Photochemistry: adiabatic and nonadiabatic molecular dynamics with

1
Photochemistry adiabatic and nonadiabatic
molecular dynamics with  multireference ab initio
methods 
Mario Barbatti Institute for Theoretical
Chemistry University of Vienna
COLUMBUS in BANGKOK (3-TS2C2) Apr. 2 - 5,
2006 Burapha University, Bang Saen, Thailand
2

• Outline
• First Lecture An introduction to molecular
  dynamics
• Dynamics, why?
• Overview of the available approaches
• Second Lecture Towards an implementation of
  surface hopping dynamics
• The NEWTON-X program
• Practical aspects to be adressed
• Third Lecture Some applications theory and
  experiment
• On the ambiguity of the experimental raw data
• On how the initial surface can make difference
• Intersection? Which of them?
• Readressing the DNA/RNA bases problem

3

• Outline
• First Lecture An introduction to molecular
  dynamics
• Dynamics, why?
• Overview of the available approaches
• Second Lecture Towards an implementation of
  surface hopping dynamics
• The NEWTON-X program
• Practical aspects to be adressed
• Third Lecture Some applications theory and
  experiment
• On the ambiguity of the experimental raw data
• On how the initial surface can make difference
• Intersection? Which of them?
• Readressing the DNA/RNA bases problem

4
Part IAn Introduction to Molecular Dynamics
Cândido Portinari, Café, 1935
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Dynamics, why?
6
Photoinduced chemistry and physics
PA photoabsorption 1 fs
VR vibrational relaxation 102-105 fs
Fl fluorescence 106-108 fs
Ph phosforescence 1012-1017 fs
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Dynamics, why?

• Why dynamics simulations are needed?
• Estimate of specific times (lifetimes, periods)
• Estimate of the kind and relative importance of
  the several available nuclear motions (reaction
  paths, vibrational modes).

• When is it not adequate to reduce the dynamics to
  the motion on a sole adiabatic potential energy
  surface?
• Electron transfer (high kinetic energy)
• Dynamics at metal surfaces (high DoS)
• Photoinduced chemistry (multireference states).
• Radiationless processes in molecules and solids
  (conical intersections)

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Main objective relaxation path
Ben-Nun, Molnar, Schulten, and Martinez. PNAS
99,1769 (2002).
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An example to start the ultrafast deactivation
of DNA/RNA bases
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An example photodynamics of DNA basis
Lifetimes of the excited state of DNA/RNA basis
Canuel et al. JCP 122, 074316 (2005)
Maybe the fast deactivation times for the DNA/RNA
basis can provide some explanation to the
photostability of DNA/RNA under the UV solar
radiation.
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An example photodynamics of DNA basis
What has theory to say?
C2
pp/S0 crossing Marian, JCP 122, 104314
(2005) Chen and Li, JPCA 109, 8443 (2005) Perun,
Sobolewski and Domcke, JACS 127, 6257 (2005)
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An example photodynamics of DNA basis
What has theory to say?
reaction coordinate
np/S0 crossing Chen and Li, JPCA 109, 8443
(2005) Perun, Sobolewski and Domcke, JACS 127,
6257 (2005)
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An example photodynamics of DNA basis
What has theory to say?
ps/S0 crossing Sobolewski and Domcke, Eur.
Phys. J. D 20, 369 (2002)
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An example photodynamics of DNA basis
What has theory to say?
Our own simulations (TD-DFT(B3LYP)/SVP) do not
show any crossing at all.
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An example photodynamics of DNA basis
What has theory to say?

• The static calculations have being done in good
  levels, for instance
• MRCI in Matsika, JPCA 108, 7584 (2004)
• CAS(14,11) in Chen and Li, JPCA 109, 8443
  (2005)
• DFT/MRCI in Marian, JCP 122, 104314 (2005).
• However, the system can present conical
  intersections but never access them due to
  energetic or entropic reasons.
• The dynamics calculations are not reliable
  enough they miss the MR and the nonadiabatic
  characters.

To address the problem demands nonadiabatic
dynamics with MR methods. We will come back to
the adenine deactivation later
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Overview of the available approaches
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The minimum energy path the midpoint between
static and dynamics approaches
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Minimum energy path in two steps

• Determine the initial
• displacement vector (IRD)

2. Search for the minimum energy path
Celany et al. CPL 243, 1 (1995)
Schlegel, J. Comp. Chem. 24, 1514 (2003)
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Minimum energy path
Three qualitatively distinct MEPs
Garavelli et al., Faraday Discuss. 110, 51 (1998).
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Minimum energy path

• Advantages
• Explore the most important regions of the PES.
• Its equivalent to one trajectory damped
  dynamics.
• Clear and intuitive.
• Disadvantages
• Only qualitative temporal information.
• Neglects the kinetic energy effects.
• No information on the importance of each one of
  multiple MEPs.
• No information on the efficiency of the conical
  intersections.

