Advanced Organic Chemistry

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1 Lalic, G. hemistry 530A Advanced rganic hemistry Lecture 11 roblems from ougherty: Kinetic Isotope ffects Kinetic Isotope ffects of lementary Reactions Kinetic Isotope ffects in Multi-Step Reactions ougherty,. A., "Modern hysical rganic hemistry", hapter 8, p & Background ougherty, p Westheimer, F.. "The Magnitude of the rimary Kinetic Isotope ffect for ompounds of ydrogen and euterium." hem. Rev. 1961, 61, 265. (pdf)

2 rimary KI Because of the greater mass of relative to, - bond is stronger than - bond. - bond also has a lower zero point energy. This is also true for other atoms and their isotopes, but the difference is biggest for hyrogen and the effect is the biggest for hydrogen. G Kinetic Isotope ffects activation energy for breaking - bond activation energy for breaking - bond - zero point energy - zero point energy - distance For the homolysis of - and - bonds the difference in Z's will be the same as the diference in activation energies ( G ). The diference in activation energies will be reflected in the corresponding rate constants (k and k ). In general, the diference in the rates of reactions as a result of the isotopic substitution ( for ) is called the KI. The ratio of k /k provides a quantitative measure of a KI. A- B A B- For other types of elementary reactions (one TS) in which - bond is being broken, situation is similar. owever, because - and - bonds are ususally not completely broken in TS, we have to consider the change in the difrence between Z for - and - in SM and TS ( Z). G G G TS Z TS Z SM Z SM - Z TS = Z SM - distance resented is the "summary" vibration, which represents all vibrational modes. Z will be a result of the changes in all vibrational modes that involve -() bond that is being broken. For the primary kinetic isotope effect, the changes in the stretching vibration will have the greatest effect. () Z will be the greatest for the homolysis reaction because Z TS = 0. For reactions with Z TS = 0 primary KI = ~6.5. The primary KI for other reactions (transfer of from one molecule to another), in general, will be smaller and will depend on the following factors. A- B [A B] A B- k /k = 1-7 xtent to which the transfer has progressed in the TS. For linear TS (AB in line) the KI will be the greatest when A- force constant is the same as the B- force constant (i.e. the strength of partially formed A- and B- bonds is the same). If A = B that will be the case for the symmetric TS. symmetric stretch A B in TS If the A- and B- force constants are the same, the high energy symmetric stretch will be the same for AB and AB. We say that we "lost" that vibrational mode in the TS because there is no Z associated with that vibration. The value of the primary isotope effect can provide information about the position of the TS on the reaction coordinate. The geometry of the TS. Linear TSs usually lead to a greater KI. In linear TS we can "lose" a high energy symmetric strech. In non-linear TS we "lose" a bending mode that has a lower vibrational frequence. Tunneling In some cases KI larger than ~7 ca be obtained if tunneling is involved. Tunneling is defined as an event in which hydrogen goes through the barrier and not over it. euterium usually can not do that because of the greater mass. eavy Atom Isotope ffects KI is directly related to a difference in masses of the two isotopes. This difference is 100% for and but it is only 8% for 12 and 13. As a result, KI for heavy atoms are hard to measure and are used much less often. 13 KI is used most offten in part because of the NMR technique developed by Singleton Singleton,. A. J. Am. hem. Soc. 1995, 117, 9357.

3 Kinetic Isotope ffects Secondary KI quilibrium Isotope ffect (I) Isotopic substitution can lead to a diference in rate constants even when X- () bond is not broken during the course of the reaction. That usually occurs if isotopic substitution is near an atom that changes hybridization during the reaction. This phenomenon is called secondary KI and it can be (isotopic substitution at the atom that changes hybridization) or (isotopic substitution at the next atom). 2 KI is mostly a consequence of the changes in frequency of out-of-plane bending vibrations with the change in hybridization of a carbon atom. The lower the frequency of a vibration, the smaller the diference in Z between and. sp 3 sp 2 k /k (max. 1.4) Isotopic substitution can effect the position of an equilibrium if there is a diference in Z for and in the summary vibration of the starting material and the product. The change in K eq is called I. Z SM - Z = G euterium substitution at the atom changing the hybridization will shift the equilibrium to the left. Z TS 1350 cm -1 Z SM sp 3 sp 2 Z G G 800 cm -1 I for equilibria that involve change in hybridization will be larger than the 2 KI for the same reaction under kinetic conditions. Z SM sp 3 sp 2 In an equilibrium, deuterium will favor the compound with a greater Z. Intrinsic KI in Multi-Step Reactions sp 2 sp 3 k /k inverse KI In general, frequency of out-of-plane bending sp 3 > sp 2 > sp The latter the TS, the greater the KI. 2 KI provides information about hanges in hybridization during the reaction ostion of the transition state along the reaction coordinate 1 and 2 KIs were so far described only in the context of elementary reactions or elementary steps with a single TS. We call these KIs, the intrinsic KIs of elementary reactions. In complex reactions involving multiple elementary steps, intrinsic KIs can have an effect on several aspects of the overall reaction. Intrisic KI will result in a change in the overall rate of the reaction if the rate constant associated with the elementary step with an intrisic KI is in the rate law for the overall reaction (i.e. if the elementary step occurs prior to or is the rate determining step). Intrinsic KI will influence product distribution in a competition experiment if the elementary step with an intrinsic KI is the product determining step of the reaction. The position of the elementary step relative to the rate determining step is irrelevent in this case.

