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Femtochemistry: A theoretical overview. Introduction. Mario Barbatti mario.barbatti@univie.ac.at. This lecture can be downloaded at http://homepage.univie.ac.at/mario.barbatti/femtochem.html lecture1.ppt. settling the bases: photochemistry, excited states, and conical intersections.

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slide1

Femtochemistry: A theoretical overview

Introduction

Mario Barbatti

mario.barbatti@univie.ac.at

This lecture can be downloaded at

http://homepage.univie.ac.at/mario.barbatti/femtochem.html

lecture1.ppt

slide2

settling the bases:

photochemistry, excited states, and conical intersections

slide3

Photochemistry & 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?
slide5

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.

slide6

The 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.

slide7

P ~ |j|m|i|2

t ~ ns

Basic process I: Radiative decay (fluorescence)

slide8

j| |i

P ~ v 

N

t~ fs

Basic process II: Non-radiative decay

slide9

The Static Problem

  • How are the excited state surfaces?
  • 2. For which geometries does the molecule have conical intersections?
  • 3. Can the molecule reach them?
slide10

Conical intersections

formamide

pyridone

Antol et al. JCP 127, 234303 (2007)

Barbatti et al., Chem. Phys. 349, 278 (2008)

slide12

Conical intersections: Twisted-pyramidalized

Barbatti et al. PCCP 10, 482 (2008)

slide14

The Dynamics Problem

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?

slide17

Programs

  • COLUMBUS
  • MRCI, MCSCF
  • Analytical gradients and non-adiabatic couplings
  • www.univie.ac.at/columbus
  • Lischka 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, DFTB
  • www.univie.ac.at/newtonx
  • Barbatti et al., J. Photochem. Photobio. A 190, 228 (2007)
slide18

1

For a fixed nuclear geometry, solve time-independent Schrödinger Eq. for electrons. Get the energy gradient

and the couplings

2

Use the energy gradient to update the nuclear geometry according to the Newton`s Eq.

3

For the new nuclear geometry (only!), solve the SC-TDSE

and correct classical solution by performing a hopping if necessary.

i)

Go back to step 1 and repeat the procedure until the end of the trajectory.

4

ii)

Repeat procedure for a large number of trajectories to have the “classical wave packet”.

5

iii)

MQCD methods: surface hopping

slide19

Transition probability is

evaluated at each time step

A stochastic algorithm decides on which surface the molecule will continue

Classical nuclear motion

on the on-the-fly BO surface

MQCD methods: surface hopping

E

Q

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

slide20

Chair

Twisted-chair

Envelope

Q

Screw-boat

q

f

Boat

Cremer-Pople parameters

Ex.: 1S6 = Screw-boat

with atoms 1 above the plane and 6 below

Cremer and Pople, JACS 97, 1358 (1975)

slide24

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.

slide25

This effect might have constituted an evolutionary advantage for the five nucleobases forming DNA and RNA.

slide26

Lifetime of nucleobases

Canuel et al. J. Chem. Phys. 122, 074316 (2005)

slide27

1 ps

30 ps

2-aminopurine

9H-Adenine

slide30

0

750

1500

delay time / fs

Experimental data on adenine

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 (pp*) [5]

2: 1 ps – relaxation into S0 (np*)

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)

slide31

Theoretical 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]
slide32

pp*imi

ps*

La

np*

ps*

Conical intersections in adenine

7T8

2H3

4H3

4S3

E8

E3

B3,6

N-H

6S1

C8-C9

2E

slide33

How does deactivation ocurr?

Barbatti and Lischka, JACS 130, 6831 (2008)

slide35

2-pyridone

Barbatti et al., Chem. Phys. 349, 278 (2008)

Excited state dynamics: what do we have learned?

9H-adenine

slide36

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.

slide37

2-aminopurine

9H-Adenine

1 ps

30 ps

slide42

About 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.
slide43

About 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.
slide45

Next lecture

  • Transient spectrum
  • Excited state surfaces

Contact

mario.barbatti@univie.ac.at

This lecture can be downloaded at

http://homepage.univie.ac.at/mario.barbatti/femtochem.html

lecture1.ppt