We report a comprehensive experimental and theoretical study of the lower-wavenumber vibrational modes in the surface-enhanced hyper-Raman scattering (SEHRS) of Rhodamine 6G (R6G) and its isotopologue R6G-d4. Measurements acquired on-resonance with two different electronic states, S1 and S2, are compared to the time-dependent density functional theory computations of the resonance hyper-Raman spectra and electrodynamics-quantum mechanical computations of the SEHRS spectra on-resonance with S1 and S2. After accounting for surface orientation, we find excellent agreement between experiment and theory for both R6G and its isotopologue. We then present a detailed analysis of the complex vibronic coupling effects in R6G and the importance of surface orientation for characterizing the system. This combination of theory and experiment allows, for the first time, an unambiguous assignment of lower-wavenumber vibrational modes of R6G and its isotopologue R6G-d4.
Rhodamine 6G (R6G), a xanthene-based dye, has been extensively employed for its remarkable two-photon photophysical properties.1 R6G and its analogs are often used in applications requiring a highly photo-stable molecule with a large two-photon cross section, such as two-photon imaging and photodynamic therapy.2–4 Despite this widespread use, R6G is not a traditional push–pull two-photon chromophore like the cyanine dyes.5 While previous studies have characterized two-photon properties such as two-photon absorption (TPA) and two-photon fluorescence cross sections, these techniques do not provide insights into the photophysics responsible for R6G’s large nonlinear response.6–8 Recent work, however, indicates that vibrational hyper-Raman scattering (HRS) is a powerful tool for studying the photophysical properties of R6G as it can provide a comprehensive picture of the excited electronic state landscape and its interaction with the local environment.
HRS is the two-photon analog of Raman scattering, which gives rise to inelastic scattering at 2ωi ± ωvib, where ωi is the incident frequency and ωvib is a molecular vibrational frequency.9,10 Additionally, resonance HRS (RHRS) is useful for studying vibronic effects and one-photon forbidden but two-photon accessible electronic excited states.11,12 While the hyperpolarizability tensor, β, can always be expanded into the Franck–Condon (A-term) and Herzberg–Teller or non-Condon (B-term) scattering components, this approach is most useful when the spectra are resonant with one or a few electronic states. A-term scattering arises when an electronic state is both one- and two-photon allowed. In the case that either the one- or two-photon transitions is disallowed, however, RHRS can still occur via Herzberg–Teller vibronic effects, known as B-term scattering. B-term scattering can be further divided into B1 and B2 scattering. The B1-terms dominate when the one-photon transition is disallowed and the two-photon transition is allowed, whereas the B2-terms dominate when the one-photon transition is allowed and the two-photon transition is disallowed.
Figure 1 overviews the electronic properties of R6G, displaying the one-photon absorption (OPA) and two-photon absorption (TPA) spectra alongside the relevant electronic states.13 S1 ← S0 occurs at 2.3 eV (λOP = 528 nm and λTP = 1056 nm), and S2 ←S0 occurs at 3.1 eV (λOP = 405 nm and λTP = 810 nm). For R6G, the RHRS at S1 is dominated by the B2-term; in contrast, the B1-term was found to play the dominant role in the RHRS at S2 because the S2 ← S0 transition is strongly two-photon-allowed but only weakly one-photon-allowed.13,14 In practice, recording the RHRS of a dye molecule coincident with a molecular electronic state is complicated by fluorescence and the weakness of the hyper-Raman effect.
Surface-enhanced HRS (SEHRS) affords signal enhancements up to 1013 and fluorescence quenching through rapid analyte to metal energy transfer facilitated by the nanoparticle, allowing for experimental on- and off-resonance studies.15,16 The presence or absence of strong non-Condon effects can be determined by comparing SEHRS and surface-enhanced Raman scattering (SERS) spectra that are on-resonance with the same, isolated electronic state, as purely A-term driven scattering would elicit the same spectra. Figure 1(c) contrasts the on-resonance SERS and SEHRS of R6G, clearly showing the importance of B-term activity in the SEHRS. Previous work combining on- and off-resonance SEHRS experiments with first-principles computations of RHRS has led to a deeper understanding of the complex nonlinear optical properties for R6G and its analogs.13,14,18–21 Briefly, the B-terms of R6G are driven by perturbations of the ground-state orbitals induced by asymmetric molecular vibrations.13 In this case, the B-terms can be more than 300 times more intense than the A-terms, in stark contrast to most other nonlinear optical dyes.14 Using the SEHRS spectra, it was also possible to identify the importance of Herzberg–Teller absorption features in the TPA spectrum of R6G.13 These strong non-Condon effects also lead to SEHRS spectra that are highly surface-geometry dependent, enabling the orientation of R6G to be determined using the intense peaks in the higher-wavenumber region (>1000 cm−1).22
Despite these previous achievements, it still remains a formidable challenge to realize single-molecule SEHRS of R6G due to the lack of pronounced isotopic effects in the higher-wavenumber region, (vide infra) unlike isotopologues of other two-photon chromophores.18,23 The isotope-affected lower-frequency modes are weaker in intensity and more anharmonic, which further complicates the comparison between theory and experiment. Although Watanabe et al.24 reported a detailed mode assignment for R6G, the lowest wavenumber mode considered in that work is 615 cm−1. This framework could be made more general if it could be extended to include accurate computations of the lower-frequency modes.
