Article pubs.acs.org/JPCC
Physical Factors Affecting Charge Transfer at the Pe-COOH−TiO2 Anatase Interface Olga A. Syzgantseva,*,†,‡ Martti Puska,‡ and Kari Laasonen† †
COMP, Department of Chemistry, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland COMP, Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
‡
S Supporting Information *
ABSTRACT: In this work we address the factors affecting the rate and the completeness of the excited state electron transfer from a COOH-anchored perylene molecule to the (101) anatase surface. To investigate the electron injection at the Pe-COOH−TiO2 interface, a pure electron dynamics and a coupled electron−ion dynamics simulations are conducted within the real-time timedependent density functional theory (RT-TDDFT) and RT-TDDFT-based Ehrenfest dynamics formalisms, respectively. The role of ionic dynamics, the influence of the adsorption mode, the surface coverage by the adsorbate, as well as the impact of the initial excitation energy on the charge transfer process are analyzed. The dissociative adsorption is shown to be less favorable for the charge transfer than the nondissociative one. The ionic dynamics turns out to have a limited effect on the total amount of the transferred charge, but it is responsible for the retardation of the electron transfer. The energy of initial excitation is revealed to be a determinant factor of the electron injection efficiency in the Pe-COOH−TiO2 system: the excitation of an electron to the LUMO+1 molecular orbital, instead of the LUMO one, doubles the total amount of the transferred charge. Meanwhile, a complete CT can only be achieved in conjunction with specific coverage and slab thickness characteristics, with all other factors being fixed. A surface coverage ratio equal to or less than 0.25 molecule/nm2 and a slab thickness of at least 4 TiO2 layers, corresponding to 192 Ti sites per 1 molecule of chromophore, are required.
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INTRODUCTION The excited state charge transfer (CT) phenomenon at the interface between an organic chromophore and a semiconductor surface, typically a metal oxide, is of primary importance in many fields of technological applications, including photovoltaic processes1−4 and photocatalysis.3−7 Understanding of these processes implies the knowledge about the time, completeness, and pathways of electron injection, as well as the moment of possible backward reinjection or recombination. Apart from the inherent systems’ properties, i.e. the nature of the dye and the type of semiconductor surface, other factors, such as the internal ionic dynamics of the complex system, the surface coverage by adsorbate, the thickness of semiconductor layer, the type of anchor, and the energy of the initial excitation are to be taken into consideration when aiming to modulate the CT-characteristics. The parameters, affecting the CT efficiency at the dye− semiconductor interface, have been widely studied both experimentally and theoretically.8−13 In particular, recent developments of ab initio modeling approaches have allowed for investigation of CT processes on the molecular level for a large set of chromophores,14,15 overcoming the experimental limitation on the number of systems and conditions, which practically can be sampled. Various theoretical methods are proposed to study CT processes at the dye−semiconductor interface. They can be © 2014 American Chemical Society
roughly classified into estimations of the injection rate through the calculation of the coupling coefficients between the donor and acceptor states14−21 and the explicit electron or electron− nuclear dynamics.22−29 The first class of methods allows the evaluation of the electron injection time, assuming the effective injection ratio equals 1, but does not account for possible ionic movements and does not contain information about the completeness of CT or the possible reinjection or recombination events. Direct dynamical simulations of the CT processes are relatively limited22−28,30−35 due to the high computational cost of these methods. Nevertheless, the recent efficient implementations of the Ehrenfest dynamics (ED) approach and the real-time time-dependent density functional theory (RT-TDDFT) into some computer codes, including the GPAW code,34,36,37 have opened a way to simulations with hundreds of atoms. The direct electron or the coupled electron−ion dynamics allows not only determination of the CT constants but also description of the role of each structural fragment of the system in the CT process. In the current study we have adopted this methodology. Some CT-factors, such as the influence of the anchoring group, have been extensively studied by computational methods;19,38−40 others, such as surface coverage and support Received: July 11, 2014 Revised: September 27, 2014 Published: October 9, 2014 25310
dx.doi.org/10.1021/jp506935a | J. Phys. Chem. C 2014, 118, 25310−25319
The Journal of Physical Chemistry C
Article
of the dye, the generalized ΔSCF method60,61 was applied. One electron was promoted from the perylene’s localized HOMOorbital to an orbital, constructed as a linear combination of empty Kohn−Sham states in order to reproduce in the best way perylene’s LUMO or LUMO+1 orbital. Core electrons were described within the PAW formalism.62 The wave functions were represented on a finite grid with the distance between grid points equal to 0.20 Å. The number of electrons treated in the calculation were 12, 6, 4, and 1 for Ti, O, C, and H atoms, respectively. The whole system was described within periodic boundary conditions in three directions. The simple orthorhombic unit cell dimensions were [35.0 (4-layer slab), 45.0 (6-layer slab)] Å, 11.3526 Å and 10.2395 Å for the x, y, z, directions, respectively. For all calculations, the (1 × 2 × 2) Monkhorst−Pack k-point set was used. The slab geometries were taken from the previous study.63 To study the volume effect on electron injection, several slab configurations were considered: simple (x1: ∼1 molecule/nm2), double (x2: ∼0.5 molecule/nm2), triple (x3: ∼0.5 molecule/nm2), and quadruple (x4: ∼0.25 molecule/ nm2) unit cells (Table 1). All of them, except triple, contain 4 layers of TiO2, while the triple cell has 6 layers. Corresponding models are given in Figure 1.
