N-719 dye (99.0%) samples were purchased commercially from Fisher Scientific and used without further purification. TiO₂ nanocrystals (99.5%, anatase) were purchased commercially from Sigma Aldrich. Triple distilled water was used for sample preparation.

Solutions of N-719 dye were prepared by dissolving the dye powder in distilled water at 10⁻⁵ M concentration. Adsorption of N-719 dye molecules on TiO₂ nanoparticles was obtained by dispersing 5 mg of TiO₂ nanoparticles in 10 ml of N-791 dye solutions. This procedure was followed for each of the different size TiO₂ nanoparticles to prepare the mixture. The mixtures were stirred overnight, and the precipitate was then centrifuged and rinsed three times with deionized water. Finally, a small amount of TiO₂ nanoparticles modified with the selected adsorbate was dropped onto a glass slide and allowed to spread into a circle of about 2 cm in diameter. After solvent evaporation, Raman measurements of these samples were investigated using Spectra Pro 2750 (0.75 m Triple Grating Monochromator 1200 gratings/Spectrograph) at the excitation wavelength of 488 nm obtained from an Ar⁺ laser (Spectra Physics). The laser was focused on the sample by using a 10× objective lens attached to a confocal microscope and the power of the laser on stage was 1.50 mW. The laser spot size was 2 µm and the slit width was 20 µm. The Raman measurement of the sample was taken with 5 accumulations over 10 s acquisition. The silicon line at 520 nm was used to calibrate the observed wavenumbers.

Figure 1 displays Raman intensity of two peaks—a narrow peak at 690 cm⁻¹ and a relatively broad peak at 790 cm⁻¹ for six different size TiO₂ crystals. Enhancements of these two peaks are observed in the SERS spectra upon the adsorption of N-719 dyes on TiO₂ crystals.

In a recent study, we showed the appearance of these same two peaks after the modification of the TiO₂ particles with N-719 dyes [2] . We showed that these two peaks belong to surface optical (SO) phonon modes of TiO₂ and only appear

upon the adsorption of N-719 dyes on TiO₂ crystals. We further identified the symmetry of these surface modes to be of Raman forbidden a_2u symmetry originating from the (100) face of TiO₂ crystals. A figure displaying the SERS enhancements of the surface modes upon the modification with N-719 dyes compared to the bare TiO₂ particles from our previous study is included in the supplemental information.

In our previous analysis of the enhancement of the Raman forbidden surface modes using 10.9 nm size TiO₂ crystals, we demonstrated the presence of charge-transfer (CT) transitions between the TiO₂ crystals, and the N-719 dyes adsorbed on the surface of the TiO₂ crystals. An energy level diagram of TiO₂ and N-719 dyes is presented in Figure 2 to illustrate the possible charge-transfer transitions between the TiO₂ crystals and the adsorbed dye. Note, this figure is reproduced from our previous study.

The diagram shows that the energy gap between the HOMO of N-719 dyes and the conduction band (CB) of TiO₂ is 1.48 eV which is within the range of the excitation laser 488 nm (2.56 eV) to excite a charge-transfer transition (μ_CT) from the (HOMO) of N-719 dyes to the (CB) of TiO₂. In addition, a molecular transition (μ_mol) can also be obtained between the (HOMO) and the unfilled (π^*) molecular orbital at −2.84 eV of N-719 dyes. In this study we concluded that the presence of the charge-transfer transitions (μ_CT) between the dye and the TiO₂ crystals indicates the energy states of these two systems must be coupled. This coupling between the dye and the TiO₂ crystals is the primary mechanism through which intensity is borrowed from the nearby excitonic (μ_exct) or molecular transition (μ_mol) for the enhancement of the surface modes in TiO₂. Enhancements of these Raman forbidden surface modes are akin to the observations of forbidden

character in both optical and Raman spectra by Albrecht contributing to the chemical enhancement in SERS [10] .

In the current study, appearance of the same Raman forbidden surface modes at 690 cm⁻¹ and at 790 cm⁻¹ in different size TiO₂ crystals suggests the presence of the same mechanism governing the SERS enhancements. While Figure 1 shows the enhancement of the same two surface modes in all different sized TiO₂ crystals, the figure also exhibits differences of SERS intensity of these two surface modes in different sized TiO₂ crystals. Among the six different sized TiO₂ crystals, the maximum enhancements for both surface modes appear in 30 nm sized TiO₂ crystals whereas the 20 nm TiO₂ crystals show the least enhancements. In Figure 3, a comparison of the SERS excitation profile for these two surface modes for all six different sized TiO₂ crystals is displayed.

