What is the course about ?

Organic Chemistry: organocatalysis

Structural Biology: peptide conformations

Photochemistry and Photobiology: olefins & vision

10-10 (1 Å) - 10-9 m

10-9 - 10-8 m

> 10-8 m (proteins)

Part 1

Part 2

Part 3

Internal Conversion in Cytosine

(100 fs) JACS 2002

Fluorescent Probes (few ps)

Ang. Chem. Int. Ed. 2001

Stereoselectivity in Pericyclic Reactions

(100 fs) J. Phys. Chem A 2001

Molecular Motion in Biological Photoreceptors

(500 fs) PNAS 2000, 2004, 2005, 2006, 2007

LIGHT ENERGY WASTAGE LIGHT ENERGY

EXPLOITATION

Fluorescent proteins (ca. 0.3 ns) JACS 2004

Fate of Light Energy at the Molecular Level

Thermal Reaction Path

Transition Structure (TS)

A B

Reaction Coordinate

Energy

Ground State

TS or “activated complex” 1935 Eyring, Evans and Polanyi

Minimum Energy Path

hν

Conical Intersection (CI) or “Photochemical Funnel”

Excited State

Ground State

Photochemical Reaction Path

Minimum Energy Paths

Energy

Reaction Coordinate

CI

Ground State Excited State

hν

A*

B A

1966 Zimmerman, 1972 Michl

TS

B

A

CI A*

B

A

Transition Vector (X 1 ) Branching (or g-h) plane (X1, X2)!Stationary Point Singularity

One Product One or More Product

X 1

X 1 X 2

Photochemical Reaction Path

ν h 254 nm

liquid state under N2 benzvalene

Benzene Photochemistry

(q.y. 0.02) (e.g. Turro 1986)

(primary) (secondary) (excited state)

prefulvene

Ground state diradical intermediate

N of absorbed photons N of photoproduct molecules

This conical intersection defines the "prefulvene" path

2.0 Å 1.4 Å

1.4 Å

ground state allyl radical

Benzene Conical Intersection: Structure

half-broken bond

unpaired electrons

The wavefunction (electronic structure) does not change when passing through the CI.

diradical

Energy

Reaction Coordinate

CI

Ground State Excited State

ΨA ΨB

Kekule

Benzene Conical Intersection: Branching Space

X 2 = δ δ q

ψ 1 ψ 2 X 1 = δ ( E - E ) δ q 1 2

Benzene Conical Intersection: Branching Space

Gradient Difference (fastest escape from energy degeneracy)

Derivative Coupling (fastest change in the electronic structure)

Benzene Conical Intersection: Wavefunction

x1 x2

Barry phase: the wavefunction (and bonding) changes sign along a loop that contains the intersection !

coupled electrons

coupled electrons

coupled electrons

Benzene Conical Intersection: the branching space χ

3!

1!

x1 x2

-x1 -x2

x1 x2

-x1

-x2

χ

1!

3!

3!1!

Branching space diagram

unstable

unstable

π12 π2π3

2π4 S1!

M*!π12 π2

1π31π4 S2!

π12 π2

2π3π4 S0! S0 σ12 π1

2π2σ2

S1 σ12 π1π2

2σ2

the first computations: 1969 Van der Lugt and Oosteroff and 1975 Devaquet et al. found that the point of return to the ground state (M*) is an energy minimum.

A bit of History

Avoded crossing

Cs symmetry!

Suggests that the non-crossing rule applies not only to diatomic but also to polyatomic molecules

interpolated and symmetric reaction coordinate

State correlation diagram

Slow decay (Fermi Golden Rule - coupling of vibrational states)

2A 1 1B 2

1A 1

E. Teller Isr. J. Chem. 7, 227, 1969

“…in a polyatomic molecule the non-crossing rule, which is rigorously valid for diatomics, fails and two electronic states, even if they have the same symmetry, are allowed to cross at a conical intersection..”.

“…radiationless decay from the upper to the lower intersecting state occurs within a single vibrational period when the system “travels” in the vicinity of such intersection points…”

A bit of History

H.C. Longuet-Higgins, “The Intersection of Potential Energy Surfaces in Polyatomic Molecules”, Proc. R. Soc. Lond. Ser. A., 344, 147-156, 1975

“…thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules...”.

Ultrafast deactivation channels are not consistent with stable M* intermediate.

