Doubly resonant sum frequency spectroscopy of mixed photochromic isomers on surfaces reveals conformation-specific vibronic effects

With the advent of powerful and tunable laser sources, various nonlinear spectroscopies have become available for probing the electronic structure and nuclear dynamics of molecular systems and their interactions with complex environments. One such spectroscopic technique is sum frequency generation (SFG)—a coherent second order nonlinear optical process resulting from the interaction of the electric fields of two incoming laser pulses with a non-centrosymmetric material.^1–3 This restriction to non-centrosymmetric media renders SFG an attractive interface-selective analytical tool.^4–6 In addition, since SFG is a coherent process, the signals from ordered structures are amplified by in-phase constructive interference. This is particularly important for in situ measurements of structurally ordered molecular interfaces.^7–12 Infrared-Visible SFG (IVSFG) may be enhanced if the incoming infrared (IR) laser frequency is resonant with a surface vibrational mode. Further enhancement may be achieved if the visible (Vis) beam is tuned into resonance with an excited electronic state.^13,14 Such doubly resonant infrared-visible sum-frequency generation (DR-IVSFG) spectroscopy offers unique opportunities for studying aligned molecular probes (for example, within cellular membranes) as DR-IVSFG is particularly sensitive to surface-bound species and their interfacial local electric fields,¹⁵ orientation, conformation, and ordering.^13,16–19 Because DR-IVSFG is a multiphoton process, electronic transitions that are weak or forbidden in linear spectroscopy may be observed and resolved through distinct selection rules,^20,21 making the development of selective DR-IVSFG molecular probes with high surface sensitivity a priority.

For a molecule to serve as an efficient probe for nonlinear spectroscopies, it needs to possess a large hyperpolarizability—the molecular quantity that governs nonlinear light-matter interactions.^22–25 It is known that push-pull substitutions on azobenzene produce an excited charge transfer state with higher dipolar character than that of the ground state. This results in large values of molecular linear and nonlinear electric properties. Azobenzene and its derivatives serve well in this regard. They have attracted much attention as photoactive molecules for applications requiring molecular photo-control, such as photo-switching for molecular electronics, biomolecular imaging and sensing, and photo-pharmacology.²⁶ Specifically, conventional symmetric trans-azobenzene derivatives respond to ultraviolet (UV) and visible (Vis) light corresponding to the symmetry allowed S₀ → S₂ (π → π^*) transition and the symmetry forbidden S₀ → S₁ (n → π^*) transition, respectively. Because of the symmetry restrictions, the S₀ → S₁ absorption band is very weak, but can still be observed in the solution spectrum due to the effect of the nuclear motion (in particular, torsion of the phenyl groups around the N—C bonds) on the electron density.

In biological applications, where cells and tissue absorb and hence may be harmed by UV photons, it is of vital importance to use visible or near-infrared (NIR) light for stimulating an optical response. Therefore, a large effort has been placed on the synthesis of azobenzene derivatives that absorb in the visible to near-infrared range, especially at the wavelengths corresponding to the biological transparency window. It has been determined that substituents on the phenyl rings can strongly influence the azobenzene absorption bands.²⁴ For instance, incorporating an electron donating group at one para-position and an acceptor group at the other para-position may lead to pronounced red-shifts. Such pseudostilbene-type derivatives are commonly termed “push–pull” azobenzenes. Azo-compounds of this type reveal a red shift in the S₀ → S₂ electronic transition upon addition of the electron donating and withdrawing groups, sometimes overlapping the much weaker S₀ → S₁ electronic transition.^24,27–29 Recently, we synthesized a push-pull azobenzene, Am-1CN Azo-OH (Fig. 1), with λ_max of 472 nm and low fluorescence quantum yield for use in Resonance Raman (RR) imaging of subcellular compartments.²⁷ This molecule may prove to be an excellent probe for studying biological interfaces with DR-IVSFG spectroscopy as there are many conceptual similarities between RR and DR-IVSFG, the most prominent one being the importance of selective vibronic coupling. However, employing Am-1CN Azo-OH in this capacity requires prior elucidation of its interfacial electronic properties and nuclear dynamics.

