Field Development I. Hybridization and Molecular Shapes · • Two sp3 hybrid orbitals have maxima...
Transcript of Field Development I. Hybridization and Molecular Shapes · • Two sp3 hybrid orbitals have maxima...
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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.
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(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
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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?
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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
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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
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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
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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
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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’.”
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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 ...”
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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.
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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
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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)
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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.
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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
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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)
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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
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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
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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
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• 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
-
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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?
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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
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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%
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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!
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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
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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
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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
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Simple (?) Geometries of Hydrides
H 2O NH 3 BH3 SF6BeH2
PtH 2 ZrH 3+ RhH 4
-PdH 3- WH 6Cu(Me) 2
-
CH 4
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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.
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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
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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.
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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)
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ZrH3+
Electron count: 6 e-
Bonding orbitals:Bonding hybrids:Expected bond angles:
sd2
90Þ
3 localized pairs
93ÞMP2 Geometry Optimization
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RuH4
Electron count: 12 e-
Bonding orbitals:Bonding hybrids:Nonbonding orbitals:Nonbonding hybrids:Expected bond angles:
4 localized pairssd3
2 lone pairsd71Þ and/or 109Þ
109.5Þ
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Shapes of 6 and 12 Electron MHn
Landis, C. R.; Cleveland, T.; Firman, T. K. J. Am. Chem. Soc. 1995, 117, 1859.
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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."
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Shapes of 12 Electron MH6
TcH6+ at MP2
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PdH3-
Electron count: 14 e-
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
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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
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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)
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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
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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
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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."
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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.
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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)
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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
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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
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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
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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
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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
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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.
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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.
Pauling, L. J. Am. Chem. Soc. 1931, 53, 1367
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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.
Pauling, L. J. Am. Chem. Soc. 1931, 53, 1367
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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.
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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.
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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.
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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
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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
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Can You Predict the Structures ofThese Molecules?
WH6 TcH6+ ZrH3
+
RhH3 PtH42- FeH6
4-
RhH4- RuH4 PtH2
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How Does Site Isomerization in ClF3 Occur?
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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.
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Shape of 16 Electron MH4
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y Functions for sdn
d Orbitals