Energy

Reaction Coordinate

CI

Ground State Excited State

hν

A*

B

A

Photophysics of octatetraene

hν’

1966, Howard Zimmerman

1970, Josef Michl

1974, Lionel Salem

A bit of History

Zimmerman, Michl and Salem were the first to suggest that, in photochemical organic reactions, the point of return M* may correspond to a conical intersection. Zimmerman and Michl call it photochemical funnel.

1982-1988 CASSCF Gradients of the Excited State Energy (Robb, Bernardi, Schlegel and Olivucci). Structure Predicted from Valence Bond

Theory

1990 First Conical Intersection “Detected” for the Ethylene Dimerization (Bernardi, Olivucci, Robb). Computation is carried out on the CRAY-XMP in London.

1.47 Å 2.17 Å

2.08 Å

1990-2000 with M. A. Robb and F. Bernardi: 25 different organic chromophores undergoing 16 different reactions

A bit of History

“statistical” demonstration using quantum chemistry

allow to draw guess structures (eg for pericyclic reactions) !

allow the use optimization methods (eg pseudo Newton-Raphson)

1989-1992

The Norfolk Building King’s College London

Michael Robb

A bit of History

0.0

40

20

0

2A 1

1B 2

1A 1

hν

real crossing between states of the same (A1) symmetry

A bit of History

First application of ab initio CASPT2//CASSCF: s-cis buta-1,3-diene J. Chem. Phys. 1995!

excited state minimum energy path

S1!

M*!S2!

S0! S0

S2

Cs symmetry!

2A 1 1B 2 S2

1A 1 S1/S0

S2/S1

S1/S0

S2/S1

S 1

S 0

CI!

π12 π2π3

2π4 S1!

M*!

Symmetry Based Coordinate!

π12 π2

1π31π4 S2!

π12 π2

2π3π4 S0! S0 σ12 π1

2π2σ2

S2 σ12 π1

1π21σ2

S1 σ12 π1π2

2σ2

Gradient Based Coordinate!

the van der Lugt and Oosteroff result is consistent with the existence of a conical intersection at the bottom of the S1 energy surfaces

A bit of History

FC!

Computational Tools

Conical Interersection Optimization (CIO)

Intrinsic Reaction Coordinate (IRC)

Initial Relaxation Direction (IRD)

Energy Minimum and Transition State Optimization

Trajectory (Classical or Semi-classical)

Construction of a Photochemical Reaction Path

TS!

reactant!

CIO!

TSO!

FC!

IRD!

product!

IRD!

IRC!

X1 X2

CI

M1

M2

TS1

TS2

Upper state!Lower state!Thermal!

Caltech

Construction of Photochemical Reaction Path

1999 Nobel Prize for Chemistry

Photochemical Reaction Path in Textbooks 2001

2008

“…the use of computational methods to elucidate reaction mechanisms has not really made a major impact on the way in which organic photochemist think about such mechanisms …”

6.13 Some Important and Unique Properties of Conical Intersections

6.12 The Non-Crossing Rule and Its Violations: Conical Intersections and their Visualization

6.30 Concerted Photochemical Pericyclic Reactions and Conical Intersections

5.6 Conical Intersections near Zero-Order Surface Crossings

1990

Photochemical Reaction Path in Textbooks

Turro, N. J. (1990). J. Photochem. Photobiol., A: Chemistry 51 63.

MOLECULAR AND ELECTRONIC STRUCTURE OF THE CROSSING: NATURE OF THE PHOTOCHEMICAL FUNNEL

EXCITED STATE REACTION PATHS: EXCITED STATE DECAY

GROUND STATE RELAXATION PATHS: PHOTOPRODUCT SELECTIVITY

TRAJECTORIES: REACTION TIME SCALES AND QUANTUM YIELDS

Computational Photochemistry

almost routine

feasible since 2007!

still unpractical or impossible

wavefunction/density (orbital occupancies)

branching plane

equilibrium geometries and transition states

Newton equations of motion

optimization of a singularity

M. Olivucci, Ed. Computational Photochemistry, Elsevier 2005

Computational Photochemistry (further info http://www.lcpp.bgsu.edu)

S1!

M*!

S0! S0

S2

2A 1 1B 2 S2

1A 1

S1/S0

S2/S1 S1!

M*!

S0! S0

S2

2A 1 1B 2

S2

1A 1

S1/S0

Avoided Crossing rule valid !

