Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 5926−5933
pubs.acs.org/JPCL
Charge Transfer Driven Structural Relaxation in a Push−Pull Azobenzene Dye−Semiconductor Complex Alberto Torres, Luciano R. Prado, Graziele Bortolini, and Luis G. C. Rego* Department of Physics, Universidade Federal de Santa Catarina, Florianópolis, SC 88040-900, Brazil
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S Supporting Information *
ABSTRACT: Photoexcited structural dynamics in azo-compounds may differ fundamentally whether the push−pull photochromic azocompound is isolated or forms a heterogeneous charge transfer complex, due to a sudden oxidation of the chromophore. Herein, we use a quantum-classical self-consistent approach that incorporates nonadiabatic excited-state electronic quantum dynamics into molecular mechanics to study the photoexcited dynamics of the push−pull azocompound para-Methyl Red in the gas phase and sensitizing the (101) anatase surface of TiO2. We find that the photoinduced S2/S0 trans-tocis isomerization of para-Methyl Red in the gas phase occurs through a pedal-like torsion around the ϕCNNC dihedral angle, without evidence to support the inversion mechanism, likewise in the parent azobenzene molecule. However, the photoexcited structural relaxation of the charge transfer complex para-Methyl Red/TiO2 contrasts essentially with the isolated azo-compounds. Immediately after photoexcitation, the excited electron flows into the TiO2 conduction band, with an injection time constant of ≃5 fs, and no indication of isomerization is observed during the 1.5 ps simulations. Instead, a strong vibronic relaxation occurs that excites the NN stretching mode of the azo-group, which is ultimately ascribed to the NA relaxation, and delocalization, of the hole wavepacket.
C
approaches to circumvent such problems consist of the application of local diabatization schemes to generate a timedependent diabatic basis,9,19,22−24 the use of grid-based direct dynamics formalisms,25,26 or partition schemes.16,27 Despite eliminating strong nonadiabatic derivative couplings, quasidiabatization schemes require on-the-fly calculation of a few Hamiltonian eigenstates, including excited states, which can be problematic for large systems. The diabatic representation, however, is well suited for wavepacket propagation schemes but is inappropriate for the concomitant nuclear dynamics propagation that occurs on the PES. This particular problem can be overcome by using analytic force fields, such as those regularly used in molecular mechanics (MM) simulations. Herein we use a quantum-classical self-consistent method that incorporates nonadiabatic excited-state electronic quantum dynamics into molecular mechanics. Semiempirical quantum mechanism and molecular mechanics schemes comprise an Ehrenfest formalism fully derived for diabatic representation, which is capable of describing complex structural dynamics phenomena of large scale systems, in particular phenomena where the molecular structure undergoes large structural deformations. The method is used to study the excited-state nonadiabatic dynamics, including long-
harge transfer (CT) and electronic excitation dynamics (EED) are ubiquitous in photochemistry.1 Besides, they are pivotal mechanisms for electron transfer reactions in biomolecules,2,3 for phototransduction phenomena in natural and artificial light-harvesting structures,4,5 among many other processes in atomic, molecular physics, chemistry and biology. These mechanisms (CT and EED) have also been relentlessly explored for potential applications in optoelectronic molecular devices.6 They are often influenced by the nonadiabatic coupling between electronic and nuclear degrees of freedom, so that dynamics simulations on a single Born−Oppenheimer potential energy surface (PES), usually in the ground state, cannot fully describe them.7,8 Molecular structures of interest for the study of nonadiabatic charge and energy transfer