field development i. hybridization and molecular shapes · • two sp3 hybrid orbitals have maxima...

Valence Bond Concepts Applied to Molecular Mechanics Force Field Development

I. Hybridization and Molecular Shapes II. Resonance in MM Computations III. Valence Bond Theory and Shapes of Covalent Transition Metal Complexes IV. Modelling the Splitting of N 2 by Simple Mo(Amide) 3 Complexes.

Funding Provided by the National Science Foundation and Molecular Simulations Inc.

Mr. Dan Root Mr. Tom Cleveland Mr. Tim Firman

CollaboratorsProf. Tony Rappè (CSU) Prof. Notker Rösch (TU-Muenchen)

Special thanks to Schrödinger, Inc.

(length = r 0; force constant = k r)

+ van der Waals + electrostatic terms

torsional motionbond angle bendbond stretch

E = k r(r-r 0)2 + kθ(θ-θ0)2 + k φ(1+cos(n φ+δ)

Bond Angle Spring

Bond Spring

A Classical Mechanical Approach (Ball and Spring)

Molecular Mechanics Computations

H H

O

Issues Impacting Rational Design of Homogeneous Catalysts

MechanisticWhat step(s) control the reaction rate and selectivity?

StructuralWhat are the important steric interactions that guide selectivity?

Can the structures of new catalyst designs be predicted?

SyntheticCan promising designs of new catalysts be synthesized?

What Makes Transition Modeling So Difficult?• Transition Metal Complexes Have Complicated and Varied Shapes

OC FeCO

CO

O C

C O

N

FeN N

N

N PR3

RhR3P

PR3

+

Trigonal Bipyramid Square Pyramid T-Shape

OC NiCO

CO

Trigonal Plane

PR3

RhPR3R3P

R3P

+

Square Plane

• Transition Metal Complexes Often Have Indistinct Topologies

ZrR

+

ClPt

Cl

Cl

-

PR3

PR3

Rh

Method Development and the Pauling Point

Too Good To Be True

Too True To Be Good

Increasing Effort

Incr

easi

ng R

elia

bilit

yPauling Point

Empirical Ab Initio

Because molecular mechanics bonded terms are based on a localized bond topology, Valence Bond Theory is the natural viewpoint for the derivation of new potential energy functions.

Premise

• Description of Inorganic Molecular Shapes Including Conformational Dynamics • Theory-based Derivation of New Potential Energy Functions • Application to Full Periodic Table • Minimal Parametrization • Accuracy in Structures and Vibrational Frequencies Similar to MM3 for Organics • Bond Making and Bond Breaking

GoalsThe VALBOND/UFF Force Field

Valence Bond Theory and Molecular Shapes

• Covalent bonds are formed by the interaction of singly-occupied orbitals of the central atom and the ligands.

• Hybridization of these orbitals provides a mechanism for maximizing bond strength by concentrating electron density in the bonding region.

• Hybrid orbitals located on the same atom must be orthogonal and normalized.

• Two sp3 hybrid orbitals have maxima in their eigenfunctions at tetrahedral angles, sp2 hybrid orbitals have maxima at trigonal planar angles, sp hybrid orbitals have maxima at linear angles, and pure p orbitals have maxima at right angles.

Principles of the Directed Covalent Bond

Construction of Hybrid Orbitals“The dependence on r of s and p hydrogen-like eigenfunctions is not greatlydifferent ... the problem of determining the best bond eigenfunctions reducesto a discussion of the θ, ψ eigenfunctions.”

For Methane ψ1 = 12

s + 32

px

ψ2 = 12

s - 12 3

px + 23

pz

“... the best bond eigenfunction will bethat which has the largest value in the bond direction ... along the x-axis thebest eigenfunction is ψ1with a maximumvalue of 2, considerably larger than 1.732for a p eigenfunction.” Pauling, L. J. Am. Chem. Soc. 1931, 53, 1367

“A second eigenfunction can be introduced in the xz plane... This eigenfunctionis equivalent and orthogonal to ψ1, and has its maximum at an angle of 109o28’.”

