Structure and Electronic Properties of Tio2 Nanoclusters and Dye–Nanocluster Systems Appropriate to Model Hybrid Photovoltaic Or Photocatalytic Applications

nanomaterials

Article Structure and Electronic Properties of TiO2 Nanoclusters and Dye–Nanocluster Systems Appropriate to Model Hybrid Photovoltaic or Photocatalytic Applications

Corneliu I. Oprea and Mihai A. Gîrt,u *

Department of Physics and Electronics, Ovidius University of Constant,a, 900527 Constant,a, Romania; [email protected] * Correspondence: [email protected]

Received: 30 January 2019; Accepted: 20 February 2019; Published: 4 March 2019

Abstract: We report the results of a computational study of TiO2 nanoclusters of various sizes as well as of complex systems with various molecules adsorbed onto the clusters to set the ground for the modeling of charge transfer processes in hybrid organic–inorganic photovoltaics or photocatalytic degradation of pollutants. Despite the large number of existing computational studies of TiO2 clusters and in spite of the higher computing power of the typical available hardware, allowing for calculations of larger systems, there are still studies that use cluster sizes that are too small and not appropriate to address particular problems or certain complex systems relevant in photovoltaic or photocatalytic applications. By means of density functional theory (DFT) calculations, we attempt to find acceptable minimal sizes of the TinO2n+2H4 (n = 14, 24, 34, 44, 54) nanoclusters in correlation with the size of the adsorbed molecule and the rigidity of the backbone of the molecule to model systems and interface processes that occur in hybrid photovoltaics and photocatalysis. We illustrate various adsorption cases with a small rigid molecule based on coumarin, a larger rigid oligomethine cyanine dye with indol groups, and the penicillin V antibiotic having a flexible backbone. We find that the use of the n = 14 cluster to describe adsorption leads to significant distortions of both the cluster and the molecule and to unusual tridentate binding configurations not seen for larger clusters. Moreover, the significantly weaker bonding as well as the differences in the density of states and in the optical spectra suggest that the n = 14 cluster is a poor choice for simulating the materials used in the practical applications envisaged here. As the n = 24 cluster has provided mixed results, we argue that cluster sizes larger than or equal to n = 34 are necessary to provide the reliability required by photovoltaic and photocatalytic applications. Furthermore, the tendency to saturate the key quantities of interest when moving from n = 44 to n = 54 suggests that the largest cluster may bring little improvement at a significantly higher computational cost.

Keywords: TiO2 clusters; electronic structure; density of states; organic dyes; dye-sensitized solar cells; penicillin; photocatalytic degradation; density functional theory

1. Introduction Nanostructured titanium dioxide is well-known for its numerous and diverse applications [1,2]. Examples of such new uses are in photocatalytic degradation of pollutants [2–4], in dye-sensitized solar cells, for energy conversion [5,6], in sensor electronics (for detection of gases, chemicals, or biological materials) [7], in coatings with antibacterial, anticorrosion, antifogging, or self-cleaning properties [8], in drug delivery [9], etc. Due to its abundance, nontoxicity, and high stability under a variety of conditions, titanium dioxide is likely to remain the material of choice for the near future [1].

Nanomaterials 2019, 9, 357; doi:10.3390/nano9030357 www.mdpi.com/journal/nanomaterials Nanomaterials 2019, 9, 357 2 of 31

The physical and chemical properties of TiO2 nanocrystals, dictated to a large extent by their electronic structure, are influenced by the size, shape, organization, and surface properties of the nanoparticles [10,11]. Consequently, understanding the structure-property correlations for TiO2 nanostructured materials is crucial for optimizing their use in practical applications; however, it remains a challenging task even after decades of extensive studies. Density functional theory (DFT) [12–14] has, over the past two decades, been the method of choice for most computational studies and quite successful at predicting TiO2 properties and explaining experimental data. Despite some inherent difficulties [14] and limitations [15], DFT methods have been able to treat molecular systems of relatively large sizes, of up to several hundreds of atoms, with moderate computational costs [16,17]. Computational studies have discussed the electronic properties of bulk TiO2 polymorphs [18], the structure and reactivity of anatase surfaces, and the modeling of bare and sensitized TiO2 nanoparticles [16,17]. It was found that rutile is thermodynamically the most stable bulk phase, whereas anatase is very common and stable in nanomaterials [17,19], displaying the highest photocatalytic activity [20,21]. As anatase is the most interesting phase of TiO2 for photovoltaic and photocatalytic applications, it will be the focus of our interest in the following. In photovoltaic and photocatalytic applications, the key role is played by some electronic properties. For instance, the energy level alignment between the conduction or valence band edges of TiO2 with the ground and excited states of the adsorbed molecule or with the redox level of the electrolyte determine whether a process can take place or not. To investigate the interaction of the individual dye with the TiO2 surface it is natural to use the cluster approach [22], whereas a periodic approach is to be preferred for studying interfaces of periodic crystalline materials, such as perovskites, on TiO2. Although the TiO2 nanoclusters have been extensively studied theoretically, as reported in recent reviews [16,17], there are still some different perspectives regarding the proper cluster size needed to tackle a particular problem or a certain complex system. For instance, Peng et al. [23] used only a simple TiO6H5 complex to model the anchoring of the dye to the oxide, with the belief that the simple complex would be ‘sufficient for the investigation of geometries, excitations, and electronic structures of the as-investigated dyes before and after binding’. However, they also note that, to study other TiO2 to dyes interactions, their model should be used with precautions [23]. Zhang et al. [24] used the same model, perpetuating the claim that it was suitable for the investigation of organic dyes bound to TiO2. Both studies could only consider bidentate chelate anchoring, in contrast with the experimental and computational data (reviewed in [25]), favoring the bidentate bridging binding of the carboxyl group to the oxide. Chen et al. [26] chose a Ti5O20H22 model system to describe the binding of several ruthenium sensitizers to the (101) anatase surface, invoking the size limitations needed to adopt a larger basis set. Although they admitted that various models, ranging from 5 to 20 Ti atoms, had been used, showing that the contributions to absorption were not equivalent [26], they went on and used the smallest cluster. There was no discussion of the impact of using one single layer of atoms and of a large number of H atoms to saturate the covalent bonds of O atoms. Wang et al. [27] used a (TiO2)6 cluster adopted in a previous work, which in fact proposed either a complex with only one Ti atom [24] or a cluster with five Ti atoms [26]. The work influenced Mendizabal et al. [28], who used a cluster with six Ti atoms, Ti6O21H18, cut from the anatase crystal and completed with H atoms to end dangling bonds, and Manzoor et al. [29], who made use of a (TiO2)6 cluster, claiming that it had been ‘extensively employed as a model semiconductor nanoparticle in several studies’. None of these three studies discussed the anchoring, although it has a major role in the charge injection from the dye into the semiconducting oxide. Analyzing the dependence of the electronic properties of the dye–oxide system on the (TiO2)n nanoclusters’ size, with n = 1, 2, 3, 6, 9, 15, and 38, Sánchez-de-Armas et al. [30] concluded that the minimal TiO4H4 model could reproduce the red shift of the optical spectra upon binding to TiO2. However, they recognized that the electronic structure of the system did change for larger systems, Nanomaterials 2019, 9, 357 3 of 31 with the orbital on the dye responsible for the excitation moving from below the conduction band edge for the minimal model to well into the conduction band for larger clusters. They concluded that the n = 6 model could provide only a semi-quantitative simulation of all the features in the electronic structure of the complex alizarin–TiO2 system [30]. The same authors argued in subsequent papers that the n = 9 cluster was suitable for larger coumarin-based dyes [31], whereas the n = 15 cluster had the minimal size to provide a complete picture in the case of the smaller catechol molecule binding to the substrate [32]. Early in-depth DFT computational studies of TiO2 clusters were performed by Persson et al. [33–35], whose strategy for n equal to 16 and 38 was to remove selected atoms from the (101) surfaces to keep the cluster neutral and stoichiometric. They also performed systematic simulations with the cluster size ranging from n = 16 to 68 [36,37] and from n = 32 to 122 [38,39]. Independently, Jug and co-workers [40] had a different approach, in which they saturated all peripheral oxygen atoms of the clusters with hydrogen atoms and all less than fivefold coordinated titanium atoms with OH groups. They studied (TiO2)n(H2O)m clusters, with n = 33–132 and m = 17–48 [40]. Starting from the original concept of Persson and co-workers [35,36], De Angelis et al. used a cluster with n = 38 [41–43] and with n = 82 [44,45]. Both clusters were shown to represent a good trade-off between accuracy and computational convenience and nicely reproduced the main electronic characteristics of TiO2 nanoparticles [41,43], the larger one being used to check the accuracy of the results [46,47]. Larger clusters have also been studied computationally. A study of clusters with n between 58 and 449 and different truncated-bipyramidal shapes chose to saturate the under-coordinated surface atoms by dissociated water molecules [48]. Later, De Angelis and co-workers examined clusters of n = 367 and 411 [49]. In the context of photovoltaic applications [50,51], we showed that, when dealing with small molecules, an n = 24 cluster provides a reasonable compromise between accuracy and computational costs [52–54]. In contrast, when studying the photocatalytic activity of TiO2 under UV and visible light [55], we examined the adsorption of various common antibiotics onto TiO2 nanoclusters, and found that the penicillin molecule is strongly distorted when binding to the substrate [56]. In summary, despite the large number of computational studies reported so far for TiO2 clusters, there are still studies that use cluster sizes that are not appropriate to address particular problems or certain complex systems. To find acceptable minimal sizes of the TiO2 nanoclusters, one should answer questions such as: Should the size of the cluster be chosen in correlation with the size of the adsorbed molecule? Does the rigidity of the backbone of the molecule play a role in choosing the appropriate cluster? Additional questions regard the way the anchoring of the adsorbed molecule affects the structure and the optical and charge transfer properties of the system. In an attempt to find answers to these questions, we report here computational studies of five different TinO2n+2H4 clusters, with n = 14, 24, 34, 44, and 54, to better understand size effects on optimized geometries and charge transfers. Our goal is to explore the structure, the anchoring, electronic spectrum, and optical properties, and the charge injection mechanisms from the adsorbed molecule to such titanium oxide clusters. We choose as adsorbed molecules simple and well-known systems, such as the coumarine-based dye, C343 [52], and penicillin V [56], as well as new molecules, such as OMCD1 [54,57].

2. Materials and Methods The titanium oxide clusters reported here, regardless of size, were initially cut from the experimental anatase structure [58] to model the (101) surface. In order to ensure the charge neutrality in the presence of under-coordinated Ti atoms [48,59,60], four hydrogen atoms were used to solve the dangling bonds of the oxygen atoms bound to the two Ti atoms at the periphery of the Ti14O30H4 cluster, or to the three-fold coordinated Ti atoms in the corners of Ti24O50H4, Ti34O70H4, Ti44O90H4, and Ti54O110H4 clusters. These structures, for the molecules investigated, C343, OMCD1, and penicillin V, both isolated and adsorbed on the cluster, were energy minimized by DFT [12–14] calculations using Nanomaterials 2019, 9, 357 4 of 31 the hybrid B3LYP exchange-correlation functional [61–63] and the split valence 3-21G(d) basis set with polarization functions [64,65]. For the density of electronic states, single-point calculations were performed using the hybrid B3LYP functional with the effective core potentials (ECPs) for Ti, P, S, and I atoms and double-ζ quality basis functions for all atoms via LANL2DZ [66] and accounting for aqueous solvent effects via the conductor-like polarizable continuum model (C-PCM) [67]. The cavity used in the C-PCM calculation was built from spheres centered on heavy nuclei based on the United Atom for Hartree–Fock procedure [68]. The lowest 50 singlet-to-singlet electronic transitions were calculated by Time-Dependent DFT (TD-DFT) [69]. Calculations were performed with the GAUSSIAN09 quantum chemistry package [70], whereas the projection of the density of states and the UV–Vis spectra on different system components were obtained with GaussSum [71].

3. Results The results of our computational study are reported in three subsections. The ﬁrst is dedicated to the clusters alone, and the following two to the clusters with adsorbed rigid and ﬂexible molecules, respectively. In each subsection, we start from the optimized geometry and then discuss the electronic spectrum.

3.1. Structure and Properties of TiO2 Nanoclusters

We performed geometry optimization of model clusters with a slight deviation from the TiO2 stoichiometry to avoid the problem of the surface states in the gap. We introduced H atoms or –OH groups to terminate the dangling bonds at the periphery, resulting in the Ti14O30H4, Ti24O50H4, Ti34O70H4, Ti44O90H4, and Ti54O110H4 model clusters (TinO2n+2H4). This approach resulted in compact structures with 4-, 5-, and 6-fold coordinated Ti ions, together with 2- and 3-fold coordinated oxygen atoms [48,52]. Following the geometry optimization, the structure is slightly distorted (see Figure1) to minimize the surface stresses. One way to examine the distortion of the lattice is by considering the average value of the Ti–O distance and its corresponding standard deviation, for the various clusters, and to compare them to the experimental values for the bulk [72], as shown in Table1. The average distance is consistently smaller than the experimental value of 1.950 Å, valid for the bulk oxide, which has two different Ti–O distances for axial and equatorial bonds. Important to note is that the average Ti–O distance increases with the cluster size, the distortion being stronger for smaller clusters, as expected. The lattice distortion is also revealed by the distribution of the Ti–O distances, which widens signiﬁcantly compared to the bulk. Moreover, the range for values of the Ti–O distances grows with cluster size. For smaller clusters, the surface-to-bulk ratio is larger, as shown below, and the distribution of distances narrower. As the cluster size increases, so does the difference between the surface and internal atoms, as the bonds are more distorted at the surface and less inside the cluster.

Table 1. Structural parameters describing the optimized geometry of TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54) performed by DFT at the B3LYP/3-21G(d) level in vacuum. The average Ti–O distance and its standard deviation, and the cluster width and length, deﬁned by the positions of the peripheral Ti or

O atoms and determined by calculations are compared to the experimental values of the bulk TiO2 [72]. All quantities are expressed in Å.

