- freely available
Computation 2013, 1(1), 1-15; doi:10.3390/computation1010001
Published: 11 March 2013
Abstract: We present the first computational study of the effects of isotopic substitution on the operation of dye-sensitized solar cells. Ab initio molecular dynamics is used to study the effect of deuteration on light absorption, dye adsorption dynamics, the averaged over vibrations driving force to injection (∆Gi) and regeneration (∆Gr), as well as on promotion of electron back-donation in dyes NK1 (2E,4E-2-cyano-5-(4-dimethylaminophenyl)penta-2,4-dienoic acid) and NK7 (2E,4E-2-cyano-5-(4-diphenylaminophenyl)penta-2,4-dienoic acid) adsorbed in monodentate molecular and bidentate bridging dissociative configurations on the anatase (101) surface of TiO2. Deuteration causes a red shift of the absorption spectrum of the dye/TiO2 complex by about 5% (dozens of nm), which can noticeably affect the overlap with the solar spectrum in real cells. The dynamics effect on the driving force to injection and recombination (the difference between the averaged <∆Gi,r> and ∆Gi,requil at the equilibrium configuration) is strong, yet there is surprisingly little isotopic effect: the average driving force to injection <∆Gi> and to regeneration <∆Gr> changes by only about 10 meV upon deuteration. The nuclear dynamics enhance recombination to the dye ground state due to the approach of the electron-donating group to TiO2, yet this effect is similar for deuterated and non-deuterated dyes. We conclude that the nuclear dynamics of the C-H(D) bonds, mostly affected by deuteration, might not be important for the operation of photoelectrochemical cells based on organic dyes. As the expectation value of the ground state energy is higher than its optimum geometry value (by up to 0.1 eV in the present case), nuclear motions will affect dye regeneration by recently proposed redox shuttle-dye combinations operating at low driving forces.
Photoelectrochemical cells, such as dye-sensitized solar cells (DSSC) , have attracted considerable and renewed interest in recent years as a possible economic alternative to silicon cells, as some long-standing issues begin to be effectively resolved [2,3,4,5]. In a typical DSSC , a surface of a wide band gap (oxide) semiconductor anode (with a gap too wide to adsorb most visible light photons) is covered-sensitized by dye molecules. The dye absorbs the solar radiation and is thereby promoted to an excited state, whose energy lies within the conduction band (CB) of the oxide. The large density of states of the CB favors the electron transfer from the molecule to the oxide . The electron can travel through the external circuit, and the resulting dye cation can be regenerated by a redox species in the electrolyte that provides ionic conductance between the sensitized surface and the cathode [7,8].
Besides the light absorption spectrum of the (adsorbed) chromophore molecule, the performance of photoelectrochemical cells largely depends on the kinetic competition between electron injection (charge separation) and dye regeneration (the desired processes), on one hand, and dye de-excitation and charge recombination of injected electrons with the dye cation or with electrolyte species, on the other (undesired processes) . All these elementary processes are due to nuclear motions. Electron injection proceeds either via a non-adiabatic mechanism of transition between different electronic states—from one localized on the dye to one localized on the semiconductor—which is governed by derivative coupling, or via an adiabatic mechanism, with nuclei moving over a barrier on the potential energy surface [9,10]. The rates of dye de-excitation (internal conversion), regeneration, and electron recombination are also governed by the interaction of electronic and nuclear degrees of freedom [11,12,13,14,15]. A key parameter governing the rates of injection and regeneration is the driving force, which can be proxied as the difference between the energies of the molecular excited state and the conduction band minimum (CBM) for injection and between the redox potential of the redox species and the dye ground state, for regeneration.
Nuclear motions not only affect injection and recombination—they also result in a broadening and a shift of the light absorption spectrum [16,17]. This is because structural changes induce shifts in energy levels. These shifts can significantly modify rates of various electronic processes to the point of making predictions based solely on optimized geometries unreliable. For example, we have shown in  that nuclear dynamics can modify the driving force to injection by tenths of eV vs. the equilibrium geometry for organic dyes adsorbed on the anatase (101) surface of TiO2, which could result in an up to an order of magnitude change in the injection rate. The magnitude of this dynamic effect was also dependent on the dye adsorption configuration on TiO2 (monodentate or bidentate). In , we predicted with molecular dynamics simulations that the rate of recombination of the injected electron with the dye cation can be enhanced by orders of magnitude by nuclear motions.
