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

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.


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


Hybridization Defects (1)


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)

cos(180-) = a2/(1-a2) (a2 = s-character, 1-a2 = p-character)

Holds only for orthogonal hybrids!

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

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……)

-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

D Ere

act.

(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

-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


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)

Cl

Si

Cl

H3CCH3

1140

1090

1070

larger angles betweenmore electropositive substituents

more s-character of central atom is directedtowards less electronegative substituent,more p-character to more electronegative substituent

Si CH3

Si Cl

e.g.:

Pb

Pb

Pb

Bent‘s rule effects in organolead fluorides

Quasirelativistic ab initio calculations, J. Am.Chem. Soc. 1993, 115, 1061.

102.80

115.50

134.80

101.40

104.10

116.40

101.10

Bent‘s Rule: Counteracting Effects

negative hyperconjugationcounteracts EN effects

negative hyperconjugation„switched off“

negative hyperconjugationsmall for heavier elements

EH3 h(E-H) h(LP-E)NH3 sp3.14 sp2.61

PH3 sp5.29 sp0.76

AsH3 sp7.08 sp0.51

Bent‘s Rule and Lone Pairs

h: NPA/NLMO Hybridization

results from DFT calculations (BP86)

Inversion Barriers and Hybridization

TS

†

pure p-character of LPhigh s-character in bondshigh 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

Further Pecularities of 1st-Row (2. Period) Elements (p-Block)

N-N P-Psingle 167 200double 418 310triple 946 490

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):

Binding Energies

increments (/, in kJ mol‑1):C-C N-N O-O

322/295 160/395 145/350Si-Si P-P S-S

195/120 200/145 270/155Ge-Ge As-As Se-Se

165/110 175/120 210/125

Preference for - multiple bonding compared to chain-linked single bonds

also: bond ionicitycf. silicates, etc…!

234213I310285Br381327Cl565485FSi-XC-XX

BDEs (kJ mol‑1):

Allred-Rochow

Pauling

OH3C CH3

Electron-Localisation-FunctionElectron-Localisation-Function

OH3Si SiH3

The Si-O Bond has a Strong Ionic Character

154o111o

Silicon-Oxygen Bonds ElectronegativitySi: 1.74 O: 3.50

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

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

directed valency, spmdn hybrids, electroneutrality principle Pauling 1931, 1940, 1948

3-center-4-electron-bondPimentel 1951; Hach, Rundle 1951

Limiting Bonding Situations: Example of Different Lewis Structures for XeF2

covalent, hypervalent

partially ionic,delocalized

ionicF - Xe2+ F -

F Xe F

F Xe + F -F - Xe+ F

F Xe + F -F - Xe+ F

3-Center-4-Electron MO Model

a

b

n

a

b

n

a

b

n

a

b

n

F Xe + F -F - Xe+ F

Modified 3-Center-4-Electron MO Model

discovery of noble-gas compoundsChernik 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:

The Early History of Hypervalency, Part 2

+ l =

The Role of d-Polarization-Functions

p + l d polarized p

electric field

Mulliken Population Analysis (1955)

MO-LCAO:

r( )rj

m

i

m

i j Pij r = electron density

n = r rr( )dj

m

i

m

P Sij ij n = total electron number

Q P Sij ij ij 2 ;( )i j Qij = overlap population

q = i P P Sii ij iji j

m

qi = gross AO population

q = qA i

A

i qA = gross atom population

weak points of Mulliken population analysis:strong basis-set dependenceunphysical (partly negative) populationsfailure for transition to ionic bonding

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. 1994 (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

“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

“natural resonance theory” (NRT)superposition of NBO-Lewis structuresWeinhold et al. 1995

occupancy-weighted Löwdin orthogonalization

- O S2+ O -

O

O 2-

- O S2+ O -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* levelWeinhold et al., 1995

O

O 2-

- O Cl3+ O -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 Cl3+ O -

further ionic structures: NRT at HF/6-31G* levelWeinhold et al., 1995

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- 0.0 (0.0) 66.2 (46.9) 23.1 (49.8)

ClO4- 0.0 (0.0) 60.9 (36.8) 31.4 (60.7)

SO30.0 (0.0) 87.9 (77.3) 5.9 (9.2)

SO20.0 (0.0) 95.2 (90.2) 4.8 (8.6)

NRT at HF/6-31G* (MP2/6-31G*) levelWeinhold et al., 1995

species

C

C

C

CC

H

H

CC

C

C

H

H

Hyperconjugation Exemplified by Cyclopentadiene

CH+C C

CC-

H

u3*

C

C

C

C-

CH+

H ......