Parameter Ti14O30H4 Ti24O50H4 Ti34O70H4 Ti44O90H4 Ti54O110H4 TiO2 r(Ti–O) 1.834 1.876 1.889 1.896 1.901 1.950 σr(Ti–O) 0.074 0.100 0.100 0.103 0.105 0.022 Width (Ti . . . Ti) 12.45 12.18 11.87 11.94 12.00 12.04 Width (O . . . O) - 13.28 13.36 13.28 13.29 12.83 Length (Ti . . . Ti) 3.55 7.20 10.67 14.47 18.05 Length (O . . . O) 4.94 8.16 12.05 15.63 18.76 Length bulk (Ti ... Ti) 3.78 7.59 11.37 15.14 18.92 Nanomaterials 2019, 9, x FOR PEER REVIEW 4 of 30

For the density of electronic states, single-point calculations were performed using the hybrid B3LYP functional with the effective core potentials (ECPs) for Ti, P, S, and I atoms and double-ζ quality basis functions for all atoms via LANL2DZ [66] and accounting for aqueous solvent effects via the conductor-like polarizable continuum model (C-PCM) [67]. The cavity used in the C-PCM calculation was built from spheres centered on heavy nuclei based on the United Atom for Hartree– Fock procedure [68]. The lowest 50 singlet-to-singlet electronic transitions were calculated by Time- Dependent DFT (TD-DFT) [69]. Calculations were performed with the GAUSSIAN09 quantum chemistry package [70], whereas the projection of the density of states and the UV–Vis spectra on different system components were obtained with GaussSum [71].

3. Results The results of our computational study are reported in three subsections. The first is dedicated to the clusters alone, and the following two to the clusters with adsorbed rigid and flexible molecules, respectively. In each subsection, we start from the optimized geometry and then discuss the electronic spectrum.

3.1. Structure and Properties of TiO2 Nanoclusters

We performed geometry optimization of model clusters with a slight deviation from the TiO2 stoichiometry to avoid the problem of the surface states in the gap. We introduced H atoms or –OH groups to terminate the dangling bonds at the periphery, resulting in the Ti14O30H4, Ti24O50H4, Ti34O70H4, Ti44O90H4, and Ti54O110H4 model clusters (TinO2n+2H4). This approach resulted in compact structures with 4-, 5-, and 6-fold coordinated Ti ions, together with 2- and 3-fold coordinated oxygen atoms [48,52]. Following the geometry optimization, the structure is slightly distorted (see Figure 1) to minimize the surface stresses. One way to examine the distortion of the lattice is by considering the average value of the Ti–O distance and its corresponding standard deviation, for the various clusters, and to compare them to the experimental values for the bulk [72], as shown in Table 1. The average distance is consistently smaller than the experimental value of 1.950 Å, valid for the bulk oxide, which has two different Ti– O distances for axial and equatorial bonds. Important to note is that the average Ti–O distance increases with the cluster size, the distortion being stronger for smaller clusters, as expected. The lattice distortion is also revealed by the distribution of the Ti–O distances, which widens significantly compared to the bulk. Moreover, the range for values of the Ti–O distances grows with cluster size. For smaller clusters, the surface-to-bulk ratio is larger, as shown below, and the distribution of distances narrower. As the cluster size increases, so does the difference between the surface and Nanomaterials 2019, 9, 357 5 of 31 internal atoms, as the bonds are more distorted at the surface and less inside the cluster.

Figure 1. Figure 1. TopTop and and lateral lateral views views of of the the optimized optimized structures structures of theof the Ti14 TiO1430OH304H, Ti4, 24TiO2450OH50H4,4, Ti Ti3434OO7070HH44, Ti O H , and Ti O H nanoclusters (from left to right, respectively) modeling the anatase titania Ti4444O90H44, and Ti5454O110110H4 4nanoclusters (from left to right, respectively) modeling the anatase titania (101)(101) surface.surface. TheThe geometrygeometry optimizationoptimization waswas performedperformed by densitydensity functionalfunctional theorytheory (DFT)(DFT) atat thethe B3LYP/3-21G(d)B3LYP/3-21G(d) level. level. Atom Atom colors colors ar aree grey grey for for Ti, Ti, red red for for O, O,and and light light grey grey for forH. In H. the In thetop topview, view, the thewidths widths and and the thelengths lengths reported reported in Table in Table 1 are1 are meas measuredured horizontally horizontally and and vertically, vertically, respectively, respectively, as asshown shown in inFigure Figure S1 S1of ofthe the Supplementary Supplementary Materials. Materials.

The values presented in Table1 are consistent with the results of DFT calculations for stoichiometric (TiO2)n clusters, with n between 16 and 68, by other groups [36]. We also note that the values reported earlier [52,53] for n = 24, 34, 44 have slight deviations from those presented here due to the different DFT functionals and basis sets used. Another way to examine the distortion of the lattice is by looking at the length and width of the various clusters and comparing those values to the corresponding distances measured in the bulk, as displayed in Table1. The length and width of the various clusters were determined between peripheral Ti as well as O atoms. The width of the clusters was measured as the amount the distance between the peripheral Ti atoms ﬂuctuates from cluster to cluster with respect to the 12.04 Å value in the bulk. However, it can be observed that, despite the ﬂuctuations, the width approaches the bulk value as the cluster size increases, as one would expect. When measuring the width between peripheral O atoms, the values are consistently larger than the one for the bulk, the range of width values being narrower. In contrast to the width, the length of the clusters, measured between peripheral Ti atoms, is consistently smaller than the corresponding values for the bulk. In the case of the cluster lengths, the tendency is, again, to approach the values for the bulk when the cluster size increases. The lengths measured between peripheral O atoms also follow this tendency. Examining in parallel the width and the length of the clusters, it can be noticed that the two quantities have opposing trends, particularly when measuring the distances between peripheral O atoms. As the cluster size increases, the width approaches the bulk value from above, whereas the length tends to the bulk from below. This tendency is illustrated in the plot of the relative variation of the cluster width and length with respect to the bulk, displayed in Figure2. The dependence on n of the relative cluster lengths shows a tendency to converge towards the bulk value, as expected. The relative variations of the cluster length (which takes values over a larger range when measuring the distance between peripheral O atoms) varies in opposition with the cluster width. The distortion allows for larger distances along one direction and shorter distances along the perpendicular direction. Overall, the distortion of the clusters is extremely large for n = 14, below ±10% for n ≥24, and less than ±5% for n = 54. Earlier in this section, we stated that the distribution of Ti–O distances widens for larger n, when the surface-to-bulk ratio decreases. To support this statement, we present in Table2 the numbers of Ti and O atoms of various coordination as well as the surface-to-bulk ratio, determined as the fraction of under-coordinated atoms [36]. The number of bulk (6-fold coordinated) Ti atoms increases slowly with n, as the clusters studied here are intended for modeling interface phenomena in hybrid photovoltaic or photocatalytic applications. For such applications, the most important anatase surface Nanomaterials 2019, 9, 357 6 of 31

is (101) [21], already shown in Figure1. Consequently, the clusters modeled here are extended along Nanomaterials 2019, 9, x FOR PEER REVIEW 6 of 30 Nanomaterialsone direction 2019 of, 9 that, x FOR particular PEER REVIEW surface and not inside, towards the bulk. 6 of 30

Figure 2. The relative cluster width, (𝑤 −𝑤bulk)/𝑤bulk, and length, (𝑙 −𝑙bulk)/𝑙bulk, of TinO2n+2H4, FigureFigure 2. The relativerelative clustercluster width, width,( w(𝑤n − −𝑤wbulkbulk)/)/𝑤wbulkbulk,, andand length,length,( l(𝑙n −−𝑙lbulkbulk))/𝑙/lbulkbulk, ofof TiTinnOO22nn+2+2HH44, , nanoclusters (where n = 14, 24, 34, 44, 54) with respect to the corresponding value for the bulk anatase nanoclustersnanoclusters (where (where n = 14, 14, 24, 24, 34, 34, 44, 44, 54) 54) with with respect respect to to th thee corresponding corresponding value value for for the the bulk bulk anatase anatase TiO2 [72]. The distances are measured between peripheral Ti (grey) or O (red) atoms. TiOTiO2 [72].[72]. The The distances distances are are measured measured between between peripheral peripheral Ti Ti (grey) or O (red) atoms.

Table 2. The number of Ti or O atoms m-fold coordinated (mx) to O or Ti atoms, respectively, and the Table 2. The number of Ti or O atoms m-fold coordinated (mx) to O or Ti atoms, respectively, and the Tablesurface-to-bulk 2. The number ratio (s/b, of Ti dete or Ormined atoms asm-fold the fraction coordinated of under-coordinated (mx) to O or Ti atoms, atoms respectively, [36]). and the surface-to-bulksurface-to-bulk ratio ratio (s/b, (s/b, dete determinedrmined as as the the fraction fraction of of under-coordinated under-coordinated atoms atoms [36]) [36]).. Parameter Ti14O30H4 Ti24O50H4 Ti34O70H4 Ti44O90H4 Ti54O110H4 TiO2 (bulk) Parameter Ti14O30H4 Ti24O50H4 Ti34O70H4 Ti44O90H4 Ti54O110H4 TiO2 (bulk) ParameterTi, 6x Ti14O0 30H4 Ti24O2 50H4 Ti34O4 70H4 Ti44O6 90H4 Ti54O 8110 H4 TiOall 2Ti(Bulk) atoms Ti, 6x 0 2 4 6 8 all Ti atoms Ti,Ti, 5x 6x 60 14 2 22 4 30 6 38 8 all Ti atoms 0 Ti, 5x 6 14 22 30 38 0 Ti,Ti, 4x 5x 8 6 148 228 8 30 38 8 0 0 Ti,Ti, 4x 4x 8 8 8 8 8 8 8 8 8 8 0 0 O, 3x 6 18 30 42 54 all O atoms O,O, 3x 3x 6 6 18 18 30 30 42 42 54 54 all all OO atoms atoms O, 2x 20 28 36 44 52 0 O,O, 2x 2x 20 20 28 28 36 36 44 44 52 52 0 0 O,O, 1x 1x 4 4 4 4 4 4 4 4 0 0 O, 1x 4 4 4 4 4 0 s/bs/b (%) (%) 86.4 86.4 73.0 73.0 67.3 67.3 64.2 64.2 62.2 0 0 s/b (%) 86.4 73.0 67.3 64.2 62.2 0

The surface-to-bulk ratio is also displayed in Figure 3. It can be seen that the slope of the curve TheThe surface-to-bulk surface-to-bulk ratio ratio is is also also displayed displayed in in Figure Figure 33.. It cancan bebe seenseen thatthat thethe slopeslope ofof thethe curvecurve decreases with nn and there is a slight tendency of saturation for the particular type of surface cluster decreasesdecreases with n and therethere isis aa slightslight tendencytendency of of saturation saturation for for the the particular particular type type of of surface surface cluster cluster of of interest here. The small clusters have a large number of under-coordinated atoms, which are likely ofinterest interest here. here. The The small small clusters clusters have have a largea large number number of of under-coordinated under-coordinated atoms, atoms, which which are are likely likely to to affect the electronic and optical properties of the system. Although still far from the bulk, the toaffect affect the the electronic electronic and and optical optical properties properties of the of system. the system. Although Although still far still from far the from bulk, the the bulk, clusters the clustersn ≥ with n ≥44, displaying the levelling-off of the surface-to-bulk ratio, are likely to be better clusterswith with44, displaying n ≥44, displaying the levelling-off the levelling-off of the surface-to-bulk of the surface-to-bulk ratio, are likelyratio, toare be likely better to candidates be better candidates for describing interface phenomena. candidatesfor describing for interfacedescribing phenomena. interface phenomena.

Figure 3. The surface-to-bulk ratio (defined (deﬁned as the fractionfraction of under-coordinated atoms) dependence Figure 3. The surface-to-bulk ratio (defined as the fraction of under-coordinated atoms) dependence on the size ofof TiTinnO22n+2HH4 4clustersclusters (n (n == 14, 14, 24, 24, 34, 34, 44, 44, 54), 54), geometry geometry optimized by DFT/B3LYP/3-21G(d)DFT/B3LYP/3-21G(d) on the size of TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54), geometry optimized by DFT/B3LYP/3-21G(d) in vacuum. in vacuum. The next step from the analysis of the optimized geometry is to compare the various clusters in The next step from the analysis of the optimized geometry is to compare the various clusters in terms of energy. For that reason, we present in Figure 4 the binding energy per atom, determined as terms of energy. For that reason, we present in Figure 4 the binding energy per atom, determined as the difference between the energy of the TinO2n+2H4 cluster and the sum of the calculated energies of the difference between the energy of the TinO2n+2H4 cluster and the sum of the calculated energies of

Nanomaterials 2019, 9, 357 7 of 31

The next step from the analysis of the optimized geometry is to compare the various clusters in Nanomaterialsterms of energy. 2019, 9, For x FOR that PEER reason, REVIEW we present in Figure4 the binding energy per atom, determined7 of as 30 the difference between the energy of the TinO2n+2H4 cluster and the sum of the calculated energies theof the constituents constituents (i.e., (i.e., of ofthe the n Tin Ti atoms, atoms, 2n 2+2n+2 O Oatoms, atoms, and and four four H H atoms), atoms), all all divided divided by by the the total number of atoms (3 n + 6). 6).

Figure 4. Dependence of the binding energy perper atom,atom, [E[𝐸n−−𝑛𝐸nETiTi−−((22𝑛n + 2 +)) 2 E𝐸OO −−4𝐸4EH]/(3𝑛]/(3n + +6 ),6), on thethe size of TinnO2nn+2+2HH4 4clustersclusters (n ( n= =14, 14, 24, 24, 34, 34, 44, 44, 54), 54), calculated calculated by by B3LYP B3LYP functional functional and and 3-21G(d) 3-21G(d) or LANL2DZ basis sets in vacuum or in water solvent.