In this work, we present a combined experimental and theoretical study of the SEHRS spectra of R6G and its isotopologue R6G-d4 on-resonance with S1 and S2 with an emphasis on the assignment of the lower-frequency modes (400 cm−1–800 cm−1). The TPA and RHRS computations are carried out using vibronic coupling models based on the time-dependent wavepacket approach.25,26 This approach is constructed by a sum-over-states scheme with a few of the lowest excited electronic states, which accurately describes the resonant nonlinear optical properties. The SEHRS computations are achieved by combining the vibronic models with a recently developed dressed-tensor formalism22,27,28 in which a silver spherical nanoparticle is used as the substrate and the adsorption geometry is chosen based on a previous prediction.22 After reviewing the theoretical framework for SEHRS calculations and the experimental methods for SEHRS measurements, we present a detailed comparison between theoretical and experimental SEHRS of R6G and R6G-d4. Taken together, the comparison of experiment and theory for both the R6G and R6G-d4 isotopologue enables an assignment of the lower-frequency modes and a detailed analysis of the relative importance of Condon and non-Condon scattering effects in a prototypical dye molecule.
II. EXPERIMENTAL METHODS
A. R6G and SEHRS substrate preparation
R6G-d4 was synthesized according to the procedure described by Blackie and co-workers,29 with the nuclear magnetic resonance spectroscopy (NMR) and mass spectrometry data of the resulting compound matching this prior report. Ag nanoparticle (AgNP) colloidal suspensions were synthesized via the Lee and Meisel method.30 Specifically, 92.0 mg of silver nitrate (Sigma-Aldrich) was added to 200 ml of boiling water, and then, 113.9 mg of tribasic sodium citrate (Sigma-Aldrich) in 10 ml of water was added drop-wise and allowed to boil for 30 min. The resulting colloidal solution was then diluted to 1 l. AgNPs are ∼40 ± 5 nm in diameter as verified by TEM analysis (see the supplementary material). Aqueous solutions of R6G (Acros) and R6G-d4 were prepared in ultrapure water (18 M Ω cm) and mixed with AgNP colloids to make a final concentration of 10−6 M R6G-functionalized AgNPs. The colloids were then destabilized using 1 M NaBr, resulting in AgNP aggregates.
B. Experimental SEHRS
The SEHRS spectra at 820 nm and 1064 nm laser wavelength were acquired using an optical parametric oscillator (APE picoEmerald), focused with an inverted microscope objective (Nikon Ti–U, 20×, NA = 0.5) with 2 mW of average power at the objective. At this power, no signal degradation is observed over the acquisition time of 30 s. The scattered light was collected in a backscattering geometry and passed through a Rayleigh rejection filter (Semrock). The scattered photons were then dispersed with a spectrometer (Princeton Instruments Acton SP2300, 1200 g/mm, BLZ = 500), detected with a back illuminated, deep depletion CCD (Excelon) and analyzed using the Winspec32 software (Princeton Instruments). The data were then analyzed and plotted in Igor Pro (WaveMetrics). The spectral resolution for the 820 nm and 1064 nm SEHRS spectra are 2.7 cm−1 and 1.5 cm−1, respectively.
III. THEORETICAL METHODS
The TPA cross sections were obtained using the imaginary part of the second hyperpolarizability γ. A vibronic coupling model26 was adopted for the complex γ calculations, and the portion in γ that corresponds to the saturated linear absorption process31,32 has been carefully excluded by construction. The key to simulating SEHRS is to calculate the transition first hyperpolarizability β′ as the square of it is proportional to the scattering intensity.16,33 In the vibronic coupling model,25 β′ can be written as the summation of the Franck–Condon34,35 (A-term) and the first Herzberg–Teller36,37 (B-term) terms, i.e., β′ = A + B1 + B2. Detailed descriptions for the A- and B-terms have been given previously,25 and here we will only provide a simplified version for clarification. With respect to the kth excited state, the A- and B-terms are given as
where represents the transition dipole moment evaluated at ground-state equilibrium geometry and ∂μ0k/∂Qa (∂Sk0/∂Qa) refers to the one-photon (two-photon) transition dipole moment derivative with respect to the normal mode. , and gk(t) stand for the electronic excitation energy, the vibronic coupling constant for the normal mode with frequency ων, the vibrational frequency, the incident frequency, and the broadening function for the kth excited state, respectively. Finally, L, Ma, and Nb are the line shape functions.
