Theory of Chemical Bonding and Reactivity
Quantitative
Orbital and Activation Strain Models

F. Matthias BickelhauptOutline
1. Activation Strain model and KS MO theory
ASM in action: bond activation
2. Bite Angle and Bite-Angle Flexibility
3. d regime and s regime catalysts

ADF: ZORA BLYP-(D3)/TZ2P

kcal/mol – Å – deg

1 - Activation Strain model& KS-MO

Theoretical ChemistryHΨ=EΨ
Numerical description[T + VNe + Vee,C + Vee,XC] ψ = E ψ

Understanding and design!
[T + VNe + Vee,C + Vee,XC] ψ = E ψphysical mechanism
Rev. Comput. Chem. 2000, 15, 1.

Activation Strain Model• Decompose barrier:[M] +X∆E≠ = ∆E≠strain + ∆E≠intM∆E ≠strain≠∆EintX∆E≠[M] + CH3–X
CH3-M-X

J. Comput. Chem. 1999, 20, 114; Chem. Soc. Rev. 2014, 43, 4953

Activation Strain Model• Analysis along reaction coordinate ζ∆E∆Estrain

∆E

∆Eint

ζ

• Interplay ∆Estrain(ζ) + ∆Eint (ζ) determines TSJ. Comput. Chem. 1999, 20, 114; Chem. Soc. Rev. 2014, 43, 4953

Fragment MO Approach
A + B  A–B"local" bond in "delocalized" modelcanonical fragment orbitals
Rev. Comput. Chem. 2000, 15, 1.

Bond Energy Decomposition
A + B  AB
∆Ebond = ∆Estrain + ∆Eint∆Eint= ∆Velstat+ ∆EPauli+ ∆Eoi,pb+ ∆Eoi,relax

A+B

A+B

AB0AB0pb

ABΨSCFΨ0pb = N |(closed-sh)A (closed-sh)B (SOMOA + SOMOB)2|
Ψ0 = N |ΨA ΨB|

ΨA, ΨB

ρ[A+B] = ρA + ρB

= N |(closed-sh)A (closed-sh)B SOMOA(1)α(1) SOMOB(2)β(2)|Rev. Comput. Chem. 2000, 15, 1.

MO model: cause and effect∆E = ∆Estrain + ∆Eint∆Velstat + ∆EPauli + ∆Eoi + ∆Edisp
δ+∆Eoi =δ–|<ψA | hKS | ψB >|2εA– εB∆Eoi ~S2∆ε– Causal relationship– Quantitative– Qualitative...

Rev. Comput. Chem. 2000, 15, 1.

Physical Understanding

ASM in action:
Bond Activation

ADF: ZORA BLYP-(D3)/TZ2P

kcal/mol – Å – deg

Catalysis• Model: Catalytic C–X Bond Activation
MLn
R–Nu

R–X

Reductive
Elimination

Oxidative
Addition

R–MLn–Nu

R–MLn–X

Nu–X–C–H vs C–C Activation• Computational and experimental facts (in kcal/mol):bondBDE

C–H
C–C

10990

C–H vs C–C Activation• Computational and experimental facts (in kcal/mol):!E≠ bond activ

bondBDE

C–H

1094

C–C

90

19

Why is C–C activ. more difficult than C–H activ. ?

C–H vs C–C Activation120!
E /(kcal/mol)
kcal mol–1
ΔE90

ΔE strain

6030

C–C
ΔE

0

C–H

-30
-60-90

ΔE int

-120
0.0

0.2

0.4

0.6

0.8

1.0

C–X
stretch (Å)
C–X
stretch/Å

1.2

1.4

1.6

C–H vs C–C Activation

C–H vs C–C Activation

C–H vs C–C Activation

C–H vs C–C Activation120!
E /(kcal/mol)
kcal mol–1
ΔE90

ΔE strain

6030

C–C
ΔE0

C–H

-30-60-90

ΔE int

-120
0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

C–X
stretch (Å)
C–X
stretch/Å

C–H bonds shield C–C bond  delayed [M]–[C–C] interaction

Bulky Substrates

ChemPhysChem 2007, 8, 1170

Fragment-oriented Designof Catalysts for C–X Activation
1: Intrinsic reactivity:
M
M + CH3–X

