Unravelling Photochemical Mechanisms with

Computational Methods

Rachel Crespo-Otero

Introduction Surface Hopping Dynamics

Excited State Proton TransferPhotodissociation

OUTLINE

0 20 40 60 80 1000

1

2

3

4

5

6

7

S3

S2

S1

S0

Energ

y (

eV

)

Time (fs)

S4

S5

III III

PHOTOCHEMICAL REACTION

IUPAC GOLD BOOK

Generally used to describe a chemical reaction caused by absorption

of ultraviolet, visible or infrared radiation. There are many ground-state reactions,

which have photochemical counterparts….

Vision

Solar Fuels

Modern Technologies

Many electronic states can be involved in a photoreaction

Coupling between nuclear and electronic motions

PHOTOMECHANISMS

Fl: FluorescencePh: PhosphorescenceISC: Intersystem crossing IC: Internal conversion

Reactants Products

E

Reaction coordinate

ISC IC

S0

S1

S2

S3

FlPh Fl

PHOTOREACTIONS

Reaction barriers are smaller in the excited state

Thermodynamically disfavoured products can be formed

PHOTODISSOCIATION

(X-Y)

*(X-Y)

X-Y distance

E

To reduce the barrier of the reaction in the excited state, an excited state with high X-Y antibonding character can be populated

EXCITED STATE PROTON TRANSFER (ESPT)

X-HY

X-HY

X-HY

+ -

e-

X-H distance

E

Population of Charge Transfer states accelerate PT process in the excited states

XH-Y

- +

XH-Y˙ ˙

EXCITED STATES REACTIONS

Breakdown of the Born-Oppenheimer approximation

Ultrafast!

Competition between different pathways

Photochemical reactions: can we use our chemical intuition?

EXCITED STATES DYNAMICS: SURFACE HOPPING

0,,

tRrH

ti e Time dependent Schrödinger equation

tRrtctRr j

j

j ,,, Approximation for the wavefunction

The dynamics of the nuclei is propagated classically on a single Born–Oppenheimer surface at any time.

The nonadiabatics events are simulated by a stochastic algorithm that allows each trajectory to jump to other states during the propagation.

Tully, J. Chem. Phys. 93, 1061 (1990)

EXCITED STATES DYNAMICS: SURFACE HOPPING

Tully, J. Chem. Phys. 93, 1061 (1990)

Semi-classical time-dependent Schrödinger equation

sN

j

jkjjk

k cHit

ci

1

0

Non-adiabatic coupling terms

nuclearvelocities

vF

kj

j

kjkt

Non-adiabatic couplings

Substitute

0,,

tRrH

ti e

tRrtctRr j

j

j ,,,

*

kMultiply by and integrate over the electronic coordinates

The SC-TDSE is solved with standard methods(Unitary Propagator, Adams Moulton 6th-order, Butcher 5th-oder)

Non-adiabatic coupling terms

nuclearvelocities

vF

kj

j

kjkt

Non-adiabatic couplings

EXCITED STATES DYNAMICS: SURFACE HOPPING

|k kj k kjΦ H V

| , 0d

k kj kj kjΦ H W F

Adiabatic basis

Diabatic basis

elementsijH

jRkkj F

2

20

c c

m m

m

d

dt M

R FNewton’s equations of motion

Fewest switches method (Tully)

EXCITED STATES DYNAMICS: SURFACE HOPPING

Granucci and Persico, J. Chem. Phys. 126, 134114 (2007)C. Zhu, S. Nangia, A. W. Jasper, and D. G. Truhlar, J. Chem. Phys. 121, 7658 (2004).