C

Negative Hyperconjugation Exemplified by Difluoromethane

......

C

H H

F F(F)

*(C-F)

C

H H

F- F+

C

H H

F+ F-

C

H H

F F

Negative Hyperconjugation in F3PO

......P+

FO-

F

F

P+F-

OFF

P+F

OF

F-

(O)(to e-MO)

*(P-F)(to e*-MO) P

FO

FF

(M)*(P-F) PF

MFF

…….and for -backbonding in phosphane complexes…….

Musher’s Classification of„Hypervalent“ Compounds

1. order 2. order

e.g. XeF2, XeF4, XeF6, SF4, ClF3,

etc….

lone pair presents-character

concentrates in LP

e.g.PF5, SF6, JF7

highest possible oxidation state

s-character in bonds

(Musher 1969)

MO-Diagram of SF6

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

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 M



(n-1)d



M L



(n-1)d




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

J. Am. Chem. Soc. 1991, 113, 6017

0.9

0.9

CaCl2CaBr2CaI2

CaF2

MgF2

MgBr2

MgI2 MgCl2

BeF2

BeCl2

BeBr2

BeI20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Ab initio Abwinkelungs-Kraftkonstanten (mdyn/Å)

Abw

inke

lung

s-K

raftk

onst

ante

nau

s po

lariz

edio

nM

odel

l (m

dyn/

Å)

0.9

0.9

CaCl2CaBr2CaI2

CaF2

MgF2

MgBr2

MgI2 MgCl2

BeF2

BeCl2

BeBr2

BeI20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Ab initio Abwinkelungs-Kraftkonstanten (mdyn/Å)

Abw

inke

lung

s-K

raftk

onst

ante

nau

s po

lariz

edio

nM

odel

l (m

dyn/

Å)

force constants from polarized ion model too low for Be and Mg complexes but too high for Ca, Sr, and Ba complexes

0 2 4 6

-0.05

0.00

0.05

0.10

0.15

0.20 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!







M

XX

(??)

M2+

X-X-

XM

X



Low Ligand-Ligand Repulsion for Neutral LigandsJ. Phys. Chem. 1992, 96, 7316

1170

DE(MP2)Lin= 0.6 kJ/Mol

Ba2+(H2O)2 Ba

O O

980 DE(HF)Plan= 0.4 kJ/Mol

Ba2+(H2O)3 Ba

O OO

1220

Cs

O O

DE(MP2)Lin= 0.2 kJ/Mol

Cs+(H2O)2







M

XX

(??)

M2+

X-X-

XM

X



X: Li BeH BH2 CH3 NH2 OH F0

5

10

15

20

25

30

C2v(in-plane)

C2v(out-of-plane)

CsDElin/

kJ mol-1

Ba Ba

N N NN

C2v(in-plane)DE(HF) = 0.0 kJ mol-1

C2v(out-of-plane) DE(HF) = +15.7 kJ mol-1

118.4º 128.8º

Effects of -Bonding

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.

Sc

Sc

H HH

F

FF

Structural Preferences of d0 MX3 Complexes

C. A. Jolly, D. S. Marynick Inorg. Chem. 1989, 28, 2893.

XX

M

XX

XX

‘ip’, ‘b2’

‘op’, ‘a2’

‘op’, a2

‘op’, b1

‘ip’, a1

-Acceptor-Type d-Orbitals for Linear and Bent MX2 d0 Complexes

180 170 160 150 140 130 120 110 100 905.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

Figure 5

av

ScF2+

ip

op

met

al ch

arac

ter o

f NLM

O (i

n %

)

F-Sc-F angle (degs)

-Bonding Favors Bent Structure in some Cases!

180 170 160 150 140 130 120 110 100 9010111213141516171819202122

Figure 6

av

ZrO2 op

ip

met

al ch

arac

ter o

f NLM

O (i

n %

)

O-Zr-O angle (degs)

-Bonding Favors Bent Structure in some Cases!