Regardless of the basis sets used and whether the calculation was performed in vacuum or in Regardless of the basis sets used and whether the calculation was performed in vacuum or in water solvent, the binding energy per atom increases with n. This result is expected, because the water solvent, the binding energy per atom increases with n. This result is expected, because the number of fully coordinated atoms increases with the cluster size and, therefore, the binding becomes number of fully coordinated atoms increases with the cluster size and, therefore, the binding becomes stronger for the larger clusters. Important Important to notice is also also the the fact fact that that the the value value of of the the binding binding energy energy n n ≥ per atom is levelling-off at high n, with less thanthan 0.040.04 eVeV differencesdifferences forfor n ≥ 44.44. For each cluster, we report in Table 3 3 the the edgeedge ofof thethe valencevalence band,band, consideredconsidered atat thethe energyenergy ofof thethe highest highest occupied occupied molecular molecular orbital orbital (HOMO), (HOMO), and and the the edge edge of of the the conduction conduction band, band, at at the the lowest unoccupied molecular molecular orbital orbital (LUMO). (LUMO). The The geometry geometry relaxation relaxation leads leads to to band band gaps gaps of of 4.38–5.15 4.38–5.15 eV, eV, values that are sensitive to the DFT functional andand basis set used. For For that reason, the band gaps n presented here have slight deviations from those reported earlierearlier forfor n == 24, 34, 44 [[52,53].52,53]. Overall, the values obtained for the band gap are larger than the experimental value of ~3.2 eV Table 3. Valence (EVB) and conduction (ECB) band edges, the band gap (ECB − EVB), the optical gap, and for anatasethe conduction titania [50,73]. band oxidation The TiO potentials2 band gap (CBOP) has (inbeen eV), overestimated calculated for clusters by many of variouscalculations sizes, usingof model clusters,DFT particularly and Time-Dependent when using DFT (TD-DFT), hybrid DFT the B3LYPfunctionals functional, [17,74]. LANL2DZ For instance, basis sets, for and the water (TiO solvent.2)38 cluster, values of 3.5 eV were obtained from configuration interaction computations using about 3000 E E E − E E CBOP configurationsCluster [33], whereas VBa band gapCB of 3.78 eVCB was VBdetermined 0-0using DFT methods [41]. It has to be noticed, however, thatHOMO the configurationLUMO interactionHL Gap (CI) calculationOptical Gap was forEVB a structure+ E0-0 cut from the bulk, withTi14 Ono30 Hgeometry4 −8.52 optimization−3.37 [33], and 5.15 that the DFT 4.23calculation was−4.29 performed on a − − − structure optimizedTi24O50H4 by Car–Parrinello7.97 3.53 molecular 4.44dynamics [41], 3.66 and not by4.31 DFT, as in our Ti34O70H4 −8.21 −3.70 4.52 3.81 −4.41 calculation. Also, the two missing O atoms in the n = 38 model are likely to affect the valence band Ti44O90H4 −8.17 −3.77 4.40 3.75 −4.42 states, as weTi shall54O110 demonstrateH4 −8.17 later in −this3.79 section, possibly 4.38 leading 3.75 to a smaller −calculated4.42 gap. HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital. Table 3. Valence (EVB) and conduction (ECB) band edges, the band gap (ECB − EVB), the optical gap, and theOverall, conduction the values band oxidation obtained potentials for theband (CBOP) gap (in are eV), larger calculated than for the clusters experimental of various value sizes, ofusing ~3.2 eV DFT and Time-Dependent DFT (TD-DFT), the B3LYP functional, LANL2DZ basis sets, and water solvent. for anatase titania [50,73]. The TiO2 band gap has been overestimated by many calculations of model clusters, particularlyE whenVB using hybridECB DFTECB functionals − EVB [17,74E0-0]. For instance,CBOP for the (TiO ) Cluster 2 38 cluster, values of 3.5 eV wereHOMO obtained fromLUMO configuration HL gap interaction Optical computations gap EVB + using E0-0 about 3000 configurationsTi14 [O3330],H whereas4 −8.52 a band gap− of3.37 3.78 eV was5.15 determined using 4.23 DFT methods−4.29 [41]. It has to be noticed, however,Ti24O50H4 that the−7.97 configuration −3.53 interaction 4.44 (CI) calculation 3.66 was for a structure−4.31 cut from the Ti34O70H4 −8.21 −3.70 4.52 3.81 −4.41 bulk, with no geometry optimization [33], and that the DFT calculation was performed on a structure Ti44O90H4 −8.17 −3.77 4.40 3.75 −4.42 Ti54O110H4 −8.17 −3.79 4.38 3.75 −4.42 HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital.

Nanomaterials 2019, 9, 357 8 of 31 optimized by Car–Parrinello molecular dynamics [41], and not by DFT, as in our calculation. Also, n theNanomaterials two missing 2019, 9 O, x FOR atoms PEER in REVIEW the = 38 model are likely to affect the valence band states, as we8 shall of 30 demonstrate later in this section, possibly leading to a smaller calculated gap. The values presented in Table3 3 are, are, overall, overall, consistentconsistent withwith thethe resultsresults of of DFT DFT calculations calculations forfor stoichiometric (TiO 2))nn clusters,clusters, with with nn betweenbetween 16 16 and and 60, 60, for for which which the the band band gap gap was was determined determined to tobe bebetween between 4.55 4.55 and and 4.94 4.94 eV, eV, with with an an anomalous anomalous value value of of 4.81 4.81 eV eV for for nn == 68 68 [36]. [36]. We We note that the values reportedreported byby us us earlier earlier [52 [52,53],53] for forn =n 24,= 24, 34, 34, 44 have44 have slight slight deviations deviations from from those those presented presented here, duehere, to due the to different the different DFT functionals DFT functionals and basis and setsbasis used. sets used. Our calculations show that the band gap is smallest,smallest, closest to the experimentalexperimental value, for the largest cluster. The gap does not vary monotonically, likelylikely becausebecause of the particular symmetry of the n = 24 cluster. The density of states displayed in Fi Figuregure 55 reﬂectsreflects thethe decreasedecrease inin thethe bandband gapgap withwith increasing clustercluster sizesize andand revealsreveals thethe anomalyanomaly forforn n == 24. It can be seen that the peak located at about −88 eV, eV, which which consists of the top two states inin thethe valencevalence bandband (of(of −−7.97 and −8.028.02 eV, eV, to to be be precise), precise), is relatively distanceddistanced fromfrom thethe adjacentadjacent lowerlower energyenergy states,states, situatedsituated atat −−8.258.25 eV. eV. This anomaly comes from thethe strongerstronger electron electron localization localization on on the the two tw centralo central oxygen oxygen atoms, atoms, which which raises raises the the energy energy of the of orbitalsthe orbitals by about by about 0.25 eV 0.25 away eV fromaway the from next the lower next states. lower For states. the other For clusters,the other the clusters, extra localization the extra doeslocalization not take does place not and take the place four and highest the four states highes in thet states valence in the band valence are all band grouped are all within grouped a narrow within 0.035a narrow eV energy 0.035 eV interval. energy interval.

Figure 5.5. The densitydensity ofof statesstates (in(in arbitraryarbitrary units)units) ofof thethe TiTinnOO22nn+2+2HH44 clustersclusters ( (nn == 14, 14, 24, 24, 34, 34, 44, 54), calculated atat thethe DFT/B3LYP/LANL2DZDFT/B3LYP/LANL2DZ level level in in wate waterr solvent. solvent. Energy Energy levels levels were convoluted with Gaussian distributions with a full width atat halfhalf maximummaximum (FWHM)(FWHM) ofof 0.10.1 eV.eV.

To betterbetter understand understand the the nature nature of of the the states states in thein the valence valence and and conduction conduction band band we examine we examine more closelymore closely the density the density of the of state the forstate the for cluster the cluster with n with= 54, n as= 54, displayed as displayed in Figure in Figure6. The 6. valence The valence band isband dominated is dominated by the contributionby the contribution of the O of atoms. the O In atoms. contrast, In thecontrast, key contribution the key contribution in the conduction in the bandconduction comes band from comes the Ti atoms,from the the Ti participation atoms, the participation of the oxygen of atoms the oxygen being small.atoms Worthbeing notingsmall. Worth is that thenoting introduction is that the of introduction the hydrogen of atoms,the hydrogen which endatoms, four which dangling end bonds,four dangling has a minor bonds, contribution has a minor to thecontribution overall density to the ofoverall states density but plays of states an important but plays role an inimportant removing role from in theremoving gap the from states the localized gap the atstates the surface.localized at the surface. The density of states curves indicate that the relative weight of the O and Ti atoms in the key molecular orbitals is consistent with the contribution of those atoms for the entire corresponding bands. Specifically, the peak at the valence band edge (the HOMO located just below −8 eV) shows a strong O contribution, whereas the peak at the conduction band edge (the LUMO situated above −4 eV) has a significant Ti weight. To visually illustrate the nature of the key orbitals discussed above, we display in Figure7 the electronic density of the highest occupied molecular orbitals and the lowest unoccupied molecular orbitals for three of the five clusters. The two orbitals are especially important as they describe the states at the edges of the valence and conduction bands, respectively.

Figure 6. Total density of states (DoS) of the Ti54O110H4 cluster, calculated at the DFT/B3LYP/LANL2DZ level in water, showing, separately, the contribution of Ti atoms, O atoms, and –OH groups. Energy levels were convoluted with Gaussian distributions with an FWHM of 0.1 eV.

Nanomaterials 2019, 9, x FOR PEER REVIEW 8 of 30

The values presented in Table 3 are, overall, consistent with the results of DFT calculations for stoichiometric (TiO2)n clusters, with n between 16 and 60, for which the band gap was determined to be between 4.55 and 4.94 eV, with an anomalous value of 4.81 eV for n = 68 [36]. We note that the values reported by us earlier [52,53] for n = 24, 34, 44 have slight deviations from those presented here, due to the different DFT functionals and basis sets used. Our calculations show that the band gap is smallest, closest to the experimental value, for the largest cluster. The gap does not vary monotonically, likely because of the particular symmetry of the n = 24 cluster. The density of states displayed in Figure 5 reflects the decrease in the band gap with increasing cluster size and reveals the anomaly for n = 24. It can be seen that the peak located at about −8 eV, which consists of the top two states in the valence band (of −7.97 and −8.02 eV, to be precise), is relatively distanced from the adjacent lower energy states, situated at −8.25 eV. This anomaly comes from the stronger electron localization on the two central oxygen atoms, which raises the energy of the orbitals by about 0.25 eV away from the next lower states. For the other clusters, the extra localization does not take place and the four highest states in the valence band are all grouped within a narrow 0.035 eV energy interval.

Figure 5. The density of states (in arbitrary units) of the TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54), calculated at the DFT/B3LYP/LANL2DZ level in water solvent. Energy levels were convoluted with Gaussian distributions with a full width at half maximum (FWHM) of 0.1 eV.

To better understand the nature of the states in the valence and conduction band we examine more closely the density of the state for the cluster with n = 54, as displayed in Figure 6. The valence band is dominated by the contribution of the O atoms. In contrast, the key contribution in the conduction band comes from the Ti atoms, the participation of the oxygen atoms being small. Worth noting is that the introduction of the hydrogen atoms, which end four dangling bonds, has a minor contribution to the overall density of states but plays an important role in removing from the gap the Nanomaterials 2019, 9, 357 9 of 31 states localized at the surface.

Nanomaterials 2019, 9, x FOR PEER REVIEW 9 of 30

The density of states curves indicate that the relative weight of the O and Ti atoms in the key molecular orbitals is consistent with the contribution of those atoms for the entire corresponding bands. Specifically, the peak at the valence band edge (the HOMO located just below −8 eV) shows a strong O contribution, whereas the peak at the conduction band edge (the LUMO situated above −4 eV) has a significant Ti weight. To visually illustrate the nature of the key orbitals discussed above, we display in Figure 7 the electronic density of the highest occupied molecular orbitals and the lowest unoccupied molecular orbitals for three of the five clusters. The two orbitals are especially important as they describe the states at the edges of the valence and conduction bands, respectively.

Upon examination of the HOMOs, we observed the two lobes of the p-type orbital, localized Figureespecially 6. Total on O density atoms, ofof and statesstates colored (DoS)(DoS) red of of the thein Ti FigureTi5454OO110110 7.H 4Moreover, cluster,cluster, calculated comparing atat thethe the DFT/B3LYP/LANL2DZDFT/B3LYP/LANL2DZ HOMOs of the three levelclusters, inin water,water, we note showing, showing, the high separately, separately, electron the thedensity contribution contributi strongly ofon Ti of atoms,localized Ti atoms, O atoms, on O atoms,the and two –OHand central –OH groups. groups.oxygen Energy Energyatoms, levels wereexplaininglevels convoluted were the convoluted higher with Gaussianenergy with Gaussian anomaly distributions distributionsmentioned with an abov with FWHMe. anFor FWHM of the 0.1 other eV. of 0.1clusters, eV. the electron density is delocalized, with a significant contribution towards the periphery of the structure.

3 Figure 7. Isodensity surfaces (0.03 e/bohr ) of the key molecular orbitals of TinO2n+2H4 clusters Figure 7. Isodensity surfaces (0.03 e/bohr3) of the key molecular orbitals of TinO2n+2H4 clusters (n = 14, (n = 14,24, 24,54, 54,fromfrom left leftto right, to right, respectively), respectively), calculated calculated by DFT byat the DFT B3LYP/LANL2DZ at the B3LYP/LANL2DZ level in water level in watersolvent. solvent. The The first ﬁrst two tworows rowsdisplay display the top and the a top perspective and a perspective view of the LUMOs, view of whereas the LUMOs, the bottom whereas two the bottomrows two show rows the showtop and the a perspective top and a view perspective of the HOMOs. view Atom of the colors: HOMOs. Ti, grey; Atom O, red; colors: and H, Ti, light grey; grey. O, red; and H, light grey.

Upon examination of the HOMOs, we observed the two lobes of the p-type orbital, localized especially on O atoms, and colored red in Figure7. Moreover, comparing the HOMOs of the three Nanomaterials 2019, 9, 357 10 of 31 clusters, we note the high electron density strongly localized on the two central oxygen atoms, explaining the higher energy anomaly mentioned above. For the other clusters, the electron density is delocalized, with a signiﬁcant contribution towards the periphery of the structure. In contrast, the LUMOs show the four lobes characteristic for d-type orbitals of Ti atoms (colored grey in Figure7). For these states, the electron density is more substantial in the central part of the structure. At the end of this section it has to be noted that, although the HOMO–LUMO gap mimics the band gap of the semiconducting oxide, a better approximation for the gap energy, particularly when analyzing the optical properties of the system, is the electronic transition energy [17,46]. The former is determined by DFT calculations at the end of the geometry optimization, whereas the latter is computed by means of TD-DFT methods. The optical gap is reported in Table3. The values obtained for the optical gap range from 3.66 to 4.23 eV, systematically smaller than those for the HOMO–LUMO gap and closer to the experimental value of ∼3.4 eV, obtained with optical absorption measurements at low temperatures [75]. Although, overall, the optical gap decreases with increasing cluster size, the variation is not monotonic, the n = 24 anomaly being present. The values presented in Table3 are, overall, consistent with the results of DFT calculations for stoichiometric (TiO2)n clusters, with n between 16 and 46, for which the TD-DFT gap was between 3.97 and 4.09 eV [36]. Adding to the HOMO energy, obtained by DFT, the energy of the optical transition, determined by TD-DFT, we can estimate the conduction band oxidation potentials (CBOP) (see Table3). This energy is important for applications, to analyze the charge transfer of the adsorbed molecule to the TiO2 nanocluster [50,51]. The transfer can occur only if there is a proper energy level alignment, such that the excited state of the molecule lies higher than the conduction band’s oxidation potential [17,46].