Figure 3 exhibits a similar trend of the excitation profile for both surface modes. Raman intensity for both of these two surface modes initially drops from 7 nm to 20 nm size TiO₂ crystals before reaching its maximum for 30 nm size TiO₂ crystals. The intensity then gradually decreases as the size for TiO₂ crystals increases to 100 nm. Results in this figure clearly show differences in SERS enhancements of the two surface modes for different sized TiO₂ crystals. Unlike PbS and CdSe quantum dots where differences in charge-transfers transitions due to quantum confinement played a major role in generating the resonance

condition, the same phenomenon cannot be attributed to differences of SERS enhancements in this study. The size of the TiO₂ crystals used in this study are well above the exciton Bohr radius thus the differences in charge-transfer transitions owing to quantum confinement does not apply here.

The differences of SERS enhancements of several different probing molecules adsorbed on larger sized crystals (larger than Bohr radius) was previously reported [8] [9] . In this study, the authors utilized the Fano solutions to vibronic coupling following the equation below to analyze the variation of the observed SERS enhancements.

SERSIntensity ∝ ( q + ε ) 2 1 + ε 2

Note, q is regarded as an asymmetry parameter which varies from 0 to larger values and measures the degree of coupling of the discrete states between the molecule and the SERS substrate. ϵ is a dimensionless parameter. The Fano line shape (Fano profile) results from this equation shows a drop in intensity at sufficiently negative values of ϵ before reaching the maximum intensity. The curve then decreases asymmetrically at higher positive values of ϵ. The maximum resonance in this Fano profile reported to indicate a strong vibronic coupling between the discrete states of an adsorbent (molecule) and a SERS substrate. On the contrary, the minimum resonance in the profile suggested to indicate a weak vibronic coupling between the two systems. To examine the correlation between the vibronic coupling and charge-transfer (CT) transitions, the authors in the previous study constructed SERS excitation profiles of different molecules based on the differences of charge-transfer (CT). Their study showed a fit between the SERS excitation profile and the Fano profile suggesting that the degree of charge-transfer (CT) transition is strongly dependent on the degree of coupling between a molecule and a SERS substrate.

In our current study, we constructed a Fano profile based on the Fano equation as previously reported to compare with the excitation profile of the two surface modes with that of the Fano profile in Figure 4(a) and Figure 4(b). The Fano line shape in this figure shows a characteristic drop in intensity (minimum resonance) at sufficiently negative values of є before reaching its maximum

intensity (maximum resonance). The line then decreases asymmetrically at higher positive values of ϵ. This Fano profile is similar to those previously reported [7] [8] [9] . The figure also shows excitation profiles of the surface modes at 690 cm⁻¹ (Figure 4(a)) and at 790 cm⁻¹ (Figure 4(b)). It can be seen that the excitation profiles of the two surface modes closely fit to that of the Fano profile. We obtained the optimum fit of the SERS profile to that of the Fano profile with a value of q = 1.0 for the surface mode at 690 cm⁻¹ in Figure 4(a) and with a value of q = 1.5 for the surface mode at 790 cm⁻¹ in Figure 4(b). The excitation profiles of the two surface modes show the presence of resonances similar to those in the Fano profile.

The figures show the highest enhancements (maximum resonance) of the surface modes at 30 nm and the lowest enhancements (minimum resonance) of the surface modes at 20 nm.

The close fit between the excitation profile and the Fano profile indicates a strong coupling between the N-719 dye and TiO₂ in 30 nm sized crystals compared to that of the 20 nm sized TiO₂. Furthermore, the strong coupling suggests a higher degree of charge-transfer between the N-719 dyes and the 30 nm size TiO₂ crystals compared to that of the 20 nm size crystals.

To quantify the degree of charge-transfer ρ_CT(k) for the enhancements of the two surface modes in different size TiO₂ crystals, we employ the following equation as previously reported to measure the degree of charge-transfer in a N-719 dye-TiO₂ complex [11] [12] :

ρ CT ( k ) = I k ( CT ) I 0 ( CT ) 1 + I k ( CT ) I 0 ( CT ) (1)

Herein, k is an index used to identify individual vibrational mode in the Raman spectrum. I^k(CT) is the Raman intensity of the vibrational mode which is strongly enhanced by charge-transfer and I⁰ (CT) is the Raman intensity of the vibrational mode whose enhancement is considered free from charge-transfer. Since the enhancements of the two surface modes are strongly affected by the charge-transfer (CT) process, we need to examine the vibrational mode which is free from the effect of charge-transfer (CT).