Hybrid Orbitals for Other GeometriesGeometry Hybridization Strength

Linear sp1

sp6d51.912.96

Trigonal Plane sp2 1.991

Tetrahedron sp3

sp1.125d1.8752.002.950

Square Plane sp2d1 2.694

Octahedron sp3d2 2.923

Pauling, L. J. Am. Chem. Soc. 1931, 53, 1367

“I have not succeeded in determining whether or not these octahedral eigenfunctions are the strongest ...”

Forty Years Later Pauling Returned to the Problem of Constructing Hybrids

“ I have now found a simple relation between the strength (the bond-forming power) of a hybrid spd bond orbital and the angles that it makes with other similar orbitals...”

S0sp(α ) = 0.5 + 1.5cos2 (α 2)

+ 0.5 − 1.5cos2 (α 2)

S0spd(α ) = 3 − 6cos2 (α 2) + 7.5cos4 (α 2)

+ 1.5 + 6cos2 (α 2) − 7.5cos4(α 2)

Pauling, L. Proc. Nat. Acad. Sci. 1975, 72, 4200.

Generalized Hybrid OrbitalsFor any pair of hybrid orbitals with hybridization spmdn making the bondangle α, the strength functions are given by

S(α) = Smax 1−1−

where ∆ = overlap inte

and Smax =1

1+ m + n1(

Root, D. M.; Landis, C. R.; Cleveland, T. J. Am. Chem. Soc. 1993, 115, 4201.

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

2

0

15 30 45 60 75 90 105

120

135

150

165

180

Bond Angle (degrees)

spsp2sp3p

O

H H'

Pair Defect Sum Approximation

E(α) = kO-H(Smax - S(α)) + kO-H'(Smax - S(α))

Pair Defect = Smax - S(α)

α

For two ligands forming electron pair bonds with two spn orbitals, the energy of bond angle distortions is approximated by the strength defects in each of the bonds.

For H2O, the total energy as a function of bond angle is given b

where kO-H is a scaling parameter (VALBOND parameter)

Strength Functions Model Potential Energy Surfaces

Assuming that

1801601401201008060400

20

40

60

80

valbondab initioharmonic

Water

Angle (degrees)

Ener

gy (k

cal/m

ol)

• hybridizations are known• potential energies scale

linearly with pair-defects

the VALBOND force fieldmodels high quality ab initioenergies over large variationsin bond angles

Root, D. M.; Landis, C. R.; Cleveland, T. J. Am. Chem. Soc. 1993, 115, 4201.

HB

F

FH

BF

Fsp2.09

sp1.81

120.9

118.1

Lewis Structure

A quantitative expression of Bent's rule is used to distribute p-character among each ligand, lone pair, and singly occupied orbital.

Bent's Rule

quantitative

3 sp2 hybridshybridization

gross

• •••••

Given hybridizations for each bond orbital, the hybrid orbital strength functions accurately simulate bending potential energy surfaces.

But how are hybridizations determined?

Assignment of Hybridizations

Organic Rad icals and Carbenes

M olecule Angle VALBON D Exp1CH 2 H -C-H 103.0 102.43CH 2 H -C-H 131.7 136

CH 3 H -C-H 120 1201CF2 F-C-F 103.8 104.8

1CH F H -C-F 103.6 101.81CCl2 Cl-C-Cl 103.9 100(9)

Am ines, Phosp hines, and ArsinesM olecule Angle VALBON D Exp.BF2N H 2 F-B-F

H -N -H119.9115.0

117.9116.9

N Cl3 Cl-N -Cl 106.5 107.1N H Cl2 H -N -Cl

Cl-N -Cl106.7106.1

102106

N O2 O-N -O 149.2 134.1N ClO Cl-N -O 120.0 113.3PH 3 H -P-H 93.8 93.3PCl3 Cl-P-Cl 100.1 100.1

CH 3PH 2 C-P-HH -P-H

97.191.3

96.593.4

AsH 3 H -As-H 91.7 92.1AsF3 F-As-F 96.0 96.0AsCl3 Cl-As-Cl 98.7 98.6AsBr3 Br-As-Br 99.6 99.7AsI3 I-As-I 100.2 100.2

