Photochemistry Meets Physics: Semiclassical Dynamics of Lightdriven Molecular Switches

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Photochemistry Meets Physics Semiclassical
Dynamics of Light-driven Molecular Switches

• Daniele Passerone
• Institute of Organic Chemistry
• University of Zurich
• Switzerland

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Collaborators

• Kim Baldridge, University of Zurich (CH)
• Massimo Olivucci, University of Siena (I)
• Adalgisa Sinicropi, Siena
• Teodoro Laino, ETH Zurich (CH)

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Outline

• Why are molecular switches important?
• Examples of experimental applications
• Hamms group
• Available theoretical studies
• Olivuccis group
• Conical intersections
• Exploration of intersection space
• Laino and Passerone
• Switches and Schiff bases intersection space
  exploration
• Modeling of semiclassical potentials
• Perspectives

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Light-Driven cis-trans switches experimental
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Efficient light-driven molecular
switchesexamples from the nature

• The isomerization of the retinal chromophore
  provides the "driving-force" underlying the
  activity of rhodopsin proteins.
• The photoisomerization happens in a fast and
  efficient way through a conical intersection

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The perfect molecular switch

• EFFICIENT
• Reaction path like (a)
• Stability of the isomers

• REACTION COORDINATE
• Dominated by the reactive mode

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The perfect molecular switch

• RADIATIONLESS DECAY
• Through a conical intersection

• EXPERIMENTALLY ACCESSIBLE
• Synthesis and biocompatibility

• COMPUTATIONALLY ACCESSIBLE
• Dimensions of the system

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Example 4-benzylidene-3,4-dihydro-
2H-pyrrolium

• Alternative decay path which is stabilized in
  acetonitrile solution and reduces the quantum
  yield this is a probem!
• It involves an additional rotation of a single
  bond

Sampedro, Migani, Pepi, Busi, Basosi, Latterini,
Elisei, Fusi, Ponticelli, Zanirato and Olivucci,
JACS 126, 9349 (2004)
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Realistic systems simulations with QM/MM

• Attaching a monomer to complex biological
  molecules and controlling their conformation

• Andruniw, Fantacci, De Angelis, Ferre, and
  Olivucci, Mechanism of the Initial Conformational
  Transition of a Photomodulable Peptide, Angew.
  Chem. Int. Ed. 2005, 44, 6077 6081

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Octapeptide

• An octapeptide derived from the thioredoxin
  reductase active site is used to prepare a
  bicyclic peptide with a photoisomerizable
  unitwith a locked backbone

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Photoinduced strain

• The central torsionof the switch is analmost
  barrierless decay
• It is studied with high level CASPT2//CASSCF
  methods
• The cis/trans transitionof the peptide is
  muchslower

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Computational methods

• QM/MM description of the whole system (examples
  Roethlisberger, Baldridge, Olivucci et al.)
• An active region of the system is described with
  high levelquantum schemes
• The environment is described through a force
  field
• A scheme for the interface between QM and MM
  parts is constructed to reproduce the correct
  electrostatic behavior

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QM calculations

• CASPT2//CASSCF can efficiently describe the
  passage from the excited state to the ground
  state
• A single Car-Parrinellotrajectory for the
  wholesystem (switchpeptide)can be afforded on
  S0

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Switch-induced cis-trans

• There is a sequential mechanism for the
  transmission of the strain generated by the
  switch with a hierarchy of timescales

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Intermezzo different photochemical mechanisms
M. A. Robb, M. Garavelli, M. Olivucci and F.
Bernardi (2000), Rev. Comp. Chem. 15 87-146.
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Fast molecular switches decay through a conical
intersection

• An excited system radiationless decays to the
  ground state.
• Contact between electronic states not dictated by
  symmetry
• Location of contact points is central for
  understanding important photoreactions.

