Quantitative structure–property relationship modeling of ruthenium sensitizers for solar cells applications: novel tools for designing promising candidates

Abstract

To date, the most common way of screening new potential sensitizers for dye sensitized solar cells is via the traditional time and money consuming trial and error approach. In this study we explore the possibility of extending drug discovery and cheminformatic approaches to the field of material science with the aim of a quantitative structure–property relationship elucidation that could lead to a fast and inexpensive in silico screening of new ruthenium sensitizers for third generation solar cells. Starting from the building of a database of already tested candidates used to train the predictive models, appropriate descriptors extracted from images of 3D molecular interaction fields (GRID/MIFs), as well as semi-empirical calculated descriptors, were chosen to describe the target structures. Then, structure–performance (J_sc, V_oc and PCE) models were built and analysed in order to elucidate structure–property relationships and interesting results were obtained. In particular, we were able to find the molecular descriptors that more contribute to enhance the performance investigated, thus finding directives for the design of potentially high-performing candidates. We also proposed an efficient correction of the experimental J_sc and V_oc based on the quantity of the LiI additive for electrolyte used to build the devices. In the early stage of this project, we demonstrated that molecular modelling methods could be successfully extended to the field of material science as alternative to the traditional expensive and time-consuming trial and error approach.

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Introduction

Research on renewable energies has become a key issue for sustainable development.

The increasing interest in the solar energy market has led to various generations of photovoltaic technologies.^1,2 The latest technology, so called third generation, includes, among others, the dye-sensitized solar cell (DSSC). DSSCs appear as one of the most promising technologies due to their low-cost, large-scale production (e.g. roll-to-roll, inkjet printing) and the appealing potential of merging the extreme versatility of thin film technology with the electronic features needed for the solar cell operation.^3–5 To this end, research is moving forward to solve the issue related to their relatively still low efficiencies and limited lifetime, if compared with the traditional silicon-based solar cells.

In DSSCs the light-to-electricity conversion is determined by a dye sensitizer, either an organic or metal–organic molecule, which absorbs the solar radiation and transfers the photoexcited electron to a wide band gap semiconductor electrode consisting of a TiO₂ network composed of nanometer-sized particles, while the concomitant hole is transferred to the redox electrolyte to generate carriers transport to the electrodes as shown in Scheme 1.⁶ The overall conversion efficiency (η) of the DSSC is determined by the short circuit current (J_sc, mA cm⁻²), the open circuit potential (V_oc, V), the fill factor (FF, adimensional parameter), and the power of the incident light (P_i, mW cm⁻²), namely:

η = (V_oc × J_sc × FF)/P_i (1)

Scheme 1 Operational principle of a DSSC based on I⁻/I₃⁻ redox shuttle.

It is well known that η markedly depends on the electronic and optical properties of the dye sensitizer. The dye is responsible for the light harvesting step and plays a crucial role in many of the key electron transfer processes occurring at the TiO₂/dye/electrolyte interface.^7,8 Therefore, by a rational design of the dye sensitizer we can tune its absorbing properties and control the electron transfer processes that ultimately would lead to optimization of the solar cell efficiency.

The sensitizer which had a key role in significantly advancing the DSSC technology was ruthenium(II) tetraprotonated[cis-(dithiocyanato)-Ru-bis(2,2′-bipyridine-4,4′-di-carboxylate)] complex (N3).⁹ Then, similar dye sensitizers with different ligands on the pyridine moiety anchoring the dyes on the surface of the TiO₂ nanoparticles have been proposed in order to elucidate structure–properties relationships and to achieve higher conversion efficiencies.^10–13

In this context, approaches that involve totally in silico screening of potential candidates could encourage researchers to substitute the traditional slow and expensive trial-and-error approach with a rational design of high-efficiency materials. Strategies combining computational chemistry methods (e.g. ab initio and semiempirical calculations) have already been explored to identify high performing materials for solar cells.^14–17 However, because of the complexity of the overall solar cell operation, these methods cannot straightforwardly predict relevant solar cell properties such as the final efficiency (η) in terms of molecular structure–properties relationships.

