Chemistry 125: Lecture 38 January 11, 2010 Reaction Rates: Trajectories, Transition State Theory, and Bond Dissociation Energies This For copyright notice see final page of this file

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Update from Prof. Leiserowitz on Hemozoin Alignment 400nm thick disk cut from chemically fixed malaria-infected red blood cell Cut into ~40 slices each imaged by SEM and reconstructed in 3D by computer tomography

Update from Prof. Leiserowitz on Hemozoin Alignment 400nm thick disk cut from chemically fixed malaria-infected red blood cell 3 or 4 hemozoin crystals identically oriented on {100} [2 (?) others may have been damaged during slicing]

Semester 1 : Bonds and Molecular Structure (and some thermodynamics) Semester 2 : Reactions and Synthesis (and some spectroscopy)

Free energy determines what can happen (equilibrium) K = e -  G/RT = 10 -(3/4)  G room Temp But how quickly will it happen? (kinetics) Energy & Entropy

Classical Trajectories & The Potential Energy Surface Visualizing Reaction

Time-Lapse “Classical” (Molecular Mechanics) Trajectory for non-reactive collision of 13 atoms 6 molecules 40 Dimensions (3n + time) by E. Heller faster slower heavier lighter rotating slowly rotating rapidly & vibrating Too Complicated (for our purposes)

Potential Energy “Surface” for Stretching Diatomic Molecule A-B A-B Distance Potential Energy Rolling Ball Maps A-B Vibration

Potential Energy Surface for Linear Triatomic A-B-C Cliff Pass (Transition State or Transition Structure) Plateau Valley ridge + maximum minimum * * So 2-D specifies structure

Vibration of A-B with distant C spectator Slice and fold back Potential Energy Surface for Linear Triatomic A-B-C Vibration of B-C with distant A spectator

Unreactive Trajectory: (A bounces off vibrating B-C) Potential Energy Surface for Linear Triatomic A-B-C

C flies away from vibrating A-B Reactive Trajectory A approaches non-vibrating B-C Potential Energy Surface for Linear Triatomic A-B-C “classical” trajectory (not quantum)

H 3 Surface Henry Eyring (1935) Crazy angle of axes means that classical trajectories can be modeled by rolling marble. Transition State (“Lake Eyring”)

H + H-Br

John McBride (1973) “I wanted to catch a little one”

Studying Lots of Random Trajectories Provides Too Much Detail Summarize Statistically with Collective Enthalpy (H) & Entropy (S)

“steepest descent” path Slice along this path, then flatten and tip up to create… (not a trajectory)

“Reaction Coordinate” Diagram (for a one-step atom transfer) Not a realistic trajectory, but rather a sequence of three species Starting Materials Products Transition “State” G each with H and S, i.e. Free Energy (G)

Free Energy determines what can happen (equilibrium) K = e -  G/RT = 10 -(3/4)  G room Temp and how rapidly (kinetics) k (/sec) = e -  G /RT ‡ ‡ = (3/4)  G room Temp Amount of ts (universal) Velocity of ts theory Since the transition state is not truly in equilibrium with starting materials, and the velocity is not universal, the theory is approximate.

Using Energies to Predict Equilibria and Rates for One-Step Reactions: Free-Radical Halogenation H CH 3 Cl H Cl CH 3 Cl CH 3 Cl Cl "free-radical chain"

Are Average Bond Energies “Real” or just a trick for reckoning molecular enthalpy ? Bond Dissociation Energies are real.

BondDissn Energies best values as of 2003

Ellison I Larger halogen  Poorer overlap with H (at normal bond distance) & less e-transfer to halogen H I H F less e-stabilization  weaker bond Diagram qualitative; not to scale.

Ellison II No special stabilization  SOMO orthogonal to  *) C - H bond unusually strong (good overlap from sp 2 C ) Vinyl C - H bond normal (sp 3 C, as in alkane) Allyl Special stabilization  SOMO overlaps  *) hard 111 Phenyl Ditto hard 113 easy 89 Ditto Benzyl easy 90 All H-Alkyl 100 ± 5 Same trend as H-Halogen Special Cases SOMO C   Are unusual BDE values due to unusual bonds or unusual radicals? or actually

H 3 C H + X X  H 3 C X + H X F Cl Br I ” Possibility of Halogenation (Equilibrium) CostReturnProfit

H 3 C H + X X  H 3 C X + H X Possibility of Halogenation (Equilibrium) F Cl Br I ” CostReturnProfit Is break-two-bonds-then-make-two a plausible Mechanism? at RT (~300K)? at ~3000K?  = /sec  = 250/sec How about rate (which depends on Mechanism)? No Way! Yes (unless there is a faster one)

H H 2 H 2 H HHHHHH H H H Henry Eyring (1935) Dissociation followed by association requires high activation energy. SLOW Make-as-you-break “displacement” is much easier. FAST

Free-Radical Chain Substitution X-HR-H X-X R-X X R cyclic machinery

End of Lecture 38 Jan. 11, 2010 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0