1. Hybridization and hypervalency
in transition-metal and main-group bonding
(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 d0 Complexes
Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec , 2009

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.
Note the nodes (zero crossings)!!
They result from the necessary
orthogonality of the modes.
2. harmonic
1. harmonic
x=0
x=l
base tone

3. The Nodes of the Radial Solutions
R is the product of an exponential e-(1/2)r and of an
associated Laguerre polynomial; r = 2Zr/na0
1s, 2p, 3d, 4f: no „primogenic repulsion“ (Pekka Pyykkö)

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

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

6. Hybridization Defects and their Consequences in p-Block Chemistry

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

8. Radial Extent and Energies of Valence Orbitals
W. Kutzelnigg Angew. Chem. 1984, 96, 262.
AO-Energies from Moore Tables
26-55%
20-33%
24-40%
10%
r-expectation values from Desclaux tables (DHF)

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

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

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

12. CH4 sp3.16 SiH4 sp2.10 GeH4 sp2.00 SnH4 sp1.81 PbH4 sp1.77
Hybridization Defects (2)
cos(180-) = a2/(1-a2) (a2 = s-character, 1-a2 = p-character)
Holds only for orthogonal hybrids!
NPA/NLMO Hybridization*
CH4
sp3.16
SiH4
sp2.10
GeH4
sp2.00
SnH4
sp1.81
PbH4
sp1.77
*A posteriori hybridization analyses from DFT calculations (BP86/TZVP)

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. inorganic lead chemistry:
Why is Inorganic Lead Chemistry Dominated by PbII,
but Organolead Chemistry by PbIV?
(J. Am. Chem. Soc. 1993, 115, 1061)
Pb(IV)
Pb(II)
inorganic lead chemistry:
PbCl4:
decomposes at low temperatures
PbCl2, PbO, Pb(OAc)2:
stable ionic compounds
PbO2 or Pb(OAc)4:
strong oxidation agents
organolead chemistry:
PbMe4, PbEt4:
stable compounds, earlier appreciable commercial value
PbMe2, PbEt2
unknown,
possibly reactive intermediates
decreasing stability:
R4Pb > R3PbX > R2PbX2 > RPbX3 > PbX4
(R = alkyl, aryl; X = halogen, OR, NR2, OOCR, etc……)

15. ) (kJ mol E D  QCISD/DZ+P data - 60 40 20 80 100 120 140 160 PbF80
100
120
140
160
PbF 4
PbMeF 3
PbMe 2 F n  +F 1
+MeF +C H 6 D E
react.
(kJ mol )
Substituent Effects on 1,1
Elimination Reactions of Pb(IV) Compounds
J. Am. Chem. Soc.
1993 ,
115
, 1061.
QCISD/DZ+P data

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

17. sp3.16 sp1.98 sp2.10 sp1.01 sp2.00 sp0.75 sp1.81 sp0.70 sp1.77 sp0.51
Hybridization Defects (3)
EH4
h(E)
charge Q(E)
EF4
CH4
sp3.16
-0.952
CF4
sp1.98
1.338
SiH4
sp2.10
0.547
SiF4
sp1.01
2.361
GeH4
sp2.00
0.392
GeF4
sp0.75
1.852
SnH4
sp1.81
0.753
SnF4
sp0.70
2.348
PbH4
sp1.77
0.519
PbF4
sp0.51
2.111
h(E): NPA/NLMO Hybridization
results from DFT calculations (BP86)

19. Bent‘s Rule: 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)

20. Bent‘s rule effects in organolead fluorides
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.

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

22. EH3 h(E-H) h(LP-E) NH3 sp3.14 sp2.61 PH3 sp5.29 sp0.76 AsH3 sp7.08
Bent‘s Rule and Lone Pairs
EH3
h(E-H)
h(LP-E)
NH3
sp3.14
sp2.61
PH3
sp5.29
sp0.76
AsH3
sp7.08
sp0.51
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. NH3 << PH3 < AsH3 < SbH3 < BiH3
NLi3 << NH3 << NF3
NH3 << NH2F << NHF2 << NF3