phenomena range from molecular dimers9,10 to polymers and11,12 molecular wires,13 from chromophores14,15 to dyesensitized interfaces16−20 and functionalized nanocrystals,21 and from proteins3 to biomolecules.2 These simulations generally adopt the intuitive adiabatic representation of PES; however, propagation of nonadiabatic dynamics in the adiabatic representation has some drawbacks. Among them, level crossings of weakly coupled adiabatic states may give rise to unphysical long distance population transfer, nonadiabatic derivative couplings are highly peaked and difficult to map at level crossings, adiabatic eigenstates are very sensitive to nuclear position, and on-the-fly calculation of the ground state and nearby excited states can be computationally expensive, especially among a dense manifold of states. Practical © XXXX American Chemical Society
Received: August 13, 2018 Accepted: September 26, 2018 Published: September 26, 2018 5926
DOI: 10.1021/acs.jpclett.8b02490 J. Phys. Chem. Lett. 2018, 9, 5926−5933
Letter
The Journal of Physical Chemistry Letters range CT effects, of the push−pull azo-compound para-Methyl Red in gas phase and sensitizing the (101) anatase surface of TiO2, whereby we demonstrate that the excited-state nonadiabatic dynamics of para-Methyl Red sensitizing the TiO2 surface is fundamentally different from the isolated azocompounds. Theoretical Method. The time-dependent Schrö dinger equation (TDSE) is solved for the electronic degrees of freedom iℏ
∂ |Ψ(r;t )⟩ = Ĥ el(R t)|Ψ(r;t )⟩ ∂t
by means of which the excited-state interatomic potential is separated as the contribution from the ground-state force field potential, VMM GS , plus a correction that is due to the electron− hole excitation, VEH[Ψel,Ψhl]. The underlying reasoning for this approximation is that VMM GS is produced by all the occupied orbitals that comprise the ground state and it is, at least in principle, well described by the force field. By creating a hole within the manifold of occupied states due to an electron that is sent to the unoccupied manifold, we produce a perturbation potential that is a functional of the electron and hole wave functions. This second term is responsible for the coupling between quantum and classical degrees of freedom in the excited state. It is calculated on-the-fly from the Hamiltonian as
(1)
where r designates the electronic coordinates, Rt ≡ R(t) are the time-dependent nuclear coordinates, and Ĥ el(Rt) is the time-dependent extended Hückel Hamiltonian operator.19,28 The nuclei are described by molecular mechanics, with the following force field (FF) MM VGS ({R}) =
∑
Kb(R − R 0)2 +
bonds
+
∑
VEH[Ψ el(R,t ),Ψhl(R,t )] = Tr[ρ EH (R,t )H(R t)]
where ρEH = |Ψel⟩⟨Ψel| − |Ψhl⟩⟨Ψhl| is the electron−hole density matrix. The force produced on atom N by an e−h excitation is given by
K θ(θ − θ0)2
angles
∑ ∑ Cn(cos ϕ)n
ÅÄÅ ÑÉ ÅÅij σ yz12 ij σ yz6ÑÑÑ ij ÅÅjj ij zz Ñ + ∑ 4εijÅÅÅjj zz − jjjj zzzz ÑÑÑÑ j z j z ÅÅ R ij R Ñ i,j≠i k ij { ÑÑÖÑ ÅÅÇk { qjqi + ∑ i , j ≠ i 4π ϵ0R ij torsions
FN = −∇N VEH[Ψ el(R,t ),Ψhl(R,t )]
n
(7)
where ∇N ≡ ∇RN. This force is responsible for the electronic back-reaction on the classical degrees of freedom and it gives rise to adiabatic (AD) and nonadiabatic (NA) nuclear dynamics effects. Furthermore, it is responsible for conservation of the total energy during the excited-state dynamics. The excited-state total energy is composed of the classical energy of the nuclei (kinetic plus potential), as given by the molecular mechanics formalism, and the quantum energy of the excited electron−hole pair EQM = Tr[ρEHH]. In the present diabatic representation we work solely with localized atomic orbitals of the Slater-type, ⟨r|α(t)⟩ = fa(r− RA(t)); thus the electron−hole wavepackets are written as |Ψ(t)⟩ = ∑αcα(t)|α(t)⟩. The numerical approach for solving the time-dependent Schrödinger equation is to divide the total evolution operator into short segments (time slices δt) and then apply the scheme