A rigorously clean (organic-free), optically flat silica slide (Electron Microscopy Sciences, 72250) was dip-coated in a 5 mM solution of Am-1CN-Azo-OH in dry tetrahydrofuran (THF) to produce a thin film. After removal from the THF solution, the sample was blown dry with pure nitrogen. More details about the slide and sample fabrication are provided in the supplementary material. The obtained optical density at the maximum of the strong S₀ → S₂ electronic transition is ∼3.6 × 10⁻²; we deduce an average surface density of roughly 6 × 10¹⁴ molecules/cm² using the literature extinction coefficient of the analog commercial dye Disperse Red 1 (∼3.5 × 10⁴ M⁻¹ cm⁻¹).³⁰ 

The DR-SFG setup has been described elsewhere.^20,31 In brief, ∼60 fs tunable mid-IR pulses (∼5 µJ/pulse) and 5 ps tunable visible (Vis) pulses (3 µJ/pulse) were overlapped spatially and temporally on the sample surface.³² The reflected incoming beams were filtered out using short-pass filters, and the collimated SFG beam was directed and focused at the entrance slit of a spectrograph, spectrally dispersed and collected with a liquid nitrogen cooled CCD camera. Spectra presented here were acquired in the ssp polarization configuration, where the indexing corresponds to the polarization of the SFG, Vis, and IR beams. This polarization combination contains a single tensor element of the nonlinear susceptibility $χyyz(2)$⁠. By contrast, ppp polarized SFG spectra contain contributions from multiple tensor elements and they are sensitive to the experimental configuration and provide a different orientational averaging. The ppp SFG response from a gold film (EMF Corp.) was acquired at each Vis wavelength for normalization, alignment, and timing purposes.^33–36 A fresh spot at the sample was used for each Vis wavelength. Spectral calibration was achieved by placing a polystyrene film in front of the IR beam while recording the gold SFG signal. The entire IR path was purged by dry, CO₂–free air. Spectra were reproducibly obtained in 3-4 independent experiments with freshly prepared samples.

Calculations were performed using a combination of NWChem 6.8³⁷ and an in-house code TD-SPEC (Time Dependent Spectroscopic Simulations of Linear and Nonlinear Optical Processes).^13,38,39 NWChem 6.8 was used for geometry, frequency, and excitation calculations of the cis and trans isomers. The range separated CAM-B3LYP functional⁴⁰ and cc-pVTZ basis set⁴¹ were used for all NWChem calculations. Excitation energy gradients were calculated using numerical three-point differentiation of the four lowest excited states for the cis isomer and the ten lowest states of the trans isomer. Only the two lowest excited states were included for both isomers when plotting the DR-IVSFG spectra. Higher excited states were investigated, but the spectra were dominated by the lowest two states in both isomers. All calculations of χ⁽²⁾ were done with ssp polarization unless otherwise noted, and all frequencies were scaled by 0.97 to match their experimental counterparts. All calculations were performed for gas phase molecules, ignoring molecule-molecule interactions and surface effects.

Results of our DR-IVSFG study are presented in Figs. 2 and 3, each of which is comprised of multiple spectra for an Am-1CN-Azo-OH thin film in two stretching regions. Each spectrum corresponds to vibrationally resolved SFG signals obtained with a broad bandwidth IR pulse (∼300 cm⁻¹ FWHM) and different narrowband visible wavelengths that span SFG photon wavelengths in the 460 nm–650 nm window of the absorption spectrum [shown in Fig. 4(a)]. For spectra in Fig. 2, the IR frequency was centered at ∼1600 cm⁻¹. First, we will focus on the two vibrational bands at 1590 cm⁻¹ and 1560 cm⁻¹. These two bands appear to be present in the bulk FTIR spectrum (see Fig. S1 in the supplementary material) but not in Raman. The lack of resolved splitting in the observed Raman spectrum may be caused by the low experimental resolution (see Fig. S2 in the supplementary material).