The surface-enhanced β′ is achieved by adapting a recently developed dressed-tensor formalism22,27 that describes the molecule as a point-dipole interacting with the enhanced local field from a spherical nanoparticle (dipolar model). This method generates a sufficiently strong local field perpendicular to the nanoparticle surface so that the surface-selection rules are obeyed. Although the relative enhancements are expected to differ in a colloidal system, no appreciable effect on the relative intensities of the resonance-hyper bands is expected. Frequency () is the same as twice of the incident frequency (ωL), the surface-enhanced β′, i.e., β′,tot, can be written as22,27,28
where δαβ is the Kronecker delta function and describes the local field enhancement in the β Cartesian direction resulting from polarization in the α direction. Note that the Einstein summation convention is employed for Greek indices. The local field provided by the model nanoparticle is given as38
where R describes the vector separation between the molecule and dipolar sphere. αS(ω) is an isotropic and frequency-dependent complex polarizability of the nanoparticle, which is constituted by the sphere radius a and material’s dielectric constants ε(ω) as
We note that due to the noticeable difference between the incident (ω) and scattered (2ω) frequencies for HRS, two separate local field calculations are needed for simulating SEHRS.
IV. COMPUTATIONAL DETAILS
Geometry optimization and normal mode calculations were performed at the B3LYP/6-311G* level of theory using NWChem.39 A scale factor of 0.98 was applied to all vibrational frequencies. Computations of the transition first hyperpolarizability (β′) were carried out using TDSPEC25,26,40 in which the dimensionless displacements (Δ), transition dipole moment derivatives (dμ/dQ), and two-photon transition moment derivatives (dS/dQ) were extracted from the corresponding response properties by means of the three-point numerical differentiation. These response properties were calculated using linear and quadratic response modules in Dalton 2.0 with B3LYP/6-311G*.41 To facilitate comparison with experiment, solvent shifts (0.20 eV–0.56 eV) have also been applied to each excitation.
The local field calculations were performed using a silver spherical nanoparticle with a diameter of about 100 nm, where the frequency-dependent complex dielectric function of silver was obtained from Ref. 42. It is important to point out that this diameter only represents the strong local field along the surface normal, which is not the actual dimensions of the nanoparticles used in the experiments.
The differential cross sections for SEHRS were calculated by assuming a perpendicular measurement of the scattered light with respect to the incident radiation, given as25
Here, α is a fine structure constant, accounts for the Boltzmann population of mode Qp (only the lowest vibrational state is often assumed significantly populated), and the hyper-Raman intensity activity coefficient,
takes various molecular orientations into account. See Ref. 25 for the detailed expressions of and . All simulated spectra in this work are convoluted with a Lorentzian line shape with 10 cm−1 width.
V. RESULTS AND DISCUSSION
Figure 2 presents the experimental SEHRS of R6G and R6G-d4 acquired on-resonance with S2 (820 nm) and S1 (1064 nm). The incident wavelengths for each resonance were chosen based on the experimental TPA spectra [Fig. 1(a)].17 Figure 2(b) presents the lower-wavenumber modes of the resonant SEHRS spectra, where peak shifts and relative intensity differences are observed between isotopologues, as these modes have more participation of the deuterated phenyl group. The higher-wavenumber modes seen in Fig. 2(c), however, do not change between isotopologues as these modes are highly B-term driven.13 Only substitutions to the xanthene ring, where the relevant electronic states are localized, will cause spectral changes.
Figure 3 compares the experimental and theoretical SEHRS of R6G and R6G-d4 on-resonance with S1 and S2, with peak positions indicated in Tables S1 and S2. Previous work indicates the importance of accurate surface orientation when simulating SEHRS and determines that R6G adsorbs with a slight tilt to the surface normal along the edge of the xanthene ring along the ethylamine group; thus, this geometry was used in the presented calculations.22 The theory does well in describing the SEHRS for both resonance conditions at low and high-wavenumber regions, accurately capturing the vibrational modes.
Figure 4 compares the orientationally averaged RHRS spectra and calculated SEHRS on-resonance with S1 and S2 for both R6G and R6G-d4. Clearly, the S1-resonant SEHRS exhibits spectral changes due to surface interactions, whereas the S2-resonant spectrum is minimally affected by the surface as the spectra are nearly identical. When on-resonance with S1, the β tensor direction depends on the symmetry of the vibrational mode; thus, the B2-type scattering will become sensitive to the molecular adsorption orientation if given a direction-fixed local field enhancement.22 Conversely, when on-resonance with S2, the B1-type scattering is dominated by modes with one fixed β direction, the βzzz component; thus, the SEHRS is not sensitive to small changes in orientation.