M. A. Robb, M. Garavelli, M. Olivucci and F.
Bernardi (2000), Rev. Comp. Chem. 15 87-146.
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Conical intersections
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How to describe the intersection space

• Conical intersections (N-2) dimensional
  hyperlines in the nuclear coordinate space
• Goal exploring the (N-2) dimensional CI space
• If the nuclei move orthogonally to certain
  vibrations, the system remains in the CI

Robb, Garavelli, Olivucci and Bernardi (2000),
Rev. Comp. Chem. 15 87-146.
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Example retinal chromophore
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Reaction paths in the excited state and CI seam
are very close. The quantum yield can be strongly
affected by the intersection space structure
GOAL A better exploration of the intersection
space
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State of the art excited states CI

• Methods for describing the excited states
• CASSCF for reaction path determination
• Multi-determinant approach (beyond Hartree-Fock)
• Subdivision of the system in active and inactive
  orbitals
• CASPT2 for refining the energetics
• They are computationally expensive
• Implemented in GAUSSIAN, MOLCAS, MOLPRO, GAMESS

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State of the art excited states CI

• Methods for finding conical intersection points
• Efficient for locating the lowest energy point of
  contact
• They can access only small portions of the
  intersection space
• Olivucci and Robb Yarkony Persico

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Challenges for the IS exploration

• Fast and accurate quantum chemistry methods
• CASSCF//CASPT2 schemes
• MOLCAS, MOLPRO, GAMESS packages
• Finding the minimum energy in the CI space
• Constrained optimization

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Challenges for the IS exploration

• Efficient sampling techniques
• Constrained molecular dynamics
• Finding low energy paths within the CI space
• Band energy minimizations with constraints (as
  standard TS searches for ground states)

Laino and Passerone (2004), Chem. Phys. Lett.,
339, 1 Passerone and Laino, Comp. Phys. Comm.
(2005)
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Conical intersections a multidimensional
hyperline

From Potential energy surfaces Ian Grant,
Bristol University http//www.chemsoc.org/exemplar
chem/entries/2002/grant/index.html
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g and h vectors
Degeneracy is not removed if the motion is
orthogonal to the two vectors g and h the
conditions for having degeneracy are
The CI is a (N-2)-dimensional surface
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Constraints

• The dynamics has to fulfill the following
  conditions
• no rotations
• no translations
• motion in the CI space

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Molecular Dynamics in a CI

• Low T MD the system remains in the starting basin

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Constrained molecular dynamics (MD)

• Starting point any configuration within the CI

• Nuclei move in the force field of the electrons
  (calculated ab initio)

Laino and Passerone (2004), Chem. Phys. Lett.,
339, 1 Passerone and Laino, Comp. Phys. Comm.
(2005)
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Scheme of the method

• Given a nuclear configuration R the electronic
  energy E2 and E1 are computed using advanced
  quantum chemistry schemes
• The electronic forces on the nuclei obtained from
  the quantum calculation are used for updating R
  and the velocities V using the velocity Verlet
  algorithm
• The corrections due to the constraints (motion in
  the CI, no rotations, no translations) are added
• Possible velocity rescaling for constant-T MD
• Go to step 1.

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Observation

• The obtained dynamics are not true dynamics
  (constraints, Born-Oppenheimer/like motion of the
  nuclei in highly degenerate zones) but allows an
  efficient exploration of the CI region.
• ALL GEOMETRIES AT SUFFICIENTLY LOW ENERGY IN THE
  INTERSECTION SPACE ARE POTENTIAL ACCESS POINTS
  FOR A RADIATIONLESS DECAY FROM THE EXCITED STATE

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Exploration of intersection space in C2H4

• Are (a), (b) and (c) connected by a seam at
  zero gap?

• Constrained dynamics starting from (b), aiming at
  (a)

Laino and Passerone (2004), Chem. Phys. Lett.,
339, 1 Passerone and Laino, Comp. Phys. Comm.
(2005)
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C2H4

• Exploration of the IS using dynamics methods

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Band energy minimization

• Pick two points from the MD trajectory

• Find the path connecting A and B that minimizes

t (fs)

• The initial path is made by points on the MD
  trajectory

• The path minimizing S overcomes a low-energy
  barrier

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Band energy minimization retinal

• Double bond rotation in retinal fragment
• A non-trivial region of intersection space is
  found the sum of two torsion angles is kept
  constant during minimization

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A novel molecular switch

• Based on the Protonated Schiff Base framework
  structure
• 4-cyclopenten-2'-enylidene-3,4-dihydro-2H-pyrrolin
  ium
• It is experimentally available (Chemistry
  Department, University of Siena, Italy)
• Desired absorption properties
• Desired rigidity
• Ab initio calculations are being performed in the
  group of Prof. Olivucci (Chemistry Department,
  University of Siena, Italy)
• CASSCF//CASPT2 level
• It is expected to have a high quantum yield

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Radiationless decay

• Are there other accesspoints for
  radiationlessdecay, that are not in theMINIMUM
  of the intersection space?

