Hybridization and hypervalency in transition-metal and main-group bonding Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 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 d0 Complexes
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Hybridization and hypervalencyin transition-metal and main-group bonding
Martin Kaupp, Winter School on Quantum Chemistry, Helsinki, Dec. 13-17, 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 d0 Complexes
Analogy between Wave Functions and Classical Standing Waves
Vibrations of a string fixed at bothends. Base tone and the first twoharmonics are shown.
base tone
1. harmonic
2. harmonic
Note the nodes (zero crossings)!!They result from the necessaryorthogonality of the modes.
x=0 x= Obj100
The Nodes of the Radial Solutions
R is the product of an exponential e-(1/2) and of an
associated Laguerre polynomial; = 2Zr/na0
1s, 2p, 3d, 4f: no „primogenic repulsion“ (Pekka Pyykkö)
1s
2p
3d
4f
2p
See also: J. Comput. Chem. 2007, 28, 320.
2p2p
See also: J. Comput. Chem. 2007, 28, 320.
P-Block Main-Group Elements
Hybridization Defectsand their Consequencesin p-Block Chemistry
Formatvorlage des Untertitelmasters durch Klicken bearbeiten
X-H Binding Energies of Monohydrides XH,and of „Saturated“ Hydrides MHn
W. Kutzelnigg Angew. Chem. 1984, 96, 262.
W. Kutzelnigg Angew. Chem. 1984, 96, 262.
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
Reasons for Hybridization (1)
better bonding overlap
reduced antibonding overlap
(angular)
(radial)
W. Kutzelnigg, Einführung in die Theoretische Chemie, Vol. 2
Reasons for Hybridization (2)
Mulliken gross populationsfor valence AOs in XHn hydrideswithout free electron pairs
W. Kutzelnigg Angew. Chem. 1984, 96, 262.
Hybridization Defects (1)
Hybridization Defects (2)
*A posteriori hybridization analyses from DFT calculations (BP86/TZVP)
Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds
J. Am. Chem. Soc.1993, 115, 1061.
QCISD/DZ+P data
-60
-40
-20
0
20
40
60
80
100
120
140
160
PbF4 PbMeF3 PbMe2F2 PbMe3F PbMe4
PbMenF4-n→ PbMenF2-n +F2
PbMenF4-n→ PbMen-1F3-n +MeF
PbMenF4-n→ PbMen-2F4-n +C2H6E
reac
t. (
kJ
mol
-1)
Substituent Effects on 1,1-Elimination Reactions of Pb(IV) Compounds
J. Am. Chem. Soc. 1993, 115, 1061.QCISD/DZ+P data
Hybridization Defects (3)
h(E): NPA/NLMO Hybridization
results from DFT calculations (BP86)
0.40.60.81.01.21.41.61.82.02.22.42.62.83.0
0.40.60.81.01.21.41.61.82.02.22.42.62.83.0
NP
A A
tomic C
harge on
Pb
p/s
rat
io o
f P
b-X
bon
din
g N
LM
O NPA Charge
Pb-F bond
Pb-C bond
Pb(CH3)4 Pb(CH3)3F Pb(CH3)2F2 Pb(CH3)F3 PbF4
Influence of Electronegative Substituents on Hybridization in PbIV Compounds
J. Am. Chem. Soc. 1993, 115, 1061.
Bent‘s Rule: Basic Principles
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)
• for the heavier p-block elements, hybridization defects are important for inert-pair effect, inversion barriers, Bent‘s rule effects, double-bond rule…..
Hypervalency?On Myth and Reality ofd-Orbital-Participationin Main-Group Chemistry
On the Definition of Hyper-(co)-Valency
MgF64- SiF62- SF6
covalency increases
ionicity increases
certainly no hypervalency hypervalency ?
A Working Definition of Hypervalency
We regard a molecule as hypervalent if at least for one atom the bonding situation requires more valence orbitalsthan available for the free atom
The Early History of Hypervalency, Part 1
electron pair theory, octet ruleLewis 1916; Kossel 1916; Langmuir 1919
BP86 data, relative energies in kJ/molAngew. Chemie 1999, 111, 3219
Formatvorlage des Untertitelmasters durch Klicken bearbeiten
The Structure of WCl4(CH3)2
trans oct. C2(min. 0.0)
“intermediate” C2(min. +6.5)
cis oct. C2v(TS +25.7)
cis tp “other face”, C2v(TS +8.5)
tp “same face”, Cs(TS +14.5)
BP86 data, relative energies in kJ/molAngew. Chemie 1999, 111, 3219
The Structure of WCl3(CH3)3
tp “across” C1(min. 0.0)
tp “same face” C3(min. +2.3)
oct. fac. C3v (TS +61.2)
oct. merid. Cs (TS +26.0)
BP86 data, relative energies in kJ/molAngew. Chemie 1999, 111, 3219
d(Si-H)=1.488Å, <H-Si-H=120.0º
d(Si-H)=1.563Å, <H-Si-H=93.3º
d(Si-H)=1.500Å, <H-Si-H=110.9º
d(Zr-H)=1.800Å, <H-Zr-H=104.8º
d(Zr-H)=1.902Å, <H-Zr-H=120.0º
d(Zr-H)=1.862Å, <H-Zr-H=116.6º
SiH
HH
+
Zr
HH
H
+
Si
HHH
.
Zr
H HH
.
-
ZrH
HHSi
HH
H
-
Limits of the Isolobal Principle
Review: M. Kaupp Angew. Chemie 2001, 113, 3642.
Examples of Unsymmetrical Metal Coordination in Oxide Materials
*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!
J. Am. Chem. Soc. 1993, 115, 11202
Structures of the Dihydride Dimers M2H4 (M = Mg, Ca, Sr, Ba)(relative MP2 Energies in kJ/Mol)
D2h
C3vC2v
C2h
D4h
C2v
0.00.0+20.1+56.0
+507.0+130.4+86.5+33.4
+115.0+5.90.00.0
+19.2+35.5
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.
Thank you for your attention!
MM
C2
C2A
C1
H1H2
H3
Structure of Mo(butadiene)3
Extreme Resonance Structures for tris(Butadiene)-Molybdenum and Related Complexes
M M
3 x 3, MoII, d43 x 4, MoIV, d2
(NRT analysis: 3x10%)
Intermediate Resonance Structures for tris(Butadiene)-Molybdenum and Related Complexes
1
2
3
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(C4H6)3 Mo(C4H6)3C3h
„Non-Berry“ Rearrangement of TaH5
Trends of the s- and d-valence orbitals in the transition metal seriesa) radial size
from Dirac-Fock calculations (Desclaux)
Trends of the s- and d-valence orbitals in the transition metal series b) orbital energies
from Dirac-Fock calculations (Desclaux)
Why??
Angew. Chem., Int. Ed. Engl. 2001, 40, 3534.
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.