It is clear that nuclear dynamics is an important factor and that the ability to control it is a way to control the electron dynamics and, with it, the overall performance of photoelectrochemical solar cells. One way to modify nuclear dynamics is structural changes of the dye or dye-surface complex [20,21]. Such changes lead to a simultaneous modification of the electronic structure, and it could be difficult to optimize both. An example of a system where a structural change leading to a desirable electronic effect-increase in photon absorption and a better overlap with the solar spectrum—also leads to undesirable effects on electron-nuclear dynamics is the dyes 2E,4E-2-cyano-5-(4-dimethylaminophenyl)penta-2,4-dienoic acid (referred to below as NK1) and 2E,4E-2-cyano-5-(4-diphenylaminophenyl)penta-2,4-dienoic acid (referred to below as NK7), shown in Figure 1. NK7 differs from NK1 by an extended π-conjugation of the electron donor moiety—a typical procedure in organic dye design. The injection rate of the excited electrons from NK7 into titania was measured to be significantly lower compared to NK1 . Likely reasons for this are increased electron-phonon coupling  and a less favorable energy level matching with TiO2 .
It is, therefore, important to explore possibilities of modifying nuclear dynamics without seriously affecting equilibrium electronic structure. This is in principle possible by: (i) introducing steric hindrance, for example, by using co-adsorbates; (ii) controlling the temperature; and (iii) isotopic substitution. The use of co-adsorbates is widespread, due to their ability to shift the conduction band minimum (CBM) of the oxide and to prevent recombination [23,24,25,26]. We have recently observed in molecular dynamics simulations that co-adsorbed water can prevent a close approach of the dye-equivalent oxidation hole to TiO2, which should hinder recombination with the dye cation [17,19]. Most co-adsorbates used in DSSC do, however, modify the electronic structure of the oxide surface [17,24,25,26]. In the Born-Oppenheimer approximation, temperature can change the vibrational dynamics of low-frequency modes without affecting electronic structure. A recent theoretical study of the temperature effect in the range 300–350 K on absorption, injection, and recombination in DSSC predicted that an increase in temperature would cause a red-shift in the absorption spectrum, but little effect on the driving force to injection, while definitive conclusions about the effect on recombination could not be drawn, due to a small time-frame of the simulations (10 ps) . While other systems could potentially be identified with stronger temperature dependence, it would likely be impractical to thermostat a real solar cell in order to maintain the optimal temperature.
Isotopic substitution, on the other hand, appears to be a much cleaner way to impact nuclear dynamics without affecting electronic structure and without changing the dye structure or environment. It will change the amplitude of atomic vibrations, as well as directions of normal mode vectors. This will affect the (averaged over nuclear vibrations) molecular energy levels , as well as the values of derivative coupling elements responsible for nonadiabatic transitions [13,15,27]. Isotopic substitution has been used to increase the excited state lifetime of organic molecules and transition metal complexes used in organic light-emitting diodes (OLED), in order to increase the luminescence yield by reducing the rate of nonradiative decay, due to vibronic coupling [28,29,30,31], but studies of the isotopic effect on the performance of photoelectrochemical cells are almost non-existent. We have recently estimated the effect of deuteration of tetracyanoethylene (TCNE), tetracyanoquinodimethane (TCNQ) and tetracyanoanthraquinodimethane (TCNAQ) on the geminate recombination in cells utilizing interfacial charge transfer bands (so-called direct injection cells) . It was predicted that deuteration significantly changes the contribution of many vibrational modes to the rate of geminate recombination, although the overall effect was mild, as the main promoting modes were little affected. To the best of our knowledge, no study of the effects of isotopic substitution on the performance of the conventional DSSC’s has been done.
Here, we study how deuteration—the most readily achievable type of isotopic substitution [31,32,33]—can change the nuclear dynamics effect on light absorption, electron injection, and recombination in NK1 and NK7 dyes on TiO2. The paper is organized as follows: in Section 2, theoretical and computational methods are described, Section 3 presents the results of comparative studies of the dynamical effects in deuterated and non-deuterated dyes, and Section 4 concludes.
