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 d 0 Complexes
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Hybridization and hypervalency in transition-metal and main-group bonding
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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=l
01
0
dxm
x
xn
The Nodes of the Radial Solutions
R is the product of an exponential e-(1/2)r and of anassociated Laguerre polynomial; r = 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 Consequences
in p-Block Chemistry
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)
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)
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
020406080
100120140160
PbF4 PbMeF3 PbMe2F2 PbMe3F PbMe4
PbMenF4-n→ PbMenF2-n +F2
PbMenF4-n→ PbMen-1F3-n +MeF
PbMenF4-n→ PbMen-2F4-n +C2H6
DEre
act. (
kJ m
ol-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)
EH4 h(E) charge Q(E)
EF4 h(E) charge Q(E)
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)
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
NPA
Atom
ic Charge on Pb
p/s r
atio
of P
b-X
bon
ding
NL
MO 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…..
• large electronegativity of 2p-elements also arises from compact 2p shell
Hypervalency?On Myth and Reality ofd-Orbital-Participation
in Main-Group Chemistry
On the Definition of Hyper-(co)-Valency
MgF64- SiF6
2- 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
• in PF5, SF6, etc., delocalization is more complex due to s-orbital participation significant hypervalent populations
3d
Transition Metal Systems
r f(r
) in
a.u.
r in a.u.J. Comput. Chem. 2007, 28, 320
Radial Orbital Densities of the Manganese Atom
M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.
M L
(n-1)s,poutermost 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.
M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.
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,poutermost core shell
Pauli repulsion stretched bond
(n-1)d
The problem of the outermost core shells in transition-metal atoms
M. Kaupp J. Comput. Chem. 2007, 28, 320. See also: M. A. Buijse, E. J. Baerends J. Chem. Phys. 1990, 93, 4129.
M L
(n-1)s,poutermost 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.
Non-VSEPR Structuresand Bonding for d0-Systems
Non-VSEPR Structures of d0-Systems
VSEPR = valence-shell electron-pair-repulsion model
Structural Preferences of d0 Systems 1 Ia 18
VIIIa 1 H 2 He 1
2 IIa
13 IIIa
14 IVa
15 Va
16 VIa
17 VIIa
3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 2
11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 3
3
IIIb 4
IVb 5
Vb 6
VIb 7
VIIb 8 9 10
VIIIb
11 Ib
12 IIb
19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 4
37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 5
55 Cs 56 Ba 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 6
87 Fr 88 Ra 104 Rf 105 Ha 106 Sg 107 Bh 108 Hs 109 Mt 110 Uun 111 Uuu 112 Uub 113 Uut 114 Uuq 115 Uup 116 Uuh 117 Uus 118 Uuo 7
119 Uue 120 Ubn 8
57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 6
89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 7
e.g. catalysis
Practical Relevance of d0-Systems
e.g. bioinorganic chemistry
Mo-Cofactor (after Rajagopalan, Johnson)
ZrO2,ferroelectric perovskites
e.g. materials
1230
Ba
F F
F Cl Br I Be linear linear
linear
linear
Mg linear linear linear linear
Ca quasilinear
quasilinear
quasilinear
quasilinear
Sr bent,
DElin = 6.6 quasilinear quasilinear quasilinear
Ba bent, DElin = 20.9
bent, DElin = 6.8
bent, DElin = 4.5
quasilinear
MgF F
linearization energies in kJ/mol from SDCI calculations(J. Am. Chem. Soc. 1991, 113, 6012)
The Question of Bendingof the Alkaline Earth
Dihalides
regular, „VSEPR“ structuresdistorted, „non-VSEPR“ structurespolarization 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
XX(??)
M2+
X-X-
XM
X
Factors Controlling the Structures of d0 Systems
Review:Angew. Chemie 2001, 113, 642.
X X
a) linear structure:
(e.g. BeX2, MgX2)
M
X
M
b) bent structure
(e.g. SrX2, BaX2)X
d-Orbital-Contributions to HOMO in d0 MX2-Complexes
M2+
X-X-
M2+ X-X-
Polarized- I on Model Explanation of Bent MX2 Structures
no permanent dipole moment
permanent dipole moment:charge-dipole and dipole-dipole interactions
Klemperer et al., 1963; Guido, Gigli, 1976.
BaH2: Electron Localization Function (ELF, color scale)
projected on electron density (cloud of points)
Bending Force Constants (at Linear Structure)for Molecular Alkaline Earth Dihalides
BP86 data, relative energies in kJ/molAngew. Chemie 1999, 111, 3219
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
H HH
-
Limits of the Isolobal Principle
Review: M. Kaupp Angew. Chemie 2001, 113, 3642.
Examples of Unsymmetrical Metal Coordination in Oxide Materialsoxide coordination 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.*
6-fold, dist. octahedral
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!
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
C3v
C2v
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, d4 3 x 4, MoIV, d2
(NRT analysis: 3x10%)
Intermediate Resonance Structures for tris(Butadiene)-Molybdenum and Related Complexes
Y1
Y2
Y3
Y4
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)3
C3h
„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.