Ino rganic Flo tsam and JetsamM olecule Angle VALBON D Exp.Sn6(Ph2)6Ph2Sn

Ph2Sn SnPh2 SnPh2

SnPh2SnPh2

<Sn-Sn-Sn>C-Sn-C

112.4105.5

112.5106.7

B3Ph3O3

Ph2BO

BPh2

OBPh2

O

<B-O-B><O-B-O>

121.8118.2

121.7118.0

PO4P3O 3

P2

O3P3 O

PO

O2O

O4P 1

O1

O1-P1-O2O2-P1-O4O2-P2-O3P1-O2-P2P2-O3-P2

114.1104.599.3122.9127.3

11510399124128

Ga2Pyr2Br4

Ga Gapyridine

pyridine

BrBr

BrBr

Br-Ga-BrGa-Ga-Br

107.0115.1

105.8116.3

As3(CH 3)6In3(CH 3)6

AsIn

As

InAs

In

C-In-CC-As-C

101.9124.7

99126

4 valbond parameters (scaling factors)

4 hybridization weighting factors

VALBOND Requires:

20 equilibrium bond angles

20 bending force constants

MM3 Requires:

A Comparison of Parametrization: VALBOND & MM3

C C CH3H CC

CH

HH

H H

HH H

C CH

H

CH3

HO

CH H H3C

OCH3

O

CH3C O

CH3

• Use of d2sp3 (e.g. SF6) and dsp3 (e.g. PF5) hybridization

schemes is incompatible with ab initio computations.

• If d-orbitals are excluded, it is not possible to generate

enough hybrid orbitals to accommodate all bonds and lone

pairs.

• Ionic resonance helps explain molecular stabilities but does

not lead to simple justification of molecular shapes.

FXe F Xe FXe

Simple Valence Bond Hybrids (Localized Bonds) Are Poor Descriptors of Hypervalent Molecules

-F

+F

+F

-

0

20

40

60

80

100

120

60 90 120 150 180

Angle (degrees)

MP21-3-van der Waals

1-3-Coulombic

MP2

VDW

Coulombic

Origins of the Angular Distortion Potential of XeF2: Orbital or 1,3 Repulsion?

Cl

F

Hypervalent VALBOND Uses Both 2c-2e and 3c-4e Bonds as Fundamental Bonding Units

Consider ClF3,

Cl

F

• Resonance structures with linear 3c-4e bonding arrangements are preferred.

F Cl

F

• VALBOND uses three resonance structures, each with twolone pairs, one 2c-2e bond, and one 3c-4e bond

F

3c-4e bond

I II III

F F FF

F F

F

FF

F F

FF F

F

F

F F

F

Resonance Structure Populations Are Geometry Dependent

FF

F

Population=Σ cos2θ

Σ Σ cos2θ

3c-4e angles

3c-4e anglesRes. Structures2c-2e bond3c-4e bond

33% 33%33%

100%

Trigonal Planar

SHAPE Resonance Structures and Populations

T-shape

0% 0%

F Xe F F Cl F

F

F

S

F

FF

F

P

F

FFF

Xe FFFF

F

S

FFFFF

Results for Hypervalent VALBOND

All structures use one set of generic VALBOND parameters

180o (180o) 178o (182o)

174o

(186o)

92o(88o)

90o

(90o)

120o

(120o)

180o (180o)

90o (90o)

90o (90o)

Inclusion of Lone Pairs Brings Computed Structures Into Agreement with Experiment!

F

PFF

F F

F

PFF

F F

Dynamic Motions of PF 5

Bending FrequenciesVALBOND

Experiment

151

500

300

520

174

175

Ab Initio

340

533

Axial - Equatorial Exchange Transition States

VALBOND

99o 101o

∆E† = 3.0 kcal/mol 2 - 5 kcal/mol

ClF F

F

ClF F

FF

ClF F

FCl F

F

ClF

FF

Dynamic Motions of ClF 3

Bending FrequenciesVALBOND Experiment

418 442

381 328

300 328

Axial - Equatorial Exchange Pathways - Possible TS's

C3v

CsC2vD3h

FCl F

F 91o

134o 130o

100o

FCl F

F

Axial - Equatorial Exchange in ClF 3

The Transition State is C 2v !