2. Theoretical and Computational Methods
The methodology here is similar to that used in [18,19], namely, the electronic and molecular structure was computed using DFT (density functional theory)  and the SIESTA code  The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional  and the DZP basis set (double-ζ polarized orbitals) were used. We used a standard DZP basis set as generated by SIESTA, but the cutoff radii were increased from the default values by choosing Eshift = 0.001 Ry to mitigate basis-set superposition errors . A large enough simulation cell was used that the Brillouin zone was sampled at the Γ point (11.36 × 10.25 × 27.0/30.0 Å for the cells containing NK1/NK7 dyes, respectively). Core electrons are treated within the effective core approximation with Troullier-Martins pseudopotentials (provided with SIESTA) . Geometries were optimized until forces on non-fixed atoms were below 0.02 eV/Å. The TiO2 anatase (101) surface was used, as it is the dominant and thermodynamically stable facet . It was modeled with a 3 × 1 slab containing four Ti layers, of which two top Ti layers were allowed to move and the bottom layers were kept frozen at their bulk position. DFT values for TiO2 lattice constants of a, c = 3.78, 9.52 Å are in excellent agreement with the experiment and other theoretical calculations . This slab thickness was shown to be adequate to simulate dye adsorption and electron injection [41,42,43,44]. Ab initio molecular dynamics (MD) simulations were performed at 300 K using a Nose-Hoover thermostat with a time step of 1 fs. The first 3 ps were discarded for equilibration before computing distributions and averages (for which data were sampled every time step). These parameters are similar to other dynamical studies of dye/titania systems [45,18,46]. The MD trajectories for free dyes were 10 ps long, which was sufficient to sample all intermolecular vibrations. In , we identified that the MD trajectory needs to be longer than 10 ps in order to account for orientational degrees of freedom of the dye with respect to the surface. Here, we therefore computed 15 ps-long trajectories for deuterated (referred to below as D-NK1 and D-NK7) and non-deuterated NK1 and NK7 dyes adsorbed on a clean surface in the monodentate and bidentate bridging configurations, for a total of eight MD simulations. As a result, the post-equilibration parts of the trajectories used to estimate the averages are almost twice as long compared to [18,19]. Figure 2 shows the optimized geometries, which served as the starting point for the MD calculations. Full deuteration is assumed.
The effect of nuclear motions of deuterated and non-deuterated dyes on the absorption spectra was estimated from the distributions obtained during MD of the HOMO-LUMO gap for free dyes or HOMO-LUMO* for adsorbed dyes, where LUMO* are orbitals of the adsorbate complex corresponding to the dye LUMO (average energies are used when there is more than one LUMO*; see  for more details). We have shown previously that the gap reproduces well the relative spectra in spite of the underestimation of the absolute energies when using a generalized gradient approximations (GGA) functional . The effect on the driving force to injection was estimated by comparing ΔGi = LUMO*-CBM, at the equilibrium, ΔGiequil, and averaged over MD trajectories, <ΔGi>. As isotopic substitution does not affect the equilibrium geometry and electronic structure, the initial configurations and their frontier orbitals are the same as in the previous study (see Figure 1, Figure 2, Figure 3 of ).
3. Results and Discussion
3.1. Effect of Deuteration on Absorption Spectra and Dye Regeneration
The distributions of the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap of the free dyes during the MD trajectories are shown in Figure 3. Nuclear vibrations cause not only a broadening of the electronic transitions, but also a red shift. The expectation value of the gap for NK1 is 1.70 eV vs. 1.88 eV at the equilibrium geometry. The corresponding values for NK7 are 1.57 eV and 1.70 eV. The lowering of the gaps is due to a destabilization of the HOMO (from −5.37 to −5.27 eV for NK1, from −5.52 to −5.36 for NK7) rather than to a stabilization of the LUMO (from −3.49 to −3.57 for NK1, a slight increase from −3.82 to −3.79 for NK7), on the average, during vibrations.
In a classic MD simulation (where the nuclei are treated classically and move on the Born-Oppenheimer potential energy surface computed quantum mechanically), deuteration is not expected to change this pattern, and indeed, the nuclear motions cause a similar red shift, with the expectation values of the gap of 1.69 and 1.56 eV for D-NK1 and D-NK7, respectively. The difference in the spectral shape can be appreciated visually by comparing solid and dotted lines in Figure 3. Overall, the computed effect of deuteration on light absorption of the free dyes is negligible and is within numeric accuracy.
For dyes adsorbed on TiO2, the comparison of spectral shapes between NK1 and NK7 and D-NK1 and D-NK7 is given in Figure 4. There is a noticeable dynamical effect on the spectrum in that the expectation value of the HOMO-LUMO* gap is 1.48/1.52 eV and 1.66/1.59 compared to the equilibrium values of 1.70 and 1.59 eV for NK1/D-NK1 and NK7/D-NK7, respectively, in the case of monodentate adsorption. For the bidentate adsorption, the expectation value of the HOMO-LUMO* gap is 1.47/1.48 eV and 1.45/1.39 compared to the equilibrium values of 1.70 and 1.53 eV for NK1/D-NK1 and NK7/D-NK7, respectively. Dynamical lowering of the gap is due to a destabilization of the HOMO (similarly to the case of the free dyes), as well as a stabilization of the LUMO*, both by up to 0.1 eV (Table 1). The exception is NK7 adsorbed in the monodentate regime, where there is little difference in <HOMO> and <LUMO*> vs. the equilibrium values for both deuterated and non-deuterated dye. This will be explained below by the specifics of dye motion with respect to the oxide surface in this system (Section 3.3).