It can be easily observed that the 1600 cm⁻¹ and 1560 cm⁻¹ SFG signals have comparable intensities at shorter visible wavelengths (≤560 nm). However, the 1600 cm⁻¹ band features a distinct electronic enhancement toward the longer visible wavelength range. The SFG spectra also exhibit bands near 1500 and 1400 cm⁻¹ that mirror the electronic intensity enhancement of the 1600 cm⁻¹ band. The spectra obtained at visible wavelengths of 500 and 530 nm reproducibly showed a larger contribution from a vibrationally non-resonant (NR) coherent SFG background above 1500 cm⁻¹.

Similarly, the nitrile C≡N stretching region was investigated by tuning our broadband IR center frequency to 2200 cm⁻¹ and repeating a stepwise Vis scan as described above. Figure 3 shows five representative ssp SFG spectra of the Am-1CN Azo-OH film at various Vis wavelengths. A vibrational band near 2230 cm⁻¹ was obtained with a measured linewidth of ∼14 cm⁻¹ (this feature is also present in experimental IR and Raman spectra as shown in Figs. S1 and S2 in the supplementary material). This vibrational response exhibited a clear electronic enhancement for the range of Vis wavelengths used, being more pronounced at longer wavelengths. Spectra in this region exhibited a significant broad non-vibrationally resonant SFG background resulting in asymmetric (dispersive) lineshapes.¹⁷ 

The SFG intensity, I_SFG, is proportional to $χ(2)2$⁠, where χ⁽²⁾ is the second order electric dipole susceptibility. The latter can be expressed as a sum of doubly resonant (R) and non-resonant (NR) contributions,

The orientationally averaged doubly resonant term, involving two electronic states with their corresponding vibrational manifolds, reads as

where g and e label the ground and excited electronic states of a molecule and ν′ and ν″ label vibrational states within the ground and the excited state manifolds, respectively. IR absorption promotes the molecule from the global minimum of a multi-dimensional potential energy surface (the zero-point energy state with vibrational quantum number, ν′ = 0) to an excited vibrational state within the ground state manifold. From now on, we will refer to the electronic transition from this excited vibrational state as “a hot band” because at the room temperature, only the zero-point energy state of such high-frequency vibrations is populated following the Boltzmann distribution. Although usually the term “hot band” is reserved for the ν′ = 1 to ν′ = 2 transition within an electronic state manifold, the fundamental concept is similar for an electronic transition from the ν′ = 1 state. The IR-absorption populates an excited vibrational state, which can be then resonantly excited by the Vis pulse to an excited vibronic state. Equation (2) is general, meaning that no steps were taken for separation of the electronic and nuclear degrees of freedom. The electronic-vibrational wavefunctions are the eigenstates of the total Hamiltonian. Huang and Shen earlier developed a theory of DR-IVSFG⁴² using the Born-Oppenheimer separation and linear coupling model. They showed that for totally symmetric normal modes, Eq. (2) can be reduced to a much simpler expression containing a product of the linear electron-vibrational coupling constant, electronic transition dipole moment at the equilibrium, squared (in the Condon approximation, neglecting the normal coordinate displacement during a vibration), and the ground state dipole moment derivative with respect to the corresponding normal coordinate.

We report the SFG excitation profiles (SFGEPs) obtained by plotting the fitted amplitudes of the 2200 cm⁻¹, 1600 cm⁻¹, and 1560 cm⁻¹ responses of the spectra in Figs. 2 and 3 as a function of the corresponding SFG wavelength (Fig. 4). The SFG intensity $I=χeff(2)2$ is fitted according to^43,44

with

where A_electr,nq and A_vib,q are the oscillator strengths relevant to the nth electronic absorption of the adsorbate and the oscillator strength of the qth SFG active mode of the adsorbate, respectively, and A_electr,nq is approximated as a Lorentzian centered at ω_n with amplitude B_nq, representing the magnitude of the electronic coupling between the qth vibration and the nth electronic state at the corresponding polarization. At a fixed Vis wavelength, A_electr,nq is approximated as a constant.