M XX

2: Improve with ligands:
MLn
MLn + CH3–X

J. Chem. Theory Comput. 2005, 1, 286
J. Organomet. Chem. 2005, 690, 2191

XMLn X

2 - Bite Angle &Bite-Angle Flexibility

Bite Angle:
steric nature

Bidentate Ligands
and the Steric Nature of the Bite Angle
LMethane C–H activation:

ML180°• ligands raise barriersML< 180°

L• smaller bite angle
è lower barrier

Chem. Eur. J. (communication) 2009, 15, 6112
ChemPhysChem. 2007, 8, 1170

Bidentate Ligands
and the Steric Nature of the Bite Angle
Bite-Angle Effect according to literature:• ligands push d AOs upè better HOMO–LUMOinteraction
σ*C-X

"dπ"

• this view is not entirelyexact

Chem. Eur. J. (communication) 2009, 15, 6112
ChemPhysChem. 2007, 8, 1170

Bidentate Ligands
and the Steric Nature of the Bite Angle
Bite-Angle Effect: Activation Strain analyses:• HOMO–LUMO interaction only
marginally improved

Chem. Eur. J. (communication) 2009, 15, 6112
ChemPhysChem. 2007, 8, 1170

Ligands

J. Organomet. Chem. 2005, 690, 2191

Bidentate Ligands
and the Steric Nature of the Bite Angle
Bite-Angle Effect: Activation Strain analyses:• HOMO–LUMO interaction
marginally improved• Instead:
Strain reduced bybuilding it into catalyst

Chem. Eur. J. (communication) 2009, 15, 6112
Org. Biomol. Chem. 2010, 8, 3118
Nature Chem. 2010, 2, 417

Variation M and L• Oxidative addition with non-chelating d10-ML2 complexes• Metal variation: metals around Pd in the periodic table:• Ligand variation: NH3, PH3 or CO

Co–

Ni

Cu+

Rh–

Pd

Ag+Ir–Pt

Au+• Text Books: d10-ML2 is in general linear
LM

MM

L'
L

L'

L

L'