3.2. Structure and Properties of TiO2 Nanoclusters with Rigid Adsorbed Molecules

In this section, we report results of calculations involving models of TiO2 nanoclusters and two adsorbed molecules of various sizes with a rigid backbone. In each case, we start from the optimized geometry, analyzing the binding to the cluster, and then discuss the electronic spectrum. The anchoring modes of the adsorbed molecules to the TiO2 surface are of crucial importance, the bonding type playing an important role in the electron injection [50,51].

3.2.1. Structure and Properties of TiO2 Nanoclusters with a Small Rigid Adsorbed Molecule To better understand the role of the cluster size in studying the binding of a small rigid molecule to the TiO2 nanocluster, we chose first the two smallest clusters (n = 14 and 24) and a small molecule with a rigid backbone, a coumarin-based molecule: 11-oxo-2,3,6,7-tetrahydro-1H,5H,11H-pyrano[2,3- f]pyrido[3,2,1-ij]quinoline-10-carboxylic acid (C343). The optimized geometry of C343 has been reported previously by us and other authors [52,76] and, therefore, here we only state that the structures are in agreement with the ones already presented. Earlier studies have shown that for the organic dyes bearing a carboxylic acid as the anchoring group, the preferred adsorption mode is bidentate bridging, with one proton transferred to a nearby surface oxygen [25,47,77]. Here we analyze the bidentate bridge anchoring of C343 to the model clusters, with two different binding sites in the case of n = 14 and one binding configuration for n = 24. The optimized geometries are displayed in Figure8 and some of the most important structural parameters are presented in Table4. The two anchoring configurations chosen for the n = 14 cluster connect the oxygen atoms of the adsorbed molecule to two neighboring Ti atoms on the same (101) surface of anatase titania. When the geometry optimization starts with the plane of the C343 molecule roughly transverse to the cluster’s width, the final structure exhibits the typical bidentate bridge binding, but with the adsorbed molecule strongly bent towards the cluster (left column of Figure8). If the optimization is initiated with the Nanomaterials 2019, 9, 357 11 of 31

C343 molecule oriented roughly along the cluster’s width, the resulting structure is highly unusual, with three Ti–O bonds (middle column of Figure8). Comparing geometry parameters for the isolated cluster and the two cluster-molecule systems (Table4), we note that both the average Ti–O distances and the standard deviation of those distances increase significantly, particularly for the three-bonds case. The n = 14 cluster is significantly distorted in both cases, as also shown by the cluster sizes. For the two-bonds system, both the width and the length of the cluster decrease, whereas for the three-bonds model the width decreases but the length increases. Table4 also presents the Ti–O distances at the binding sites. The values are significantly larger than the average distance of 1.950 Å in the bulk anatase titania, suggesting that the bonds are weak, particularly for the smallest cluster. The n = 14 system with two bonds has highly disproportionate NanomaterialsTi–O distances 2019, 9 (differences, x FOR PEER REVIEW of 0.15 Å), whereas the three-bonds structure has more even distances11 of 30 (differences to within 0.06 Å).

Figure 8. Top (ﬁrst row), side (second row), and front (third row) views of the optimized structures Figure 8. Top (first row), side (second row), and front (third row) views of the optimized structures of the C343 dye molecule adsorbed on the Ti14O30H4 cluster (left and middle column) and on the of the C343 dye molecule adsorbed on the Ti14O30H4 cluster (left and middle column) and on the Ti24O50H4 cluster (right column). Calculations performed by DFT at the B3LYP/3-21G(d) level in Ti24O50H4 cluster (right column). Calculations performed by DFT at the B3LYP/3-21G(d) level in vacuum. The side and front views also show the three neighbouring Ti atoms to which the molecule vacuum. The side and front views also show the three neighbouring Ti atoms to which the molecule can bind. Atom colors are: C, grey; O, red; N, blue; and H, light grey. can bind. Atom colors are: C, grey; O, red; N, blue; and H, light grey.

Comparing geometry parameters for the isolated cluster and the two cluster-molecule systems (Table 4), we note that both the average Ti–O distances and the standard deviation of those distances increase significantly, particularly for the three-bonds case. The n = 14 cluster is significantly distorted in both cases, as also shown by the cluster sizes. For the two-bonds system, both the width and the length of the cluster decrease, whereas for the three-bonds model the width decreases but the length increases. Table 4 also presents the Ti–O distances at the binding sites. The values are significantly larger than the average distance of 1.950 Å in the bulk anatase titania, suggesting that the bonds are weak, particularly for the smallest cluster. The n = 14 system with two bonds has highly disproportionate Ti–O distances (differences of 0.15 Å), whereas the three-bonds structure has more even distances (differences to within 0.06 Å).

Nanomaterials 2019, 9, 357 12 of 31

Table 4. The structural parameters of the model system consisting of the TinO2n+2H4 clusters (n = 14, 24) with an adsorbed C343 molecule, obtained after geometry optimization by DFT with the B3LYP functional, in vacuum. The basis sets used were 3-21G(d) for n = 14 and 3-21G(d), LANL2DZ, and a combination of LANL2DZ on Ti and 6-31G(d,p) on O, C, N, and H atoms (DZ&6-31G) for n = 24. Geometrical parameters describing the adsorption modes: bond lengths (in Å), torsion angle of the carboxyl group relative to the coumarin plane, and dihedral angle deﬁned by the coumarin plane and the plane of the three neighbour Ti atoms (both in deg).

C343 on Ti O H C343 on Ti O H C343 on Ti O H Parameter 14 30 4 14 30 4 24 50 4 (Two Bonds) (Three Bonds) 3-21G(d) LANL2DZ DZ&6-31G † r(Ti–O) 1.852 1.880 1.887 1.891 1.891 σr(Ti–O) 0.090 0.119 0.108 0.121 0.116 Width (Ti . . . Ti) 12.41 12.07 11.98 12.44 12.23 Width (O . . . O) - - 13.13 13.41 13.49 Length (Ti . . . Ti) 3.48 3.75 7.25 7.26 7.30 Length (O . . . O) 5.09 5.64 8.28 8.36 8.35 r(O1–Ti) 2.128 2.068 1.972 1.951 1.956 r(O2–Ti) 1.976 2.039 1.999 2.053 2.058 r(O3–Ti) - 2.096 - - - <(O–C–C–C) 2.0 31.8 −4.3 0.2 −1.3 <(C343;3Ti) 8.3 52.2 81.7 88.8 85.8 † combination of LANL2DZ on Ti and 6-31G(d,p) on O, C, N, and H atoms.

On the other hand, the two-bonds structure has a smaller torsion angle of the carboxyl group relative to the coumarin plane, compared to the three-bonds system, a fact easily seen in Figure8. This result suggests that the price paid for more even binding distances is a twisted anchor. Further, examining the dihedral angle between the molecule and the Ti atoms in the cluster, we note that the two-bonds system has the C343 dye highly tilted, almost parallel with the cluster. Of the three models analyzed, the molecule is most upright for the n = 24 cluster. In contrast to the smallest cluster, the n = 24 system is also less distorted, a fact revealed by all key geometry parameters, starting with the average Ti–O distance and its standard deviation and continuing with the width and the length of the cluster. Moreover, the Ti–O distances at the anchoring sites differ by less than 0.03 Å, suggesting a signiﬁcantly smaller distortion compared to the n = 14 cluster. Also, the torsion angle of the carboxyl group relative to the coumarin plane is relatively small. To evaluate the role of the basis set on the structural parameters resulting from DFT calculations for the C343-Ti24O50H4 system we also used, aside from 3-21G(d), larger basis sets, LANL2DZ and a combination (DZ&6-31G) consisting of LANL2DZ on Ti and 6-31G(d,p) [78] on O, C, N, and H atoms. Table4 shows that the average Ti–O distance increases with larger basis sets, getting closer to the value for the bulk. The difference in the length of the Ti–O bond is less than 0.22%, leading to increases in the width and the length of the cluster of about 2.8%. Puzzled by the unusual bending, by the triple binding, and by the high distortion of the anchoring distances, we explored the energetics of the three systems. Table5 presents the adsorption energy, determined as the difference between the calculated energy of the constituents (i.e., the oxide cluster and the C343 molecule) and the energy of the system. Binding in the two-bonds C343-Ti14O30H4 system is consistently the weakest, regardless of the basis set used or whether the calculation was in vacuum or in water solvent. Moreover, in one of the calculations the value is positive, indicating that the system would be better off separated. The three-bonds C343-Ti14O30H4 structure is also relatively weakly bound compared to C343-Ti24O50H4, which has the most stable structure of the three. Nanomaterials 2019, 9, x FOR PEER REVIEW 13 of 30

Table 5. The adsorption energy of the C343-TinO2n+2H4 systems (n = 14, 24), defined as the difference between the calculated energy of the bound system and the sum of the energies for the separated constituents (isolated Ti2nOn+2H4 and C343), (in eV), calculated by the DFT/B3LYP method with 3- 21G(d) or LANL2DZ basis sets, in vacuum or in water solvent.

C343-Ti14O30H4, C343-Ti14O30H4, C343-Ti24O50H4 Method two-bonds three-bonds NanomaterialsB3LYP/3-21G(d)2019, 9, 357 vacuum −2.473 −3.075 −3.254 13 of 31 B3LYP/3-21G(d) solvent −1.961 −2.574 −2.835 B3LYP/LANL2DZ solvent 0.429 −0.242 −1.188 Table 5. The adsorption energy of the C343-TinO2n+2H4 systems (n = 14, 24), deﬁned as the difference between the calculated energy of the bound system and the sum of the energies for the separated The contribution of the C343 molecule to the density of states is more significant in the valence constituents (isolated Ti2nOn+2H4 and C343), (in eV), calculated by the DFT/B3LYP method with band3-21G(d) and particularly or LANL2DZ in the basis gap, sets, where in vacuum the HOMO or in water of the solvent. complex system is located. The information provided by the density of state curves in Figure 9 is completed by the electron densities displayed in Figure 10 for the key molecular orbitals.C343-Ti For14O 30instance,H4, forC343-Ti all three14O30 systems,H4, the HOMO level clearly Method C343-Ti24O50H4 has a dominant contribution from theTwo-Bonds adsorbed molecule,Three-Bonds the orbital having a π nature due to the conjugatedB3LYP/3-21G(d) character of vacuum the organic dye.−2.473 In contrast, the−3.075 LUMOs have the−3.254 most significant − − − contributionB3LYP/3-21G(d) from the oxide, solvent the nature of1.961 the molecular orbital2.574 being determined2.835 by the d atomic B3LYP/LANL2DZ 0.429 −0.242 −1.188 orbitals of Ti. However,solvent neither the HOMOs nor the LUMOs are pure. A small weight from the cluster in the HOMOs and from the molecule in the LUMOs (contributions seen both in the density of state curves and in the electron density plots) make possible optical transitions in the visible region, as we Next, we examine the density of states for the three model systems considered in this section and shall see in the electronic spectra. compare them to the corresponding curves for the bare TinO2n+2H4 (n = 14, 24) clusters (Figure9).

(a) (b) (c)

Figure 9. The density of states (DoS) of the systems consisting of the C343 molecule adsorbed on the Figure 9. The density of states (DoS) of the systems consisting of the C343 molecule adsorbed on the Ti14O30H4 cluster via (a) two or (b) three O–Ti bonds and on the Ti24O50H4 cluster (c). Dotted curves Ti14O30H4 cluster via (a) two or (b) three O–Ti bonds and on the Ti24O50H4 cluster (c). Dotted curves represent the density of states of the corresponding bare TinO2n+2H4 clusters (n = 14, 24). Calculations represent the density of states of the corresponding bare TinO2n+2H4 clusters (n = 14, 24). Calculations were were performed by DFT at the B3LYP/LANL2DZ level in water solvent. Energy levels were convoluted performed by DFT at the B3LYP/LANL2DZ level in water solvent. Energy levels were convoluted with with Gaussian distributions with of 0.1 eV full width at half maximum. Gaussian distributions with of 0.1 eV full width at half maximum. The contribution of the C343 molecule to the density of states is more signiﬁcant in the valence To examine the influence of the molecule adsorbed on the cluster on the density of states of the band and particularly in the gap, where the HOMO of the complex system is located. The information cluster, we compared the curves with the ones for the bare corresponding cluster (dotted lines in provided by the density of state curves in Figure9 is completed by the electron densities displayed in Figure 10 for the key molecular orbitals. For instance, for all three systems, the HOMO level clearly has a dominant contribution from the adsorbed molecule, the orbital having a π nature due to the conjugated character of the organic dye. In contrast, the LUMOs have the most signiﬁcant contribution from the oxide, the nature of the molecular orbital being determined by the d atomic orbitals of Ti. However, neither the HOMOs nor the LUMOs are pure. A small weight from the cluster in the HOMOs and from the molecule in the LUMOs (contributions seen both in the density of state curves and in the Nanomaterials 2019, 9, x FOR PEER REVIEW 14 of 30

Figure 9). It can be seen that significant differences occur, particularly for the smallest cluster. For instance, the large peaks in the valence band at about −9.32 and −8.55 eV for the bare n = 14 cluster are much less intense for both types of binding and the higher one moves even higher, to −8.46 eV, for the system with three bonds. Similarly, in the conduction band, the peaks at −2.69 and −2.30 eV for the bare cluster are much less intense in the complex system. Moreover, new peaks occur at −2.96 eV. In contrast, the influence of the adsorbed molecule seems to be less significant for the n = 24 cluster. By enlarging the basis set in the density of states calculations for the C343–Ti24O50H4 system, we found some systematic changes towards higher energies (see Figure S2 of the Supplementary Materials). The valence band edge moves up by up to 0.28 eV, the HOMO by 0.22 eV, and the conduction band edge by 0.19 eV, leading to a decrease in the band gap of 0.09 eV. We note that by using the LANL2DZ basis set on structures optimized with 3-21G(d) and LANL2DZ functions the effect on the energy of the dye states is minor. Moving on to the electron density of the key orbitals, particularly of the ones in the conduction band, we note that despite the delocalization of the electron over the Ti atoms of the cluster, some charge is present on the atoms of the anchoring group. This fact can be seen in the LUMOs but is much more obvious for the LUMO+5 orbital of the two-bonds and the LUMO+3 of the three-bonds n = 14 complex system, and for the LUMO+2 of the n = 24 model structure (see Figure S3 of the Nanomaterials 2019, 9, 357 14 of 31 Supplementary Materials). The presence of charge on the anchor plays an important role in charge transfer properties and has to be well-described by the structure used to model the experimental electronsystems. density plots) make possible optical transitions in the visible region, as we shall see in the electronic spectra.