Garavelli et al., Faraday Discuss. 110, 51
(1998). Cembran et al. JACS 126, 16018 (2004).
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SiCH4 MRCI/CAS(2,2)/6-31G
Also for SiCH4 one expects the basic scenario
torsiondecay at the twisted MXS. 68 of
trajectories follow the torsional coordinate, but
do not reach the MXS die to the in-phase
stretching-torsion motion. The lifetime of the
S1 state is 124 fs.
This and other movies are available
at homepage.univie.ac.at/mario.barbatti
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SiCH4 MRCI/CAS(2,2)/6-31G
The other 32 follow the stretch-bipyramidalizatio
n path. And reaches quickly the bipyramid. region
of seam. The lifetime of the S1 state is 58 fs.
This and other movies are available
at homepage.univie.ac.at/mario.barbatti
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SiCH4
Zechmann, Barbatti, Lischka, Pittner and
Bonacic-Koutecký, CPL 418, 377 (2006)
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The time-dependent self-consistent field the
basis for everything
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Time-dependent SCF
Time dependent Schrödinger equation (TDSE)
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Wave packet dynamics

• Time evolution - I
• Wave packet propagation
• 1) The nuclear wave function is expanded as
• f is the number of nuclear coordinates (ltlt 3N).

MCTDH (multiconfigurational time-dependent
Hartree) (Meyer, Manthe and Cederbaum, CPL 165,
73 (1990))
2) Solve TDSE using c. z ? Hermite/Laguerre
polynomials (DVR, discrete variable
representation) z ? Plane waves (FFT, fast
Fourier transform)
Advantage it is the most complete
treatment Limitation it is quite expansive to
include all degrees of freedom
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Wave packet dynamics
C. Lasser, TU-München
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Wave packet example HBQ
H
O
N
de Vivie-Riedle, Lischka et al. (2006)
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Multiple spawning

• Time evolution - II
• Multiple Spawning dynamics (Martínez et al., JPC
  100, 7884 (1996))

Nuclear wave function is expanded as a
combination of gaussians
The centroids RC and PC are restricted to move
classically.
Advantage very reliable quantitative
results Limitation it is still quite expansive
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Semiclassical approaches

• Time evolution - III
• Mean Field Surface Hopping.

Nuclear wave function is restricted to be a
product of d functions
RC is restricted to move classically.
Advantage large reduction of the computational
effort Limitation they cannot account for
nuclear quantum effects
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Classical limit of the Schrödinger equation
Nuclear wave function in polar coordinates
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Classical TDSE limit and minimum action
Newton
Hamilton-Jacob
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TDSE and Multiconfigurational expansion
where
Time derivative
Nonadiabatic coupling vector

• Diabatic representation fi ? hij 0.
• Adiabatic representation fi ? Hij 0 (i ? j).

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Mean Field (Ehrenfest) dynamics
Advantage Computationally cheap Limitation
wrong assymptotical description of a pure state
(there is no decoherence) Solution (?) Impose a
demixing time (Jasper and Truhlar, JCP 122,
044101 (2005))
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Surface hopping

• At each time, the dynamics is performed on one
  unique adiabatic state.
• In the adiabatic representation Hii Ei(R),
  ?Ei, and hji are obtained with traditional
  quantum chemistry methods.
• aji is obtained by integrating
• Nuclear motion is obtained by integrating the
  Newton eq.

• The transition probability between two
  electronic states is calculated at each time step
  of the classical trajectory.
• The system can hop to other adiabatic state.

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Mean Field and Surface hopping
Mean Field system evolves in a pure
state (superposition of several states)
Surface Hopping system evolves in mixed state
(several independent trajectories)
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What are we loosing?
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Multiconfigurational approach in polar coordinates
Lets start again, but now with a
multiconfigurational wave function.
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Approximation 1 Classical independent
trajectories
where
and
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Approximation 1 Classical independent
trajectories
0
where
and
Example Surface hopping. Mean Field.
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Approximation 1 Classical independent
trajectories
Example Surface hopping. Mean Field.
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Approximation 2 Classical coupled trajectories
where
and
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Approximation 2 Classical coupled trajectories
0
where
and
Example Bohmian Dynamics Velocity Coupling
Approximation (VCA, Burant and Tully, 2000).
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Approximation 2 Classical coupled trajectories
where
Example Bohmian Dynamics Velocity Coupling
Approximation (VCA, Burant and Tully, 2000).
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Approximation 3 Coupled trajectories
where
and
Example Classical Limit Schrödinger Equation
(CLSE, Burant and Tully, 2000)
(Yarkony, JCP 114, 2601 (2001)
One problem get Dkl
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Comparison between methods
Tully, Faraday Discuss. 110, 407 (1998).
surface-hopping (diabatic)
surface-hopping (adiabatic)
mean-field
wave-packet
Landau-Zener
Burant and Tully, JCP 112, 6097,(2000)
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Comparison between methods
Butatriene cation
Worth, hunt and Robb, JPCA 127, 621 (2003).
Oscillation patterns are not necessarily quantum
interferences
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Hierarchy of methods
Quantum
Classical
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• This lecture
• Dynamics reveal features that are not easily
  found by static methods
• From the full quantum treatment to the classical
  approach, there are several available methods
• Semiclassical approaches (classical nuclear
  motion quantum electron treatment) show the
  best cost-benefit ratio

• Next lecture
• How to implement the surface hopping dynamics
• The on-the-fly surface-hopping dynamics program
  NEWTON-X