∆E†= 40 kcal/mol ∆E†= 37 kcal/mol

VALBOND MP2

Simple (?) Geometries of Hydrides

H 2O NH 3 BH3 SF6BeH2

PtH 2 ZrH 3+ RhH 4

-PdH 3- WH 6Cu(Me) 2

-

CH 4

Hybridization and Metal Complexes: the Intriguing Case of WH 6

• 1989 Girolami reports that ZrMe 62- is not octahedral

Morse, P. M.; Girolami, G. S. J. Am. Chem. Soc. 1989, 111, 4547

• 1990 Haaland demonstrates that WMe 6 is not octahedral (either C 3v or trigonal prismatic) Haaland, A. et al. J. Am. Chem. Soc. 1990, 112, 4547

• 1992/1993 Albright and Schaefer independently report that WH 6 : • is not octahedral • exhibits four minima of nearly equivalent energy • two minima are C 3v and two are C 5v • distortion to octahedral geometry requires ca. 130 kcal Kang, S. K.; Tang, H.; Albright, T. J. Am. Chem. Soc. 1993, 115, 1971.

Shen, M.; Schaefer, H. F.; Partridge, H. J. Chem. Phys. 1992, 98, 508.

0102030

4050

60708090

100

Sr Y Zr Nb

Mo Tc Ru

Rh Pd Cd

%s %p %d

Transition Metal Bonds Have Little p-Orbital CharacterSchilling, Goddard, Beauchamp J. Am. Chem. Soc. 1987, 109, 5565.

Hybridizations of M-H+ Bonds

* NBO values

*p

*s*d

*d

*s*p

Hybridization Rules for Transition Metal Complexes

• Use only s and d orbitals in forming hybrid orbitals.

• To form n covalent electron-pair M-H bonds use sdn-1 hybridization.

• Lone pairs prefer high d-orbital character.

• When the metal valency exceeds 12 electrons, delocalized bonding unitsare used (e.g. hypervalent, linear 3-center 4-electron bonds).

Landis, C. R.; Cleveland, T.; Firman, T. K. J. Am. Chem. Soc. 1995, 117, 1859.

sd sd4

sd2 sd5

sd3 d

90Þ

90Þ

71Þ 109Þ 55Þ 125Þ

63Þ 117Þ

66Þ 114Þ

30 60 90 120 150/ 30

60 90 120 150

0.20

0.15

0.10

0.05

0.00

0.20

0.15

0.10

0.05

0.00

0.20

0.15

0.10

0.05

0.00

0.25

Ene

rgy

Angle (degrees)

ZrH3+

Electron count: 6 e-

Bonding orbitals:Bonding hybrids:Expected bond angles:

sd2

90Þ

3 localized pairs

93ÞMP2 Geometry Optimization

RuH4


Bonding orbitals:Bonding hybrids:Nonbonding orbitals:Nonbonding hybrids:Expected bond angles:

4 localized pairssd3

2 lone pairsd71Þ and/or 109Þ

109.5Þ

Shapes of 6 and 12 Electron MHn

Landis, C. R.; Cleveland, T.; Firman, T. K. J. Am. Chem. Soc. 1995, 117, 1859.

The Beguiling Case of WH6

Shen, Schaefer, Partridge J. Chem. Phys. 1993, 98, 508.Four Local Minima Were Proposed

C3v

116o

63o

116o

63o

C5v116o

63o

63o

"To inorganic chemists comfortable with the idea that WMe6 is effectively octahedral, the present theoretical results for WH6 will bunsettling."