An alternative approach could be the use of chemometric tools to elucidate quantitative structure–property relationships (QSPR) and to build models that establish a mathematical relationship between a set of molecular descriptors characterizing the target molecule and a property of interest.¹⁸ This approach is, for instance, currently and successfully employed in the drug design field^19–21 and other statistical approaches have recently been used to rationalize experimental data and to optimize the fabrication process of Grätzel solar cells.^22–24

We propose in this study an innovative approach of extending the molecular modelling and drug design techniques to the photovoltaic material research field. By exploiting an existing data-set of photovoltaic efficiencies for ruthenium-based dyes, we find that combining calculated semiempirical descriptors (HOMO, LUMO, bandgap), chosen descriptors extracted from images of 3D molecular interaction fields (GRID/MIFs) and 2D structural descriptors also used in drug design we can have an exhaustive and target-oriented description of the dye molecule of interest and a Partial Least Squares PLS models can be built to both rationalize experimental data and to predict new compounds photovoltaic performance.

Methodology

For the purpose of efficiently describing entire dataset of molecules, we used VolSurf+, a completely automated procedure to convert 3D molecular fields into physicochemical relevant molecular descriptors that are computationally efficient and well suited for fast quantitative structure–property relationship studies.^25,26 The basic concept of VolSurf+ is to extract the information present in 3D molecular field maps into few quantitative numerical descriptors that are easy to understand and to interpret. VolSurf+ provides a set of 135 descriptors that are relevant for drug design applications, but some of them nonetheless can be useful in the description of OPV donor materials (Fig. 1).²⁷ In particular, the VolSurf+ chosen descriptors were (ESI 1.1†):

Fig. 1 Example of (a) shape and (b) hydrophobic (red) and hydrophilic (blue) molecular interaction fields (MIFs) for ligand 11.

(1) Structural descriptors: molecular weight, molecular volume, molecular surface, rugosity, molecular globularity, flexibility parameters, number of charged centers.

(2) Hydrophilic/hydrophobic and H-bond donor/acceptor regions descriptors: hydrophilic/hydrophobic volumes, capacity factors, interaction energy moments, polar and hydrophobic surface areas, H-bond donor/acceptor volumes, polarizability and dispersion forces.

(3) Mixed descriptors: critical packing, diffusivity, log P octanol/water and cyclohexane/water, percentage of unionised species at different pH.

As a fourth set of descriptors, we introduced electronic properties descriptors: the HOMO, LUMO, HOMO–LUMO gap and the molecular electrostatic potential. The electronic properties were computed by semiempirical methods with the Gaussian09 package.²⁸ To find the best compromise between reliability of results and time of computing, we screened different DFT models chemistry for geometry optimization (B3LYP,^29,30 AM1 (ref. 31)) and for excited states TDDFT calculation (B3LYP, MPW1K,³² ZINDO³³) and we chose the combination of semiempirical AM1 for ground-state geometries optimization and ZINDO for excitation energies calculation.

Combining such semi-empirical calculated descriptors, models predicting structure–photovoltaic property relationships (open circuit voltage, current intensity or power conversion efficiency) have been built. Considering the database of already tested ruthenium sensitizers collected by Yin et al.,³⁴ a subset of 73 dyes able to include significant structural and performance variation (the training set, ESI 1.2†) was chosen. The dyes mentioned in the paper are referred to with the same label used in ref. 33 and are reported in Table 1. Then, partial least squares algorithm³⁵ from the VolSurf+ package has been used to find the best molecular descriptors correlation with different performances of interest. The correlation coefficient R² (amount of performance “explained”, ranging from 0 to 1) and the cross validated correlation coefficient Q² (amount of performance “predicted”, ranging from 0 to 1) were then used to analyse the goodness and reliability of the obtained models. Weights plot (see e.g. Fig. 4) have been used to elucidate structure–property relationships as well as descriptors–performances correlations and interpreted in term of descriptors positioning (blue dots) in respect to the axis origin and the performance (yellow dot): descriptors important for the n^th latent variable fall far from the origin along the n^th axis in the plot, and descriptors more related to the performance lay near the performance itself (directly correlated) or in its symmetric to the origin space (inversely correlated).³⁶ Descriptors–performances correlation was also explicitated by reporting the Variables Importance on PLS (VIPs).³⁷

Table 1 Substituents fragments of the mentioned dyes, ref. 33

A: 4,4′-dicarboxylic acid-2,2′-bipyridine scaffold
1		2
3		4
5		6
23		25
26		27
30		32
39		46
53		54
56
B: 1,10-phenantroline scaffold
60	X^1 = H, X^2 = NH2, Y = Z = H	61	X^1 = X^2 = NH2, Y = Z = H
62	X^1 = H, X^2 = NO2, Y = Z = H	63	X^1 = X^2 = NO2, Y = Z = H
64		65

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Results and discussion

We applied the cheminformatic approach described above to build structure–property relationships models for a series of ruthenium sensitizers effectively employed in DSSCs. Various bipyridine-based ligands were chosen to define a training set of 73 heteroleptic ruthenium dyes (see methodology). The ruthenium scaffold is unchanged for all the molecules of the training set and only the 4,4′-dicarboxylic acid-2,2′-bipyridine (dcbpy, Fig. 2a) – or 1,10-phenanthroline (1,10-phen, Fig. 2b) – or dipyridylamine (DPA, Fig. 2c)-based ancillary ligands are systematically substituted.

