Theoretical Photochemistry WiSe 2016/17

Lecture 5

Irene Burghardt (burghardt@chemie.uni-frankfurt.de)

http://www.theochem.uni-frankfurt.de/teaching/ −→ Theoretical Photochemistry

1

Topics

1. Photophysical Processes

3. Wavepackets

5. The Franck-Condon picture of electronic transitions

6. What do we measure experimentally?

2. The Born-Oppenheimer approximation

4. Beyond Born-Oppenheimer – non-adiabatic transitions

7. Conical intersections

8. Some electronic structure & dynamics aspects

9. Examples: Ethene, PYP

10. More on dynamics: trajectories or wavefunctions?

11. Wavefunction propagation techniques

2

12. Trajectory surface hopping techniques

13. Non-linear optical spectroscopy: calculation of spectroscopic signals

14. Extended systems: Excitons, light-harvesting, etc.

15. Solvent/environmental effects

3

Literature

1. P. W. Atkins and R. Friedman, Molecular Quantum Mechanics, 5thEdition, Oxford University Press (2011).

2. D. Tannor, Introduction to Quantum Mechanics: A Time-DependentPerspective, University Science Books (2006).

3. M. Klessinger, J. Michl, Excited States and Photochemistry of OrganicMolecules, VCH-Wiley (1995).

4. I. N. Levine, Quantum Chemistry, 6th Edition, Pearson InternationalEdition (2009).

5. F. Jensen, Introduction to Computational Chemistry, 2nd Edition, Wiley(2007).

6. C. J. Cramer, Essentials of Computational Chemistry – Theories andModels, 2nd Edition, Wiley (2004).

4

How does ethylene isomerize?

5

Singlet electronic states

Omitting σ framework, consider only “Huckel-type” π and π∗

configurations:

N(π2) = “Normal”

V (ππ∗) = “Valence”

Z(π∗2) = “Zwitterionic”

experimental observation: V lifetime around 20-100 femtoseconds

6

Normal Modes

TABLE I. Ground-state harmonic frequencies of ethene ~in cm21).

Frequency

Symmetry Mode MP2 ~this work! CCSD~T!a Expt.b Description

ag n1 3196 3157 3156 C–H sym. stretch

n2 1684 1672 1656 C–C stretch

n3 1384 1369 1372 CH2 sym. scissor

au n4 1076 1044 1045 torsion

b1u n5 3178 3139 3130 C–H sym. stretch

n6 1485 1479 1472 CH2 antisym. scissor

b2g n7 960 942 960 CH2 pyramid. ~wagging!

b2u n8 3293 3246 3239 C–H antisym. stretch

n9 828 823 844 CH2 sym. rocking

b3g n10 3266 3219 3207 C–H antisym. stretch

n11 1247 1242 1249 CH2 antisym. rocking

b3u n12 984 967 968 CH2 pyramid. ~wagging!

aReference 71.bReference 74.

NB. Symmetry determines vibronic coupling!

7

Zeroth-order picture: torsion only

cies of ethene are summarized. Compared to other

the error of the

At the ground-state equilibrium geometry, single-point

CASSCF and MS-CASPT2 calculations have been per-

large V −N gap!

CASSCF/CASPT2 calc’s

Krawczyk et al., JCP 119, 1397 (2003)8

Torsion plus pyramidalization

• There is a CoIn if the pyramidalization mode is added to the picture!

the missingcut is found at a C–C distance which is about 0.1 Å shorterthan the minimum of the same cut for

C. Two-dimensional cuts

of the torsion and the coordinatesFigs. 5–7. Theare shown as the dotted lines. The full lines represent theglobal analytic fit to thetwo-dimensional cut as a function ofcomputed at the CASSCF level only, as explained in Sec. II.A cubic-spline interpolation of these data in theis shown in Fig. 8.

face along torsion and pyramidalization, which has been dis-cussed previously.

FIG. 3. Adiabatic PEs of the valence states of perpendicular ethene (r51.332 Å) as a function of the one-sided pyramidalization angle q.Crosses: ab initio data; full lines: global analytic fit ~see text!.

calculations for

could not be determined from

. From the MS-CASPT2

and CASSCF results, the following potentials have been de-

19a

19b

19c

19d

TABLE VI. Parameters of the fit of the antisymmetric scissor coordinate

FIG. 9. Conical intersection of the S0 and S1 surfaces of ethene in w,q

space. The other coordinates (r ,as ,aa) have been relaxed to minimize the

energy of the intersection.

Krawczyk et al., JCP 119, 1397 (2003)9

Torsion plus pyramidalization

• . . . and that’s far from the whole story: complex CoIn seam• ethylidene formation is another pathway (via H migration)

10

Photoactive Yellow Protein (PYP)

Tyr98

P h e 96

A rg 5 2

C h ro m o p h o re

C ys 6 9

P h e 6 2V a l6 6

Th r5 0

G lu 4 6

Tyr4 2

(a)

O

S

O

• biological local environments (e.g., individual amino acids) can be ofkey importance

• how is the chromophore’s quantum dynamics concerted with theenvironmental dynamics/fluctuations?

Gromov, Burghardt, Koppel, Cederbaum, JACS, 129, 6798 (2007)

11

PYP chromophore: A complicated photoswitch!

O O

H

H

O

H

H

O

S CH3

a

b

Phenol part

Alkene part

0.0

1.0

2.0

3.0

En

erg

y(e

V)

-0.53/-0.47-0.25/-0.75 -0.76/-0.24

-0.39/-0.61

-0.87/-0.13

-0.71/-0.29

S 0,eqS 1,mina

S 1,minb

S1

S1

S0

S0

S1

S0

• double and single-bond isomerisation12

PYP chromophore: S1 potential surface

100

150

200

250

100

150

200

2.5

3.0

3.5

b a

100150200250

80

100

120

140

160

180

200

a

b

aa

b

P

(a)

• CC2 calculations

• barrier towards double-bond isomerisation but essentially no barrier tosingle-bond isomerisation

• another important mode: hydrogen-out-of-plane (HOOP) mode13

FC geometry: combined effect of local AA environment

CC2

supermolecular

calculations

Gromov, Burghardt, Koppel, Cederbaum, J. Am. Chem. Soc., 129, 6798 (2007)14

Influence of the protein environment on the CoIn (QM/MM)

• the CoIn can be significantly shifted due to the local protein environment

Groenhof et al. JACS, 126, 4228 (2004) 15

Influence of water environment on the CoIn (QM/MM)

• selective hydrogen bonding interactions determine the twisting pathway!

Groenhof et al. Meth. Mol. Biol. (2013)

16