A One-Slide Summary of Quantum Mechanics Fundamental Postulate: O Ψ = a Ψ operator wave function (scalar) observable What is Ψ? Ψ is an oracle! Where does Ψ come from? Ψ is refined Variational Process H Ψ = E Ψ Energy (cannot go lower than "true" energy) Hamiltonian operator (systematically improvable) electronic road map: systematically improvable by going to higher resolution convergence of E truth What if I can't converge E ? Test your oracle with a question to which you already know the right answer...
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A One-Slide Summary of Quantum Mechanics
Fundamental Postulate:
O Ψ = a Ψoperator
wave function
(scalar)observable
What is Ψ? Ψ is an oracle!
Where does Ψ come from? Ψ is refined
Variational Process
H Ψ = E ΨEnergy (cannot golower than "true" energy)
Hamiltonian operator(systematically improvable)
electronic road map: systematicallyimprovable by going to higher resolution convergence of E
truth
What if I can't converge E ? Test your oracle with a question to which youalready know the right answer...
ligand with attachedphotoaffinity label inenzyme active site
N3binder
hν NH
–N2binder
Photoaffinity Labeling 1
singlet nitrene covalentlymodifies enzyme — activesite can be identified bysequencing of protein
hν
But:
N3
–N2
Attractive features of aromatic nitrenes as photoaffinity labels: 1) Generated with light outside of protein absorption bands 2) Highly reactive singlets 3) N2 is an innocuous byproduct of activation
Photoaffinity Labeling 2
bond insertion
N
ISC to triplet state(H-atom abstraction)
didehydroazepine
k1
kISC
k3
Practical concern—must minimize
N
singlet
N3
N
hν
–N2
Photoaffinity Labeling 3bond insertion
ISC to triplet state(H-atom abstraction)
didehydroazepine
k1
kISC
k3
k3 > k1 k1 > k3 k3 > k1Platz et al.
N
singlet
N N N
F F
F F
Contributing to the Delinquency of a Theorist
High level ab initio calculations of 2,6-difluorophenylnitreneand 3,7-difluoro-[1,2]-didehydroazepine (and their 3,5-disubstituted isomers, where there is no fluorine effect)would be most welcome and instructive!
M. S. Platz, Accounts Chem. Res. 1995, 28, 487.
Configuration Cartoons
N
N
N
N
3A2 (T0) 1A2 (S1)
11A1 (S2) 21A1 (S3)
Relative E (kcal/mol) for PhN
N
π
σ
.:. 3A2
1A2 11A1 21A1
MRCISD/DZP 0.0 21.0 39.8 (52)CASPT2N(8,8)/TZP 0.0 19.3 34.8 54.5CCSD(T)/DZP 0.0 — 35.2 (47.2)BLYP/TZP 0.0 (14.3) 29.5 (41.0)Expt. 0.0 18 30 ?Kim, S.-J.; Hamilton, T. P.; Schaefer, H. F. J. Am. Chem. Soc. 1992, 114, 5349;Hrovat, D. A.; Waali, E. E.; Borden, W. T. ibid. 1992, 114, 8698; Smith, B. A.;Cramer, C. J. ibid. 1996, 118, 5490; Travers, M. J.; Cowles, D. C.; Clifford, E. P.;Ellison, G. B. ibid. 1992, 114, 8699.
Ring Expansion Mechanism
Wagner-Meerwein shift ofCH to aligned in-plane
(empty) N p orbital
The electronic configurationof the didehydroazepine
correlates with the S3 nitrene
N N
Avoided Crossing
S1
S3
NN
S1
S3
NN
∆E1‡
∆E2‡
π-Electron-donating groups should slow ring expansion
F F
F
F
0
10
20
30
40
50
60
70
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Hammett σ
CASP
T2 E
rel,
kcal
/mol
Phenylnitrene Energies With 32 Different meta and para Substituents
S3
S2
S1
some widening
N
Photoaffinity Labeling 5
Gritsan, N. P.; Tigelaar, D.; Platz, M. S. J. Phys. Chem. A 1999, 103, 4465.
k3
R
R = H, CH3, CF3, CH3C(O), F, Cl
"Measured" Ea = 5.7 ± 0.4 kcal/mol in every case
For R = I, OCH3, N(CH3)2, ISC too fast to measure k3
N
R
E
nitrene didehydroazepine
Actual Ring Expansion Reaction Coordinate
Substituent Effects on Ring Expansion CoordinateRelative 298 K enthalpies in kcal/mol
12.38.58.99.5
NHMeHF
NO2
8.52.73.03.7
13.35.87.34.8
1.7–1.9–1.6–0.7
Substituent Effects Rationalized
N
NO
O
N
NO
O
EWGsstabilize
R
+ +
–5.50.00.50.2
NHMeHF
NO2
EDGs stabilize
N N
R
N
Photoaffinity Labeling 4
Karney, W. L.; Borden, W. T. J. Am. Chem. Soc. 1997, 119, 3347.