Fig. 2 Molecular structures of investigated ruthenium photosensitizers with various (a) bipyridine- (b) phenanthroline- and (c) bipyridylamine-based ancillary ligands; example of electronic structure of investigated electronic scaffold.

Selected VolSurf+ molecular descriptors were used to describe the selected structures (see methodology). However, electronic properties cannot be neglected when considering this class of materials because it is well known that the HOMO, but in particular LUMO (Fig. 2d), positioning can dramatically affect the electron injection step.³⁸ Therefore, we added three semiempirical calculated descriptors (geometry optimization with AM1 followed by excited states calculation with ZINDO) in order to evaluate the HOMO, the LUMO and the bandgap.

Experimental J_sc, V_oc and PCE were simultaneously modelled with the PLS algorithm. The first step of the obtained model analysis was to look for evident outliers, because the presence of outliers generally means that some molecular descriptors are missing to properly catch their structure–property relationship, or that experimental data contain alteration in respect to the rest of the database. Two strong outliers (dye 60 and 63) could be detected on the bottom left part of the predicted versus experimental plot for the PCE model on the whole training set (Fig. 3a). To figure out why the model is unable to correctly catch structure–properties relationships for the outliers we looked at the dye structures and considered them with respect of the entire training set.

Fig. 3 Predicted versus experimental plot for PCE model for (a) the whole training set and (b) after the outliers exclusion (6, 65), coloured by PCE value: red-low PCE, blue-high PCE.

Fig. 4 Weights plot of the model after the outlier exclusion.

Ligands 60 and 63 belong to the same family of dyes 61 and 62: they all have at least one –NO₂ or –NH₂ on the 1,10-phenanthroline-based ancillary moiety (Table 1B) and they show the lowest performance of the series. It is known that –NH₂ groups on the dye structure lead to a decreasing of all the performances with respect to the same dye without this substituent.³⁹ At the same time, the –NO₂ moiety leads to a quenching of fluorescence in organometallic complexes, thus competing with charge injection and decreasing the solar cell operation.⁴⁰ Our model succeeds in reproducing the performance trend and, even if overestimated in case of dyes 60 and 63, predict their performances as the lowest of the series. Indeed, despite the fact that the two moieties are very different from a chemical point of view, they are projected in the same chemical space which means that our model have found as detrimental to the performance the presence of both –NO₂ or –NH₂ as it actually is.

A second group of outliers could be identified in dye 6 and 65 (Fig. 3a).

Ligand 6 differs from the analogues 1, 2, 3, 4, 5 for the alkyl chain length (Table 1A). Usually long alkyl chains on the dbpy ligand function as an electrical insulating barrier layer between the sensitizer dye and the hole-transporting medium, thereby reducing interfacial charge recombination losses and increasing the open circuit potential (V_oc) and short-circuit photocurrent (J_sc). As the PCE is increasing when elongating the chain length for dye 1, 2, 3, 4, 5, the linear regression algorithm used takes this feature as important for the PCE enhancement. However, dye 6 deviates from this trend because of the observed slower charge recombination between the electrolyte and the injected electron⁴¹ and the inhomogeneous dye-loading on the TiO₂ surface due to the folding of the long C18 chains reducing the recombination blocking effect of the alkyl chain spacer.⁴² In dye 65 (CYC-P2), as in the correctly estimated 64 (CYC-P1, Table 1B), the ancillary ligand is an alkylthiophene and they only differ for the conjugation length. In the more conjugated CYC-P2 the HOMO is localized on the ligand-P2, resulting in a weak oscillator strength of the MLCT transition that could be the major reason for its low cell efficiency.

