Transition state theory (TST):

Deduction of Mechanisms 4.2 Transition State Theory Observations: Reaction rates increase almost ever with increasing T this relation k vs Ea is consistent with the Arrhenius equation k describes the overall reaction rate "constant" A and Ea are considered T independent, mostly correct over a small range of DT Transition state theory (TST): kB: Boltzmann h: Planck  = Übergangsfaktor, generally = 1

Deduction of Mechanisms 4.2 Transition State Theory Arrhenius: plot lnk vs. 1/T liefert A und Ea DH DS kB h k T - ln ln + = translates into TST: RT R ln(k/T) vs. T-1yieldsH(slope) andDSwithln(kB/h) = 23.76 relation between Arrhenius and TST and 2.6 kJ/mol bei RT the activation parametersHandDS are very indicative for the mechanism

Deduction of Mechanisms 4.2 Transition State Theory Example: DH = 37 kcal/mol DS= + 25 e.u. relates to volume of activation DV thermodynamics: dG = -SdT + Vdp kinetics: lnk depends linearly on the pressure lnk (or logk) vs p gives a straight line with V as slope assuming that V is pressure independent what does this tell us with respect to mechanism ?

Deduction of Mechanisms 4.2 Transition State Theory it gives an insight into the intimate mechanism of the rds transition states ground state Ia D Id I A DS ++ + 0 - -- DV ++ + 0 - -- D and Id and A and Ia are often difficult to differentiate DS and DV  give us a clear insight into the mechanism, e.g. ligand exchange

Deduction of Mechanisms 4.2 Transition State Theory interpretationofS interpretationof V ligand self exchange V represents the sum of the partial mol volumina in the transitions state V° (H2O) = 18 cm3 / mol  associative V = - 15 cm3 / mol  A – process = + 15 cm3 / mol  D – process  dissociative

Deduction of Mechanisms 4.2 Transition State Theory [M(OH2)6]n+ kex + OH2 [M(OH2)5(OH2)]n+ + H2O kex covers an extremely broad range for D processes k = kex „no reaction" reaction Go = O

Deduction of Mechanisms 4.2 Transition State Theory water self exchange rates: indicative for substitution mechanisms in general Ka [M(OH2)6]n+ [M(OH2)5(OH)] + H+ kexH2O kex / H+ [M(OH2)6]n+ [M(OH2)6]n+ kex· Ka [M-OH2] v = kex [M-OH] = [H]+

Deduction of Mechanisms 4.2 Transition State Theory back to data interpretation: most reactions are not one step… let's look at a pH dependent scheme Ka k2 p.m. A + B P AH+ H+ + A the composed rate constant is: k2·KA applying TST and van'tHoff

Deduction of Mechanisms 4.2 Transition State Theory back to data interpretation: most reactions are not one step… linearization: we do not get H but-H - H we must know pre-equilibrium (Ka in this case) to get the "true" H Question: find a situation for which DG is negative e.g. the reaction becomes slower with increasing temperature k3 k4 I P A + B I steady state System: k-3 k-3 >> k4then:

Deduction of Mechanisms 4.2 Transition State Theory back to data interpretation: most reactions are not one step… we also get a "linear" profile, the parameters are composed of the individual values deviations from linearity in practice a typical Eyring (or Arrhenius) plot: lnk/T slope yields DH intercept yields DS 1/T

Deduction of Mechanisms 4.2 Transition State Theory but sometimes, the "straight line" looks rather like this lnk/T 1/T or like this … what does that mean ? lnk/T 1/T non-linearity ! often, even in professional presentations still considered as linear…

P1 k1 A k2 P2 Deduction of Mechanisms 4.2 Transition State Theory concurrent reaction schemes will result in non-linearity what about a simple consecutive scheme like this one k1 A + B {AB} k-1 k2 {AB} + C E + F

Deduction of Mechanisms 4.2 Transition State Theory the T profile of such a scheme is non-linear it can however be "dissected" in two linear profiles

Deduction of Mechanisms 4.2 Transition State Theory an simple example from practice: a linkage isomerization Co Rh Ir DS -17+/-3 -33+/-7 -11+/-4 e.u DH 92 80 95 kJ/mol DV -6.7 -7.4 -5.9 cm3/mol activation parameters is there an isokinetic relationship ? what mechanism of isomerization do you suggest ?