For comparison, the film linear absorbance spectrum is shown. All three SFGEP plots display a peak in the shorter wavelength range (below 500 nm) that closely matches the absorbance spectrum. However, the SFGEPs of the 1600 cm⁻¹ and 2200 cm⁻¹ responses also feature a distinct intense peak with a maximum at lower energies (∼560 nm) with no apparent correspondence in the linear absorbance spectrum. A similar tendency seems to be present in a control measurement of a well-known commercial push-pull azobenzene, Disperse Red 1 (see Fig. S6 in the supplementary material). We attribute this low energy signal to the S₀ → S₁ electronic transition, forbidden for the trans-isomer but allowed (albeit weak) on the cis-isomer.

Intuitively, the most intense DR-IVSFG signal should originate from a symmetry allowed electronic transition preceded by a resonantly driven vibration, whose coupling to the electron density is the strongest. In what follows, we analyze our experimental observations and discuss on possible mechanisms that explain the spectral features of the observed DR-IVSFG signals in the context of the resonance Raman cross sections.⁴⁵ 

The density functional theory (DFT) simulations of vibrational frequencies feature several distinct bands in the IR and resonance Raman spectra near 1600 cm⁻¹ (Table I). The calculated vibrational frequencies agree with the splitting between the experimentally observed 1560 cm⁻¹ and 1590 cm⁻¹ bands (∼40 cm⁻¹) only when considering the non-degenerate modes of trans- and cis-isomers involving the azo group stretching (see the discussion below). The DFT vibrational analysis reveals a split between the convoluted non-degenerate stretching modes of these two isomers that agree with the experimental observations (Table I). Other reports have shown two bands with comparable frequencies for similar compounds, albeit without much interpretation.^46,47 The dihedral angle between the phenyl rings was determined to be 0.9°. The calculated S₀ → S₁ and S₀ → S₂ transition energies and oscillator strengths are provided in Table II. Computed frontier molecular orbitals (MOs) and first hyperpolarizabilities are provided in the supplementary material.

The theory behind TD-SPEC for DR-SFG was explained in a previous study.¹³ The most important parts are summarized below. TD-SPEC follows the work of Heller et al. of the time dependent wavepacket approach.^48–52 In SFG, the intensity is related to the second order nonlinear susceptibility in the following manner:

where $χIJK2$ is described by

where R represents the Euler angle rotational elements, N_s is the molecular surface density, and β is the microscopic hyperpolarizability. The orientation of both isomers used for the simulated DR-IVSFG spectra relative to the surface can be found in Fig. 5; the orientation chosen best reproduced the experimental spectra. In the trans isomer, the simulations seem to indicate that the OH and the CN groups have comparable affinity toward the surface silanols.

In DR-SFG, both vibrational and electronic states are on resonance, which allows us to write β in the following fashion once the Born-Oppenheimer approximation has been applied:

Here, the symbols I₀ and L₀ are the ground and excited state vibrational states, $μβk0$ is the electronic transition dipole integral between the ground electronic state and the excited electronic state, $0$ and $k$⁠, respectively, while E is the corresponding energy of that state, ω is the energy of the IR or SFG laser, and Γ is the electronic or vibrational lifetime depending on superscripts. The equation is separated into two terms which represent the transition polarizability and the IR transition. The hyperpolarizability can be further split by taking a Taylor series expansion of the electronic transition dipole moment coordination dependence, which looks like β = A + B₁ + B₂ + ⋯, which results in the Franck-Condon (A) and the first Hertzberg-Teller (B₁ and B₂) terms. Sum over all intermediate vibrational states K is avoided by converting (7) into a time dependent formalism, the derivation of which can be seen in previous studies.^48,51,52 The A term is given by