While deuteration has little effect on the HOMO-LUMO* gap in NK1/TiO2, there is clearly a red shift induced by isotopic substitution in D-NK7/TiO2. Such a dependence on molecular structure can be rationalized by the presence of floppy C6H5 moieties in NK7. The low-frequency torsional dynamics of these moieties can be impacted to a larger degree by deuteration than the CH3 ligands in NK1 and, with it, the overall vibrational dynamics of the molecular backbone. The resulting larger deviations from the equilibrium geometry are likely to enhance the dynamical effect on the spectrum, i.e., the red shift. Why did this effect appear in the adsorbed, but not in the free dyes? The answer must lie in the orientational motions with respect to the surface of TiO2. There is a significant hybridization of molecular energy levels with those of the oxide , and these motions are expected to influence the energies of the adsorbate complex, while molecular orientation has no effect on energy levels of a free dye. Indeed, in D-NK7/TiO2, the expectation values of HOMO are increased and simultaneously the expectation values of LUMO* are lowered by up to 0.04 eV each vs. H-NK7/TiO2. As a result, the spectrum is red-shifted by about 0.1 eV or about 5%–6%. Considering typical underestimation of the gap by GGA DFT, this should result in a shift on the order of dozens of nm in real cells, which could have a significant effect on the overlap with the solar spectrum.
|Table 1. The energies of the dyes’ frontier orbitals and the gap between them, the energy of the conduction band minimum (CBM) of TiO2 and the driving force to injection ΔGi, in eV, at the equilibrium configuration and averaged over nuclear motions for the non-deuterated and deuterated NK1 and NK7 dyes adsorbed on TiO2 in the monodentate and bidentate configurations, as shown in Figure 2.|
|System||Equilibrium/MD averaged (non-deuterated)/MD averaged (deuterated)|
The average over nuclear motions energy of the dye ground state permits a preview into the effect of nuclear motions on regeneration. As room temperature vibrations are able to destabilize the HOMO level in (deuterated or non-deuterated) dyes/TiO2, this could decrease the driving force to regeneration <ΔGr> by the electrolyte by up to 0.1 eV vs. the static estimate ΔGrequil, which could have a noticeable effect on the regeneration rate, depending on the redox shuttle used [7,8]. This effect is expected to be important for the development of new redox shuttles, which operate at low driving forces, to gain a higher open-circuit voltage—which is currently an area of active research [7,8]. Indeed, it has been established that effective regeneration can be possible with ΔGr as low as 0.2–0.3 eV, and a number of redox shuttle-dye couples operating in these regimes have been proposed [7,8,47,48,49]. On the other hand, the deuteration effect on the regeneration rate is unlikely to be significant, as the change in the average HOMO level predicted here is within 0.05 eV.
3.2. Effect of Deuteration on Injection Conditions
Even as the equilibrium electronic structure is the same for H-NK1,7 and D-NK1,7, deuteration is expected to influence injection conditions via different nuclear dynamics, as normal mode vectors are mass-dependent. This affects the temporal distribution of the adsorbate system’s energy levels and its average over nuclear motions. In Table 1, we list the driving force to injection in the eight systems: at the equilibrium geometry ΔGiequil and averaged over nuclear motions <ΔGi>, for the non-deuterated and deuterated dyes. An example distribution of the energy levels relevant for electron injection and dye regeneration following from the MD trajectory of the dye/TiO2 system is shown in Figure 5. The distributions are similar to those reported in  for shorter (10 ps) trajectories and for non-deuterated dyes and do not visually differ between deuterated and non-deuterated dyes. These calculations showed that nuclear motions exert a strong effect on injection conditions, with the expectation values of ΔGi differing by up to 0.1 eV from those computed at the equilibrium geometry. This dynamic effect is dependent on the dye molecular structure, as well as on the adsorption mode, being stronger for monodentate adsorption. The magnitude of the difference between <ΔGi> and ΔGiequil is significant, as it has been estimated that the injection rate changes by a factor of two when ΔGi changes by 100 meV [50,51].
It is striking that despite the fact that the dynamic effect (the difference between ΔGiequil and <ΔGi>) is large, deuteration has a negligible effect on <ΔGi>. This must mean that it is the distribution of configurations of the molecular backbone that determines the dynamic effect on injection and that the nuclear dynamics of the CH(CD) bonds do not affect this distribution much. Interestingly, it was recently shown that deuteration does not change the rates of geminate recombination much in organic dye/TiO2 adsorbate complexes, which are also driven by the nuclear dynamics . This suggests that deuteration may not be an effective way to control electronic processes which depend on the backbone’s structure and dynamics. The question remains open whether other types of isotopic substitution (in the backbone itself) could achieve such control.
