +6.5) cis oct. C 2v (TS +25.7) cis tp “other face”, C 2v (TS +8.5) tp “same face”, C s (TS +14.5) BP86 data, relative energies in kJ/mol Angew. Chemie 1999, 111, 3219

90 The Structure of WCl 3 (CH 3 ) 3 tp “across” C 1 (min. 0.0) tp “same face” C 3 (min. +2.3) oct. fac. C 3v (TS +61.2) oct. merid. C s (TS +26.0) BP86 data, relative energies in kJ/mol Angew. Chemie 1999, 111, 3219

91 Examples of Unsymmetrical Metal Coordination in Oxide Materials oxidecoordinationrelated material properties ZrO 2 7-fold coordination (baddeleyite) vs. cubic high- temperature form refractive ceramics (stabilization of cubic form) WO 3 6-fold, dist. octahedral electrochromic ceramics MoO 3 6-fold, strongly dist. octahedral heterogeneous catalyst BaTiO 3, etc.* 6-fold, dist. octahedral ferroelectric and piezoelectric ceramics *5d vs. 4d comparisons: KTaO 3 is regular octahedral (cubic) and paraelectric, KNbO 3 is distorted (rhombohedral) and ferroelectric at lower temperatures. LiTaO 3 has a ferroelectric transition at lower temperature (950 K) than LiNbO 3 (1480 K). More ionic bonding and larger band gap with 5d vs. 4d, due to relativistic effects!

92 J. Am. Chem. Soc. 1993, 115, Structures of the Dihydride Dimers M 2 H 4 (M = Mg, Ca, Sr, Ba) (relative MP2 Energies in kJ/Mol) D 2h C 3v C 2v C 2h D 4h C 2v

93 Summary: Understanding Non-VSEPR Structures in d 0 -Complexes -d 0 complexes with purely  -bonded ligands tend to violate VSEPR and related models, in spite of increased ligand repulsion. -while extended VSEPR models are not useful in rationalizing the distorted structures, both MO and VB models are successful for simple homoleptic complexes. -  -bonding is much more important in d 0 complexes than in related p-block complexes, due to the avalability of inner d-orbitals. -the interrelation between  -bonding and bond angles is complicated, due to the involvement of different d ‑ orbitals. -the “anti-Bent’s-rule” structure of TiCl 2 (CH 3 ) 2 is due to Ti ‑ Cl  -bonding! -additional  -donor ligands influence the angles between  -donor ligands in heteroleptic complexes.

94 Thank you for your attention!

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

96 NRT Weights (w) for Various Lewis Structures in Oxo Anions and Sulfur Oxides „w mod “(%)„w orig“ (%)„w alt “(%) „hypervalent“„original Lewis“ „no-bond/ double-bond“ PO (0.0)71.0 (53.1)20.3 (28.4) SO (0.0)66.2 (46.9)23.1 (49.8) ClO (0.0)60.9 (36.8)31.4 (60.7) SO (0.0)87.9 (77.3)5.9 (9.2) SO (0.0)95.2 (90.2)4.8 (8.6) NRT at HF/6-31G* (MP2/6-31G*) level Weinhold et al., 1995 species

97 M M C2 C2A C1 H1H2 H3 Structure of Mo(butadiene) 3

98 d(Si-H)=1.488Å,

99 Extreme Resonance Structures for tris(Butadiene)-Molybdenum and Related Complexes

100

101 11 22 33 44 a‘ e‘ a‘‘ e‘‘ e‘ a‘ e‘‘ a‘‘ 3e‘ 2e‘‘ 3a‘ 2a‘ 2e‘ 1a‘‘ 1e‘‘ 1e‘ 1a‘ a‘‘,e‘ a‘ a‘,e‘,e‘‘ 5p 5s 4d Mo(C 4 H 6 ) 3 Mo(C 4 H 6 ) 3 C 3h

102 „Non-Berry“ Rearrangement of TaH 5

103

104

105 Trends of the s- and d-valence orbitals in the transition metal series a) radial size from Dirac-Fock calculations (Desclaux)

106 Trends of the s- and d-valence orbitals in the transition metal series b) orbital energies from Dirac-Fock calculations (Desclaux)

107 Why??

108 Angew. Chem., Int. Ed. Engl. 2001, 40, 3534.

109 On the relative energies of 3d- and 4s orbitals The 3d orbitals are always lower in energy (and smaller!) than 4s. Stronger electron repulsion in 3d may nevertheless favor 4s occupation.

110 Ca atom: radial orbital densities 3p orbital (outermost core shell) 3d orbital (valence shell) Malrieu et al. Chem. Phys. Lett. 1983, 98, 433.


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