and the first and second B terms are described as

Here, the superscript “eq” refers to a property measured at the ground state equilibrium, $Δvk0$ is the vibronic coupling constant for the normal mode with frequency ω_v, ω_E is the incident frequency, and g_k(t) is a homogeneous and inhomogeneous broadening function for the k state. L, M_a, and N_b are all line shape functions, which are explained in more detail in previous studies.^38,39 It is important to note that this method relies on the harmonic oscillator model for overlapping vibrational states. This means that any normal modes that have significant anharmonicity will be poorly described using this approach.

The calculated orientation of the cis and trans isomers is shown in Fig. 5. These are the respective angles used for the ssp polarized DR-SFG simulations. Euler angles were scanned in 5° increments for both isomers. The orientations were selected to best match the number and position of peaks seen in the experiment. Simulated waterfall plots of a linear combination of the cis and trans isomers show a distinct peak near 1550 cm⁻¹ and 1600 cm⁻¹ in Fig. 6 and a peak near 2330 cm⁻¹ in Fig. 7.

For Fig. 6, there are clear enhancements of the 1600 cm⁻¹ peak when scanning toward lower wavelengths. This trend follows for the 2330 cm⁻¹ peak as in the experimental trend. Our simulated DR-IVSFG spectra, however, lack the mode at 1400 cm⁻¹, especially in the tracking regions where the signal is enhanced in the experiment. For both Figs. 6 and 7, the spectra include both Franck-Condon and Hertzberg-Teller contributions. The trans isomer is A term dominant, while the orientation and geometry of the cis isomer contains large B term contribution, which can be seen in Figs. S11–S14 in the supplementary material.

The results presented here provide an opportunity for the fundamental understanding of DR-IVSFG with coexisting isomers and multiple electronic transitions. The main absorption band in Fig. 4(a) is attributed to the S₀ → S₂ transition of the trans isomer. The S₀ → S₁ transition was not observed in the absorption spectrum of the film; it is expected to be significantly less intense and is possibly below the sensitivity of our measurement. Some reports in the literature describe this absorption band having its energy similar to that of the S₀ → S₂ transition^53,54 in which case the S₀ → S₁ band is buried under the more intense S₀ → S₂ band. Our gas-phase calculations (Table II) do not support this hypothesis.

It is clear that the high energy band in the SFGEP in Fig. 4 directly corresponds to the absorption spectrum; thus, we confidently assign this high energy band for all three traces as vibronic coupling with the S₀ → S₂ electronic transition. This band is the dominant coupling for the ν_trans stretch at 1560 cm⁻¹. However, the well-resolved, red-shifted, SFGEP contribution seen more strongly for the ν_cis stretch at 1590 cm⁻¹ and in the nitrile stretch responses in Figs. 4(b) and 4(c) can be identified as the S₀ → S₁ electronic transition, which is symmetry-allowed for the cis-isomer but forbidden for the trans-isomer. A weak S₀ → S₁ response at a comparable energy has been reported in the bulk absorption spectrum of a similar compound.⁵⁵ Resonance Raman has been used to probe this forbidden transition of trans-azobenzene in the bulk.⁵⁶ However, the authors only saw a weak contribution of the S₀ → S₁ (n → π^*) transition to the Raman intensity of their 1592 cm⁻¹ peak.

