Basics of Catalysis and Kinetics
Nobel laureates in catalysis:
Haber (1918) Ziegler and Natta (1963) Wilkinson, Fischer (1973) Knowles, Noyori, Sharpless (2001) Grubbs, Schrock, Chauvin (2006) Ertl (2007) Heck, Negishi, Suzuki (2010)
G. Poli Definition
The concept of catalyst was first introduced by Berzelius in the 19th century.
Subsequently, Ostwald came up with the definition that we still use today:
“A catalyst is a substance that increases the rate of a chemical reaction, without being consumed or produced”…
Berzelius, J. J. Ann. Chim. Phys. 1836, 61, 146-151 Ostwald, W. Z. Phys. Chem. 1894, 15, 705-706
G. Poli The Catalyst and the Rate of a Reaction
ΔG non catalyzed
catalyzed
A B Reaction coordinate
The catalyst changes only the rate of the reaction, and does not change the thermodynamics.
However, the temperature can affect equilibrium concentrations: ΔG = ΔH - T ΔS
G. Poli Historical basis for the Analysis of Catalytic Kinetics
The Michaelis-Menten Kinetics
G. Poli Thermal, Catalyzed, Inhibited, and Promoted Reactions
I II III IV
uncatalyzed catalysis inhibition stoichimetric process (no catalysis) promotion (no catalysis)
A A A A Acat Bcat Ainhib Binhib Aprom
B B (+ cat) B Bprom SM is stabilized SM is stabilized more than TS --> a further reaction is less than TS the uncatalyzed path needed to liberate B is preferred
G. Poli Thermal, Catalyzed, Inhibited, and Promoted Reactions
O NH HN CCl3 Ar O CCl3 xylenes 140°C type I Ar
CCl3 CCl3 O NH PdCl2(PhCN)2 (5 mol%) O NH type II THF, rt
N H H N B N N N N B Pt N N 1. N N Me N N O O n Pt trispyrazolylborate-platinum(methyl) type III NH NMe2 NH NMe 2 2. H Pd/C 2, O O
- PdCl (MeCN) [H ] type IV 2 2 N N Pd Cl HN O O O stable
G. Poli Thermal versus TM-catalyzed Paths
Often the catalytic reaction occurs by a mechanism that is completely different from that of the corresponding uncatalyzed process. In the catalyzed process the reaction typically occurs by more steps, but the activation energy of each step is lower than that of the uncatalyzed process. The resulting global energetic barrier is thus lower that of the uncatalyzed reaction.
Alkene hydroboration with (RO)2BH is an example.
- Oxidative addition - Coordination - Migratory insertion - Reductive elimination
- Alkene-borane π-complex
- Concerted 4-membered step G. Poli Efficiency of the Catalytic Cycle (TON and TOF)
A catalyst is not eternal and after certain number of turns it decomposes, thereby losing its catalytic activity. It is thus useful to define the turnover number (TON) of a catalyst as the number of moles of substrate that a mole of catalyst can convert before becoming inactivated. Of course, the TON is a function of the chemical yield. The turnover frequency (TOF) is the number of moles of product per mole of catalyst per unit time, that is to say, the turnover number per unit time. As the rate may change with the time, reported TOF‘s are usually average.
moles of product TON TON = TOF = moles of catalyst used h
O cat: {[PdCl(allyl)] / L} : 1/2 B(OH) 2 2 K2CO3 O + L = Br xylenes, 120 °C, 7d ArBr / cat 333 333 333 2.0 equiv 1.0 equiv TON = 240 000 000
TOF = 1 400 000 Chem. Commun., 2011, 47, 9206-9208
G. Poli The Hammond’s Postulate
The Hammond's postulate is a hypothesis derived from transition state theory, and states that the structure of a transition state resembles that of the species nearest to it in free energy. That is to say, that the transition state of an endothermic reaction resembles the products (late transition state), while that of an exothermic reaction resembles the reactants (early transition state) .
Hammond, G. S. (1955). J. Am. Chem. Soc. 1955, 77, 334–338
G. Poli The Curtin-Hammett Principle
The Curtin-Hammett principle states that, for a reaction that has a pair of reactive intermediates or reactants that interconvert rapidly (for example conformers), each going irreversibly to a different product, the product ratio will depend both on the free energy of the transition state going to each product (usually essentially) and the difference in energy between the two conformers (usually to a little extent). Hence, the product distribution will not necessarily reflect the equilibrium distribution of the two intermediates
Seeman J. I. (1983 Chemical Reviews 1983, 83, 83–134 G. Poli Example of a Generic Tolman Catalytic Cycle
precatalyst
Product Substrate cat I promoter or co-catalysts may be needed
A catalyst cat IV turnover cat II deactivation limiting step B resting state (i.e. dimer) dormant cat III
The Tolman cycle is a clockwise catalytic cycle composed only by organometallic species. The concentration of the active catalyst is represented by the sum of the concentrations of all catalytic species within the cycle. Maximum efficiency is achieved when all of the catalyst is active and lies within the catalytic cycle. If the rate of a step is sufficiently high, it may overwhelm an unfavorable preceding equilibrium present in the cycle (kinetic coupling). G. Poli Kinetics of the Catalytic Cycle
In a catalytic cycle the net rates of step are identical
Although the rate constants of the different steps in a catalytic cycle may be different, once the system has reached the steady state, the net rates1 of each step are identical. Indeed, the rate of each step is proportional to the rate constant and to the concentration of the reagents and species involved in the catalytic cycle. As a consequence, the concentrations of the species that lie in the cycle vary to make the rate of each step of the catalytic cycle identical!