Deduction of Mechanisms 4.3 Microscopic Reversibility The reaction mechanisms for the forward and the backward reaction are identical, they are mirror images of each other This principle is always valid, even when multiple steps, equilibria or branched reactions are involved if it were not valid, we would run into problems with thermodynamics let's look at the simple reaction [Fe(NCS)(OH2)5]2+ + H2O [Fe(OH2)6]3+ + NCS- is pH dependent and can be described with: k1 k2 A I I P k-1 k-2

Deduction of Mechanisms 4.3 Microscopic Reversibility the rate law: backward reaction forward reaction after equilibrium is achieved: pH dependent and K becomes which it is obviously not according to reaction equation ??

Deduction of Mechanisms 4.3 Microscopic Reversibility Without consideration of the individual steps, pH dependence conflict with thermodynamics the problem is solved by considering the microscopic reversibility of all individual equilibria involved separately pH independent path: pH dependent path: hence: as it should be

Deduction of Mechanisms 4.3 Microscopic Reversibility a mechanism proposed once upon a time in square planar complexes ligand substitution, illustrative for microscopic reversibility +Cl- -Cl- no mirror plane in the mechanism, impedes the m.r. principle instead -Cl- +Cl- tbp transition state

Deduction of Mechanisms 4.4 Solvent effects solvents protic aprotic others H-bonds, high degree of association H-bonds weakly dipolar dipolar apolar aromatic apolar strongly dipolar polarizable strong dipoles dipoles e- pair donors aromatics polar try to find examples for this classification!

Deduction of Mechanisms 4.4 Solvent effects The solvent of a reaction may not only influencethe rate but also the overall mechanism path in inorganic or organometallic reactions, solvents often act as "true" ligands solvents may stabilize / destabilize ground – transition states or intermediates … or they may be completely innocent +I2 2 +I- CHCl3 hexane 2

Deduction of Mechanisms 4.4 Solvent effects solvents may provide a "solvent cage" as the "reaction vessel" the longer the reactants reside, the faster the reaction cage effect - - - - D B C A contact ion-pair ion-pair separated by solvent layers ion-pair separated by one solvent layer separated ion-pairs z1 = z2 = 1  357 pm z1 = z2 = 2  1428 pm z1 = z2 = 3  3213 pm + + + + critical distances for ion-pair formation strongly dependent on dielectric constant e

Deduction of Mechanisms 4.4 Solvent effects residence time in the cage given by the rate of diffusion in water, typically 10-12 bis 10-11 sec time to collide 10 – 100 times consequence: short lived intermediates can not be detected since the immediately react further the entity of compounds in a cage is called "encounter complex" the solvation of the encounter complex strongly contributes to DS ReactionReactandsactivatedcompoundincreasedpolarity SN1 R—X Rd+·····Xd- ++ SN1 R—X+Rd+·····Xd+ - SN2 Y + R—X Yd+·····R······Xd- ++ SN2 Y- + R—X Yd-······R······Xd- - SN2 Y + R—X+Yd-······R······Xd+ - SN2 Y- + R—X+Yd-······R······Xd+ --

Deduction of Mechanisms 4.4 Solvent effects the solvation of the encounter complex strongly contributes to DS ML5= Cr(OH2)5, Cr(NH3)5, Co(NH3)5, Rh(NH3)5 How to interpret these data with respects to the solvent water?

Deduction of Mechanisms 4.4 Solvent effects donor/acceptor numbers are an indication for the behaviour of solvents Gutmann: DZ(SbCl5) = -DH B + SbCl5 B-SbCl5 useful to compare relative characters of solvents no obvious relationship to e Drago: concept doesn't consider hard/soft (electrostatic – covalent) new definition Drago und Weyland: -DH = EaEb + CaCb E = electrostatic, C = covalent a=acid, b=base

Deduction of Mechanisms 4.4 Solvent effects new definition Drago und Weyland: -DH = EaEb + CaCb I2 + Pyridin I2·C5H5N -DHber = (0.5 ·1.78) + (2.0 · 3.54) = 7.97 kcal/mol (-DHexp = 7.8 kcal/mol) "acidic" solvents which tend to interact electrostatically (large Es) interact preferentially with bases with large Eb and acids which prefer covalent interaction (large Ca) interact with bases of large Cb

Deduction of Mechanisms 4.4 Solvent effects: Drago-Weyland,Donor and Acceptor numbers

Deduction of Mechanisms 4.4 Acids as solvents and super acids most Brønsted acids show auto dissociation, like water pH-scale and value defined by the degree of auto dissociation therefore, each acid has its individual pH-scale all acid/base pairs which are inside these limits act as electrolyte all acid/base pairs outside these limits will be levelled by the acid solvent CH3COOH is an acid in water and an electrolyte CH3COOH in H2SO4 is a base, base strength levelled by [HSO4]- more practical: dissolution of amide H2N- is levelled by base strength of [OH]- since outside the pH scale of water