All these considerations reveal why elongating the conjugation length of the ligand is not a must for improving the conversion efficiency of the ruthenium.⁴³ Indeed, all the evident outliers are overestimated because compared with the analogues in the training set, but it is reasonable to understand that a simple linear regression model could not catch cut-off and non-linear structure–property relationships. Therefore, we decided to exclude only the second two outliers from the training set, those related to clearly non linear structure–properties relationships. By excluding these molecules from the training set, both R² and Q² statistical parameters, thus the overall predictive ability, increase: the starting model for PCE showed, with two latent variables, R² and Q² value of 0.58 and 0.44, respectively (Fig. 3a). By excluding the outliers these values increase to 0.67 and 0.56, respectively (Fig. 3b and Table 2). The good R² and Q² values of the model indicate that we should be able to predict with confidence the performance of novel candidates: for instance, considering those among the best performing materials, dye 32 (oligophenylenevinylene based, Table 1A) is recalculated at a PCE of 11.2% as actually is, dyes 39 and 46 (hexylthio-terminal chain on the dbpy, Table 1A) are recomputed to be 11.0% and 10.0% when they are 11.5% and 11.2% PCE, respectively.

Table 2 PLS models performances on the initial dataset (73), after outliers exclusion (73 no out.) and after the proposed J_sc and V_oc correction (LiI corrected)

Performance modelled	73		73 no out.		LiI corrected
	R^2	Q^2	R^2	Q^2	R^2	Q^2
a Models built with two latent variables.b Models built with three latent variables.
Jsc	0.59^b	0.41^b	0.68^b	0.55^b	0.75^a	0.66^a
Voc	0.54^b	0.38^b	0.56^b	0.43^b	0.79^b	0.64^b
PCE	0.58^a	0.44^a	0.69^a	0.59^a	0.75^a	0.60^a

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In order to elucidate relationships within the investigated performances and in respect to the molecular descriptors to identify directives for the design of novel candidates, we interpreted the weights plot of the model (Fig. 4). The first observation which can be noted is the almost complete overlap between the J_sc and the PCE data set, which means that molecular features important for an increase in J_sc play a more important role than those for the V_oc to increase the PCE. However, the V_oc values do not lay distant, so we can define parameters that could simultaneously improve J_sc and V_oc, thus the final PCE. In particular, among the most inversely correlated descriptors we find the USR 6 (which accounts for the presence of NO₂ and NH₂), PHSAR/PSAR (considering the ratio between the polar surface area and the hydrophobic surface area and the ratio between the polar surface area and the surface, respectively) and WO4 and WO5 (H-bond donor volumes), while among the most directly correlated we found log P n-oct and log P c-Hex (the logarithm of the partition coefficient between 1-octanol and water and cyclohexane and water), log D5/log D10 (accounting for the log P at different pH), G (globularity) and FLEX_RB (the ratio between flexibility and the number of rotable bonds).

These findings indicate that promising candidates should not have NO₂ and NH₂ moieties, as expected; they should have small polar regions or polar regions balanced with hydrophobic regions and not have wide molecular regions able to generate attractive H-donor interactions. At the same time, they should be hydrophobic and possibly have a certain extent of globularity and flexibility but avoiding too many rotational bonds. Although these indications may seem difficult to understand, the advantage in using the employed molecular field interaction (MIF)-based descriptors is that they are immediately calculated as soon as we design the molecule of interest so that we can easily visualize and verify the previously suggested directives. Moreover, by projecting new candidates on the proposed models, a quick estimation on their performance can be obtained. For instance, a straightforward way to use this model is by plotting the LV1/LV2 plot, colour it by the performance value and colour the object by their performance value (Fig. 5a). New candidates can then be projected on this plot and the performance directly estimated from their positioning: if the projections lay on the blue area, they will be promising sensitizers and worth synthesizing and testing. Moreover, a cluster in the LV1/LV2 plot indicates that similar features associated with the modelled performance have been found in the dyes that are therefore grouped together. It is interesting to note that clear clusters can be identified on the obtained LV1/LV2 plot: dyes 25, 26, 27 are the only containing hydrophobic fluorous chains which allow these dyes to adsorb on the TiO₂ surface more strongly and provide higher dye density than alkyl chains, and 23 contains with Li⁺-coordinating oxyethylene side chains (Table 1A); sensitizers 60–63, as already pointed out, contain at least one NO₂ or NH₂; 53, 54, 56 contain carbazole substituted thiophene moieties and 30 and 32 both contain oligophenylenevinylene groups as an ancillary ligand (Table 1A) and all have a PCE in the range of 9–11% (Fig. 5b). The great advantage in using cheminformatic tools is that sometimes these feature-associations would not have been deducible only by looking at the structure. Therefore, when looking for new sensitizers and to gain insights into uncovered structure–property relationship we would save time and money by finding candidates that lay on the not-yet-explored chemical space.