Avoided Crossing rule invalid

Avoided Crossing rule invalid

Different Electronic States = Different Conical Intersection Structure =

Different Chemistry

- +

- + (π π*)2 π π*

Hydrocarbons Schiff bases

σ-Bond Making

σ-Bond Breaking

C

Group (or σ-Bond) Exchange

The Chemistry of Conical Intersections: Bond-Making, Bond Breaking and Group Transfer

1

3 6

1 6

3

Polyenes (and polyene radicals)

Benzene Cyclohexadienes

The Chemistry of Conical Intersections: Conjugated Hydrocarbons

1 . 4 1 . 4 2 . 0

J. Am. Chem. Soc. 1995, 117, 11584-11585

Crossing between the ground state and a (π-π*) doubly excited state

S1

S0 π π*

π π*

The Chemistry of Conical Intersections: Multiple conical intersections

E / k

cal m

ol-1

3 5 7 9

0

10

20

30

40

The Chemistry of Conical Intersections: Selectivity

cyclizations

Z/E isomerization

90°

Selectivity may be due to differences in energy

S1 S0

+ + hν

2.12 2.22

The Chemistry of Conical Intersections: Cyclohexadiene/Hexatriene

Allyl radical moiety

triradical moiety

X 2 X 1

The Chemistry of Conical Intersections: Multiple products

x1

x2

-x1

-x2

χ

5! 6!

5!

6!

The Chemistry of Conical Intersections: Change in bonding

unstable

Selectivity may be affected by the excited state dynamics

5!

6!

5!

6!

N H 2 ( + ) 1

2 3

4 5

N H 2 ( + )

trans

1

2 3

4 5

The Chemistry of Conical Intersections: Protonated Schiff Bases

cis

Cis Form

Light

Retinal Rhodopsin

Trans Form

NH + 1 1 1 1 NH +

(Appears in ca. 200 fs)

- +

1.46 Å

1.40 Å

1.38 Å

1.33 Å

1.38 Å

90°

e- +

Crossing between the ground state and a (π-π*) singly excited state

S1

S0

π π*

π π*

hν

N

The Chemistry of Conical Intersections: Charge Transfer

+

90°

Newman projection

X1

X2

N H 2 +

N H 2 +

+ N H 2

+

x1

x2

-x1

-x2

χ

N H 2

N H 2

The Chemistry of Conical Intersections: Charge Transfer

N

N

Unstable (TS)

Unstable (TS)

Stretching

Motion Coupled to the Torsion

χ

x1 x2

-x1 -x2

N H 2

+ N H 2

breaks the double bond homolitically

+

breaks the double bond hetherolitically

The Chemistry of Conical Intersections: Charge Transfer

N H 2

N H 2 +

N H 2 +

+

1.35

1.461.36

1.43

1.29

MEP co-ordinate (a. u.)

0.0 5.0 10.0 15.0 20.00

20

40

60

80

100

hν

1.39

1.391.46

1.42 1.3076.8

(291 nm)

91.2

1.36

1.431.42

1.43 1.30

FC

120

1.42

1.37

1.53

1.37

1.35

24.7

12.5

1.51.37 1.37

1.351.41

S1

S0

0.0

1.35

1.451.36

1.431.29

trans

180.0

S2

CI

The Chemistry of Conical Intersections: Barrierless Photoisomerization Path

Ener

gy (k

cal m

ol-1

) π π*

π π*

Crossing between the ground state and a (n-π*) singly excited state

S1

S0 n π*

n!π*

The Chemistry of Conical Intersections: Azoalkane Fluorescence Quenching

N

NCl

ClClH

τ=930 nsec, Φf=0.56 N

N

τ=13 nsec, Φf=0.01

hν

N

N n!π*

O O

N N

X2 (ring-puckering)

N N

X1 (coupled electron-proton transfer)

The Chemistry of Conical Intersections: Azoalkane Fluorescence Quenching

Azoalkane (pyrazoline)

CH2Cl2

N N

Cl

Cl

S1

S0 n π*

n!π*

hν

x1 x2

NN H C

ClH

Cl

Rαδιχαλ Παιρ!NN H C

ClH

Cl+ -

Ion Παιρ! TS (electron transfer)!

The Chemistry of Conical Intersections: Electron Transfer

δ- δ+

- +

δ- δ+