thickness,14 the role of internal ionic dynamics,19−21 and the impact of the initial excitation energy,14 are addressed less often. To approach these issues, we have chosen as a model system the perylene-3-carboxylic acid (Pe-COOH), attached to the TiO2 anatase (101) surface via a COOH anchor group. The (101) surface of anatase is known to be the most abundant face in the TiO2 material, used in Grätzel-type solar cells,41,42 while the perylene derivatives are selected as sensitizers in DSSC, as in these compounds the intramolecular decay channels are not competing with the electron transfer to the TiO2 surface.38,43 Experimentally, the excited state charge transfer from a perylene molecule or its derivatives to a TiO2 surface was extensively studied by Willig’s group.28,38−40,43−54 In particular, it has been established that the time constant of the primary charge transfer equals 13 fs.44,52 Troisi’s group14−17 has theoretically modeled the injection times for a wide range of chromophores (particularly perylene with different anchor groups, adsorbed on the (101) anatase surface), relating the injection rate to the imaginary part of the self-energy. In particular, they have considered the impact of COOH anchor dissociation on the electron transmission from Pe-COOH to anatase TiO214 and investigated the influence of the TiO2 crystallographic surface on the charge injection rate.18 Although this approach reveals an estimate of the CT time, it does not address the CT completeness. Apart from this work, the electron transfer dynamics in a Pe-COOH−anatase TiO2 system was modeled by Li and co-workers for dissociative and nondissociative adsorption modes of the COOH group19,21 by a method based on a model Hamiltonian,19 in conjunction with the ML-MCTDH approach.21 The effect of the surface size (finite or infinite) on the completeness of CT was revealed in their study. At the same time, the questions on the role of ionic dynamics, the surface coverage, the system’s size, and the energy of the initial excitation were not explicitly addressed for this system in the literature. To the best of our knowledge, this is the first study applying the ED and RT-TDDFT techniques to describe the electron injection at the Pe-COOH−anatase TiO2 interface.
Table 1. Characteristics of Different Surface Models Used in This Work Model name
TiO2 layers
x1 x2 x3 x4
4 4 6 4
Volume, Coverage, molecules/nm2 nm3/molecule 1 0.5 0.5 0.25
1.5 3.0 4.5 6.0
Load, molecules/ Ti atom
Load molecules/ slab atom
1
1
1
1
/48 /96 1 /144 1 /192
/144 /288 1 /432 1 /576
Two adsorption modes of perylene-3-carboxylic acid (dissociative and nondissociative) were considered. To quantify the charge transfer, the total electron density at each instant of time was partitioned into atomic contributions according to Bader’s64 scheme and the amount of transferred charge was
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COMPUTATIONAL DETAILS Electron injection studies were conducted using real time propagation of electronic wave functions, within time-dependent density functional theory (RT-TDDFT)37,55 and TDDFTbased Ehrensfest dynamics (ED).34,56 Pure electron dynamics was studied with RT-TDDFT, using a 25 as (attosecond) propagation time step. Coupled electron−ion dynamics simulations were performed within the Ehrenfest dynamics formalism, in which electrons are described by quantum mechanics and nuclei move classically according to Newtonian equations of motion in the mean field potential of the electrons, with a 20−25 as time step. In both cases, the semi-implicit Crank−Nicolson algorithm was applied for electronic wave function propagation.57 Ionic steps in ED were realized according to the velocity−Verlet algorithm.58 The PBE59 density functional was applied to solve electronic equations. For a molecule adsorbed on a surface, the initial molecular electronic states might be changed due to the coupling with the surface states. For the perylene-3-carboxylic acid, absorbed on the anatase (101) surface, the HOMO orbital is localized in the TiO2 band gap, while the LUMO and LUMO+1 interfere with TiO2 states in the TiO2 conduction band (CB). To reproduce resonant molecular excitations between two molecular orbitals
Figure 1. Surface models and adsorption modes. Left panel: x1, x2, x3, x4 models (see Table 1 for characteristics). Right panel: nondissociative and dissociative adsorption modes. Atoms: C (yellow), H (blue), Ti (red), O (green). 25311
dx.doi.org/10.1021/jp506935a | J. Phys. Chem. C 2014, 118, 25310−25319
The Journal of Physical Chemistry C
Article