In Figure 5, we display the comparison of the Raman spectra of N-719 dyes with that of N-719 dyes adsorbed on different size TiO₂ crystals. The figure shows enhancements of the molecular peaks of N-719 dyes at 1030 cm⁻¹, 1268 cm⁻¹, 1472 cm⁻¹, 1542 cm⁻¹ and 1610 cm⁻¹.

The molecular line at 1030 cm⁻¹ corresponds to ring breathing (bpy) mode, the line at 1268 cm⁻¹ corresponds to inter-ring (bpy) mode, and the three lines at 1472 cm⁻¹, 1542 cm⁻¹ and 1610 cm⁻¹ correspond to ring stretching mode (bpy) [13] [14] . Among these molecular lines, the ring breathing mode at 1030 cm⁻¹ is

considered to be least affected by the charge-transfer (CT) effect [11] [12] . Therefore, to quantify the degree of charge-transfer, we select the surface mode at 690 cm⁻¹ and at 790 cm⁻¹ which are strongly affected by CT process as I^k (CT) and the N-719 dye line as I⁰ (CT). Thus, to measure the degree of charge-transfer for the enhancement of the surface mode at 690 cm⁻¹ Equation (1) can be expresses as follows:

ρ C T ( k ) = I 690 I 1030 1 + I 690 I 1030 (2)

Note, to measure the degree of charge-transfer for the enhancement of the surface mode at 790 cm⁻¹, we simply replace I₆₉₀ with I₇₉₀ in Equation (2).

In Figure 6, we plot the degree of charge-transfer of the two surface modes based on different particle sizes. The figure shows the 30 nm sized TiO₂ crystals have the highest degree of charge-transfer whereas the 20 nm sized crystals have the lowest degree of charge-transfer.

In addition, for 690 cm⁻¹ peak, the degree of charge-transfer gradually decreases between 7 nm to 10 nm and between 50 nm to 100 nm. For 790 cm⁻¹ peak, the degree of charge-transfer level off between 7 nm to 10 nm and between 50 nm to 100 nm. The degree of charge-transfer in Figure 6 is similar to the excitation profiles of the two surface modes in Figure 3. Results in Figure 6 suggest that higher degree of charge-transfer in 30 nm sized TiO₂ is due to strong coupling between the TiO₂ and N-719 dye contributing to maximum SERS

enhancements. This coupling is the weakest in 20 nm sized TiO₂ crystals resulting in a smaller degree of charge-transfer generating the weakest enhancements. The figure also shows the relative degree of charge-transfer resulting in the enhancement of the 790 cm⁻¹ in each of the TiO₂ crystals is higher than that of the 690 cm⁻¹. In addition, in Figure 4, the best fit between the excitation profile of 790 cm⁻¹ and the Fano profile was achieved for the value of q = 1.5 whereas for 690 cm⁻¹, the value of q = 1.0 shows the optimum fit. The higher value of q for 790 cm⁻¹ indicates that the coupling between the N-719 dye and the TiO₂ crystals generating is stronger for 790 cm⁻¹ line compared to the 690 cm⁻¹ line. We do not know why the coupling and the degree of charge-transfer is different for the two surface modes in each of the different size crystals.

Looking back at Figure 5, we can see that the molecular enhancements of N-719 dyes are similar to the enhancements of the surface modes. It can be seen in the figure that the 30 nm size TiO₂ crystals produce the strongest enhancements of N-719 dyes while the 20 nm size TiO₂ crystals show the least. To compare the relative enhancements of the molecular modes to those of the surface modes, the SERS excitation profiles of the 1542 cm⁻¹ line of N-719 dyes and the two surface modes at 690 cm⁻¹ and at 790 cm⁻¹ are presented in Figure 7.

Note, the molecular line at 1542 cm⁻¹ is selected as it is the most enhanced molecular peak in all six different size TiO₂ crystals. The figure shows the excitation profile of N-719 dyes follows the same trend as the excitation profile of the two surface modes. Similar to the excitation profile of the surface modes, Raman intensity of the N-719 dye at 1542 cm⁻¹ initially drops for 7 nm to 20 nm size TiO₂ crystals before reaching its maximum for 30 nm size TiO₂ crystals. The intensity then gradually decreases as the size for TiO₂ crystals increases to 100 nm. Similarity of this enhancement pattern between the surface modes and the molecular mode suggests that the degree of charge-transfer between N-719 dye and

the TiO₂ crystals is governed by the strength of vibronic coupling which plays an important role in SERS enhancements of the surface modes and of N-719 dyes.