Competitive Kinetics Isotope Effects - Advanced Organic Chemistry, Harvard University, Lecture notes of Chemistry

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Compe&&ve  Kine&c  Isotope  Effects   Intermolecular  Compe//on:  measure  in  same  flask  using  two  isotopomeric  substrates     Intramolecular  Compe//on:  measure  in  same  flask  using  one  substrate  that  can  choose   between  two  isotopes     The  methods  are  more  accurate  but  the  results  must  be  interpreted  cau&ously.                 References:  Hartwig  ACIE  2012  51  3066;  Sierra  Chem.  Rev.  2011,  4857;  Singleton  JACS  1995  117  9357,  JACS  1999  121  9455;  Saunders   Reac&on  Rates  of  Isotopic  Molecules  Wiley,  1981   Absolute  Rates:     -­‐  measure  rate  of  H  vs.  D  in  separate  flasks   -­‐  observa&on  of  primary  KIE  is  unambiguous   evidence  for  rate-­‐determining  C-­‐H  cleavage   -­‐  subject  to  rela&vely  large  experimental  errors   Intermolecular  Compe&&on   At  low  conversions,  the  ra&o  of  product  isotopomers  will   reflect  the  KIE.     At  high  conversions,  the  product  ra&o  will  equal  the  star&ng   material  distribu&on.  ! SMH kH⎯→⎯ PH SMD kD⎯→⎯ PD Simula&on  for  kH  =  0.05  s-­‐1  and  kD  =  0.01  s-­‐1  (KIE  =  5.0):   The  blue  and  green  lines  show  the   product  concentra&ons  over  the   course  of  the  reac&on.     The  red  line  shows  the  product   isotopomer  ra&o.     This  uses  a  first-­‐order  model,  but   the  conclusions  do  not  change  with   other  models.   Intramolecular  Compe&&on   In  an  intramolecular  compe&&on   experiment,  only  the  product  ra&o  is   available.    This  ra&o  always  reflects  the   KIE  directly.   !PD kD←⎯D− SM −H kH⎯→⎯ PH In  a  first-­‐order  model,  this  is  easy  to   see  mathema&cally  (see  le`).    The   integral  of  an  exponen&al  is  another   exponen&al,  which  will  result  in  a   term  that  is  the  same  for  the   differen&al  equa&on  in  PD.    These   terms  will  cancel,  leaving  kH/kD  =  KIE.     Intui&vely,  this  occurs  because  the   star&ng  material  ra&o  is  constrained   to  1:1,  so  every  moment  is  like  the   start  of  an  intermolecular   compe&&on.     ! [SM]= [SM]0 exp − kH +kD( )t⎡⎣ ⎤⎦ dPH /dt = kH[SM]= kH[SM]0 exp − kH +kD( )t⎡⎣ ⎤⎦ dPH = kH[SM]0 exp − kH +kD( )t⎡⎣ ⎤⎦dt Scenario  1:  The  Trivial  Case   In  a  one-­‐step  reac&on,  whether  the  KIE  is  measured  from   absolute  rates  or  intermolecular  compe&&on,  the  result  will   be  the  same.   ! SMH kH⎯→⎯ PH SMD kD⎯→⎯ PD If  a  reac&on  proceeds  via  a  mechanism  in   which  the  first  step  is  rate-­‐determining  and   involves  C-­‐H  cleavage,  then  both  experiments   will  also  show  a  KIE.    (Intramolecular   compe&&on  would  also  show  a  KIE.)     However,  the  situa&on  becomes  more   complicated  if  C-­‐H  cleavage  is  post-­‐rate-­‐ determining.    In  general,  compe//ve  KIEs  do   not  have  to  reflect  the  KIE  of  the  rds.   Scenario  2:  Rate-­‐Determining  Catalyst  Ac&va&on   For  example,  consider  another  trivial  example   where  the  rate  (or  turnover)  limi&ng  step   involves  catalyst  ac&va&on.    This  could  be  a   ligand  dissocia&on  or  reduc&ve  elimina&on   from  a  metal  complex.     Absolute  rates  will  just  measure  the  rate  of   catalyst  ac&va&on,  which  is  obviously  not   sensi&ve  to  whether  the  substrate  has  H  or  D.     Compe//on  experiments  could  show  a  KIE,   however!    The  slow  catalyst  ac&va&on  process   trickles  ac&ve  catalyst  into  the  reac&on.     Imagine  running  the  experiment  by  trickling  in   ac&ve  catalyst.    Clearly,  a  compe&&ve  KIE   would  be  observed.    In  this  case,  the  absolute   rate  measures  the  rate  of  the  catalyst  addi&on,   while  the  compe&&ve  KIE  measures  the   preference  of  the  catalyst  for  H  vs.  D.   ! preCAT k1⎯→⎯ CAT CAT + SMH kH⎯→⎯ CAT +PH CAT + SMD kD⎯→⎯ CAT +PD Scenario  4:  Pre-­‐Equilibrium  Cleavage   What  if  C-­‐H  cleavage  occurs  before  the  rate-­‐ determining  step?     Assuming  pre-­‐equilibrium  kine&cs,  the  rate  law   in  this  situa&on  is:     vH  =  k2[BH]  =  KH  k2H  [AH]   vD  =  k2[BD]  =  KD  k2D  [AD]     Measuring  the  KIE  amounts  to  measuring     (KH/KD)  (k2H/k2D)     which  is  the  product  of  the  equilibrium  isotope  effect  (EIE)  and  KIEs.     Regardless  of  how  the  KIE  is  measured,  the  isotope  effect  will  be  much  smaller  because   EIE  <<  KIE.    Absolute  rates  will  show  the  effect  because  it  is  in  the  rate  law.    Rela&ve  rates   will  show  the  effect  because  the  reac&on  is  commiied  to  an  isotope  at  the  rds.     If  both  steps  1  and  2  are  isotopically  sensi&ve,  the  two  isotope  effects  will  be   superimposed.   Scenario  5:  Post-­‐Rate-­‐Determining  Equilibrium  Cleavage   If    equilibrium  C-­‐H  cleavage  occurs  a@er  the   rate-­‐determining  step,  the  rate  law  cannot  be   affected.     Absolute  rates:  No  KIE.     Compe//on:  EIE.     However,  compe&&on  experiments  can  show   an  EIE  because  it  can  perturb  the  rate  of  the   product-­‐determining  step.    In  this  diagram,  the   product  is  commiied  to  an  isotope  in  step  k2.     This  rate  of  this  step  depends  on  [B],  which  is   affected  by  the  EIE.     Example  1   This  means  that  C-­‐H  cleavage  is  not  rate-­‐determining.    In  fact,  oxida&ve  addi&on  to  the  C-­‐ Cl  bond  is  rate-­‐limi&ng.    In  experiment  a),  the  substrate  is  not  commiied  to  an  isotope  at   this  stage,  so  an  intramolecular  KIE  can  be  observed.    In  experiment  b),  the  substrate  is   commiied  to  an  isotope  during  C-­‐Cl  oxida&ve  addi&on,  so  an  intermolecular  KIE  cannot   be  observed.    Geary  Eur.  JOC    2010  5563   Intramolecular  KIE:  yes               Intermolecular  KIE:  no