Upon creation of localized LUMO and LUMO+1 orbitals via the ΔSCF procedure, the HOMO−LUMO (LUMO+1) separation rises slightly to 1.7 and 3.0 eV, respectively. In the dissociative mode, the HOMO−LUMO separation is of 1.5− 1.8 eV in the ground state and 1.8 eV in the excited state. As follows from the DOS structure of dissociated acid, the position of hybridized LUMO states is much more spread over the conduction band than in the case of undissociated substrate. Indeed, three maxima can be distinguished at ∼1.5 eV, ∼1.6 eV, and ∼1.8 eV. The experimentally determined position of the first excited state level is ∼0.9 eV above the bottom edge of the conduction band.38 The electronic structure of our system, reproduced by the PBE functional, is in excellent agreement with this experimental fact (LUMO is 0.7−1.0 eV above the lower CB edge, see Figure 2). A thorough consideration of the DOS-structure makes it obvious that the choice of a resonant excitation avoids an arbitrary selection of one of the numerous close-lying mixed TiO2−Pe-COOH states with a great contribution of molecular LUMO or LUMO+1. Besides, the oscillator strength of the resonant excitation would be greater than that of any other excitation between localized molecular HOMO and hybridized acceptor. For both cases, the DOS structures reveal that the number of states, in particular of surface states of the first TiO2 layer, available for injection after excitation to the LUMO orbital is smaller compared to LUMO +1 excitation. The charge transferred from Pe-COOH to the TiO2 surface in the ground state is less than 0.06e− for both adsorption modes. The Bader’s charge of the H atom, adsorbed on the surface within dissociative adsorption, equals 0.39e− and stays unchanged during the wave function propagation. If the bond breaking upon OC−O−H group dissociation is considered as homolytic (one electron of the O−H bond stays on the H atom and another on the Pe−COO group), then the Pe−COO moiety withdraws 0.61e− backward and becomes negatively charged. Thus, in the ground state Pe−COOδ− holds in total 153.6e− compared to 154.0e− in the undissociated Pe-COOH state. Upon excitation one electron is promoted from the molecular HOMO of the perylene, situated in the band gap, to the molecular LUMO in a way that CT from the Pe-COOδ− moiety to the surface, produced by initial excitation, is less than 0.04 e− for 1 molecule/nm2 coverage. Using the excited state wave functions, produced as described above, at the first step, the impact of ionic dynamics on the electron injection rate is considered, as the inclusion of ionic motion via the Ehrenfest dynamics formalism is a more timeconsuming procedure than pure electron dynamics, realized via RT-TDDFT, and its possible elimination allows a substantial reduction of the CPU time consumption. Then, the possibility of CT enhancement via COOH anchor dissociation is analyzed, as the dissociative adsorption is reported14,32 to be favorable to the electron injection process in similar systems. Finally, the impact of the initial excitation energy on the rate and amount of transferred charge and the “size effect” are addressed. 2. Impact of Ionic Dynamics. We have performed ED and RT-TDDFT simulations for nondissociatively adsorbed perylene-3-carboxylic acid for 70 fs. The obtained CT results are presented in Figure 3. At the initial stage of the process (10 fs, the electron injection process has a clearly oscillatory character with no tendency toward a complete injection, as the oscillations have a decreasing amplitude. Starting from 20 fs, a distinguishable retardation effect is observed in the charge transfer within the coupled electron− ion dynamics simulation. This effect is expected, as the depletion of the electronic charge on the perylene molecule will result in ionic relaxation, stabilizing the positively charged organic moiety. Such stabilization slows down the electron transfer. As a result, the first maximum, simulated with ED, lies below one, observed for the fixed geometry. The next maxima are higher than the first one and ED has a bit longer oscillation period. The additional charge transfer due to the ionic relaxation does not exceed 5%, staying within the precision of the electron density integration and partitioning. Such a moderate impact of ionic dynamics on the charge transfer can be easily rationalized. The system properties are such that the greatest part of the charge is transferred during the first 6 fs, that can be qualified as an ultrafast charge injection and is known to be almost unaffected by the nuclear motion.21 With this respect, it should be mentioned that in the Ehrenfest dynamics the ionic relaxation is only due to the changes of the total electron density of the system (nuclei are moving in the changing electronic potential). Unlike various Molecular Dynamics (MD) approaches, this does not account for the thermal motion of nuclei. The temperature effects within the ED are usually addressed by averaging the CT profiles, obtained for a set of initial geometries sampled in the ground state by MD-techniques. In our particular case the thermal motion can be ignored, as its time scale is orders higher (100 fs −1 ps) than the time scale of the ultrafast electron injection process (∼10 fs) that we have studied. Thus, there is very little interference between the thermal motion and the charge transfer for the TiO2−PeCOOH system. Besides, the molecular LUMO in the ground state is situated well above the conduction band edge and the thermal fluctuations are not needed to raise the LUMO into the conduction band. For this reason we perform the simulations for the best single geometry, corresponding to the minimum of the ground state. Tracing the changes of the electron density of the excited one-electron state, one can notice that the first almost linear part of the CT curve (