(Adiabatic Representation)

Decoherence corrections

liik

k

ik ccc

tP *

2Re

2,0max

Comparison to other methods

• Cattaneo and Persico, J. Phys. Chem. A 101, 3454 (1997)

• Worth, Hunt, Robb, J. Phys. Chem. A 107, 621 (2003)

Comparison between hopping algorithms

• Zhu, A. W. Jasper, and D. G. Truhlar, JCTC 1, 527 (2005)

• Fabiano, Groenhof, Thiel, Chem. Phys. 351, 111 (2008)

Conceptual background

• Herman, J. Chem. Phys. 103, 8081 (1995)

• Schwartz, Bittner, Prezhdo, Rossky, J. Chem. Phys. 104, 5942 (1996)

• Tully, Faraday Discuss. 110, 407 (1998)

• Schmidt, Parandekar, Tully, J. Chem. Phys. 129, 044104 (2008)

Surface hopping reviews

• Doltsinis, NIC series, 2002

• Barbatti, WIREs: Comp. Mol. Sci. 1, 620 (2011)

SURFACE HOPPING: SOME USEFUL REFERENCES

QM/MM

MM

QM

TDDFT

CC2

ADC(2)

MCSCF

CCSD(T)/MP2

TDDFT

MCSCF

MRCI

MCSCF

TDDFT

M. Barbatti, G. Granucci, M. Ruckenbauer, F. Plasser, R. Crespo-Otero, J. Pittner, M. Persico and H. Lischka, NEWTON-X: a package for Newtonian dynamics close to the crossing seam, 2013, http://www.newtonx.org

NEWTON-X: A package for Newtonian dynamics close to the crossing seam

NEWTON-X: A package for Newtonian dynamics close to the crossing seam

Web: http://www.newtonx.org

Wiki:https://en.wikipedia.org/wiki/Newton-X

NX forum at Google: https://groups.google.com/forum/?fromgroups#!forum/newtonx

ELECTRONIC METHODS

Multi-Reference Methods

Common methods used with Surface Hopping

CASSCF: Lack of dynamic correlation

MRCI: Too computationally expensive for most applications

Disadvantage: It is challenging to find a stable active state, which can represent all regions of the potential energy surface that can be explored during the dynamics.

Advantage: Appropriate description of the S1/S0 crossing seam region.

Coupled Cluster to the second order (CC2, RI-CC2): Numerical instabilities closeto quasi-degenerate excited states. It seems to provide a proper description of conical interceptions(Tuna et al. JCTC 11, 5758 (2015))

Algebraic-Diagramatic-Construction ADC(2) : Dynamics is very stable. (Plasser et al. JCTC 10, 1395 (2014))

Common methods used with Surface Hopping

Advantage: Black box methods, they do not require much user intervention, which is very convenient for dynamics simulations.

Single-Reference Methods

ELECTRONIC METHODS

Diagonal XC kernel for CT stateshas wrong behavior

Single-determinant KSapproximation fails; self-interaction errors

Linear response and ALDA approximations may fail

No problem, in principleFunctional-dependent

predictions

DFT is, in principle, valid

Functional-dependentpredictions

Energy

xy Linear response fails for

multiple excitations

DFT/TDDFT

Incorrect descriptionof S1/S0 crossing seam

Common methods used with Surface Hopping

Single-Reference Methods

ELECTRONIC METHODS

Barbatti, M.; Crespo-Otero, R.; Surface hopping with DFT excited states. Top. Curr. Chem. 368, 415 (2016).

time

ener

gy

time

ener

gy

Multireference method

TDDFT

w1<0

e1=e0

a

a

b

b

c

c

d

d

e

e

MULTIREFERENCE METHODS vs TDDFT

Barbatti, M.; Crespo-Otero, R.; Surface hopping with DFT excited states. Top. Curr. Chem. 368, 415 (2016).

ADENINE: LEVEL OF THEORY

6

N

N

2

NH

9

N

NH2

C6-puckered CI C2-puckered CI

C2-puckered S1 min

Adenine conical intersections

Exp

erim

enta

l

ADC(2

)

MRCIS

OM2/

MRCI

TD-P

BE

TD-w

B97

XD

TD-B

3LYP

TD-P

BE0

TD-C

AM-B

3LYP

TD-B

HLY

P

TD-M

06-H

F

0

20

40

60

80

S0 p

op

ula

tio

n a

t 1

ps (

%)

C2 puckering

C6 puckering

H elimination

Experimental68 2

57 12

85 8

59 8

5 8

12 8

20 15

0

20 2125 16

10 16

Population of S0 at 1ps

Tested functionals do not explain the photochemistry . Best results: ADC(2).