Figure 10. Isodensity surfaces (0.03 e/bohr3) of the key molecular orbitals of the systems consisting of Figure 10. Isodensity surfaces (0.03 e/bohr3) of the key molecular orbitals of the systems consisting of the C343 molecule adsorbed on the Ti14O30H4 cluster via two (left column) or three (middle column) the C343 molecule adsorbed on the Ti14O30H4 cluster via two (left column) or three (middle column) O–Ti bonds and on the Ti24O50H4 cluster (right column), calculated by DFT at the B3LYP/LANL2DZ O–Ti bonds and on the Ti24O50H4 cluster (right column), calculated by DFT at the B3LYP/LANL2DZ level in water solvent. The first row displays the LUMOs, whereas the bottom row shows the HOMOs. level in water solvent. The first row displays the LUMOs, whereas the bottom row shows the HOMOs. Atom colors: Ti, grey; O, red; and H, light grey. Atom colors: Ti, grey; O, red; and H, light grey. To examine the influence of the molecule adsorbed on the cluster on the density of states of the To understand the effect of the cluster size and the binding configuration on the optical cluster, we compared the curves with the ones for the bare corresponding cluster (dotted lines in Figure9). properties of the system, the electronic spectra of the three structures investigated in this section are It can be seen that significant differences occur, particularly for the smallest cluster. For instance, the large displayed in Figure 11. The spectra of the complex system of the C343 molecule with the n = 14 cluster peaks in the valence band at about −9.32 and −8.55 eV for the bare n = 14 cluster are much less intense exhibits some differences between the two-bonds and the three-bonds configurations. Most peaks for both types of binding and the higher one moves even higher, to −8.46 eV, for the system with three bonds. Similarly, in the conduction band, the peaks at −2.69 and −2.30 eV for the bare cluster are much less intense in the complex system. Moreover, new peaks occur at −2.96 eV. In contrast, the influence of the adsorbed molecule seems to be less significant for the n = 24 cluster. By enlarging the basis set in the density of states calculations for the C343–Ti24O50H4 system, we found some systematic changes towards higher energies (see Figure S2 of the Supplementary Materials). The valence band edge moves up by up to 0.28 eV, the HOMO by 0.22 eV, and the conduction band edge by 0.19 eV, leading to a decrease in the band gap of 0.09 eV. We note that by using the LANL2DZ basis set on structures optimized with 3-21G(d) and LANL2DZ functions the effect on the energy of the dye states is minor. Moving on to the electron density of the key orbitals, particularly of the ones in the conduction band, we note that despite the delocalization of the electron over the Ti atoms of the cluster, some charge is present on the atoms of the anchoring group. This fact can be seen in the LUMOs but is much more obvious for the LUMO+5 orbital of the two-bonds and the LUMO+3 of the three-bonds n = 14 complex system, and for the LUMO+2 of the n = 24 model structure (see Figure S3 of the Supplementary Materials). The presence of charge on the anchor plays an important role in charge transfer properties and has to be well-described by the structure used to model the experimental systems. To understand the effect of the cluster size and the binding configuration on the optical properties of the system, the electronic spectra of the three structures investigated in this section are displayed in Nanomaterials 2019, 9, x FOR PEER REVIEW 15 of 30 occur together, at 575/565 nm, 508/514 nm, or 411/408 nm, for the two-bonds/three-bonds configurations of the n = 14 complex system. There are also two exceptions. The lowest energy transition is relatively low and occurs at 630 nm (~1.97 eV), only for the system with the two-bonds configuration, whereas a high energy transition, of higher intensity, is located at 369 nm and belongs only to the three-bonds system (involving the presence of charge density on the atoms participating inNanomaterials the extra 2019bond)., 9, 357 15 of 31 When comparing the n = 14 with the n = 24 spectra, we notice the expected similarities in terms of peak positions, particularly between the systems with analogous bidentate bridge anchoring. However,Figure 11. Thethe intensity spectra of is the not complex as well-described, system of the particularly C343 molecule for the with 569 the nmn and= 14 465 cluster nm exhibitstransitions some of thedifferences n = 24 system, between which the two-bondsare HOMO andLUMO+2 the three-bonds and HOMO configurations.LUMO+13, Most respectively peaks occur (see Table together, S1 ofat the 575/565 Supplementa nm, 508/514ry Materials). nm, or 411/408 nm, for the two-bonds/three-bonds configurations of the n = 14Bycomplex enlarging system. the basis There set arein the also TD-DFT two exceptions. calculations The for lowest the C343-Ti energy24 transitionO50H4 system, is relatively we found low a redand shift occurs by at up 630 to nm 12 (~1.97nm of eV), the onlyhigh for wavelength the system band. with the This two-bonds tendency configuration, is consistent whereaswith the a DFT high densityenergy transition,of states ofcalculations, higher intensity, where is locatedwe obse atrved 369 nmunequal and belongs shifts onlyup for to thethe three-bonds HOMO and system the conduction(involving the band presence edge, leading of charge to densitya smaller on energy the atoms difference participating between in the the two. extra bond).

Figure 11. 11. SimulatedSimulated UV–Vis UV–Vis absorption spectra of thethe systemssystems consisting of of the the C343 C343 dye dye molecule

adsorbed on the Ti nOO22nn+2+2HH4 clusters,4 clusters, calculated calculated in water in water solvent solvent by TD-DFT by TD-DFT at the at B3LYP/LANL2DZ the B3LYP/LANL2DZ level forlevel n = for 14.n For= 14. n = For 24, nthe= 24,calculations the calculations were performed were performed with the withLANL2DZ the LANL2DZ basis set on basis the setgeometry on the optimizedgeometry with optimized 3-21G(d) with or 3-21G(d)LANL2DZ or and LANL2DZ a combinat andion a combinationof LANL2DZ offor LANL2DZ Ti atoms and for 6-31G(d,p) Ti atoms and for on6-31G(d,p) O, C, N, and for onH atoms O, C, (DZ N, and & 6-31G) H atoms on the (DZ structure & 6-31G) determined on the structure with the same determined functions. with The the spectral same −1 linesfunctions. were convoluted The spectral with lines Gaussian were convoluted distributions with of Gaussian 1000 cm distributions−1 full width at of half 1000 maximum. cm full width at half maximum. At this point, it is worth strengthening a remark made earlier, in the discussion of the density of When comparing the n = 14 with the n = 24 spectra, we notice the expected similarities in terms of states, regarding the low intensity of the low-energy transitions. These transitions are made possible peak positions, particularly between the systems with analogous bidentate bridge anchoring. However, by the fact that the HOMOs and the LUMOs are not pure but mix to different degrees small weights the intensity is not as well-described, particularly for the 569 nm and 465 nm transitions of the n = 24 from the cluster in the HOMOs and from the molecule in the LUMOs. This mixture is important for system, which are HOMO→LUMO+2 and HOMO→LUMO+13, respectively (see Table S1 of the the photovoltaic and photocatalytic applications. Supplementary Materials). By enlarging the basis set in the TD-DFT calculations for the C343-Ti O H system, we found 3.2.2. Structure and Properties of TiO2 Nanoclusters with a Large Rigid Adsorbed24 50 4 Molecule a red shift by up to 12 nm of the high wavelength band. This tendency is consistent with the DFT densityHaving of states discussed calculations, comparatively where we the observed anchoring unequal of a shifts small up rigid for the molecule HOMO on and two the conductionclusters of differentband edge, sizes, leading we now to a smallermove on energy to a larger difference molecu betweenle, but thestill two. rigid, to explore the influence of the size ofAt the this adsorbed point, it ismolecule worth strengthening on the entirea syst remarkem. Again, made earlier, we start in thefrom discussion the optimized of the geometry, density of analysingstates, regarding the binding the low to the intensity cluster, of and the then low-energy discuss transitions.the electronic These spectrum transitions and optical are made properties. possible by theWe fact report that here the HOMOs results obtained and the LUMOsfor a new are dye, not an pure oligomethine but mix to differentcyanine molecule: degrees small 5-carboxy-2- weights (3-(7-((4-(diphenylphospho)from the cluster in the HOMOs phenyl)ethynyl)-1,1,3- and from the moleculetrimethyl-1H-benzo[e] in the LUMOs. This indol-2(3H)-ylidene)prop- mixture is important for 1-en-1-yl)-1,3,3-trimethyl-3H-indol-1-iumthe photovoltaic and photocatalytic applications. iodide, OMCD1 [54,57] (see Figure 12). We note that the OMCD1 dye has to be a cationic species in order to ensure the π conjugation over the nitrogen atoms in3.2.2. the Structurecyanine constituents. and Properties For of the TiO calculation,2 Nanoclusters to ensure with the a Large overall Rigid neutralit Adsorbedy, we Moleculeplaced a negative

Having discussed comparatively the anchoring of a small rigid molecule on two clusters of different sizes, we now move on to a larger molecule, but still rigid, to explore the inﬂuence of the size of the adsorbed molecule on the entire system. Again, we start from the optimized geometry, analysing the binding to the cluster, and then discuss the electronic spectrum and optical properties. We report here results obtained for a new dye, an oligomethine cyanine molecule: 5-carboxy-2- (3-(7-((4-(diphenylphospho) phenyl)ethynyl)-1,1,3-trimethyl-1H-benzo[e] indol-2(3H)-ylidene)prop- Nanomaterials 2019, 9, x FOR PEER REVIEW 16 of 30 Nanomaterials 2019, 9, 357 16 of 31 iodine ion in the vicinity of the cyanine parts, at distances of 5 Å and 5.6 Å to the N atoms. This modeling and computational artifice is particularly appropriate when modeling systems with applications1-en-1-yl)-1,3,3-trimethyl-3H-indol-1-ium in dye-sensitized solar cells, where iodide, iodine OMCD1 is already [54,57 present] (see Figure in the 12 electrolyte.). We note that the OMCD1Comparing dye has geometry to be a cationicparameters species for the in orderbare clus to ensureter and thethe πcluster-moleculeconjugation over system the nitrogen(Table 6 andatoms Figure in the 12), cyanine we note constituents. that the average For Ti–O the calculation, distances and to ensurethe standard the overall deviation neutrality, of those we distances placed area negative both very iodine close, ion indicating in the vicinity only ofa thesmall cyanine distor parts,tion of at the distances cluster ofdue 5 Åto and the 5.6adsorbed Å to the molecule. N atoms. Similarly,This modeling the width and computationaland the length of artiﬁce the cluster is particularly both have appropriate a small variation when from modeling the isolated systems cluster, with confirmingapplications the in minor dye-sensitized distortion solar caused cells, by where the molecule. iodine is already present in the electrolyte.

(a) (b) (c)

Figure 12. Optimized structures of the OMCD1OMCD1 moleculemolecule ((aa)) andand thethe systemsystem OMCD1–Ti OMCD1–Ti2424OO5050H4,, side side view ( b) and front view (c), calculated by DFT at the B3LYP/3-21G(d)B3LYP/3-21G(d) level. level. Atom Atom colors colors are: are: C, C, grey; grey; O, red; N, blue; P, orange;orange; I,I, purple;purple; andand H,H, lightlight grey.grey.

TableComparing 6. The structural geometry parameters parameters of forthe themodel bare system cluster consisting and the of cluster-molecule the Ti24O50H4 clusters system with(Table an 6 and Figureadsorbed 12 ),OMCD1 we note molecule, that the averageand of the Ti–O bare distances cluster, andobtained the standard after geometry deviation optimization of those distances by are bothDFT/B3LYP/3-21G(d) very close, indicating in vacuum. only Geometrical a small distortion parameters of thedescribing cluster the due adsorption to the adsorbed modes: bond molecule. Similarly,lengths the (in width Å), the and torsion the lengthangle of of the the carboxyl cluster grou bothp relative have a smallto the indoline variation plane, from and the the isolated dihedral cluster, confirmingangle defined the minor by the distortion indoline plane caused and by the the plane molecule. of the three neighbor Ti atoms on the cluster surface (bothTable in6 also deg). presents the Ti–O distances at the binding sites. The values are larger than the average distance of 1.950 Å in the bulk anatase titania.OMCD1 The two on bonding Ti–O distances are relatively close, at about 0.02 Å. The torsionParameter angle of the carboxyl group relative toTi the24O indoline50H4 ring plane is relatively Ti24O50H4 small and the dihedral angle between the molecule and the Ti atoms on the surface of the cluster is r(Ti–O) 1.880 1.876 close to a right angle, indicating that the molecule is upright. All parameters indicate that the adsorbed σr(Ti–O) 0.102 0.100 molecule, despite its size, has only a minor effect on the cluster, the distortion being small. Width (Ti…Ti) 12.20 12.18 The density of states for the model system consisting of the Ti O H clusters with the adsorbed Width (O…O) 13.22 2413.2850 4 OMCD1 molecule as well as the corresponding curve for the bare Ti O H cluster is displayed Length (Ti…Ti) 7.21 7.2024 50 4 in Figure 13. As in the case of the smaller adsorbed molecule, presented in the previous section, Length (O…O) 8.15 8.16 the contribution of the OMCD1 molecule to the density of states is more significant in the valence r(O1–Ti) 2.012 - band and particularly in the gap, where the HOMO of the complex system is located. The HOMO r(O2–Ti) 1.989 - level clearly has a dominant contribution from the adsorbed molecule, the orbital having a π nature. <(O–C–C–C) −4.2 - In contrast, the LUMO has most significant contribution from the oxide, the nature of the molecular

Nanomaterials 2019, 9, 357 17 of 31 orbital being determined by the d atomic orbitals of Ti. We note that in this case too, the HOMO and the LUMO are not pure, a small contribution being present from the cluster in the HOMO and from the molecule in the LUMO. Nanomaterials 2019, 9, x FOR PEER REVIEW 17 of 30 Table 6. The structural parameters of the model system consisting of the Ti24O50H4 clusters with an adsorbed OMCD1 molecule,<(Phenyl;3Ti) and of the bare87.2 cluster, obtained after - geometry optimization by DFT/B3LYP/3-21G(d) in vacuum. Geometrical parameters describing the adsorption modes: bond lengthsTable (in 6 Å), also the presents torsion angle the Ti–O of the distances carboxyl at group the binding relative tosites. the indolineThe values plane, are andlarger the than dihedral the averageangle deﬁned distance by theof 1.950 indoline Å in planethe bulk and anatase the plane titania. of the The three two neighbor bonding Ti Ti–O atoms distances on the clusterare relatively surface close,(both inat deg).about 0.02 Å. The torsion angle of the carboxyl group relative to the indoline ring plane is relatively small and the dihedral angle between the molecule and the Ti atoms on the surface of the cluster is close to a rightParameter angle, indicating OMCD1that the molecule on Ti24O is50 Hupright.4 Ti 24AllO 50parametersH4 indicate that the adsorbed molecule, despiter(Ti–O) its size, has only a minor 1.880 effect on the cluster, 1.876 the distortion being small. The density of states for the model system consisting of the Ti24O50H4 clusters with the adsorbed σr(Ti–O) 0.102 0.100 OMCD1 molecule as Widthwell as (Ti the . . .corresponding Ti) curve 12.20 for the bare Ti24O 12.1850H4 cluster is displayed in Figure 13. As in the caseWidth of (Othe . .smaller . O) adsorbed molecule, 13.22 presented 13.28in the previous section, the contribution of the OMCD1Length molecule (Ti . . . Ti) to the density 7.21of states is more significant 7.20 in the valence band and particularly in theLength gap, where (O . . . O)the HOMO of the 8.15 complex system is 8.16 located. The HOMO level clearly has a dominant contributionr(O1–Ti) from the adsorbed 2.012 molecule, the orbital - having a π nature. In contrast, the LUMO has mostr(O2–Ti) significant contributi 1.989on from the oxide, the - nature of the molecular orbital being determined<(O–C–C–C) by the d atomic orbitals of −Ti.4.2 We note that in this - case too, the HOMO and the LUMO are not pure,<(Phenyl;3Ti) a small contribution being present 87.2 from the cluster - in the HOMO and from the molecule in the LUMO.