Inversion of Bent’s rule for d0-Systems

(CH3)2TiCl2

GED data, Haaland et al., 1996.Explanation via -contributions: Chem. Eur. J. 1999, 5, 3632.

Si

CC

ClCl

107.50

114.20

(CH3)2SiCl2

Ti

CC

ClCl

117.30

102.80

The Structural Preferences of TaX5 d0 Complexes

TaCl5 trigonal bipyramid

(square pyr. TS, +7 kJ/Mol)

TaH5 square pyr.

(trig. bipyr, +84 kJ/Mol)

Ta(CH3)5 square pyr.

(trig. bipyr. TS, +32 kJ/Mol) MP2 energies from: Kang et al. J. Am. Chem. Soc. 1993, 115, 1971

S- S-

H2H2

S- S-

HH

S S

HH

typical ligand types:

Examples for Nonoctahedral Complexes with Sulfur Ligands

See, e.g.: Can. J. Chem. 1989, 67, 1914Inorg. Chem. 1993, 32, 2085Inorg. Chem. 1989, 28, 773, etc.....

The Structure of W(CH3)6

C3

D3

minimumtransition state

+17 kJ/mol CCSD(T)

2.15 Å

2.21 Å

95.60

75.60

2. 18 Å

84.60

W W

M. Kaupp J. Am. Chem. Soc. 1996, 118, 3018.

Structural Preferences of Hexamethyl Complexes

species: config. structure, DEa

WMe6

MoMe6

CrMe6

d0

d0

d0

C3, 25 (NR: 53)

C3, 39

C3, 12

MMe6- (M=V,Ta)

NbMe6-

d0

d0

D3

(C3, 1)

MMe62- (M=Ti,Zr,Hf) d0 D3

ReMe6+

TcMe6+

d0

d0

C3, 93

C3, 112

ReMe6, TcMe6 d1 D3

OsMe6, RuMe6 d2 D3

aenergy difference between D3 and C3 structure in

kJ/Mol (GGA-DFT level)

MO Rationalization of Nonoctahedral d0 Structures

S. K. Kang, H. Tang, T. A. Albright J. Am. Chem. Soc. 1993, 115, 1971.

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

Landis’ sd-Hybridization Model (2)(J. Am. Chem. Soc. 1998, 120, 1842)

Preferred coordination arrangements for sd5 hybrids.

Relative energies (kJ mol—1) between D3h and Oh structures of group 6 hexahalide complexes

Cr Mo WF 61.6 27.1 42.9Cl 56.4 62.6 78.7Br -a 61.9 74.9I -a -a 66.4

aDFT-BP86 results, Angew. Chem., Int. Ed. Engl. 2001, 40, 3534. No convergence for CrBr6, CrI6, MoI6.

minimum

transition stateMM

D3h

Oh

Energetics of Baylar Twist for MX6 d0 Complexes

2.414 Å

88.7º

2.406 Å

83.5º

Mo

SSS

S SS

dihedral d = 26º

d / deg

Erel /kJ mol-1

0 5 10 15 20 25 30 35 40 45 50 55 600

5

10

15

20

25

30

35

40

Mo(SH)6:intermediate

between octahedraland trigonal prismatic

Importance of trigonal prismatic intermediates and transition structures of certain molybdenum enzymes

Review: M. Kaupp Angew. Chemie, Int. Ed. Engl. 2004, 43, 546.

minimumtransition state

+19 kJ/mol BP86/A

2.34 Å

W

The Structure of WCl5CH3

2.22 Å

2.35 Å

C

Cl1

Cs oct. Cs trig. prism

Cl4

Cl3Cl2

Cl5

79.90

2.35 Å

83.30

85.30

75.6081.10

W

C

Cl1

Cl4

Cl3

Cl2

Cl5

2.33 Å

2.19 Å

2.39 Å

2.35 Å

2.32 Å78.10

102.10

81.90

<Cl1-W-Cl5 = 97.90

<Cl1-W-Cl2 = 179.80

<Cl3-W-Cl4 = 166.30

<Cl1-W-Cl3 = 87.00

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)


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)


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)

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.

Ca atom:radial orbital densities

3p orbital (outermost core shell)

3d orbital (valence shell)

Malrieu et al. Chem. Phys. Lett. 1983, 98, 433.

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

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