3.3. Effect of Deuteration on Orientational Motions and Recombination to the Dye Cation
In Figure 6, we show the temporal evolution of the distance, z, between the amino group and the oxide surface for all studied cases. It shows an approach of the electron donating group to the surface, which is a purely dynamic effect and is not due to a lower electronic energy in the tilted configuration, as discussed in . It will have an enormous effect on the back-donation rate, which has been shown to depend exponentially on this distance [52,53]:
Here, we observe that deuteration does little to change it, even if the details of the dynamics are different. This can be rationalized, on one hand, by a relatively small change of the dye molecular mass due to deuteration, which is not expected to have a strong effect on how the configuration space of orientational degrees of freedom is sampled, and, on the other hand, by the fact that the amplitude of vibrations, including dye wagging around the surface, is mass-independent in classical MD.
Figure 6 also shows that the (H-, D-) NK7 dye adsorbed in the monodentate configuration spends most of the trajectory in a near vertical configuration (Figure 2), with a significant tilt occurring only after 10 ps. This explains the smaller destabilization of the frontier orbitals by nuclear motions vs. the other systems described in Section 3.1 and corroborates the idea that orientational motions with respect to the surface play an important role in the dynamical effect on energy levels and in the red-shift of the absorption spectrum predicted in Section 3.1.
We have studied the effect of an isotopic substitution—deuteration—on the conditions determining the efficiency of dye-sensitized solar cells, namely, light absorption and energy level matching, which, in turn, determines the rates of electron injection and recombination and of dye regeneration by electrolyte species. Nuclear dynamics affect the electronic structure and energy levels of the dye-semiconductor system by modulating its molecular structure. This nuclear dynamics effect can be significant, and here, we investigated how it can be modulated by using isotopic substitution. In a classical MD study, it is impossible to capture the quantum isotopic effects, such as changes in the zero-point energy, which will also affect the average geometry. The classical study presented here captures the isotopic effect wrought via changes in the direction and amplitude of atomic vibrations. This mass-dependence is unique to polyatomic molecules in a non-isotropic space (the presence of the surface) when masses of all atoms do not change in the same proportion, as reflected in the mass-dependence of normal mode displacement vectors, in contrast to a one-dimensional classical oscillator, where the amplitude of vibrations and the average geometry are mass-independent at a given total energy. While the thermostat imposes the same average kinetic and, therefore, potential energy, in a multi-atomic system, these can be realized at different average conformations.
We found a noticeable effect of deuteration on the HOMO-LUMO gap of the adsorbate system, causing a red shift on the order of 5%, which should translate into a shift of dozens of nm in real cells and significantly impact the overlap of the absorption and the solar spectra. On the other hand, and surprisingly, the effect on energy level matching with the TiO2 conduction band was negligible, i.e., the difference between <∆GiH> and <∆GiD> is much smaller than between <∆GiH> and ∆Giequil. This leads us to conclude that deuteration could be used to fine-tune vibrationally-averaged energy levels of adsorbed dyes, but not in a major way. This conclusion might not, however, hold for other isotopic substitutions.
Nuclear dynamics is likely to have a strong effect on the rate of parasitic electron back-donation from TiO2 into the oxidation equivalent hole formed on the dye’s electron-donating group upon injection. The approach of this group to the oxide surface can lead to an increase of the back-donation rate by orders of magnitude. Here, too, the effect of deuteration was found to be minor. Other strategies are therefore recommended to prevent a close approach to the surface of the electron donating group, such as the use of co-adsorbents .
Nuclear motions are likely to affect dye regeneration by the electrolyte, as the expectation value of the ground state energy can be higher vs. the static (optimum geometry) estimate, by about 0.1 eV in the present case. The development of efficient and mass-producible dye-sensitized cell is closely dependent on the development of alternative (to iodide/triiodide) redox shuttles, specifically those which are able to operate at smaller driving forces to achieve a higher open-circuit voltage [7,8]. Redox species-dye combinations (e.g., Co-based [8,47,49] or ferrocene  redox shuttles combined with Ru-free dyes) operating at ΔGr as low as 0.2–0.3 eV are being actively researched [7,8]. For such systems, the dynamic effect described here should be taken into account.
This work was supported by the Tier 1 AcRF grant from the Ministry of Education of Singapore.
Conflict of Interest
The authors declare no conflict of interest.
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