24. Further Pecularities of 1st-Row (2. Period) Elements (p-Block)
important: size, electronegativity, hybridization defects
particularly weak bonds for F2, H2O2, N2H4,
e.g. BDE (kJ mol‑1): F2 155, Cl2 240, Br2 190, I2 149.
(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.: O2 vs S8, CO2 vs. SiO2, ketones vs. silicones
e.g. BDE (kJ mol‑1):
N-N
P-P
single
167
200
double
418
310
triple
946
490

25. Binding Energies

26. 234 213 I 310 285 Br 381 327 Cl 565 485 F Si-X C-X X BDEs (kJ mol‑1):
Preference for - multiple bonding compared to chain-linked single bonds
increments (/, in kJ mol‑1):
C-C
N-N
O-O
322/295
160/395
145/350
Si-Si
P-P
S-S
195/120
200/145
270/155
Ge-Ge
As-As
Se-Se
165/110
175/120
210/125
also: bond ionicity
cf. silicates, etc…!
234
213 I
310
285 Br
381
327 Cl
565
485 F
Si-X
C-X X
BDEs (kJ mol‑1):

27. Pauling
Allred-Rochow

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

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. MgF64- SiF62- SF6 covalency increases ionicity increases
On the Definition of Hyper-(co)-Valency
MgF SiF SF6
covalency increases
ionicity 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, spmdn hybrids,
electroneutrality principle
Pauling 1931, 1940, 1948
3-center-4-electron-bond
Pimentel 1951; Hach, Rundle 1951

34. F Xe F F - Xe+ F F Xe + F - F - Xe2+ F - covalent, hypervalent
Limiting Bonding Situations:
Example of Different Lewis Structures for XeF2
F - Xe2+ F -
F Xe F
F Xe + F -
F - Xe+ F
covalent, hypervalent
partially ionic,
delocalized
ionic

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

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

37. 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:

38. + l = pp + l dp = polarized pp The Role of d-Polarization-Functions
electric field

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

40. Improved Analyses of Accurate Wave Functions
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.)

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

42. - O Cl3+ O - - O Cl3+ O - 0% 60.9% 12x2.0% = 24.0% 15% O O Cl O - O
Which NRT-Lewis Structure Describes the Perchlorate Ion Best?
NRT weight: O 0%
O Cl O - O
O -
- O Cl3+ O -
60.9%
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. H C C C C C H p3* su Hyperconjugation Exemplified by Cyclopentadiene
...... H C C
p3* su C C C H

44. F F C H H p(F) s*(C-F) F F- F+ F+ F- C C C H H H
Negative Hyperconjugation Exemplified by Difluoromethane C H F C H F- F+ C H F+ F-
......
p(F) F F
s*(C-F) C H H

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

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

47. e.g. XeF2, XeF4, XeF6, SF4, ClF3, etc….
Musher’s Classification of
„Hypervalent“ Compounds
(Musher 1969)
1. order
2. order
e.g. XeF2, XeF4, XeF6, SF4, ClF3, etc….
lone pair present
s-character
concentrates in LP
e.g.
PF5, SF6, JF7
highest possible
oxidation state
s-character in bonds

48. MO-Diagram of SF6

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 PF5, SF6, etc., delocalization is more complex due to s-orbital participation  significant hypervalent populations

50. Transition Metal Systems3d

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

52. M L (n-1)d (n-1)s,p Pauli repulsion outermost  stretched bond
The problem of the outermost core shells in transition-metal atoms M L
(n-1)s,p
outermost
core shell
Pauli repulsion
 stretched bond
(n-1)d
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. Kaupp J. Comput. Chem. 2007, 28, 320.
See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.