FigureFigure 13. Density13. Density ofstates of states of theof the OMCD1–Ti OMCD1–Ti24O24O5050HH44 system, compared compared toto the the bare bare Ti24 TiO2450HO4 50cluster,H4 cluster, calculatedcalculated by DFTby DFT at theat the B3LYP/LANL2DZ B3LYP/LANL2DZ level in in water water solvent. solvent. The The contributions contributions of the of various the various atomsatoms are: are: Ti, blue;Ti, blue; O, O, red; red; –OH –OH groups, groups, grey;grey; dye mo molecules,lecules, black; black; iodine iodine anion, anion, green. green. Energy Energy levels levels were convoluted with Gaussian distributions with a full width at half maximum of 0.1 eV were convoluted with Gaussian distributions with a full width at half maximum of 0.1 eV.

We noticedWe noticed in thein the density density of of states states of the complex complex system system a peak a peak at about at about −5.86 −eV5.86 (HOMO-3 eV (HOMO-3 in Figure 13), which is due to three occupied 5p orbitals of the negative iodine ion included in the in Figure 13), which is due to three occupied 5p orbitals of the negative iodine ion included in the modeling of the OMVD1 molecule. They are localized just below the HOMO and are not contributing modelingto the ofregeneration the OMVD1 process molecule. of the dy Theye in arethe localizedphotovoltaic just applications. below the HOMO and are not contributing to the regenerationTo examine processthe influence of the of dye the inmolecule the photovoltaic adsorbed on applications. the cluster on the density of states of the cluster,To examine we included the influence in the plot of the the moleculecurve for adsorbedthe bare cluster. on the It clustercan be seen on the that density some differences of states of the cluster,occur, we for included instance, in at theabout plot −8.95 the and curve −8.59 for eV, the in the bare valence cluster. band It and can at be −3.20 seen eV that in the some conduction differences occur,band. for instance,We note that at about the states−8.95 at and the −edges8.59 of eV, the in valence the valence and conduction band andat bands−3.20 are eV not in influenced the conduction band.significantly We notethat by the the presence states atof the adsorbed edges of molecule. the valence and conduction bands are not influenced significantlyThe byelectron the presence density of of some the adsorbed key orbitals molecule. is displayed in Figure 14. Electron density plots are shownThe electron for HOMO-3 density (at of−5.86 some eV), key a molecular orbitals orbital is displayed with a strong in Figure contribution 14. Electron from the density 5p atomic plots are orbitals of I-, and HOMO (at −5.54 eV), corresponding to the ground state of OMCD1. From the shown for HOMO-3 (at −5.86 eV), a molecular orbital with a strong contribution from the 5p atomic conduction band, we represent the LUMO (at −3.50 eV), the band edge of the oxide, and two − orbitalsmolecular of I-, andorbitals HOMO with some (at charge5.54 eV),density corresponding delocalized also to on the the ground adsorbed state molecule, of OMCD1. LUMO+2 From (at the conduction−3.34 eV) band, and weLUMO+11 represent (at the−2.92 LUMO eV). These (at − states3.50 eV),can thebe readil bandy edgeidentified of the in oxide, the density and two of states molecular

Nanomaterials 2019, 9, 357 18 of 31 orbitals with some charge density delocalized also on the adsorbed molecule, LUMO+2 (at −3.34 eV) Nanomaterials 2019, 9, −x FOR PEER REVIEW 18 of 30 and LUMO+11Nanomaterials 2019 (at, 9, x 2.92FOR PEER eV). REVIEW These states can be readily identiﬁed in the density of states18 of 30 graph, thegraph, HOMO, the and HOMO, the excited and the states excited of OMCD1 states of being OMCD1 able being to contribute able to contribute to light absorption to light absorption followed by a chargefollowedgraph, transfer the by HOMO,a charge in photovoltaic andtransfer the excited in or photov photocatalytic statesoltaic of orOMCD1 photocatalytic applications. being able applications. to contribute to light absorption followed by a charge transfer in photovoltaic or photocatalytic applications.

HOMO-3HOMO-3 HOMOHOMO LUMO LUMO LUMO+2 LUMO+2 LUMO+11LUMO+11 Figure 14. Isodensity surfaces (0.03 e/bohr3) of the key molecular orbitals of the system consisting of FigureFigure 14. 14. Isodensity Isodensity surfacessurfaces (0.03 e/bohre/bohr3)3 )of of the the key key molecular molecular orbitals orbitals of ofthe the system system consisting consisting of of the OMCD1 molecule adsorbed onto the Ti O H cluster, calculated by DFT at the B3LYP/LANL2DZ the OMCD1 molecule adsorbed onto the Ti2424O50H4 4cluster, calculated by DFT at the B3LYP/LANL2DZ the OMCD1 molecule adsorbed onto the Ti24O50H4 cluster, calculated by DFT at the B3LYP/LANL2DZ level in water solvent. Atom colors: T, light grey; C, grey; O, red; N, blue; P, orange; I, purple; and H, levellevel in in water water solvent. solvent. AtomAtom colors: T,T, lightlight grey; grey; C, C, grey; grey; O, O, red; red; N, N, blue; blue; P, P,orange; orange; I, purple; I, purple; and and H, H, smallsmall light light grey. grey. small light grey. 3.3. Structure and Properties of TiO Nanoclusters with Flexible Adsorbed Molecules 3.3. Structure and Properties of TiO2 2 Nanoclusters with Flexible Adsorbed Molecules 3.3. Structure and Properties of TiO2 Nanoclusters with Flexible Adsorbed Molecules In theIn previousthe previous section, section, we we presented presented thethe results of of a acalculation calculation involving involving twotwo molecules molecules with with In the previous section, we presented the results of a calculation involving two molecules with a rigida rigid backbone backbone but but of of different different sizessizes adsorbed adsorbed on on small small clusters clusters (n = 14 (n and= 14 24). and In 24).this section, In this we section, a rigid backbone but of different sizes adsorbed on small clusters (n = 14 and 24). In this section, we we investigateinvestigate the the case case of of molecules molecules with with a flexible a flexible backbone backbone and study and the study optimized the optimized geometry, geometry, the investigate the case of molecules with a flexible backbone and study the optimized geometry, the the bindingbinding to the cluster, and and the the electronic electronic spectrum. spectrum. The The goal goal is to is find to find the theoptimal optimal cluster cluster size to size to binding to the cluster, and the electronic spectrum. The goal is to find the optimal cluster size to modelmodel the complexthe complex system. system. model the complex system. TheThe molecule molecule of of choice choice in in this this sectionsection is is penicillin penicillin V (phenoxymethylpenicillin, V (phenoxymethylpenicillin, 3,3-Dimethyl-7- 3,3-Dimethyl- oxo-6-(2-phenoxyacetamido)-4-thia-1-azabicyclo[3.2The molecule of choice in this section is penicillin.0]heptane-2-carboxylic V (phenoxymethylpenicillin, acid) (PV), a3,3-Dimethyl-7- member of 7-oxo-6-(2-phenoxyacetamido)-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid) (PV), a member of oxo-6-(2-phenoxyacetamido)-4-thia-1-azabicyclo[3.2a group of antibiotics still widely used today in human.0]heptane-2-carboxylic and veterinary medicine, acid) and present(PV), a inmember waste of a groupa groupwater of from antibioticsof antibiotics the pharmaceutical still still widely widely industry used used today today and in animalin humanhuman farms. and The veterinary structures medicine, medicine, of PV, in and neutral and present present as well in in wasteas waste waterwaterinfrom deprotonated from the the pharmaceutical pharmaceutical forms, are presented industry industry in andFigure and animal animal 15. It was farms.farms. reported The structures structures earlier [56] of ofthat PV PV, ,the in in neutraldeprotonation neutral as as well well asas in deprotonatedinof deprotonated the carboxyl forms, groupforms, are has are presented some presented influence in in Figure Figure on the 15 15.entire. ItIt waswas structure reported in the earlier earlier case of[56] [ 56penicillin ]that that the the G deprotonation but deprotonation less so of theoffor the carboxyl penicillin carboxyl group V. group Two has angles, has some some which influence influence are of interest on on the the entire andentire will structurestructure be further in used, the case casethe angleof of penicillin penicillin of the PV G G relativebut but less less soso forfor penicillinto penicillin the carboxyl V. V. Two Twogroup angles, angles, and whichof which the rest are are of of ofthe interest interest PV with and and respect will will be beto furtherfurtherthe phenyl used, used, grou the thep, angle have angle valuesof of the the PVof PV 28.5° relative relative to thetoand the carboxyl 1.1°carboxyl for groupthe group neutral and and molecule of of the the rest rest and of of 23.5° the the PV andPV with with1.4° for respectrespect the deprotonated toto the phenyl phenyl molecule, grou group,p, haverespectively. have values values of of 28.5° 28.5 ◦ andand 1.1 1.1°◦ for for the the neutral neutral molecule molecule and and 23.5 23.5°◦ and and 1.41.4°◦ for the deprotonated molecule, molecule, respectively. respectively.

(a) (b)

Figure 15. The optimized(a) structure of (a) neutral and (b) deprotonated penicillin(b) V calculated by DFT at the B3LYP/3-21G(d) level. Atom colors: C, grey; O, red; N, blue; S, yellow; and H, light grey. FigureFigure 15. 15.The The optimized optimized structure structure of of ( a(a)) neutral neutral andand ((bb)) deprotonated penicillin penicillin V V calculated calculated by by DFT DFT at theatGiven the B3LYP/3-21G(d) B3LYP/3-21G(d) the known adsorption level. level. Atom Atom tendencies colors: colors: C,C, of grey;grey; molecu O, red; les ontoN, blue; blue; anatase S, S, yellow; yellow; titania and and [47,77], H, H, light light we grey. performed grey. DFT calculations to determine the optimized geometry of the complex systems starting from the penicillinGivenGiven the Vthe knownmolecule known adsorption withadsorption bidentate tendencies tendencies bridge anchoring of of moleculesmolecu throughles onto the anatase carboxyl titania titania group, [47,77], [47 with,77], wethe we performed proton performed DFTDFTleaving calculations calculations the antibiotic to to determine determine and binding the the optimized tooptimized an O atom geometrygeom of theetry oxide. of the Figure complex 16 andsystems systems Table starting 7 starting present from fromthe the the penicillin V molecule with bidentate bridge anchoring through the carboxyl group, with the proton leaving the antibiotic and binding to an O atom of the oxide. Figure 16 and Table 7 present the

Nanomaterials 2019, 9, 357 19 of 31 penicillin V molecule with bidentate bridge anchoring through the carboxyl group, with the proton leavingNanomaterials the antibiotic 2019, 9, x FOR and PEER binding REVIEW to an O atom of the oxide. Figure 16 and Table7 present19 of 30 the optimized geometry and the most important structural parameters for the PV molecule adsorbed on all ﬁveoptimized clusters. geometry and the most important structural parameters for the PV molecule adsorbed on all five clusters.

Figure 16. Top view (first column), side view (second column), and perspective view (third column) Figure 16. Top view (first column), side view (second column), and perspective view (third column) of the optimized structures of the Penicillin V molecule adsorbed on TinO2n+2H4 clusters, with n = 14, of the optimized structures of the Penicillin V molecule adsorbed on Ti O H clusters, with n = 14, 24, 34, 44, 54, on the first, second, third, fourth, and fifth rows, respectively.n 2 nCalculations+2 4 performed 24, 34,by 44, DFT 54, at on the the B3LYP/3-21G(d) first, second, level third, in fourth,vacuum. and Atom fifth colors rows, are: respectively. C, grey; O, red; Calculations N, blue; S, yellow; performed by DFTand at H, the light B3LYP/3-21G(d) grey. level in vacuum. Atom colors are: C, grey; O, red; N, blue; S, yellow; and H, light grey. Examining Figure 16, the first and most important observation is that the PV molecule stands out on the smallest cluster, whereas on the other clusters it is strongly distorted, in different ways, depending on the cluster size. The energy of the total system is minimized by bending and twisting

Nanomaterials 2019, 9, 357 20 of 31

Table 7. The structural parameters of the model system consisting of the TinO2n+2H4 clusters (n = 14, 24) with an adsorbed penicillin V molecule, obtained after geometry optimization by DFT/B3LYP/3-21G(d) in vacuum. Geometrical parameters describing the adsorption conﬁgurations: bond lengths (in Å) and torsion angles (in deg.) of the PV relative to the Ti–O bond, to the carboxyl group, and of the rest of the PV with respect to the phenyl group 1.

