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Femtochemistry: A theoretical overviewFemtochemistry: A theoretical overview
Mario [email protected]
This lecture can be downloaded athttp://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture1.ppt
Introduction
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settling the bases: photochemistry, excited states, and conical intersections
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Photochemistry & PhotophysicsPhotochemistry & Photophysics
Stating the problem:
• What does happen to a molecule when it is electronically excited?• How does it relax and get rid of the energy excess?• How long this process take?• What products are formed?• How does the relaxation affect or is affected by the environment?• Is it possible to interfere and to control the outputs?
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Why to study it?Why to study it?
Basic sciences Interaction photon/matterCoeherence/decoherenceNature of transition statesNon-adiabatic phenomena
Biology Light and UV detectionPhotosynthesisGenetic code degradationCellular proton pump
Atmospheric sciences
UV induced chemistryGreenhouse effect
Astrophysics Interstellar molecular synthesis
Technology Control of chemical reactionsMolecular photo-switches
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Why to study it?Why to study it?
Pump-probe experiments based on ultra-fast laser pulses have increased the resolution of the chemical measurements to the femtosecond (10-15 s) time scale.
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The need for TheoryThe need for Theory
Theory is necessary to map the ground and excited state surfaces and to model the mechanisms taking place upon the photoexcitation.
Theory is indispensable to deconvolute the raw time-resolved experimental information and to reveal the nature of the transition species.
In particular, excited-state dynamics simulations can shed light on time dependent properties such as lifetimes and reaction yields.
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Basic process I: Basic process I: Radiative decay (fluorescence)Radiative decay (fluorescence)
P ~ |j| |i|2
~ ns
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P ~ v j| |iN
~ fs
Basic process II: Basic process II: Non-radiative decayNon-radiative decay
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1.How are the excited state surfaces?
2. For which geometries does the molecule have conical intersections?
3. Can the molecule reach them?
The Static ProblemThe Static Problem
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Conical intersectionsConical intersections
Antol et al. JCP 127, 234303 (2007)Barbatti et al., Chem. Phys. 349, 278 (2008)
pyridonepyridoneformamideformamide
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Conical intersection Structure Examples
Twisted Polar substituted ethylenes (CH2NH2+)
PSB3, PSB4HBT
Twisted-pyramidalized Ethylene6-membered rings (aminopyrimidine)4MCFStilbene
Stretched-bipyramidalized
Polar substituted ethylenesFormamide5-membered rings (pyrrole, imidazole)
H-migration/carbene EthylideneCyclohexene
Out-of-plane O FormamideRings with carbonyl groups (pyridone,cytosine, thymine)
Bond breaking Heteroaromatic rings (pyrrole, adenine, thiophene, furan, imidazole)
Proton transfer Watson-Crick base pairs
Primitive conical intersectionsPrimitive conical intersections
X C
R1
R2
R3
R4
X C
R1
R2R3
R4
X C
R1
R2 R3
R4
C
R1R2
R3
H
C O
R1
R2
X Y
R1
R2
X
R1 R2
H
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(b)
3 2
1
65
4(a)
(b)
3 2
1
65
4(a)
(b)(b)
3 2
1
65
4(a)
3 2
1
65
4(a)
Conical intersections: Conical intersections: Twisted-Twisted-pyramidalizedpyramidalized
Barbatti et al. PCCP 10, 482 (2008)
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Paths to conical intersections: Paths to conical intersections: AdenineAdenine
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
0 1 2 3 4 5 60
1
2
3
4
5
6
7
dMW
(amu1/2Å)
6S1
n*
dMW
(amu1/2Å)
E8
*
4H3
*
dMW
(amu1/2Å)
Ene
rgy
(eV
)
2E
*
B3,6
n*
Ene
rgy
(eV
)
2H3
*
Ene
rgy
(eV
)
E3
*
4S3
n*
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At a certain excitation energy:
1. Which reaction path is the most important for the excited-state
relaxation?
2. How long does this relaxation take?
The Dynamics ProblemThe Dynamics Problem
15about methods & programs
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General methodologyGeneral methodology
Subject Approach Methods
Vertical excitation spectra
Conventional adiabatic quantum chemistry
MRCI, CC2, TD-DFT
Stationary points in excited states
Conventional adiabatic quantum chemistry
MRCI, CC2, TD-DFT
Conical intersections Non-adiabatic quantum chemistry
MRCI, MCSCF
Reaction paths Convent. adiabatic quantum chemistry (multireference)
MRCI, CASPT2, MCSCF
Lifetime and yields Mixed quantum-classical dynamics methods
MRCI, MCSCF
(+ MM)
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COLUMBUS• MRCI, MCSCF• Analytical gradients and non-adiabatic couplingswww.univie.ac.at/columbusLischka et al. PCCP 3, 664 (2001)
NEWTON-X• Mixed quantum-classical dynamics (surface hopping)• Excited-state Born-Oppenheimer dynamics• Absorption/emission spectrum simulation• General, modular, flexible• Interfaces to COLUMBUS, TURBOMOLE, DFTBwww.univie.ac.at/newtonxBarbatti et al., J. Photochem. Photobio. A 190, 228 (2007)
ProgramsPrograms
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MQCD methodsMQCD methods: : surface hoppingsurface hopping
2
2
dtd
MEcI
Ii
R Use the energy gradient to update the nuclear geometry according to the Newton`s Eq.
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sN
k
ckik
ci i
t 1
RhvR
For the new nuclear geometry (only!), solve the SC-TDSEand correct classical solution by performing a hopping if necessary.