2 The rate with the smallest pseudo-first order rate constant (kn[reagentn]) is called turnover-limiting step (TLS). This step controls the efficiency of the catalytic process as the rate of a catalytic reaction cannot exceed . kTLS [catn][reagentn]. Most of the catalyst consists of the species preceding the TLS,3 which is normally the resting state, the species present in the highest amount.
1) For a step catn + reagentn catn+1 the net rate is kn [catn][reagentn] menus the reverse rate 2) Within the cycle the concentration of the catalyst remains constant. 3) It is erroneous to call the TLS the “slow step”, as all the steps proceed with the same net rate.
G. Poli The Energetic Span
E
The energetic span (E) is related to the turnover frequency TOF of the catalytic cycle. The smallest it is, the fastest the catalysis. Thus, a good catalytic cycle must consist of low-lying transition states with high-lying intermediates!
Amatore, C.; Jutand, A. J. Organomet. Chem. 1999, 576, 254. Kozuch, S.; Amatore, C.; Jutand, A. Shaik, S. Organometallics, 2005, 24, 2319. Kozuch, S.; Shaik, S. Acc. Chem. Res. 2011, 44, 101-110. Kozuch, S.; Martin, J. M. L. ChemPhysChem 2011, 12, 1413.
G. Poli Recall: Solvent Effect in SN2
- __ - Nu + RCH2-X > Nu-CH2R + X Nu- = F-, I-
G. Poli The Energetic Span
E E
Ea1 Ea E cat a1 cat n1 E1 cat c cat c1 cat a cat 1 cat b E1 cat b1 E
cat n cat n1
Reaction coordinate Reaction coordinate Trying to improve the rate of the slowest step of a catalytic cycle by increasing the energy of its reactant, so as to decreases its Ea, has (in contrast to a stoichiometric reaction) no chance of success, if the catalytic sequence is preserved otherwise. Indeed, the result is opposite, as the gain in lowering Ea is more than lost due to the increase of ΔE! As a result, the net effect is that the energetic span E increases and the global rate decreases.
G. Poli About the Definitions of Rate Determing Step
1. The step with the smallest rate constant 2. The step with the highest energy TS 3. The step with the rate constant that exerts the strongest effect (IUPAC)
smallest k: OK smallest k: NON smallest k: OK highest energy TS: OK highest energy TS: OK highest energy TS: NON TLS TLS E E E TLS T1 T2 k1 < k2 ! T1 T T2 T 1 k1 2 k I1 k-1 k -1 2 k1 I2 I2 k2 k 2 k1 I1 I2 I 3 I1 I3 I3
Rxn coordinate Rxn coordinate Rxn coordinate k k1 k k < k 1 I I 1 -1 2 I1 I2 k -1 > k2 1 2 k -1 < k2 I1 I2 k-1 steady state k-1 pre-equilibrium both irreversible k2 k2 k2 I I3 I3 3 Result: The RDS is a bad model. The States [TOF determining Intermediate (TDI) and TOF determining TS (TDTS)] exert the strongest effect on the overall rate.
G. Poli The Energetic Span
Product Substrate I1
I3 I2 lowest k and highest TS but not RD step !
te T1 TDTS a tr s t b c u T3 u S dT1' k ro 1 P TDTS I k 1 T2 3 T3' I3 k2 Gr T2' I2 I I3' 1' I TDI I 4' energetic span 2' TDI energetic span T3 – I2 > T1 – I1
G. Poli The Energetic Span
Product Substrate rate limiting TS (TDTS) I1 T1 I3 I2 E T 2 I1 Gr
Gr E T 1' T 3 resting T2' state I (TDI) 2 I1'
T 3' I3 maximal I energetic span 2' I3'
Cycle 1 Cycle 2 Rxn flow
T2 – I2 > T1’ – I3 > T1 – I1 G. Poli - PhBr + PhB(OH)3 PhPh (L = SPhos)
MeO Cy Cy HO OH P Br B cat cat MeO Pd OMe HO - B(OH) , -Br P 3 Cy Cy OMe
Kozuch, S.; Martin, J. M. L. Chem. Commun., 2011, 47, 4935 - PhBr + PhB(OH)3 PhPh (L = InPhos)
MeO *Cy Cy* P MeO Pd OMe HO OH P Br cat cat B *Cy Cy* HO - B(OH)3, -Br OMe cy* = Me
G. Poli