53. M (n-1)d (n-1)s,p Pauli repulsion outermost  stretched bond
The problem of the outermost core shells in transition-metal atoms M
(n-1)s,p
outermost
core shell
Pauli repulsion
 stretched bond
(n-1)d
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. Kaupp J. Comput. Chem. 2007, 28, 320.
See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.

54. M L (n-1)d (n-1)s,p Pauli repulsion outermost  stretched bond
The problem of the outermost core shells in transition-metal atoms M L
(n-1)s,p
outermost
core shell
Pauli repulsion
 stretched bond
(n-1)d
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. Kaupp J. Comput. Chem. 2007, 28, 320.
See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.

55. Non-VSEPR Structures
and Bonding for d0-Systems

56. Non-VSEPR Structures of d0-Systems
VSEPR = valence-shell electron-pair-repulsion model

58. Practical Relevance of d0-Systems
e.g. catalysis
e.g. bioinorganic chemistry
ZrO2,
ferroelectric perovskites
e.g. materials
Mo-Cofactor (after Rajagopalan, Johnson)

59. The Question of BendingMg F
The Question of Bending
of the Alkaline Earth
Dihalides
1230 Ba F
linearization energies in kJ/mol from SDCI calculations
(J. Am. Chem. Soc. 1991, 113, 6012)

60. M X Factors Controlling the Structures of d0 Systems
maximization of d-orbital participation in -bonding
mutual repulsion and polarization of the ligands
distorted, „non-VSEPR“ structures
regular, „VSEPR“ structures
polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation
maximization of -bonding M X
(??)
Review:
Angew. Chemie 2001, 113, 642.

61. d-Orbital-Contributions to HOMO in d0 MX2-Complexes

63. projected on electron density (cloud of points)
BaH2: 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. Radial Distribution of (Pseudo)-Valence Orbitals of Barium
0.20 5p
0.15 6p 5d
0.10
r f(r) (a.u.)
0.05 6s
0.00
-0.05 2 4 6
r (Å)
outer-core polarization and d-orbital participation cannot be separated completely!

66. M X Factors Controlling the Structures of d0 Systems
maximization of d-orbital participation in -bonding
mutual repulsion and polarization of the ligands
distorted, „non-VSEPR“ structures
regular, „VSEPR“ structures
polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation
maximization of -bonding M X
(??)
Review:
Angew. Chemie 2001, 113, 642.

67. Low Ligand-Ligand Repulsion for Neutral Ligands
J. Phys. Chem. 1992, 96, 7316
Ba2+(H2O)2 Ba
DE(MP2)Lin= 0.6 kJ/Mol O O
1170
Ba2+(H2O)3 Ba O O O
DE(HF)Plan= 0.4 kJ/Mol
980

68. Cs+(H2O)2 Cs O O
1220
DE(MP2)Lin= 0.2 kJ/Mol

69. M X Factors Controlling the Structures of d0 Systems
maximization of d-orbital participation in -bonding
mutual repulsion and polarization of the ligands
distorted, „non-VSEPR“ structures
regular, „VSEPR“ structures
polarization of central-atom semi-core orbitals by the ligands, „inverse polarization“ of cation
maximization of -bonding M X
(??)
Review:
Angew. Chemie 2001, 113, 642.

70. X: Li BeH BH2 CH3 NH2 OH F C2v(in-plane) Cs C2v(out-of-plane) Ba Ba
Effects of p-Bonding
C2v(in-plane)
X: Li BeH BH2 CH3 NH2 OH F 5 10 15 20 25 30
DElin/
kJ mol-1 Cs
C2v(out-of-plane) Ba Ba N N N N
118.4º
128.8º
C2v(in-plane)
DE(HF) = 0.0 kJ mol-1
C2v(out-of-plane)
DE(HF) = kJ mol-1

71. MR2 (M = Ca, Yb, Eu; R = C[Si(CH3)3]3 )
Eaborn et al. Organomet. 1996, 15, 4783.
J. Chem. Soc., Chem. Commun. 1997, 1961.