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Go back to step 1 and repeat the procedure until the end of the trajectory.
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Repeat procedure for a large number of trajectories to have the “classical wave packet”.
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0 iEH ieFor a fixed nuclear geometry, solve time-independent Schrödinger Eq. for electrons. Get the energy gradientand the couplings
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iE.kiik h
2/1cii tt RRR
i) k
k k
ii) 0NT
iii)
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Q
E
Transition probability is Transition probability is evaluated at each time stepevaluated at each time step
Classical nuclear motion Classical nuclear motion on the on the on-the-flyon-the-fly BO surface BO surface
Tully, J. Chem. Phys. 93, 1061 (1990)
A stochastic algorithm A stochastic algorithm decides on which decides on which surface the molecule surface the molecule will continuewill continue
MQCD methodsMQCD methods: : surface hoppingsurface hopping
tP jkjkjjk
hv*2Re2
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Q
Boat
Chair
Envelope
Twisted-chair
Screw-boat
Ex.: 1S6 = Screw-boat with atoms 1 above the
plane and 6 below
Cremer and Pople, JACS 97, 1358 (1975)
Cremer-Pople parametersCremer-Pople parameters
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dynamics: adenine
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Photochemical processPhotochemical process
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Photophysical processPhotophysical process
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A short lifetime can enhance the photostability because the
molecule does not remain long enough in the reactive excited state so as to have chance to
isomerize.
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This effect might have constituted an evolutionary advantage for the five nucleobases forming DNA and
RNA.
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Lifetime of nucleobasesLifetime of nucleobases
Canuel et al. J. Chem. Phys. 122, 074316 (2005)
N
N
NH
N
NH2
N
NH
NH2
O N
NH
NH
N
NH2
O
NH
NH
O
O NH
NH
O
O
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1 ps 30 ps
9H-Adenine 2-aminopurine
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29
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0 750 1500delay time / fs
Lifetime:Something between 750 fs [1] and 1.1 ps [2]
Mechanism:Single-exponential decay [3]Double-exponential decay [2]
1: 100 fs – relaxation into S1
[4]2: 1 ps – relaxation into S0
1: 100 fs – relaxation into S0 (*) [5]
2: 1 ps – relaxation into S0 (n*)Triple-exponential decay! [1]
[1] Ullrich et al. JACS 126, 2262 (2004)[2] Canuel et al. J. Chem. Phys. 122, 074316 (2005)[3] Kang et al. JACS 124, 12958 (2002)[4] Perun et al. JACS 127, 6257 (2005)[5] Serrano-Andrés et al. PNAS 103, 8691 (2006)
Experimental data on adenineExperimental data on adenine
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Theoretical methodsTheoretical methods
Static calculations• MR-CIS(6,5)/SA3-CAS(12,10)/6-31G* (optimizations)• CASPT2/CASSCF(16,12)/6-31G* (single points)
Dynamics simulations• 60 trajectories of 600 fs with 0.5 fs time step (~1 month each)• Surface hopping with four electronic states• MR-CIS(6,4)/SA4-CAS(12,10)/[6-31G*,3-21G]
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Conical intersections in adenineConical intersections in adenine
1 2 3 4 5 6
4.0
4.5
5.0
5.5
La
En
erg
y (e
V)
FC-MXS Distance (amu1/2Å)
N-H
2E
C8-C9
E3
E8
2H3
4S3
4H3
B3,6
6S1
La
*
*
7T8
*imi
n*
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0 100 200 400 600
0.0
0.2
0.4
0.6
0.8
1.0
S2
Occ
upat
ion
Time (fs)
S3
S1
S0
Barbatti and Lischka, JACS 130, 6831 (2008)
How does deactivation ocurr?How does deactivation ocurr?
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35
0 90 180 270 3600
90
180
(°)
(°
)
0 90 180 270 3600
90
180
(°)
(°
)
0 fs
120 fs
170 fs
200 fs
Excited state dynamics: Excited state dynamics: what do we have what do we have learned?learned?9H-adenine
0 90 180 270 3600
90
180
(°)
(°)
2-pyridone
Barbatti et al., Chem. Phys. 349, 278 (2008)
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Adenine is trapped close to 2E conformation and because of
this it has time enough to tune the coordinates of the conical intersection. Adenine is a non-
fluorescent species.
Pyridone does not stay close to any specific conformation long enough in order to have time to tune the coordinates of the conical intersections.
Pyridone is a fluorescent species.
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1 ps 30 ps
9H-Adenine 2-aminopurine
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conclusions
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Simple pictureSimple picture
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Beyond the simple pictureBeyond the simple picture
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Beyond the simple pictureBeyond the simple picture
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About the methodsAbout the methods
• MQCD simulations at ab initio multireference level start to be feasible for molecules with about 10 heavy atoms (+MM) with the current computational capabilities.
• They are still a new field being explored by few groups around the world.
• NEWTON-X is the first freely available program dedicated to this kind of simulations.
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About the methodsAbout the methods
• MQCD simulations are not a substitute for the conventional quantum-chemistry calculations, but a complementary tool to be used carefully given their high computational costs.
• They can be specially useful to test specific hypothesis raised either by experimental analysis or conventional calculations.
44Zewail, J. Phys. Chem. A 104, 5660 (2000)
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This lecture can be downloaded athttp://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture1.ppt
Next lecture
• Transient spectrum• Excited state surfaces