PV on PV on PV on PV on PV on Parameter Ti14O30H4 Ti24O50H4 Ti34O70H4 Ti44O90H4 Ti54O110H4 r(Ti–O) 1.822 1.884 1.896 1.900 1.903 σr(Ti–O) 0.180 0.104 0.104 0.103 0.107 Width (Ti . . . Ti) 12.34 12.21 11.87 11.95 12.01 Width (O . . . O) 13.27 13.34 13.35 13.32 Length (Ti . . . Ti) 3.63 7.40 10.90 14.53 18.11 Length (O . . . O) 4.81 8.82 11.64 15.30 18.80 r(O1–Ti) 2.040 2.073 2.077 2.041 2.044 r(O2–Ti) 2.035 2.102 2.100 2.119 2.110 <(Ti–O–C–C) 159.4 129.1 129.7 130.0 130.4 <(O–C–C–N) 25.7 0.8 1.0 −0.8 −0.5 <(C–C–O–C) 0.6 −30.4 79.9 47.4 42.3 1 See Figure S4 in the Supplementary Materials for details.

Examining Figure 16, the first and most important observation is that the PV molecule stands out on the smallest cluster, whereas on the other clusters it is strongly distorted, in different ways, depending on the cluster size. The energy of the total system is minimized by bending and twisting of the molecule with a flexible backbone, such that extra bonds can occur and π–π interactions [79] are made possible. The extra bond occurs, in the case of n = 24, between the central O atom of the PV backbone and a Ti atom on the oxide, the peripheral phenyl group being roughly transverse to the surface. In the case of the n = 34 cluster, the additional bond involves the O atom connected to the phenyl group and the peripheral ring is roughly parallel to the surface. In the case of n = 44 and 54, there are two extra bonds to surface Ti atoms: one involves the O atom next to the phenyl ring (just as for n = 34) and one engaging the S atom. The tendency already observed for n = 34 continues, with the phenyl ring parallel to the surface, at about 2.95 Å, interacting through π–π interactions with the atoms at the surface of the oxide [79]. Comparing the data presented in Tables1 and7, we observed that the presence of the adsorbed penicillin V molecule on the clusters causes some distortions to the structure. The presence of the PV causes the average Ti–O distance to be smaller by 0.65% for the n = 14 cluster. For the other clusters, the average distance is larger, the relative difference decreasing monotonically in absolute value with increasing n, from 0.43% to 0.11%. The standard deviation of the complex systems is significantly different from the values of the isolated cluster only for n = 14, the much wider range of distances indicating significant distortion of the structure. For the cluster width, the relative differences are less than 1% even for n = 14, whereas for the length the relative differences are larger than 2% for n = 14, 24, and 34 and smaller than 0.5% for n = 44 and 54. The torsion angle between the PV backbone and the Ti–O bond is about 160◦ for the smallest cluster and around 130◦ for all others, consistent with the bending of the molecule observed in Figure 16. The angle between the carboxyl branch and the PV backbone is similar to the value for the isolated PV (28.5◦) only for the smallest cluster; for the larger ones, the angle is close to 0◦. At the other end of the molecule, the PV backbone suffers some mechanical stress, revealed by the torsion angle of the phenyl ring. For the smallest cluster, the angle is close to the value of the isolated PV (1.1◦), whereas for the other clusters the differences are significant, going both ways. The adsorption energy, determined as the difference between the calculated energies of the entire system and of the separated constituents, is displayed in Figure 17. We note that the binding NanomaterialsNanomaterials 20192019,, 99,, 357x FOR PEER REVIEW 2121 ofof 3130 is weak for the smaller clusters and stronger, with a tendency to saturate, for the larger clusters. This result is consistent with the extra bonds that occur when the cluster surface increases, allowing forNanomaterials structural 2019 relaxation., 9, x FOR PEER REVIEW 21 of 30

Figure 17. Adsorption energy of PV on the TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54), calculated by DFT at the B3LYP/3-21G(d) level in vacuum and in water solvent.

Next, we examined the density of states for the PV molecule adsorbed on TinO2n+2H 4 to examine the roleFigure of the 17. Adsorptionsize of the cluster. energy of An PV examinatio on the TinOn of HFigureclusters 18 reveals (n = 14, 24,the 34, valence 44, 54), gap calculated located by below Figure 17. Adsorption energy of PV on the TinO2n2+2nH+24 clusters4 (n = 14, 24, 34, 44, 54), calculated by DFT roughly -8 eV and the conduction band above −4 eV, as seen in Figure 5 for the isolated clusters. What DFTat the at B3LYP/3-21G(d) the B3LYP/3-21G(d) level levelin vacuum in vacuum and in and water in water solvent. solvent. is new is the presence of new states in the gap that were not present in the case of the bare clusters. BothNext, the density we examined of states the calculation density of statesand the for elec thetron PV moleculedensity plots adsorbed for the on key TinO orbitals2n+2H4 to(Figure examine 19) Next, we examined the density of states for the PV molecule adsorbed on TinO2n+2H4 to examine the role of the size of the cluster. An examination of Figure 18 reveals the valence gap located theindicate role ofthat the the size additional of the cluster. states An in theexaminatio gap representn of Figure a contribution 18 reveals of the the valence PV molecule. gap located below below roughly -8 eV and the conduction band above −4 eV, as seen in Figure5 for the isolated clusters. roughlyIn the -8 eVcase and of the conductionsmallest cluster, band when above the −4 PVeV, molecule as seen in is Figure only slightly 5 for the distorted, isolated clusters.the numerous What What is new is the presence of new states in the gap that were not present in the case of the bare clusters. issuch new states is the that presence occur areof new similar states to inthose the ofgap the that isolated were notmolecule. present As in the the cl caseuster of size the increasesbare clusters. and Both the density of states calculation and the electron density plots for the key orbitals (Figure 19) Boththe energy the density is lowered of states by extracalculation bonding and and the π –elecπ interactions,tron density theplots additional for the key states orbitals in the (Figure gap suffer 19) indicate that the additional states in the gap represent a contribution of the PV molecule. indicatesignificant that changes the additional in their statesposition. in the gap represent a contribution of the PV molecule. In the case of the smallest cluster, when the PV molecule is only slightly distorted, the numerous such states that occur are similar to those of the isolated molecule. As the cluster size increases and the energy is lowered by extra bonding and π–π interactions, the additional states in the gap suffer significant changes in their position.

FigureFigure 18.18. DensityDensity of of states states (DoS) (DoS) of of the the systems systems consisting consisting of ofthe the PV PVmolecule molecule adsorbed adsorbed on the on

theTinO Ti2n+2OH2n4 +2clustersH4 clusters (n = ( n14,= 14,24, 24,34, 34,44, 44, 54). 54). Calculations Calculations were were performed performed by by DFT DFT at at the thethe B3LYP/LANL2DZB3LYP/LANL2DZ level in water solvent. Energy levels were convoluted with GaussianGaussian distributionsdistributions withwith aa 0.10.1 eVeV fullfull widthwidth atat halfhalf maximum.maximum. Figure 18. Density of states (DoS) of the systems consisting of the PV molecule adsorbed on the InThe the electron case of density the smallest of the cluster, key molecular when the orbitals PV molecule of the is complex only slightly systems, distorted, shown the in numerousFigure 19, TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54). Calculations were performed by DFT at the the suchindicate states that that for occurall HOMOs are similar the charge to those is mostly of the isolatedlocated on molecule. the phenyl As group, the cluster whereas size for increases all LUMOs and B3LYP/LANL2DZ level in water solvent. Energy levels were convoluted with Gaussian distributions thethe energycharge is distributed lowered by on extra Ti atoms, bonding with and a πhigh–π interactions, contribution thefrom additional d atomic statesorbitals. in the gap suffer signiﬁcantwith a changes0.1 eV full in width their at position. half maximum. The electron density of the key molecular orbitals of the complex systems, shown in Figure 19, The electron density of the key molecular orbitals of the complex systems, shown in Figure 19, indicate that for all HOMOs the charge is mostly located on the phenyl group, whereas for all LUMOs indicate that for all HOMOs the charge is mostly located on the phenyl group, whereas for all LUMOs the charge is distributed on Ti atoms, with a high contribution from d atomic orbitals. the charge is distributed on Ti atoms, with a high contribution from d atomic orbitals.

Nanomaterials 2019, 9, x FOR PEER REVIEW 22 of 30

Nanomaterials 2019, 9, 357 22 of 31 Nanomaterials 2019, 9, x FOR PEER REVIEW 22 of 30

Figure 19. Isodensity surfaces (0.03 e/bohr3) of the key molecular orbitals of the systems consisting of

the PV molecule adsorbed on the TinO2n+2H4 cluster (n = 14, left; n = 24, middle; and n = 34, right column), calculated by DFT at the B3LYP/LANL2DZ level in water solvent. The first row displays the LUMOs, whereas the bottom row shows the HOMOs. Atom colors: Ti, light grey; C, grey; O, red; N, blue; S, Yellow; and H, very light grey.

FigureTheFigure states 19. 19.Isodensity Isodensityin the gap surfaces surfaces having (0.03(0.03 an obvious e/bohre/bohr3)) dominantof of the the key key molecular molecularPV contribution orbitals orbitals ofare of the the in systems systemsfact mixed, consisting consisting with of some small weight from the oxide. This mixture allows, with a small oscillator strength, for transitions that ofthe the PV PV molecule molecule adsorbed adsorbed on the on Ti thenO2 Tin+2nHO42 clustern+2H4 cluster(n = 14, left; (n = n 14, = 24,left middle;; n = 24, andmiddle n = 34,; right and column),n = 34, otherwiserightcalculated columnwould by), DFThave calculated at beenthe B3LYP/LANL2DZ byforbidden. DFT at the To B3LYP/LANL2DZ understandlevel in water the solvent. leveleffect The in of waterfirst the row cluster solvent. displays size The the on ﬁrst LUMOs, the row optical propertiesdisplayswhereas of the the LUMOs, bottomsystem, whereasrow the shows electronic the the bottom HOMOs. absorption row showsAtom spectra thecolors HOMOs.: ofTi, three light Atom grey;complex colors: C, grey; structures Ti,light O, red; grey; N,areC, blue; displayed grey; S, in FigureO,Yellow; red; 20. N, and blue; H, S,very Yellow; light andgrey. H, very light grey. The adsorbed PV molecule introduces states in the gap that move the absorption band from the UV towardsTheThe states states the in in visible the the gap gap range having having of the an an spectrum. obvious obvious dominant dominant This behaviour PV PV contribution contribution is important are are for in in fact bothfact mixed, mixed,photovoltaic with with some some and smallphotocatalyticsmall weightweight fromfrom applications. the oxide. AThis This careful mixture mixture examination allows, allows, with with of a smallFigure a small oscillator 20 oscillator reveals strength, strength, the presence for fortransitions transitions of weak that thatabsorptionotherwise otherwise wouldbands would havein the have been blue/violet been forbidden. forbidden. region To To ofunderstand understandthe spectrum, the the effect which effect of ofcorrespond the the cluster cluster tosize HOMO–LUMO onon thethe opticaloptical propertiestransitions.properties of ofThe the the system,positions system, the theofelectronic the electronic optical absorption absorptionbands, ca spectralculated spectra of with of three three TD-DFT complex complex methods, structures structures vary are are displayedsignificantly displayed in Figurewithin Figure the 20 cluster. 20. size, consistent with the DFT calculations that provided the density of states. The adsorbed PV molecule introduces states in the gap that move the absorption band from the UV towards the visible range of the spectrum. This behaviour is important for both photovoltaic and photocatalytic applications. A careful examination of Figure 20 reveals the presence of weak absorption bands in the blue/violet region of the spectrum, which correspond to HOMO–LUMO transitions. The positions of the optical bands, calculated with TD-DFT methods, vary significantly with the cluster size, consistent with the DFT calculations that provided the density of states.

Figure 20. Simulated UV–Vis absorption spectra of the systems consisting of the PV molecule adsorbed Figure 20. Simulated UV–Vis absorption spectra of the systems consisting of the PV molecule on the TinO2n+2H4 clusters (n = 14, 24, 34, 44), calculated by TD-DFT at the B3LYP/LANL2DZ level adsorbed on the TinO2n+2H4 clusters (n = 14, 24, 34, 44), calculated by TD-DFT at the B3LYP/LANL2DZ in water solvent. The inset shows details of a higher wavelengths range. The spectral lines were level in water solvent. The inset shows details of a higher wavelengths range. The spectral lines were convoluted with Gaussian distributions of 1000 cm−1 full width at half maximum. convoluted with Gaussian distributions of 1000 cm−1 full width at half maximum. The adsorbed PV molecule introduces states in the gap that move the absorption band from the UV towards the visible range of the spectrum. This behaviour is important for both photovoltaic and photocatalyticFigure 20. Simulated applications. UV–Vis Aabsorption careful examinationspectra of the of systems Figure consisting20 reveals of the the presence PV molecule of weak absorptionadsorbed bands on the in Ti thenO2 blue/violetn+2H4 clusters region(n = 14, 24, of 34, the 44), spectrum, calculated which by TD-DFT correspond at the B3LYP/LANL2DZ to HOMO–LUMO level in water solvent. The inset shows details of a higher wavelengths range. The spectral lines were convoluted with Gaussian distributions of 1000 cm−1 full width at half maximum.

Nanomaterials 2019, 9, 357 23 of 31 transitions. The positions of the optical bands, calculated with TD-DFT methods, vary signiﬁcantly with the cluster size, consistent with the DFT calculations that provided the density of states.