72. Sc H H H F Sc F F Structural Preferences of d0 MX3 Complexes
C. A. Jolly, D. S. Marynick Inorg. Chem. 1989, 28, 2893.

73. p-Acceptor-Type d-Orbitals for Linear and Bent MX2 d0 Complexes
‘pip’, ‘b2’
‘pop’, ‘a2’ X
‘pip’, a1
‘pop’, a2 M X X
‘pop’, b1

74. p-Bonding Favors Bent Structure in some Cases!

75. p-Bonding Favors Bent Structure in some Cases!

76. Cl Cl Ti Si C C (CH3)2SiCl2 (CH3)2TiCl2
Inversion of Bent’s rule for d0-Systems Ti C Cl
117.30
102.80 Si C Cl
107.50
114.20
(CH3)2SiCl2
(CH3)2TiCl2
GED data, Haaland et al., 1996.
Explanation via p-contributions: Chem. Eur. J. 1999, 5, 3632.

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

80. 95.60 2.15 Å 2. 18 Å 2.21 Å 75.60 84.60 The Structure of W(CH3)6 W WD3 C3
transition state
minimum
+17 kJ/mol
CCSD(T)
M. Kaupp J. Am. Chem. Soc. 1996, 118, 3018.

82. MO Rationalization of Nonoctahedral d0 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 sd5 hybrids.

85. Energetics of Baylar Twist for MX6 d0 Complexes
D3h M M
transition state Oh
minimum
Relative energies (kJ mol—1) between D3h and Oh
structures of group 6 hexahalide complexes Cr Mo W F
61.6
27.1
42.9 Cl
56.4
62.6
78.7 Br -a
61.9
74.9 I
66.4
aDFT-BP86 results, Angew. Chem., Int. Ed. Engl. 2001, 40, 3534.
No convergence for CrBr6, CrI6, MoI6.

86. and trigonal prismatic
dihedral d = 26º
2.414 Å
88.7º
2.406 Å
83.5º Mo S 5 10 15 20 25 30 35 40 45 50 55 60
Mo(SH)6:
intermediate
between octahedral
and trigonal prismatic
Erel /
kJ mol-1
d / deg

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

88. The Structure of WCl5CH3
83.30
79.90 C
Cl3
2.19 Å
2.32 Å
Cl2
78.10 C
Cl4
102.10
2.35 Å W
2.22 Å
Cl2
Cl1
81.10
Cl3 W
2.39 Å
2.33 Å
75.60
2.34 Å
81.90
2.35 Å
2.35 Å
Cl5
Cl1
Cl5
Cl4
85.30
<Cl1-W-Cl5 = 97.90
<Cl1-W-Cl2 =
<Cl3-W-Cl4 =
<Cl1-W-Cl3 = 87.00
Cs oct.
Cs trig. prism
transition state
minimum
+19 kJ/mol
BP86/A
BP86 data, relative energies in kJ/mol
Angew. Chemie 1999, 111, 3219

89. tp “same face”, Cs (TS +14.5) cis oct. C2v (TS +25.7)
The Structure of WCl4(CH3)2
tp “same face”, Cs
(TS +14.5)
cis oct. C2v
(TS +25.7)
cis tp “other face”, C2v
(TS +8.5)
trans oct. C2
(min. 0.0)
“intermediate” C2
(min. +6.5)
BP86 data, relative energies in kJ/mol
Angew. Chemie 1999, 111, 3219

90. oct. fac. C3v (TS +61.2) oct. merid. Cs (TS +26.0) tp “across” C1
The Structure of WCl3(CH3)3
oct. fac. C3v
(TS +61.2)
oct. merid. Cs
(TS +26.0)
tp “across” C1
(min. 0.0)
tp “same face” C3
(min. +2.3)
BP86 data, relative energies in kJ/mol
Angew. Chemie 1999, 111, 3219

