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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)