Non-Linear d10-ML2
L-M-L

∆Elin

L-M-L

∆Elin

L-M-L

∆Elin

Co(NH3)2–

1800Ni(NH3)2

1800Cu(NH3)2+1800Co(PH3)2–

132

6Ni(PH3)2

1800Cu(PH3)2+1800Co(CO)2–

129

20Ni(CO)2145

2Cu(CO)2+

1800Rh(NH3)2–

1800Pd(NH3)2

1800Ag(NH3)2+

1800Rh(PH3)2–

141

2Pd(PH3)2

1800Ag(PH3)2+

1800Rh(CO)2–

131

10Pd(CO)2

156

1Ag(CO)2+1800Ir(NH3)2–

1800Pt(NH3)2

1800Au(NH3)2+1800Ir(PH3)2–

144

2Pt(PH3)2

1800Au(PH3)2+1800Ir(CO)2–

134

13Pt(CO)2

159

1Au(CO)2+1800Non-Linear d10-ML2
L-M-L

∆Elin

L-M-L

∆Elin

L-M-L

∆Elin

Co(NH3)2–

1800Ni(NH3)2

1800Cu(NH3)2+1800Co(PH3)2–

132

6Ni(PH3)2

1800Cu(PH3)2+1800Co(CO)2–

129

20Ni(CO)2145

2Cu(CO)2+1800Rh(NH3)2–

1800Pd(NH3)2

1800Ag(NH3)2+1800Rh(PH3)2–141

2

Pd(PH3)2

1800Ag(PH3)2+1800

Rh(CO)2–

131

10Pd(CO)2

156

1Ag(CO)2+1800Ir(NH3)2–

1800Pt(NH3)2

1800Au(NH3)2+1800Ir(PH3)2–

144

2Pt(PH3)21800Au(PH3)2+1800Ir(CO)2–

134

13Pt(CO)2

159

1Au(CO)2+1800

Non-Linear d10-ML2
L-M-L

∆Elin

L-M-L

∆Elin

L-M-L

∆Elin

Co(NH3)2–

1800

Ni(NH3)2

1800Cu(NH3)2+1800Co(PH3)2–

132

6Ni(PH3)2

1800Cu(PH3)2+1800

Co(CO)2–

129

20

Ni(CO)2145

2

Cu(CO)2+1800

Rh(NH3)2–

1800Pd(NH3)2

1800Ag(NH3)2+1800

Rh(PH3)2–

141

2

Pd(PH3)2

1800Ag(PH3)2+1800Rh(CO)2–

131

10Pd(CO)2156

1Ag(CO)2+1800Ir(NH3)2–

1800Pt(NH3)2

1800Au(NH3)2+1800Ir(PH3)2–

144

2Pt(PH3)2

1800Au(PH3)2+1800Ir(CO)2–

134

13Pt(CO)2

159

1Au(CO)2+

1800better π-accepting ligand à smaller bite angle

Non-Linear d10-ML2
L-M-L

∆Elin

L-M-L

∆Elin

L-M-L

∆Elin

Co(NH3)2–

1800Ni(NH3)2

1800Cu(NH3)2+1800Co(PH3)2–

132

6Ni(PH3)2

1800Cu(PH3)2+1800Co(CO)2–

129

20Ni(CO)2145

2Cu(CO)2+1800Rh(NH3)2–

1800Pd(NH3)2

1800Ag(NH3)2+1800Rh(PH3)2–1412Pd(PH3)2

1800Ag(PH3)2+1800Rh(CO)2–

131

10Pd(CO)2

156

1Ag(CO)2+

1800Ir(NH3)2–

1800Pt(NH3)2

1800Au(NH3)2+

1800Ir(PH3)2–

144

2Pt(PH3)2

1800Au(PH3)2+

1800Ir(CO)2–

134

13Pt(CO)2

159

1Au(CO)2+

1800

better π-backdonating metal à smaller bite angle

ML–L Bonding Analysis
weak"π∗""s"π∗"dσ""dδ""dπ" π∗"π∗""s"π∗"dσ""dδ""dδ" π∗"dπ""dπ"strongσ"σ"π"π"OC PdOCPdCOCOσ"σ""dπ"π∗π"π"OC PdOCPd"dπ" π∗CO90º CO180ºbending provides access for π* to fresh d electrons

Application to H3C–H Activation
smaller bite à less cat. strain

higher d à more stab. int.

design principles

Bite-Angle Flexibility:“it is not about the angle”

Steric Attraction !
• Crank up steric bulk Pd(PR3)2• Since Pd(PH3)2 is linear, all are... or not ??
This image cannot currently be displayed.

•R = H:Yes•

R = Me: Yes•

R = iPr: Yes•

R = tBu: Yes•

R = Cy: NoSteric Attraction !

big surfaces stick together through Van der Waals forces“Anisotropic Bulk” + Room = Steric Attraction

Bite-Angle Flexibility• Energy profiles for bending Pd(PR3)2Dispersion pulls minimum to 148° ...
... 132° for Pd(PPh3)2 !

Application to H3C–H Activation

More flexible bite angle à less activation strain
The "right bulk" provides steric protection + low barrier

3 - Electronic Regimesof Catalysts

electronic regimes
E∆E strain*C–H0d∆E∆E intCH4M–

RhCO → RhPH3ASM and MO work perfectlyè rational design, but...

∆ε HOMO+0.6 eV

E–3.4 kcal/mol≠–!

AgCO+ → AgPH3+∆ε HOMO+1.7 eV

E+9 kcal/mol≠!

Break-down of model ?

electronic regimes
Break-down of model ?
NO, we just went from d-regime to s-regimescatalyst tuning

*C–H

*C–H

catalyst tuning

ds

C–H

C–H

dCH4

M

d-regime

CH4Ms-regime

Conclusions• Bite-angle effect on reaction has steric origin...
• actually, what matters is bite-angle flexibility• d-regime or s-regime, that is the question

Take-Home Message• KS-MO is physically sound causal model• EDA without bonding mechanism is incomplete• Activation Strain model (ASM) is a powerfulgeneralization to reactions...

Further reading
1. Reviews in Computational Chemistry; Wiley-VCH: New
York, 2000, Vol. 15, pp. 1-86
2. Chem. Soc. Rev. 2014, 43, 4953
3. WIRES Comput. Mol. Sci. 2015, 5, 324