4 Kinetic Isotope ffects omatic lectrophilic Substitution xample 1: N 2 BF 4 2 N B N 2 Mechanism: B lah, G. A. J. Am. hem. Soc. 1961, 83, k obs /k obs = 0.89 reaction is pseudo first order (reaction done in ) [][B]/( [B])/ [][B]/( [B]) = 0.89 A relativelly small inverse kinetic isotope effect on the overall rate of the reaction indicates that is associated with the step that most likely occurs after the rate limiting step. [B] >> rate = [][] / = d[]/dt = [][B] rate = [][][B]/( [B]) [B] >> rate = [][] [B] << rate = K eq [][][B] Steady state approximation: d[]/dt = 0 [][] = [] [][B] [] = [][]/( [B]) What are the intrinsic KIs for the elementary steps involved? consider 6 6 and 6 6 is associated with a 2 KI (inverse KI, going from sp 2 to sp 3 ) is associated with the same 2 KI (small normal KI 1.1 to 1.3) is associated with a primary KI (values 3-7) Because of the rate law for this reaction only the intrinsic KI associated with has an effect on the overall rate of the reaction. The experimental value is a result of one secondary KI. Most electrophilic aromatic substitutions give similar results. What value for KI would you expect in a competition experiment in which same concentrations of 6 6 and 6 6 were used? raw energy diagram for the competition experiment. xample 2: Br k obs /k obs = ~5.5 Br B Steric hindrance has greater effect on the deprotonation step than on the first step of the reaction. [B] << rate = K eq [][][B] rate /rate = K eq /K eq bserved isotope effect is a combination of the equilibrium isotope effect and the primary KI of the second step. It is a combination of all intrinsic isotope effects. N 2

5 Kinetic Isotope ffects xample 3: N 3 2 S 4 2 N B N 2 k obs /k obs = 1 measured value Williams, G. J. Am. hem. Soc. 1952, 74, It means that either all of the steps are after the rate limiting step or that for some reason some or all of the intrinsic KIs are small. In this case the formation of N 2 from N 3 and 2 S 4 is the RS. Stepwise Mechanism -Ac l l Zn 3 Znl Ac 3 Ac 3 This idea is supported by the fact that competition experiment in which 6 6 and 6 6 were present in the reaction mixture at the same time leads to a KI of 0.9. N 3 2 S 4 N 2 S 4 2 rate limiting step rate = f([n 3 ], [ 2 S 4 ]) rate determining step product determining step verall KI obtained from independant rate measurements is 1.0. That is inconsistent with the concerted mechanism which should exhibit a primary KI. It indicates stepwise mechanism with a first step being the RS. A 3 Ac 2, Znl Znl RS N 3 3 N 2 oncerted Mechanism N N 2 Alkene Acylation 3 Znl2 Znl 2 Beak,. J. Am. hem. Soc. 1980, 102, In the competition experiment KI = 3.2. This KI is a combination of a relatively small primary KI and an inverse secondary KI. Small primary KI may be a result of the nonlinear cyclic TS. The difference in KIs obtained in the competition and independent rate measurement experiments is a sign of a multistep mechanism in which RS preceeds the product determining step. KIs obtained in intramolecular competition experiments are called intramolecular KI. What result would you expect from a competition experiment in which a mixture of fully proteated and fully deuterated substrates is used in the reaction. xplain, and draw an energy diagram for this competition experiment and for the intramolecular competition experiment. Would you expect positive or a negative value for a ammett plot made for the following set of reactions. R 3 Ac 2, Znl 2 = X