Deduction of Mechanisms 4.4 Acids as solvents and super acids R(H), potentiometric acidityfunction Strehlow-function -3 41 R(H+) Super base media 40 34 -2 30 31 27.5 30 26.2 NH3 ETA 23 NMP 21 20 18.7 DMA HMPT py 17.7 N2H4 DME 20 16 14 -1 13 13 13.2 THF DMSO 10 DMF acetone 4 10 H3CNO2 MeOH HCONH2 EtOH H2O H3CCN 6.3 8.5 6.7 1 TMS 4.8 0 4 0 1 1 1 1 0 -1 -8 -5 -3.7 HF -7 -5.2 -7 -10 -10.3 -14 HCO2H -16 -16 1 H3CCO2H -20 -20 F3CCO2H Super acid media H2SO4 -30 -28 2 E (V) vs. NHE -40 B. Trémillon, D. Inman, Reactions in Solution, An Applied Analytical Approach, Wiley, 1997, pp. 227-300

Deduction of Mechanisms 4.4 Acids as solvents and super acids acids which are more acidic than sulfuric acid are called super acids [BH+] B = nitroanilinindicator Hammett acidity function H0 = pKBH+ - log [B] H2SO4 + H2S2O7 [H3SO4]+ + [HS2O7]- Pyroschwefelsäure H2SO4 -11.9 HF -11.0 HClO4 -13 HSO3F -15.6 HSO3F/SbF5 -21.0 bis -25.0 super acids H0:

Deduction of Mechanisms 4.4 Acids as solvents and super acids very strong acids in H2SO4 H3BO3 + H2SO4 3 [H3O]+ + B(HSO4)4]- + 2 [HSO4]- with SO3[H3O]+and [HSO4]-is removed + 2 SO3 3 [H3O]+ + [B(HSO4)4]- + 2 [HSO4]- [H3SO4]+ + [B(HSO4)4]- + 4 H2SO4 „Magic acids“ HF/SbF5 -21.0 bis -28.0 2 HF H2F+ + F- 2 HSO3F H2SO3F+ + SO3F- 2 SbF5 2 SbF5 H[Sb2F11] H[Sb2F10(SO3F)]

Deduction of Mechanisms 4.4 Acids as solvents and super acids - the strongest known acids are based on Carborane anions the conjugate base of the super acid may not coordinate or oxidize need for delocalization over many atoms principle behind synthesis: Brønsted acidity induced by Lewis acidity H-LB + LS-A LS-LB + H-A a classical hard-soft problem extrem starke LS: Silylkationen {R3Si}+ starke LB: Cl- A: extrem schwaches Nucleophil e.g. Ch. Reed, Angew. Chem. Int. Ed.2004, 43, 5352

Deduction of Mechanisms 4.4 Acids as solvents and super acids Carborane anions are extremely acidic and not oxidizing! [CB11H13] [CB11H12]- + H+ ICl / Cl2 [CB11H12]- [CB11H6X6]- the H+ can only be introduced via LA-LB interactions [Ph3C][CB11H6X6] + [R3Si-H][R3Si-CB11H6X6] + Ph3C-H [R3Si-CB11H6X6] + HCl [H-CB11H6X6] + R3Si-Cl super-super acid formal {R3Si+} cation !!

Deduction of Mechanisms 4.4 Acids as solvents and super acids what can we do with super-super acids? AuF3 + 6Xe + 3H+ [AuXe4]2+ + [Xe2]2+ + 3HF HF/SbF5 mechanistic principle: super-super acid protonates AuF3 AuF3 + 3H+ [Au(FH)3]3+ very strong oxidant 2[Au(FH)3]3+ + 6Xe [AuXe4]2+ + [Xe2]2+ + 3HF [Sb2F11]- is the counter-ion S. Seidel, K. Seppelt, Science 2000, 290, 117. T. Drews, K. Seppelt, Angew. Chem. Int. Ed.1997, 36, 273

Deduction of Mechanisms 4.4 Acids as solvents and super acids Protonation of CO and generation of the formyl cation HCO+ [H2F]+[SbxF5x+1]- [HCO]+[SbxF5x+1] + HF CO CO(sol) HF + SbF5 HF + SbF5 [HCO]+[SbF6]- Variable-temperature1H, 13C, and 19F HP NMR spectra of 13CO (5.38 mmol) in HF-SbF5 (16.4 mmol) in a sapphire NMR tube (total pressure, 26 atm at 25°C). The broad resonance at δ(19F) = −113 (Table 1) is not shown in the 19F spectrum.