Figure 5 displays the A-term component of the total SEHRS of R6G and R6G-d4 resonant with S1 and S2 in the 400 cm−1–800 cm−1 range. While B-term scattering dominates much of the high-wavenumber SEHRS spectrum, we are able to observe lower-frequency modes with considerable A-term contributions when on-resonance with S1, as it is one-photon allowed and weakly two-photon allowed [Fig. 1(a)]. When nn-resonance with S2, however, the SEHRS is purely B-term driven as only the two-photon transition is allowed. In this lower-wavenumber region, we can identify modes with unique vibronic activity: the 451 cm−1 mode is purely B-term driven, the 614 cm−1 mode has A- and B-term effects, and the 772 cm−1 is highly A-term driven, for R6G.
In Fig. 5(b), we present a comparison of the experimental SEHRS and theoretical SEHRS at both resonance conditions for both isotopolgues, focusing on the vibrational band appearing at 772 cm−1. Unlike other lower-frequency modes, this mode is resonantly enhanced via the S1 state through mostly A-term scattering (∼78% contribution). S1-resonant A-term contributions can be observed in other modes such as the 614 cm−1 mode; however, the 772 cm−1 mode is unique in that it is not present in the S2-resonant SEHRS. Unlike other S1 correlated modes, this mode does experience a slight frequency shift in R6G-d4, from 772 cm−1–771 cm−1 in the theory and 774 cm−1 to 769 cm−1 in experiment. The peak shift is not as drastic as other modes as this vibration involves minimal displacement of the deuteriums (presented in the supplementary material as the R6G ν9 mode and R6G-d4 ν7 mode). Agreement between the experimental and calculated SEHRS for this unique mode confirms the level of accuracy and detail achieved through the computations.
Figure 6 displays the vibrational mode vector diagrams of the vibrations that comprise the experimentally observed bands around 615 cm−1 in both the R6G and R6G-d4 spectra. Even though these bands do not change significantly as a function of the excitation wavelength, the theory shows that the identity of the vibrational mode changes with the excitation wavelength. When on-resonance with S2, the spectra is dominated by the A-term driven modes, R6G ν6 and R6G-d4 ν3 modes, respectively, while on-resonance with S1, the spectra is dominated by R6G ν7 and R6G-d4 ν4 modes. Interestingly, the small shift (e.g., from 612 cm−1–618 cm−1 in the R6G) when going from S1 to S2 is accurately described by the theory as different vibrational modes. The B-term active ν6 R6G mode corresponds to asymmetric out-of-plane phenyl vibrations, whereas the A-term active ν7 mode corresponds to symmetric in-plane phenyl vibrations. This is consistent with our previous observations that anti-symmetric vibrations are required for generating the large B-term activity in rhodamine molecules.13,20 The thorough theoretical computations allow elucidation of nuanced A- and B-term effects of the lower-wavenumber region that experimental data are unable to discern.
In this work, we present a combined experimental and theoretical study of wavelength-scanned SEHRS of R6G and its isotopologue, R6G-d4. Our results show that first-principles HRS computations can correctly capture a vast amount of the experimental SEHRS features, especially those in the lower-wavenumber regime, under multiple resonance conditions. Through comparison of experiment and theory, we demonstrate that a better agreement can be reached by introducing accurate surface effects into the computations, given that the adsorption geometry of R6G onto the nanoparticle has been reasonably predicted. Furthermore, we show the ability to assign A- and B-term activity contributions of specific vibrational modes on-resonance with different electronic states. As a whole, elucidation of the A- and B-terms of specific vibrational modes further explains why assignment of the lower-frequency modes is challenging. The high-wavenumber modes are mostly B-term dependent, and their peaks change much more drastically as a function of surface orientation. The lower-wavenumber modes, however, have a much more complex variation in their A- and B-term dependencies, in addition to their surface orientation dependence. The culmination of experimental data and theoretical models to accurately elucidate the non-Condon effects and surface orientation of R6G has proved powerful for overcoming such an intricate problem. This unique achievement facilitates the mode assignment in the lower-wavenumber region for R6G and its isotopologues, which motivates future efforts toward SM-SEHRS of R6G.
This work was supported by the Pennsylvania State University, the Research Computing and Cyberinfrastructure, and the U.S. National Science Foundation under Grant No. CHE-1856419 (L.J.). This work was also supported by the University of Notre Dame and the U.S. National Science Foundation under Grant No. CHE-1709566 (J.E.O. and J.P.C.).
The data that support the findings of this study are available from the corresponding author upon reasonable request.