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4 Application of the Nonadiabatic Dynamics ``on the fly'' for the Simulation of Ultrafast Observables of Furan: Comparison with Experiment

4 Application of the Nonadiabatic Dynamics ``on the fly'' for the Simulation of Ultrafast Observables of Furan: Comparison with Experiment

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R. Mitri´c et al.

Fig. 17.1 Comparison of the theoretical thermally broadened absorption spectrum of furan (red)

for the first S1 [1 A2 (π 3s)] ← S0 (1 A1 ) and second S2 [1 B2 (ππ ∗ )] ← S0 (1 A1 ) excited state obtained

from 240 structures sampled from the thermal ensemble at T = 300 K with the measured absorption

spectrum at room temperature (blue). The discrete absorption lines for each member of the

ensemble were convoluted with a Lorentzian function with a width of 0.1 eV and added together.

The equilibrium structure of furan in the neutral ground state as well as the dominant excitations

of the transitions to the S1 (π 3s) and S2 (ππ ∗ ) states are also shown

experimental data have been obtained by TR-PEI with an unprecedented time

resolution of 22 fs [79] using sub-20 fs pulses at 260 and 200 nm generated by the

multi-colour filamentation method [80, 81]. The combination of the experimental

findings with the theoretical simulations reveals ultrafast deactivation of excited

furan through internal conversion from S2 over S1 to the ground state [79].

The simulations have been performed in a manifold consisting of the ground

and the three lowest excited states. The energies, gradients as well as nonadiabatic

couplings needed to carry out the nonadiabatic dynamics have been calculated “on

the fly” using the hybrid PBE0 functional [82] combined with the 6-311G**++

basis set [83] containing also diffuse functions. This level of theory for electronic

structure describes accurately the stationary absorption properties and is suitable

for performing the dynamics simulations as discussed in Ref. [79]. Notice that

recently the accuracy of the TDDFT method for the description of nonadiabatic

dynamics in heterocyclic organic molecules has been validated against the highly

correlated multireference ab initio methods on the example of the pyrrole molecule

[84]. For the further computational details cf. Ref. [79] Based on the nonadiabatic

MD trajectories, the TRPES signal was calculated according to Eq. 17.11, assuming

a constant value for the transition dipole moments μik in the whole energy range.

The experimental photoabsorption spectrum of furan vapour at room temperature

as well as our TDDFT absorption spectrum simulated also at room temperature are

shown in Fig. 17.1. The good agreement between experiment and theory allows

17 Nonadiabatic Dynamics in Complex Systems


Fig. 17.2 Time-dependent ionization energy IE calculated along 240 nonadiabatic trajectories

for (a) the cationic ground state D0 and (b) the cationic first excited state D1 . The red line at

4.7 eV indicates the experimental probe pulse energy. Reprinted with permission from Ref. [79].

Copyright 2010, American Institute of Physics

for straightforward assignment of the transitions. The strong absorption feature

between 5.8 and 6.2 eV is caused by the S2 [1 B2 (ππ ∗ )] ← S0 (1 A1 ) transition. The

weak feature in the low energy part (5.6–6.0 eV) of the absorption spectrum is due

to the S1 [1 A2 (π 3s)] ← S0 (1 A1 ) transition involving the Rydberg 3s state, which

is in agreement with previous work [85, 86]. Since both the oscillator strength of

this state and the overlap with the pump pulse spectrum peaked at 6.2 eV are very

small we expect that the dominant excitation occurs to the S2 state which overlaps

well with the pump pulse spectrum. This state is thus used as the starting point for

the nonadiabatic dynamics simulations discussed below. The probe pulse (260 nm,

4.7 eV) has no overlap with the UV absorption spectrum of furan. Since the sum of

the pump (6.2 eV) and probe (4.7 eV) photon energies is 10.9 eV, it is energetically

possible to ionize furan at equilibrium geometry to two cation states, D0 (ionization

energy, IE = 8.9 eV [87]) and D1 (IE = 10.3 eV [88]) by (1+1’) resonance-enhanced

multiphoton ionization.

The nature of the ionization process can be determined from the calculated

time-dependent ionization energies between the current excited state in which the

dynamics takes place, and the cationic D0 and D1 states as shown in Fig. 17.2. It can

be seen that at very short time <10 fs both cationic states are accessible by the

experimental probe pulse, but after t >10 fs the only energetically possible transition

occurs to the D0 state. After the ensemble of trajectories returns to the ground state

S0 no cationic states are accessible anymore, therefore, no photoionization occurs.

This is clearly evidenced by the simulated TRPES shown in Fig. 17.3a which reflects

ultrafast deactivation of furan by the decreasing intensity of the signals in the time

regime between 10 and 100 fs. The calculated photoelectron intensities at selected

PKEs presented in Fig. 17.3c show an increase of the signals for decreasing PKEs,

exhibiting maxima at short time delays which are shifting to longer time delays for

lower PKE values. This is in agreement with the experimental findings presented

in Fig. 17.3b and d, which were obtained by photoelectron imaging spectroscopy

with a time resolution of 22 fs [79]. It should be noticed that for very short time


R. Mitri´c et al.

Fig. 17.3 (a) Simulated TRPES of furan. (b) Experimental TRPES obtained from pump-probe

photoelectron imaging spectroscopy of furan. (c) Time evolution of theoretically obtained photoelectron intensities at selected PKE values. (d) Time-evolution of experimental photoelectron

intensities at selected PKEs

delays our simulation provides only qualitative results for TRPES, since we excite

S2 instantaneously and do not consider the overlap between pump and probe pulses.