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Constrained dynamics in the intersection space

• Starting from the MINIMUM in the IS, explore this
  space at high nuclear temperature
• The gap is between 0.25 and 1.4 Kcal/mol

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Relevant coordinates

• Central dihedral

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Relevant coordinates

• C-N bond

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Relevant coordinates

• Pentagon distorsion

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Relevant coordinates

• Improper torsions

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Why is it important?

• A photochemical process does not occur with a
  single reaction trajectory from the excited state
  (intrinsic reaction coordinate)
• The exploration of the intersection space
  provides alternative access points
• To harvest more dynamical trajectory one needs a
  classical parametrization
• The more information on the ground and excited
  state energy surface, the better parametrization
  of a two-state potential

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Classical parametrization of ground/excited state

• The system will be described by a MMVB-like
  scheme (Bernardi, Olivucci and Robb, JACS 1992
  (original approach for hydrocarbons and
  radicals))
• The inert framework of the molecule is described
  by a MM2 force field
• A parametrized Heisenberg (2x2) Hamiltonian is
  used to simulate CASSCF//CASPT2 active orbitals
  in a valence bond space.

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Classical parametrization of ground/excited state

• Reproduces bond forming/breaking and sp2/sp3
  hybridizations for covalent systems
• The functional form and the parameters are chosen
  to fit the ab initio data validated on
  experimental spectroscopic quantities
• Within the new formulation, the Heisenberg
  Hamiltonian will describe the ground state and
  the excited state surface also in presence of
  charge transfer and ionic behavior

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Creation of the potential

• Relevant coordinates can describe the behavior
  of the ground excited states of the switch

MM FRAGMENT
QM FRAGMENT
MM FRAGMENT
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Main coordinates

• They are bond alternation, group torsion,
  stretching, wagging

a
a
a
b
h2
a3
a2
a1
h1
C1
C2
C4
C3
C5
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Dynamical properties

• Using the MMVB scheme, trajectories can be
  harvested starting from the excited state
• As the system reaches the crossing region, a
  surface hopping criterion (Tully and Preston)
  based on the coupling between the states is used

• The trajectory continues on the ground state
• An ensemble of trajectories determines the
  quantum yield

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From reaction path to dynamics

• Surface-hopping method
• Examplephotochromism of dyarilethenes
  (Boggio-Pasqua, Ravaglia, Bearpark, Garavelli
  and Robb, J. Phys. Chem. A 107, 11139 (2003)).

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Perspectives

• A complete semiclassical dynamics for a joint
  system switch polypeptide using classical force
  fields
• Studying an experimentally available switch (a
  modifiation of the one shown here)
• Direct comparison with the experiments at all
  levels and timescales, from the subpicosecond
  (radiationlessdecay) to the gt nanosecond
  (peptide conformational changes)

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Conclusions

• MOLECULAR SWITCHES CAN INDUCEIMPORTANT
  CONFORMATIONAL CHANGES IN LARGE BIOMOLECULES
• MOLECULAR SWITCHES DECAY THROUGH CONICAL
  INTERSECTIONS
• THE COMPUTATIONAL DESCRIPTION OF THE INTERSECTION
  SPACE IS IMPORTANT
• THE FORCE FIELD OF THE SWITCH CAN BE MODELLED ON
  HIGH-LEVEL QUANTUM CALCULATION DESCRIBING
  GROUNDEXCITED STATES
• THE DYNAMICS OF THE SYSTEM SWITCH BIOMOLECULE
  CAN BE STUDIED WITH SEMICLASSICAL METHODS

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THANK YOU!