4. Discussion We are now in a position to interpret our results and discuss their relevance. We start by noting that our DFT calculations performed for the different TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54) revealed the existence of some distortions with respect to the bulk, which decrease with the increase of n. As the cluster size increases the surface-to-bulk ratio decreases and, as expected, the properties of the model cluster mimic better and better those of the nanoparticles used in typical photovoltaic and photocatalytic applications (whose average size is about 20 nm [50,51], leading to over 15,000 Ti atoms [80]). Our clusters have much smaller sizes, of less than 2 nm, and were intentionally constructed to model interface phenomena, which involve the anatase titania (101) surface to be well-approximated. That is why, when enlarging our clusters, we did not add layers in depth, which would have increased the number of 6-fold coordinated Ti atoms, and decreased the surface-to-bulk ratio. On the contrary, we enlarged the surface to better describe the interface effects, a fact that proved to be crucial in the proper treatment of flexible adsorbed molecules, such as PV. Our results for the cluster structures compare well, particularly with those obtained by Persson et al. [33–39], who also used DFT, and to some extent with those of De Angelis et al. [41–47], who obtained the geometry by molecular dynamics simulations. More recently, Chen and Dixon [81] used a hybrid generic algorithm to determine the equilibrium structure of ultra-small nanoparticles of TiO2, with n from 1 to 384, and for n up to 80 the geometry optimization being finalized with DFT at the B3LYP/DZVP2 level. They report similar tendencies of the TiO2 nanoclusters to display distortions from the bulk, particularly for clusters of smaller sizes. We note that our n = 14 and 24 clusters have a similar structure with their 14a and 24b clusters; for the other sizes, the numbers of Ti atoms are different, similarities being identified between our n = 34 and their 36b as well as our n = 44 and their 48a [82]. Moreover, consistent with our results, their study demonstrated that the band gap of the ultra-small nanoparticles is strongly affected by the particle shape and surface structure, the gap decreasing with cluster size (scaling with n−1/2). Our calculations indicated, through the tendency to saturate of (i) the surface-to-bulk ratio, (ii) the binding energy per atom, (iii) the DFT calculated HOMO–LUMO band gap as well as (iv) the TD-DFT determined optical gap, that the cluster with n = 54 brings little improvement compared to the one with n = 44, but increases significantly the computational cost. Our findings are consistent with previous reports, particularly those of Persson and co-workers, who used clusters with n = 38 [35] or 46 [37] and, later, 92 [39], and De Angelis and co-workers, who employed clusters with n = 38 [43] and with n = 82 [44]. Jug and co-workers used free and hydrogen-saturated clusters for the simulation of anatase surfaces by means of semi-empirical methods and found that the influence of the cluster size on the convergence of the adsorption energies in the series n = 33, 56, 72, 132 was insignificant [40]. Our DFT calculations, performed on clusters saturated with four peripheral –OH groups, suggest that these groups play a minor role in the density of states of the clusters and, in any case, not for the states that are crucial for photovoltaic or photocatalytic applications. Studying clusters with n = 29 70, and 121, Vorontsov [82,83] used the self-consistent-charge density-functional tight-binding method (SCC-DFTB) and found, on one hand, that the energy of the HOMO and especially the LUMO substantially depends on the location of the surface hydroxyl groups and, on the other hand, that the band gap is underestimated with respect to the experimental value [50]. The study of rigid adsorbed molecules allowed for a double analysis with respect to the size of the cluster as well as the size of the molecule. The anchoring of the C343 molecule on the n = 14 cluster revealed significant distortions of both the cluster and the molecule, with highly either uneven Ti–O bond lengths for the bidentate bridge anchoring, associated with strong bending of the molecule towards the surface or with unusual tridentate binding configurations. Such unusual behavior is not Nanomaterials 2019, 9, 357 24 of 31 seen for larger clusters, not even for n = 24, as for such structures the adsorbed molecule tends to stand upright, almost perpendicular to the oxide surface. The adsorption energy comparisons showed significantly weaker bonding for n = 14 with respect to n = 24, the increase in size leading to more stable structures. When contrasting the optical spectra, we noticed some similarities in terms of peak positions, particularly between the systems with analogous bidentate bridge anchoring. However, the intensity was not as well-described, particularly for the higher wavelength transitions occurring in the visible range of greater interest for photovoltaic and photocatalytic applications. As our results contradict those of several previous studies, which used very small clusters, we argue that the TiO6H5 complex used by other authors [23,24] cannot be ‘sufficient for the investigation of geometries, excitations, and electronic structures of the as-investigated dyes before and after binding’ and should be used with precautions. One obvious reason is that such a complex could only consider bidentate chelate anchoring, in contrast with the vast experimental and computational data, indicating bidentate bridging [25]. Moreover, we warn that small clusters, such as Ti5O20H22 [26], (TiO2)6 [27,29,30], Ti6O21H18 [28] (TiO2)9 [31,84], and even (TiO2)15 [32] or (TiO2)16 [85], may not reproduce sufficiently well the electronic structure and optical spectra of the small molecules bound to the substrate. When attaching the larger but still rigid OMCD1 molecule onto the n = 24 cluster, we observed relatively small distortions of either the cluster or the molecule. The binding configuration was the expected bidentate bridge, with the adsorbed molecule almost perpendicular to the surface. The density of states showed that, although the large molecule adsorbed on the relatively small cluster affected some of the states in the valence and conduction bands, the key orbitals at the edges of the bands were not altered significantly. The adsorption of a molecule with a flexible backbone on the different clusters showed important differences, which cannot be ignored. The anchoring of the PV molecule on the n = 14 cluster left the molecule almost unaffected. However, that situation proved to be deceiving, as attaching the molecule onto increasingly larger clusters demonstrated that the energy of the system can be lowered substantially by distorting the PV. The bending and twisting of the backbone allowed for energy minimization due to extra bonds and π–π interactions. The tendency to saturate of the adsorption energy indicated that the benefits brought about by the cluster with n = 54 are not significant compared to the one with n = 44. The same tendency to saturate comes from the analysis of the density of states, obtained by DFT calculations, and of the electronic absorption spectra, determined by TD-DFT methods. Our results compare well with the pioneering work of Persson et al. [36,37] and De Angelis et al. [41,44], as well as with more recent reports [86–89], which use clusters with an n of at least 38. Now, to link the results of our calculations, summarized above, to practical applications, such as in hybrid photovoltaics or in photocatalytic degradation of pollutants under visible light, we need to address two key processes: light absorption and charge transfer from the molecule to the oxide. For that reason, it is useful to recall the typical approach used to investigate whether a molecule is a good candidate as a dye to sensitize TiO2 in dye-sensitized solar cells (DSSC) [50,51]. One condition that a sensitizer has to fulfil is the proper anchoring to the oxide, which is considered a precondition for a high rate of charge transfer. The –COOH group at the periphery of a dye has the right positions of the atoms and the right symmetry of the molecular orbital to ensure both a strong mechanical binding but also a high overlap of the p orbitals of O and the d orbitals of Ti, for a sizeable electron transfer probability. A second criterion is the matching of the absorption spectrum of the dye with the solar irradiation spectrum [51]. Our results showed that the optical spectra, provided by TD-DFT calculations for clusters of various sizes, indicate significant changes in both wavelength and intensity of the electronic transitions in the visible range, where the solar intensity reaches its maximum. Moreover, we found that the spectra were generally insufficiently described by the small clusters, sizes of n = 34 and 44 being sufficient for most practical purposes (given the molecules studied here), whereas n = 54 brought little further improvement. Nanomaterials 2019, 9, 357 25 of 31

Another condition for the dye is the charge injection into the oxide. The high rate of charge injection for typical organic sensitizers is achieved if the molecule exhibits the “push→pull” effect [51]. This effect is seen in dyes with an electron-rich donor part at one end and an acceptor part at the opposite side, ending in an anchoring group (such as the carboxyl group), and kept together by a π bridge. The key for charge injection is the alternant single/double bond character of the molecular backbone, which allows for electron delocalization. A push-pull effect occurs when the ground state of the dye has the charge localized on the donor part and the excited state, reached after light absorption, has the charge localized on the acceptor part, right next to the TiO2. The push→pull effect can be studied by analyzing how the electron density is localized in the ground and excited states of the dye adsorbed on the cluster. A proper description of the charge delocalization is crucial for this purpose, which, as our results demonstrated, requires a suitable account of the structure, by an adequate choice of the TiO2 cluster. The charge injection also depends on the proper alignment of the excited state of the dye with respect to the conduction band edge of the oxide. Additionally, another criterion is the dye regeneration, by returning the electron to the dye after passing through and performing work in the external circuit. In DSSCs, this process is performed by the electrolyte (or, equivalently, by a hole conductor) if the redox level of the electrolyte is situated above the ground state of the dye. The calculations leading to the density of states reveal the position of the ground state and the excited state resulting after light absorption, allowing for the analysis of the energy level alignment. Moreover, the use of TD-DFT calculations providing the optical gaps lead to the conduction band oxidation potential (see Figure S5 of the Supplementary materials), which can be used as an alternate to the conduction band edge in the discussion of the alignment. Our results show that both the conduction band edge and the ground state of the dye are influenced, to various extents, by the size of the cluster. The differences can be observed from the density of states calculations for the C343-TinO2n+2H4 systems, where they are small but significant, but more so for the PV-TinO2n+2H4 structures, where they become important. Under these circumstances, the influence of the cluster size on the proper description of the energy level alignment has to be taken into account when choosing the cluster size used in the simulation. As a ﬁnal point, Illas and co-workers [80] showed that the exchange contribution to the hybrid DFT functional strongly affects the calculated bang gap of TiO2. We performed calculations of the C343-Ti24O50H4 system with the B3LYP functional and various basis sets for determining the optimized geometry, the electronic structure, and the UV–Vis spectra. Our calculations are consistent with the early work of Persson and co-workers [36], emphasizing the need for consistency in computations.

5. Conclusions

We reported DFT calculations of several TiO2 clusters and complex systems consisting of the cluster with an adsorbed molecule to study the influence of the cluster size on the electrical and optical properties of materials/interfaces, having in mind hybrid photovoltaic and photocatalytic applications. We performed calculations for different TinO2n+2H4 clusters (n = 14, 24, 34, 44, 54), which revealed the existence of some distortions with respect to the bulk, which are larger for smaller clusters. The tendency of the cluster with n = 54 to saturate the surface-to-bulk ratio, the binding energy per atom, the electronic (DFT) band gap, as well as the optical (TD-DFT) gap brings about little improvement compared to the one with n = 44, but increases significantly the computational cost. The study of the complex systems, consisting of the cluster with the adsorbed molecule, demonstrated for the n = 14 case significant distortions of both the cluster and the molecule and unusual tridentate binding configurations. Such behaviour is not seen for larger clusters, not even for n = 24. The adsorption energy comparisons showed for n = 14 significantly weaker bonding, differences in the density of states (particularly the positions of the key orbitals and their relative intensity), and in the optical spectra (both in terms of peak wavelength and intensity). Under these Nanomaterials 2019, 9, 357 26 of 31 circumstances, we conclude that the n = 14 cluster is a poor choice for simulating the materials used in the practical applications envisaged here. The use of the n = 24 cluster has provided mixed results. First, the inner symmetry of the cluster structure causes stronger electron localization of the electron density at the centre of the cluster, causing the HOMO to move higher in energy and split away from the immediately lower energy states. This anomaly leads to a smaller DFT band gap and TD-DFT optical gap. The cluster showed some distortions but described qualitatively well the binding of the rigid molecules, even for those of a larger size. For flexible molecules, the n = 24 cluster indicated correctly the bending and twisting of the adsorbed molecule but, due to its small size, was not able to describe the correct geometry and the π–π interactions. Consequently, we conclude that the n = 24 cluster can be used well for qualitative calculations, particularly when the adsorbed molecule is rigid, or to obtain some initial information to set up further more elaborate, computational experiments. However, if accuracy is important or the molecule is flexible, the structure is unlikely to provide the precision required by such applications as hybrid photovoltaics or photocatalytic degradation of pollutants under visible light. When the molecule is adsorbed on the larger clusters, starting from n = 34, the structure and the electronic and optical properties are described in a more reliable way. We reviewed the important criteria used in computational studies to explain or predict the suitability of various dyes as TiO2 sensitizers in DSSCs or the likelihood of the degradation of organic pollutants under visible light irradiation using anatase titania as a photocatalyst. We emphasized the influence of the cluster size on the proper description of the anchoring to the oxide, ruling out the n = 14 cluster for all systems and using with high caution the n = 24 cluster when molecules are flexible. The analysis of the matching between the absorption spectrum of the dye with the solar irradiation spectrum relies on quality UV–Vis simulated spectra. Our results showed significant changes in both wavelength and intensity of the electronic transitions in the visible range, the spectra being qualitatively described by the n = 24 cluster, and more accurate results being obtained for larger systems. The charge injection into the oxide is influenced by the anchoring, by the push→pull effects determined by the charge distribution of the ground and excited states of the dye, and by the energy level alignment between the excited state of the dye and the conduction band edge of the oxide. Hence, the accuracy of the geometry optimization, of the density of states, and of the optical spectrum calculations are very important. Such accuracy is obtained with larger clusters. The dye regeneration, by passing the electron from the electrolyte back to the dye, can happen only if the redox level of the electrolyte lies higher than the ground state of the dye. A proper approach to check this criterion requires a reliable calculation of the density of states, which, again, is high for larger clusters. In summary, our results lead us to the conclusion that cluster sizes larger than or equal to n = 34 are necessary to provide the reliability required by photovoltaic and photocatalytic applications. The tendency to saturation of the key quantities of interest when moving from n = 44 to n = 54 suggests that the largest cluster may bring little improvement at a significantly higher computational cost. Probably, for many molecules of practical interest, sizes of n = 34 and particularly n = 44 may be an appropriate choice. Finally, an important word of caution is mandatory. Consistency in calculations may be an even more important rule in the simulation of practical systems, as the functionals and the basis sets used in the DFT and TD-DFT computations may have an even stronger influence on the final results than the size of the TiO2 cluster.

Supplementary Materials: The following are available online at http://www.mdpi.com/2079-4991/9/3/357/s1, Figure S1: a Ti54O110H4 nanocluster illustrating how the widths and the lengths reported in Table1 were measured, Figure S2: Density of states of the C343-Ti24O50H4 system calculated by DFT using the B3LYP functional and three different basis sets, Figure S3: Electron density of key orbitals C343-TinO2n+2H4 (n = 14, 24), Table S1: Energy, wavelength, oscillator strength and composition of the most intense optical transition for C343-TinO2n+2H4 clusters (n = 14, 24), Figure S4: Structure of PV-Ti14O30H4 to illustrate the geometrical parameters mentioned in Table7, Figure S5: Energy level alignment for TinO2n+2H4 (n = 14, 24, 34, 44, 54). Nanomaterials 2019, 9, 357 27 of 31

Author Contributions: Conceptualization, C.I.O. and M.A.G.; methodology, C.I.O.; validation, M.A.G.; formal analysis, C.I.O.; investigation, C.I.O.; resources, M.A.G.; data curation, C.I.O.; writing (original draft preparation), C.I.O.; writing (review and editing), M.A.G.; visualization, C.I.O.; supervision, M.A.G.; project administration, M.A.G. Funding: This research was funded, in part, by SNSF and UEFISCDI, under the Romanian-Swiss Research Programme, through the grant RSRP #IZERO-142144/1—PN-II-ID-RSRP-1/2012 and by JINR (Dubna, Russia) –Romania grant programme, project no. 91, topic number 04-4-1121-2015/2020, JINR 322/21.05.2018. Acknowledgments: The authors acknowledge Professor Reda M. AbdelAal from Suez University, Egypt for the useful discussions regarding the OMCD1 molecule. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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