A One-Slide Summary of Quantum Mechanics

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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...

Transcript of A One-Slide Summary of Quantum Mechanics

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

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

–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