Barbatti, M.; Lan, Z. G.; Crespo-Otero, R.; Szymczak, J. J.; Lischka, H.; Thiel, W., J. Chem. Phys. 2012, 137, 22A503Plasser, F.; Crespo-Otero, R.; Pederzolli, M.; Pittner, J.; Lischka, H.; Barbatti, M. J. Chem. Theory Comput. 2014, 10, 1395

NON-ADIABATIC COUPLINGS IN NEWTON-X

Analytical evaluation of Fkj

- MCSCF, MRCI (H. Lischka et al. Phys. Chem. Chem. Phys., 3, 664 (2001) )

Numerical Evaluation

vF

kj

j

kjkt

The Newton-X implementation for TDDFT, ADC(2), CC2 is based on approximate CIS wavefunctions.

Finite difference method (S. Hammes-Schiffer and J. C. Tully. J Chem Phys 10, 4657(1994))

jRkkj F

22222

1 tt

tt

tt

tt

tjkjkkj

)()()(3)(34

1ttSttStStS

tjkkjjkkj

ttttS jkkj )(

TDDFT AND TDA: THE CASIDA’S ANSATZ

,K

K ov ov

o v

C

1/2

( ),K K Kv oov K ov ov

K

C A X YE

e e

1/2

2

,

| | ,K

K ov

o v

A C

0 ,K KV VE vectors from linear response

Energies of the Kohn-Sham orbitals

Normalization factor

0K

ovY for TDA

Tapavicza E, Tavernelli I, Rothlisberger U. Phys. Rev. Lett. 98, 023001 (2007).Barbatti M, Pittner J, Pederzoli M, Werner U, Mitrić R, Bonačić-Koutecký V, Lischka H. Chem. Phys. 375, 26 (2010).Plasser, F.; Crespo-Otero, R.; Pederzolli, M.; Pittner, J.; Lischka, H.; Barbatti, M. J. Chem. Theory Comput. 10, 1395 (2014).

NAD WITH NEWTON-X

Generation of absorptionspectrum

Selection of initial conditions

Dynamics simulations

Analysisof trajectories

SPECTRA SIMULATIONS AND INITIAL CONDITIONS

Crespo-Otero, R.; Barbatti, M., Theor. Chem. Acc. 2012, 131, 1237

2

2

00 0, 0

0

1,

2

fs pN N

l n l n l l n

n lr p

eE E f g E E

mc n E N

e R R R R

Gaussian or

Lorentzian

Cross Section: E

pN

fsN

Number of geometries

Number of states

1/2

3 62 2

00

1

exp /N

j j

j j j

j

q w

w

q Wigner distribution

SPECTRA SIMULATIONS AND INITIAL CONDITIONS

Spectrum

Equilibrium Geometry

Wigner Distribution

TDDFT (B3LYP/TZVP+mod)

Crespo-Otero, R.; Barbatti, M.; Yu, H.; Evans, N. L.; Ullrich, S., ChemPhysChem. 2011, 12, 3365

The mechanism depends on the initial excitation

Window Apump: 240 nm Window Bpump: 201 nm

IMIDAZOLE: DYNAMICS

00N-METHYLFORMAMIDE PHOTOCHEMISTRY

Monomer

Dimers

Crespo-Otero, R.; Mardyukov, A.; Sanchez-Garcia, E.; Barbatti, M.; Sander, W., ChemPhysChem 2013, 14, 827

Argon matrix

N-METHYLFORMAMIDE: MONOMER

QM

MM

Matrix conditions:QM (NMF): SA-3-CASSCF(10,8)/6-31G(d,p)MM (Argon matrix) : OPLSAA force field

Gas phase dynamics: SA-3-CASSCF(10,8)/6-31G(d,p)