The agreement between simulated and measured TRPES in the low energy

regime as evidenced by Fig. 17.3 allows for complete assignment of the underlying

ultrafast processes to the measured features. For most trajectories, the transition

from S2 to S1 occurs at very short times, resulting in a lifetime of the adiabatic

S2 state of 9.2 fs, as can be seen from the time-dependent adiabatic populations

shown in Fig. 17.4a. The S2 population is almost completely transferred into the

S1 state after 20 fs. The lifetime of the adiabatic S1 state is ∼60 fs, and return to

the ground state is completed after 140 fs (cf. Fig. 17.4a) which is also reflected

in the decrease of TRPES signal intensities. Despite the very fast S2 –S1 transition,

the π − π ∗ diabatic character remains largely preserved, such that transition to the

ground state occurs mostly directly from the π − π ∗ state. This is illustrated in

Fig. 17.4b which shows diabatic state populations obtained by decomposing the

adiabatic populations in terms of the diabatic characters of the involved states. As

can be seen, the diabatic π − 3s Rydberg state is only weakly populated during the

simulation. Although the theoretically obtained lifetime of the S1 state of ∼60 fs is

17 Nonadiabatic Dynamics in Complex Systems


Fig. 17.4 Time-dependent (a) calculated adiabatic and (b) approximate diabatic populations of

the ground and two excited states of furan. The characters of the adiabatic states (S0 , S1 and S2 ) as

well as the diabatic states (S0 , π − π ∗ and π -3s) are given. The lifetime τ = 9.2 fs of the adiabatic

S2 state was determined by exponential fit (dashed line) (Reprinted with permission from Ref. [79],

Copyright 2010, American Institute of Physics)

longer than the experimental value of 29 fs [79], the theory correctly predicts the

trends for timescales of internal conversions: short for S2 –S1 (∼9 fs) and longer

for S1 –S0 (∼60 fs). Analysis of the nonadiabatic MD trajectories reveals that the

geometric relaxation in excited states takes place within the C–O–C subunit [79]

and the main channel after returning to the ground state leads to formation of

hot furan (I), as also illustrated in Fig. 17.5. Two other possible minor channels

involving breaking of the C–O bond and leading to formation of 2,3-butadienal

(II) and cyclopropen-3-carbaldehyde (III) are reached with very low probability (cf.

Fig. 17.5) at later times after the transition to the ground state. Thus, bond breaking

occurs sequentially in the ground state.

In summary, time-resolved photoelectron imaging spectroscopy with the very

high time-resolution of 22 fs using two-colour deep UV pulses and ab initio nonadiabatic dynamics simulations have for the first time revealed the ultrafast deactivation

processes from S2 to S0 state in furan. Joint theoretical and experimental results

represent a general approach for investigation of ultrafast photochemical reactions,

allowing to identify the fingerprints of the character of electronic states with an

unprecedented precision.

17.5 Field-Induced Surface-Hopping Method (FISH)

for Simulation and Control of Ultrafast Photodynamics

The simulation of laser-induced dynamical phenomena provides a basis for a

deeper understanding of molecular processes under the influence of light. This is

particularly interesting in the context of optimal control by shaped laser pulses.

In order to address complex systems, semiclassical methods in which the nuclear

degrees of freedom can be treated efficiently have been developed in the frame of the

Wigner distribution approach [56–58]. However, since the interaction with the laser


R. Mitri´c et al.

Fig. 17.5 Schematic representation of the photodynamics of furan obtained from nonadiabatic

dynamics. The S2 /S1 and S1 /S0 internal conversions and the corresponding time scales are shown

in red while the products in the ground state are indicated by black arrows (main product bold

arrow, other two products thin arrows). The minor channels have energies of 1.2 (II) and 2.1 eV

(III) above the main channel (I)

field has been described using perturbation theory these methods are limited only

to processes in relatively weak fields. For this reason, new theoretical approaches

for the simulation of dynamics driven by moderately strong laser fields (below the

multielectron ionization limit) are particularly desirable. Such fields open a rich

variety of pathways for the control of ultrafast dynamics in complex systems.

Therefore, we present here our semiclassical “Field-Induced Surface Hopping”

(FISH) method [59] for the simulation and control of the laser-driven coupled

electron-nuclear dynamics in complex molecular systems including all degrees of

freedom. It is based on the combination of quantum electronic state population

dynamics with classical nuclear dynamics carried out “on the fly”. The idea of the

method is to propagate independent trajectories in the manifold of adiabatic electronic states and allow them to switch between the states under the influence of the

laser field. The switching probabilities are calculated fully quantum mechanically.

The application of our FISH method will be illustrated in Sect. 17.6 on the example

of optimal dynamic discrimination (ODD) of two almost identical flavin molecules.

The starting point for the description of laser-driven multistate dynamics is the

semiclassical limit of the Liouville-von Neumann (LvN) equation for the quantum

mechanical density operator ρˆ ,

i¯hρ˙ˆ = [Hˆ 0 − μ · E(t), ρˆ ].


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