Shapes of 12 Electron MH6

TcH6+ at MP2

PdH3-


Bonding orbitals:

Bonding hybrids:Nonbonding orbitals:Nonbonding hybrids:Expected bond angles:

2 localized pairs

sd4 lone pairsd90Þ 180Þ delocalized bond

1 3-center 4-electron bond

190Þ

85Þ

MP2 Optimized Geometry

PtC6F5 C6F5

C6F5 C6F5

The Structures of Homoleptic Pt-Aryls

Pt(C 6F5)42- (Usón, R., Forniés, J., et al., J. Chem. Soc.,

Dalton Trans. 1980, 2, 1386)

Electron Counting

PtC6Cl5

C6Cl5

C6Cl5

C6Cl5

16 e- - 12 e- >> 2 3center- 4e - interactions >> sd hybridization (90 o) >> 4 pure d lone pairs

Square Planar

Pt(C 6Cl5)4 ( Forniés, J., et al., J. Am. Chem. Soc. 1995, 117, 4295

Electron Counting

14 e- - 12 e- >> 1 3center- 4e - interaction >> sd 2 hybridization (90 o) >> 3 pure d lone pairs

See-Saw Geometry

Seam-Searching: Approximation of Transition States

Reaction Coordinate

Seam CC

C

C

CCEn

ergy

ReactantProduct

True TS

Rappè, Landis

Example: Diels-Alder Reaction

2.11Å (2.24)

1.42Å (1.38)

1.42Å (1.39)

102o

(102o)1.44Å (1.40)

H

CHH

HH

HH

Bond Breaking/ Making: Homolytic Cleavage of CH4

H

+

sp3 sp2p

VALBOND/UFF Models this by:

• Extended Rydberg Function for Bond Stretch Energy

• VALBOND for Angle Energy

• Bond Order Dependent Hybridization

• For 90o<θ<120o, 1.0Å< RC-H< 5.0Å

the Maximum Energy Deviation < 3 kcal/mol !!

Rappè, Landis

MoNN

N Mo'RRN

NRR'NRR'

MoN N

N

NN

R

'R R'

R

R'R

N

N

MoN N

NR

'R R'

R

R'R

Mo

N

N

Mo

'RRN NRR'NRR'

'RRNNRR'NRR'

N

MoN N

NR

'R R'

R

R'R

N

Mo'RRN NRR'

NRR'

purple, paramagnetic

2

N2

red-orange, paramagnetic

gold, diamagnetic

Simple Mo(NRR') 3 Complexes Effect N2 Cleavage

Laplaza, C.E.; Cummins, C. C. Science 1995,268,861-863

Why Does the Cummins Complex Split N 2?

" It is thought that the M-N triple bond is one of the strongest metal-ligand bonds, and its formation clearly provides the thermodynamic driving force for the N 2 cleavage reaction elucidated here."

"Monomeric Mo(NRAr) 3 is formally related to the well-known dimeric Mo(III) complexes X 3Mo-MoX 3(X=alkyl, amide, alkoxide), which have unbridged metal-metal triple bonds. Severe steric constraints apparently render Mo(NRAr) 3 immune to dimerization, endowing the complex with the stored energy required for the observed reactivity toward N 2."

Mo N N

N

N

N

SiR3

SiR3SiR3

N

Mo

N

N

N

R3Si

R3SiR3SiN

V N N

Why Does the Cummins Complex Split N 2?Closely related complexes form µ-N2 bridged dimers ...

V

Shih, K.Y.; Schrock, R. R.; Kempe, R. J. Am. Chem. Soc. 1994, 116, 8804-8805.

2-

Ferguson, R.; Solari, E.; Floriani, C.; Chiesi-Villa, A., Rizzoli, C. Angew. Chem. Int. Ed. Engl. 1993, 32, 396-397.

... but do not cleave N 2 to yield metal nitrides.

MoH 2N NH 2

NH 2

N

N

MoH 2N NH 2NH 2

N

MoH 2N NH 2

NH 2

Is N 2 Cleavage Thermodynamically Favorable for Simple Mo(NR 2)3 Complexes?