singlet didehydroazepine
k3
~>k3:N
F F
N
H3C CH3
N
N
Theoretical Recommendation
Optimal photoaffinity labels will be aromatic azidescombining steric bulk at ortho positions with strong
electron-donating group at para position
What is a Block CoPolymer?Situation:
Consequence:If you want to design new materials that incorporate properties of both polymers on small length scales, you must keep the polymers from phase separating by covalently attaching chains of one type to chains of the other type, e.g., AAAAAAAAAAAAA–BBBBBBBBBBBBBBB
UsesThermoplastic elastomers (e.g., running shoe soles)Pressure sensitive adhesives (Post-It™ Notes)Viscosity modifiers for oilsCompatibilizers (the polymer equivalent of a soap)
Mixtures of two polymers—even seemingly very similar polymers—nearly always phase separate rather than "alloy"
Challenge:How can you synthesize a well-defined BCP (e.g., having low polydispersity)?
R2
F
F
R1
• mild• selective (no other insertion products)• quantitative• experimentally simple
R2
O
FF
FCF3
O
F CF3
FF
R1
+
n
polyisoprene H Mepolybutadiene H H
polydimethylbutadiene Me Me
R1 R2
n
180 °C
One Technique for Making Fluorinated BCPs
R2
CnF2n
CnF2n
R1 R2
CnF2nF2nCn
R1
n
n
If One Fluorine is Good... (E. I. DuPont)
Are there concerns?
Carbene Rearrangements in Hydrocarbons
CH3
CH3
HH
CH3
CH3
HH
HHH
CH3
H
H
H
CH3
HCH3
1,2-H shift
ΔG‡ = 5.2 kcal/mol
1,3-H shift
ΔG‡ = 8.3 kcal/mol
1,2-CH3 shift
ΔG‡ = 18.1 kcal/mol
Kinetics 101Carbene additions typically proceed without an activation barrier. The rates of barrierless reactions in solution are typically "diffusion controlled". Over a reasonable range of viscosities, an appropriate rate expression is:
Ratebi (M sec–1) ≈ 1010 • [A] [B]
Unimolecular rearrangements typically follow a particularly simple rate law:
Rateuni (M sec–1) ≈ 1014 • [A] • exp(–ΔG‡ / RT)
We would like the ratio of bimolecular reaction to unimolecular rearrangementto be at least a factor of 100, i.e.,
Ratebi (M sec–1)Rateuni (M sec–1)
= 100 = 10–4 • [B] • exp(ΔG‡ / RT)
Given a realistic maximum [B] (molar concentration of double bonds) of about1 M, this implies the minimum activation energy for unimolecular rearrangement cannot be lower than 12.9 kcal/mol at 200 °C
Carbene Rearrangements in Fluorocarbons
CF3
F
FF
CF3
FF
F
FFF
F
F
F
F
FF
CF3
1,2-F shiftΔG‡ = 25.9 kcal/mol
1,3-F shift
ΔG‡ = 36.4 kcal/mol
1,2-CF3 shift
ΔG‡ = 18.5 kcal/mol
Because fluorine holds electrons more "tightly" than hydrogen, it is muchharder to insert into C–F bonds than into C–H bonds. Interestingly, the
accessibility of C–C bonds is relatively unperturbed by H vs. F.
C
F
1.8191.723
1.963 2.091
1.897
1.561
Feasibility Study on Epoxide Cracking
Kinetics 102: Left path preferred by about 5,000,000 to 1 at 200 °C
‡ ‡
++
COF
ΔG‡ = 32.0kcal/mol
ΔG‡ = 46.7kcal/mol
Feasibility Study on Epoxide Cracking 2
Kinetics 103: Half-life for a unimolecular process (like cracking) is roughly
COF
ΔG‡ = 52.1kcal/mol
‡
+
t1/2 (sec) ≈ ln2 • 10–14 • exp(ΔG‡ / RT)
For above reaction at 200 °C, 50% cracking takes 317 years . . .(4.8 hours for previous example via its preferred path)
Conclusions
1. Perfluorocarbenes, once generated, are remarkably stable to intramolecular rearrangement.
2. Epoxide cracking reactions to generate perfluorocarbenes larger than CF2 arenot practical.
3. Alternative reactions can generate perfluorocarbenes larger than CF2 with considerably lower activation energies.
CF3CF2SiF3
CF3CF + SiF4
ΔG‡ = 33.9kcal/mol
NN O
FCF3 CF3CF
+
+N2
acetone
ΔG‡ = ???kcal/mol
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