Fig. 5 LV1/LV2 plots for the 73_no_out model, (a) background coloured by PCE (from red-low PCE- to blue-high PCE) and compounds by experimental PCE value: red PCE < 7, blue PCE > 7 and (b) with clusters highlighted.

Modelling of the effect of Li⁺ ions

Inspired by the known effect of the LiI electrolyte additive on the electric properties of the device, we also investigated this effect in modeling our target experimental data. In particular, it is known that by adding LiI, the V_oc tends to decrease while the J_sc increases due to a down-shift of the TiO₂ conduction band and induced shortest lifetime.^44,45

Considering what has already been observed experimentally on the entity of this effect, we suggest two corrections for the values of J_sc and V_oc as:

J_sc = J_[Li] − (1 + log[LiI]) (2)

V_oc = V_[Li] + 0.05 × (1/p[LiI] − 1) (3)

where [LiI] is the molar concentration of the LiI used to build the tested device and J_[LiI] and V_[LiI] are the measured short circuit current and open circuit voltage, respectively.

By applying the proposed correction to both J_sc and V_oc on the subset of the 54 dyes for which the LiI additive concentration used to build the solar device have also been reported (ESI 1.2†), we obtain models that show an improved correlation and successfully predict the trend of the investigated performances, confirming either the reliability of the proposed correction and the understanding of structure–property relationships by the model (Fig. 6). In particular, the models obtained by applying these considerations show R² and Q² values of 0.75 and 0.66 when correcting J_sc for the LiI effect, which further improve to 0.79 and 0.64 for V_oc considering two latent variable (Table 2, LiI corrected). In order to investigate the single performance contribution we then separated and analysed the coefficient of the linear regression model. In Fig. 7 we reported the coefficient of the linear regression with an absolute value higher than 0.3 for every performance.

Fig. 6 Experimental/recomputed plot for (a) J_sc, (b) V_oc and (c) PCE models corrected for the LiI concentration.

Fig. 7 Coefficients for (a) J_sc, (b) V_oc and (c) PCE models corrected for the LiI concentration.

For J_sc, the more negative coefficients are referred to descriptors of the presence of NH₂/NO₂, polar surface area, percentage of unionised species is calculated at pH 4 and H-bond donor volumes calculated at different energies (USR6, PSAR/PHSAR, %FU4, WO1–WO6, Fig. 7a). At the same time the more positive coefficients belong to descriptors of flexibility/rotable bond ratio, partition coefficient cyclohexane/water and unbalance between the centre of mass of a molecule and the barycentre of the hydrophobic/hydrophilic regions (FLEX_RB, log P c-Hex, ID/IW).

The PCE coefficients plot shows very similar correlation to J_sc: the only difference is that in the PCE the log P c-Hex descriptor plays a more important role. Also V_oc shows similar correlation but with higher coefficient. It is worth noting that among the directly correlated descriptors, the calculated LUMO (USR2), more than the HOMO (USR1), plays a crucial role (Fig. 7b), in fact having the highest positive contribution to the definition of the second latent variable. This is an important statement because, in agreement to what has already been reported, an increase of the LUMO energy of the sensitizers would increase the V_oc, while the HOMO plays a less significant role.⁴⁶ This last analysis reveals as important the same molecular descriptors discussed for the not [LiI]-corrected model, confirming the reliability of the already given design rules.

Conclusions

In this work we demonstrated that cheminformatic and molecular modelling techniques, successfully applied in drug design, could be in principle extended to the material design field.

This first attempt was focused on elucidating structure–property relationships on an extensively experimentally investigated class of ruthenium sensitizers for Grätzel third generation solar cells.

A combination of semi-empirical calculated, 2D structural descriptors and descriptors extracted from images of 3D molecular interaction fields (GRID/MIFs) have been used to describe the dyes. Then, cheminformatic algorithm PLS (Partial Least Squares) has been used to build structure-J_sc/-V_oc/-PCE models to find directives for designing promising candidates.

Moreover, for a subset of dyes we proposed a correction of the J_sc and V_oc based on the quantity of the LiI additive for electrolyte used to build the device.

The obtained models correctly predict the trend of performance for the training set and show encouraging value of R² and Q², therefore could be easily and quickly used to project new candidates as well as big database of molecules to have an estimation of the expected photovoltaic performances.

The goal of this totally in silico and high throughput approach is to offer novel instruments to both overcome the traditional trial-and-error approach and to look differently into experimental data by means of statistical and molecular modeling tools.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra01906k

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