Results of DFT Computations A collaboration with the research group of Prof. Notker Rösch, TU-Muenchen

distances: DFT (Schrock Structure)

2

6 kcal/mol

1.67Å 2.00Å

1.99Å (2.00)

1.20Å(1.20)

1.90Å(1.91)

Reaction Coordinate

Ener

gy (k

cal/m

ol)

Mo'RRN NRR'

NRR'

N

N

Mo'RRN NRR'

NRR'

N

Mo'RRN NRR'

NRR'

Mo'RRN NRR'

NRR'

N

N

Mo'RRN NRR'

NRR'

UFF/VALBOND Evaluation of Ligand Effect

distances: R,R'=t-Bu; 3,5-Me 2Ph (R,R'=H)

*-10 kcal/mol

Reaction Coordinate

Ener

gy (k

cal/m

ol)

2.05Å(2.03)

1.39Å(1.35)

1.81Å (1.80)

2.02Å (1.99)

1.21Å(1.20)

1.94Å(1.90)

2

1.69 (1.69)Å 2.00(2.00)Å

* With DFT-based exothermicity correction

39.7 kcal/mol

7.0 kcal/mol

5.0 kcal/mol

Developments in Progress• New Valence Bond Consistent Improper, π-Bond, and Torsional Terms

• Improved Hypervalent Descriptions for Transition Metal Complexes

• Explicit Application of Resonance for

• Conjugated Aromatics

• Ionic-Covalent Resonance

• Hypervalency (esp. Metal Complexes)

• Donor Bonding

• Reactant-Product Mixing

MoH2N NH 2

NH 2

N

N

MoH2N NH 2NH 2

N

MoH2N NH 2

NH 2

MoH2N NH 2

NH 2

N

N

MoH2N NH 2NH 2

(NH 2)3Mo-N 2-Mo(NH 2)3 2 NMo(NH 2)3

UFF2/VALBOND Transition State Searching

distances: MM (DFT)

1.69 (1.67)Å

2

1.99Å (2.00)

46.6 kcal/mol

*6 kcal/mol

2.00(2.00)Å

* Adjusted to match DFT exothermicity

Ener

gy (k

cal/m

ol) 1.20Å(1.20)

1.90Å(1.90)

Reaction Coordinate

2.03Å

1.80Å

1.35Å

99.99%sp4.49 (O-H) sp0.57 (lone pair) pure p (lone pair)

sp2.18 (lone pair)

sp3.37 (N-H)

H2O

99.98%sp2BH3

99.99%NH3

99.98%sp3CH4

Natural Bond Orbital (NBO) Analyses

Fraction of e- density in Localized HybridsHybridizationMolecule

Localized Hybrid Orbitals Are Good Descriptors of Molecular Electron Densities

The Remarkable Robustness of the Pauling Legacy

Explorations of the Directed Covalent Bond• Mathematical Formulation of Hybrid Orbitals• Molecular Mechanics and Valence Bond Concepts• Bent’s Rule and Molecular Shapes• Hypervalent Molecules and Resonance• Simple Transition Metal Complexes• New Rules for Hybridization in Simple Metal Complexes

Is the Pauling Legacy More Harmful than Helpful?" Pauling's enormous influence has entrenched VB theoryto a degree that it still receives consideration and deference,

which some believe excessive. In the final analysis, only the MO theory (at the first approximation level) provides a unified,self-consistent view of bonding that is equally applicableacross the periodic table."

Butler, I. S.; Harrod, J. F. Inorganic Chemistry. Principles and Applications Benjamin/Cummings: Redwood City, CA, 1989;page 75.

Principles of the Directed Covalent Bond: Lewis’ Rules Updated

• The electron-pair bond is formed through the interaction of an unpaired electron on each of the two atoms.

• The spins of the electrons are opposed when the bond is formed, so that cannot contribute to the paramagnetic susceptibility of the substance.

• Two electrons which form a shared pair cannot take part in forming additional pairs.


Principles of the Directed Covalent Bond: Qualitative Interpretation of Wave Equations• The main resonance terms for a single electron-pair bond are those involving only one eigen-function from each atom.

• Of two eigenfunctions with the same depen-dence on r, the one with larger value in the bond direction will give rise to the stronger bond, and for a given eigenfunction the bond will tend to be formed in the direction with largest value of the eigenfunction.

• Of two eigenfunctions with the same depen-dence on θ and φ, the one with the smaller mean value of r will give rise to the stronger bond.


The Pair-Defect Approximation“ The approximate bond strength (Sapprox) of an orbital i at angles αij with theother orbitals j is given by...”