Deduction of Mechanisms 4.4 Acids as solvents and super acids Beside CO, super acids also protonate alkanes, but also small molecules like N2, Ara.o. fullerene [H-CB11H6X6] + C60 [CB11H6X6][HC60] benzene derivatives [H-CB11H6X6] + C6H6 [CB11H6X6][C6H7]

Deduction of Mechanisms 4.4 Acids as solvents and super acids Beside CO, super acids also protonate alkanes, but also small molecules like N2, Ara.o. protonation frequently under alkane elimination, makes s.a. synthetically useful a tbutyl cation which can be stored in bottles

Deduction of Mechanisms 4.5 Diffusion controlled reactions if the rate of a reaction is given by the collision probability, it runs at maximum speed. such a reaction runs at a diffusion controlled rate the frequency is defined by the Fick law of diffusion the relevant relationship is (Smoluchowski) rAB is the reaction cross section, DAB = DA + DB the diffusion constant, a typical range for DAB is 210-9 m2sec-1, for rA 0.2 nm or 210-10 m depends on the viscosity of the solvent the resulting rate constant is kdc 6109 M-1 sec-1

Solvent /10-4 kg m-1 s-1 kdc/L mol-1 s-1 n-Pentane 2.15 3.1·1010Diethyl ether 2.22 3.0·1010Acetone 3.16 2.1·1010Benzene 6.03 1.1·1010Water 8.98 7.4·109Acetic acid 11.6 5.7·109Benzonitrile 14.5 4.6·109Ethylene glycol 136 4.9·108Cyclohexanol 410 1.6·108Glycerol 9450 7.0·106 Deduction of Mechanisms 4.5 Diffusion controlled reactions kdcdoes not depend significantly on the reaction partners a big molecule diffusesslower but may have a larger reaction cross section for other solvents, the diffusion constant can be calculated according to Einstein-Stokes kB·T DA = 6·p·rA·h ifvA vB mit  = Viskosität resulting activation energy from kdc Ea 4 - 20 kJ/mol

Deduction of Mechanisms 4.5 Diffusion controlled reactions example for a rapid reaction

Deduction of Mechanisms 4.5 Diffusion controlled reactions

Deduction of Mechanisms 4.6 Kinetic Isotope Effect Exchanging isotopes is often a good hint to a reaction mechanism and the relevance of individual elementary steps If a reaction rate depends on the isotope (H/D), then this step is rate determining An isotopic effect is generally observable with H/D but is very difficult to detect with other isotopes e.g.12C/13C En=(n+1/2)hn vibrational energy of a molecule: n harmonic oscillator: if force constants for R-H and R-D are equal:

Bond H/cm-1 kH/kD C-H 2900 7.8O-H 3300 10.3 N-H 3100 8.9 S-H 2600 6.3 Deduction of Mechanisms 4.6 Kinetic Isotope Effect Principle of kie: Difference of activation energy is equal to the difference of ground state energies since R-H(D) bonds must be broken AH AD DE RT from Arrhenius: - ln or = kH kD and for R = C follows that kH/kD = 7.8 ln accordingly:

Deduction of Mechanisms 4.6 Kinetic Isotope Effect Beispiel: Nitrierung von C6H6 zeigt keinen Isotopeneffekt und nicht

Deduction of Mechanisms 4.6 Kinetic Isotope Effect the following reaction has a kie of 0.45, why? [PtH2(PMe3)2] [Pt(PMe3)2] + H2

Deduction of Mechanisms 4.6 Kinetic Isotope Effect How thermodynamics influences the magnitude of the kie

Deduction of Mechanisms 4.6 Kinetic Isotope Effect a few examples for normal and inverted kie's M.A. Sierra et al. Chem. Rev.2011, 111, 4857

Deduction of Mechanisms 4.6 Kinetic Isotope Effect a few examples for normal and inverted kie's what would you expect?

5. Linear Free Energy Relationships LFER Kinetic rate laws describe the time course of a reaction as a function of the elementary steps a relationship between kinetics and thermodynamics of a reaction is called a Linear Free Energy Relationship LFER LFER are a semi quantitativeway of “systematizing” our ideas about the similarity of reactions. Gand Gare correlated, although they have sometimes nothing to do with each other only sets of closely related reactions should be compared in that way

Linear Free Energy Relationships LFER only sets of closely related reactions should be compared in that way the most useful examples have well-defined domains of applicability, such as the Hammett equation, the Brønsted catalysis law and the Marcus equation (see later). an LFER is of the general form lnk= mlnKc+ bsince DG* RT kT h lnk = ln - DG* = mDG0 + b' DG0 RT - lnKc = whereas the parameters m and b' may tell us something about the mechanism

Transition state theory (TST):