- 3 states- Maximum Simulation time: 2000 fs- Total of 400 trajectories

N-METHYLFORMAMIDE: QM/MM SIMULATIONS

Active Space: n(O), CN, *CN , CH, *

CH, 2, *

cis trans

rC-N= 1.38ÅOCNH =0N

CC

O

rC-N= 1.38ÅOCNH =180

S0 minima

rC-N= 1.43ÅOCNH =50

cis1-S1cis2-S1

rC-N= 1.43ÅOCNH =309

trans1-S1 cis3-S1

rC-N= 1.44ÅOCNH =173

rC-N= 1.44ÅOCNH =289

S1 minima

CI-cis CI-transrC-N= 2.42ÅOCNH =179

rC-N= 2.43ÅOCNH =0

S1/ S0 conical intersections

Structures optimized at SA-3-CASSCF(10,8)/6-31G(d) level of theory

N-METHYLFORMAMIDE: CONICAL INTERSECTIONS

0 1 2 3 4

0

1

2

3

4

5

6

7

0 1 2 3 4

0

1

2

3

4

5

6

7

Energ

y(e

V)

Energ

y(e

V)

Mass-weighted distance (Å.amu1/2

)

cis

trans

dots: MS-CASPT2line: CASSCF

N-METHYLFORMAMIDE:

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

Energ

y(e

V)

Energ

y(e

V)

Mass weighted distance (Å.amu1/2)

trans1-S1 cis1-S1

cis3-S1 cis2-S1

dots: MS-CASPT2line: CASSCF

N-METHYLFORMAMIDE:

SA-3-CASSCF(10,8)/6-31G(d,p)

First step in the photo-mechanism: C-N dissociation

N-METHYLFORMAMIDE: GAS PHASE

QM (NMF): SA-3-CASSCF(10,8)/6-31G(d,p)MM (Argon matrix) : OPLSAA force field

1.) C-N photo -dissociation

2.) Hydrogen transfer

3.) CH3NH2…CO complex

Photo-mechanism

MATRIX EFFECTS: QM/MM

S0

LE(A)

LE(B)

E

CT(A B)

R-N●..●HOC-R’

R-NH..OC-R’

R-N-..+HOC-R’

R-NH+..-OC-R’

distance (H..O)

This mechanism protects biomolecules from UV-irradiation

PROTON TRANSFER MECHANISM

A

B

S0/S1 CROSSING GEOMETRIES

C-N dissociation

Proton Transfer

TD/LC-BLYP(μ=0.2)/6-311+G(d)

Crespo-Otero, R., Mardykov, A., Sanchez-Garcia, E., Sander, W, Barbatti, M. Phys. Chem. Chem. Phys. 2014, 16, 18877

C-N DISSOCIATION IN THE DIMER

A TYPICAL TRAYECTORY

72 % of the trajectories deactivated through the ESTP mechanism

Crespo-Otero, R., Mardykov, A., Sanchez-Garcia, E., Sander, W, Barbatti, M. Phys. Chem. Chem. Phys. 2014, 16, 18877

A

B

TDDFT/LC-BLYP(μ=0.2)/6-311+G(d)

Proton transfer mechanism protectsthe dimer from photo-dissociation

Experiments: The dimer does not dissociate under same irradiation conditions

Proton-transfer is faster than C-N dissociation (50 fs vs 400 fs).

N-METHYLFORMAMIDE: THE DIMER

Orange Green

DOUBLE PROTON TRANSFER IN … DIMERS

7-Azaindole (7AI) dimer: Concerted vs Stepwise ESPT

Crespo-Otero, R.; Kungwan, N.; Barbatti, M. Chem. Sci., 2015, 6, 5762.

CONCERTED MECHANISM

Most electronic methods fail to provide a balance description of the different regions of the excited state.

RI-CC2/TZVP

Orange Green

DOUBLE PROTON TRANSFER IN … DIMERS

RI-CC2/TZVP ADC(2)/SV(P)

Low energy window (4.1 ± 0.1 eV) DPT: 80%, SPT: 15%, MPT: 5%

CONCLUSIONS

- Surface Hopping is very useful to explore photochemical mechanisms.

- Be careful before starting running long NAD dynamics simulations. Make sure that the level of theory is appropriate!

ACKNOWLEDGMENTS

Mario Barbatti (Air Marseille Université )

Newton-X team

Elsa Sanchez (MPI, Mülheim)

Artur Mardykov (University of Bochum)

Wolfram Sander (University of Bochum)

Susanne Ulrich (University of Georgia)

Nawee Kugnwan (University of Chiang Mai)

Michael Dommett (Queen Mary University of London)