Sapprox = Smax − Smax − S0 (α i )[ ]i

∑

“ We now have subjected it to an extensive test ... it is seen that the pair-defect-sum approximation to the bond strength seems to be an excellent one.”

Pauling, L.; Herman, Z.; Kamb, B. J. Proc. Natl. Acad. Sci., USA 1982, 79, 1361.

Are Hybrid Orbitals Good Descriptors of Electron Density?

99.15%sp9.6d2.0 (axial Cl-F) sp11.3d6.9 (eq. Cl-F)

ClF3

99.99%sp4.49 (O-H) sp0.57 (lone pair) pure p (lone pair)

sp2.18 (lone pair)

sp3.37 (N-H)

H2O

99.98%sp2BH3

99.99%NH3

99.98%sp3CH4

Fraction of e- density in Localized HybridsHybridizationMoleculeNatural Bond Orbitals analysis

provides a method for extract-ing localized bond descriptionsfrom high quality electronicstructure computations.

For non-hypervalent moleculeslocalized bond descriptions account for >99.98% of thedensity matrices.

Reed, A. E.; Curtiss, L. A.; Weinhold, F.Chem. Rev. 1988, 899.

How are Hybridizations Determinedin VALBOND?

Based on Pauling’s rules and a simple, parametrized algorithm based onBent’s rule†, hybridizations for simple non-hypervalent molecules of the p-block are determined readily.

sp2.09

sp1.81

120.9

118.1

Lewis Structure

Bent's Rule

quantitative

3 hybrids with ~sp2

hybridization

gross• •

••••H

B

F

F

H

B

F

F

† Bent, H. Chem. Rev. 1961, 275.

Hypervalency Challenges VB-Based Bonding Descriptions

• spmdn hybridization schemes are incompatible with high level electronicstructure computations.

Magnusson, E. J. Am. Chem. Soc. 1990, 112, 1434.

• therefore simple hybridization schemes cannot be used to create one electron-pair bond between the central atom and each ligand.

• Resonance is important

but why is ClF3 T-shaped?F-

F-F-F Cl+

F

Cl+

F

F F Cl+ F

Ionic-Covalent Resonance Maximizes at Linear Arrangements

F-

θMaximum stabilization

at θ = 180oF

F

NBO analyses indicate that the 3-center 4-electron bond is modeledwell as donation of a lone pair fromF- into a localized σ* orbital of theClF2

+ fragment.

According to Natural Resonance Theory† analysis, two resonance structuresaccount for 99.95% of the total MP2 electron density.

F-

F-F-F Cl+

F

Cl+

F

F F Cl+ F

50% 50% <1%

† Glendening, E. D.; Weinhold, F. “Natural Resonance Theory” University of WisconsinTheoretical Chemical Institute, 1994

Can You Predict the Structures ofThese Molecules?

WH6 TcH6+ ZrH3

+

RhH3 PtH42- FeH6

4-

RhH4- RuH4 PtH2

How Does Site Isomerization in ClF3 Occur?

Structures of Simple Metal Hydrides Challenge All Bonding Models

• On the basis of ab initio computations Albright et al.1 and Schaefer et al.2suggest that WH6 is not octahedral. Instead they propose that four lowersymmetry minima (2 C3v and 2 C5v) exist at nearly equal energies.

• Schaefer estimates that the octahedral structure lies ~140 kcal/mol aboveglobal minimum!

• Gas phase diffraction data3 for WMe6 and the crystallographic structure4 ofZrMe6

+ demonstrate non-octahedral structures.

1 Albright, T. A.; Kang, S. K.; Tang, H. J. Am. Chem. Soc. 1993, 115, 1971.2 Shen, M.; Schaefer, H. F.; Partridge, H. J. Chem. Phys. 1992, 194, 109.3 Haaland, A. et al. J. Am. Chem. Soc. 1990, 112, 4547.4 Morse, P. M.; Girolami, G. S. J. Am. Chem. Soc. 1989, 111, 4114.

Shape of 16 Electron MH4

y Functions for sdn

d Orbitals

field development i. hybridization and molecular shapes · • two sp3 hybrid orbitals have maxima...

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