91. Examples of Unsymmetrical Metal Coordination in Oxide Materials oxide
related material properties
ZrO2
7-fold coordination (baddeleyite) vs. cubic high-temperature form
refractive ceramics
(stabilization of cubic form)
WO3
6-fold, dist. octahedral
electrochromic ceramics
MoO3
6-fold, strongly dist. octahedral
heterogeneous catalyst
BaTiO3,
etc.*
ferroelectric and piezoelectric ceramics
*5d vs. 4d comparisons:
KTaO3 is regular octahedral (cubic) and paraelectric, KNbO3 is distorted (rhombohedral)
and ferroelectric at lower temperatures.
LiTaO3 has a ferroelectric transition at lower temperature (950 K) than LiNbO3 (1480 K).
More ionic bonding and larger band gap with 5d vs. 4d, due to relativistic effects!

92. Structures of the Dihydride Dimers M2H4 (M = Mg, Ca, Sr, Ba)
(relative MP2 Energies in kJ/Mol)
C2h
D2h
+19.2
+35.5
0.0
+20.1
+56.0
C2v
C3v
+115.0
+5.9
0.0
D4h
+507.0
+130.4
+86.5
+33.4
C2v
J. Am. Chem. Soc. 1993, 115, 11202

93. Summary: Understanding Non-VSEPR Structures in d0-Complexes
-d0 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 d0 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 TiCl2(CH3)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
occupancy-weighted Löwdin orthogonalization
NAO basis
“natural atomic orbitals”
“natural minimal basis set” (strongly occupied)
“natural Rydberg basis set” (sparsely occupied)
NHO basis
“natural hybrid orbitals”
“natural bond orbitals”
NBO-Lewis-structure
NBO basis
“natural resonance theory” (NRT)
superposition of NBO-Lewis structures
Weinhold et al. 1995
NLMO basis
“natürliche lokalisierte Orbitale”

96. NRT Weights (w) for Various Lewis Structures
in Oxo Anions and Sulfur Oxides
„wmod“(%)
„worig“(%)
„walt“(%)
„hypervalent“
„original
Lewis“
„no-bond/
double-bond“
PO43-
0.0 (0.0)
71.0 (53.1)
20.3 (28.4)
SO42-
66.2 (46.9)
23.1 (49.8)
ClO4-
60.9 (36.8)
31.4 (60.7)
SO3
87.9 (77.3)
5.9 (9.2)
SO2
95.2 (90.2)
4.8 (8.6)
species
NRT at HF/6-31G* (MP2/6-31G*) level
Weinhold et al., 1995

97. M C2
C2A C1 H1 H2 H3 M
Structure of Mo(butadiene)3

98. Si H + Zr H + Si H . Zr H . Si H - - Zr H
Limits of the Isolobal Principle Si H + Zr H +
d(Si-H)=1.488Å, <H-Si-H=120.0º
d(Zr-H)=1.800Å, <H-Zr-H=104.8º Si H . Zr H .
d(Si-H)=1.500Å, <H-Si-H=110.9º
d(Zr-H)=1.862Å, <H-Zr-H=116.6º Si H - - Zr H
d(Si-H)=1.563Å, <H-Si-H=93.3º
d(Zr-H)=1.902Å, <H-Zr-H=120.0º
Review: M. Kaupp Angew. Chemie 2001, 113, 3642.

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

101. a‘‘,e‘ 5p
a‘‘ Y4
e‘‘ a‘ 5s
3e‘
2e‘‘ a‘
3a‘ Y3 e‘
2a‘ 4d
a‘,e‘,e‘‘
2e‘
e‘‘ Y2
1a‘‘
a‘‘
1e‘‘ e‘
1e‘ Y1 a‘
1a‘
(C4H6)3
Mo(C4H6)3
C3h Mo

102. „Non-Berry“ Rearrangement of TaH5

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