An intuitive explanation for the observed results is the partial isomerization of Am-CN trans-Azo-OH at the surface. The ground state of charge-transfer molecules is predominately aromatic with some quinonal character, while the opposite is true for the excited state.²² The non-bonding n-orbital (HOMO) is predominantly localized on the central Azo group (see Fig. S4 in the supplementary material), while the π−orbital (HOMO-1) is delocalized along the whole structure, with the electron density weight shifted toward the electron donating amine group. As stated above, the nonbonding n- and bonding π-orbitals of trans-azobenzene are orthogonal because the molecule retains an essentially flat geometry with co-planarity of the aryl rings. Nuclear motion may affect the intensity of the forbidden S₀ → S₁ transition in trans-azobenzene through the torsional motion of the aryl rings around the C—N bonds.⁵⁷ The cis-isomer, on the other hand, has its aryl rings bent and twisted with respect to each other, which results in mixing of non-bonding HOMO and bonding HOMO-1 orbitals (see Fig. S4 in the supplementary material). This mixing results in the allowed S₀ → S₁ electronic transition in the SFG spectrum.

The experimental results can be well-explained by our interpretation that the separate vibrational bands in the spectra at 1560 and 1590 cm⁻¹ (Fig. 2) represent the signals originating from the coupling of azo N=N stretching modes to electronic transitions on trans- and cis-isomers. In this case, at the frequency of S₀ → S₂ transition, the stronger coupling seems to occur for trans-isomer (∼1560 cm⁻¹, ν_trans peak), which is consistent with our calculations of the oscillator strengths and resonance Raman cross sections (Tables I and II). The blue-shifted SFG peak of the cis-isomer (1590 cm⁻¹, ν_cis peak) has lower intensity in the range of this electronic transition because of the smaller value of its oscillator strength and also the fact that the cis S₀ → S₂ transition energy is blue-shifted, in which case the visible wavelength upconversion is somewhat off resonance. On the contrary, on the red side of the visible excitation, corresponding to the frequency of the S₀ → S₁ transition, the coupling of the ν_trans stretching mode to the electron density changes is not favorable for the trans-isomer, which account for the disappearance of the 1560 cm⁻¹ peak in the SFG spectrum. At the same time, the distorted, non-planar geometry of cis-isomer facilitates the coupling of the electron density localized on the Azo-bond to the normal vibrational modes, associated with the ν_trans stretching mode which manifests in the enhanced SFG signal at 1590 cm⁻¹.

We have examined the possibility that irradiation of the sample with the Vis photons may cause cis-trans isomerization by one or two-photon absorption (see Figs. S8–S10 in the supplementary material). These photons are most likely not the same photons that play an active role in the DR-IVSFG measurement. It is also likely that our raw sample contained cis-isomers that are stabilized at the surface by favorable interactions with silica.

Recent VSFG experiments of cis-trans azobenzene isomerization in immobilized films^58,59 do not show the vibrational splitting structure in Fig. 2. Those experiments were done with a Vis wavelength of 800 nm (off electronic resonance) and focused on the nitrile and CH stretches. DR-SFG depends on resonant Raman contributions, instead of off resonance Raman contributions, and differences can explain the results in Fig. 2. A first order approximation of the DR-IVSFG spectra can be made by analyzing the IR intensity and the resonance Raman intensity of different vibrational modes. The most relevant modes have been included in Table I. Our original hypothesis revolved around the idea that the symmetric stretching modes present on the phenol rings would contribute highly to the spectra near 1600 cm⁻¹. However, by looking at the IR and resonance Raman intensities in Table I, it is clear that the azo stretching modes from the cis and trans isomers are by far the largest when both large IR and resonance Raman contributions are required. This approximation also carries over to the simulated DR-IVSFG spectra seen in Figs. 6 and 7 for the 1600 cm⁻¹ and 2300 cm⁻¹ regions, respectively. When analyzed, the simulated DR-IVSFG spectra’s most dominant peak is from the azo stretching mode of both the cis and trans isomers in the 1600 cm⁻¹ region and the nitrile stretch in the 2300 cm⁻¹ region.

While a study of isomerization kinetics was out of the scope of this work, our theoretical model allowed us to estimate the relative fraction of the cis-isomer in the film. The linear combination used to obtain the simulated DR-SFG spectra was 65% cis and 35% trans isomer. This amount reproduces the enhancement seen at both lower and higher wavelengths as well as the absorbance spectrum (see Fig. S15 in the supplementary material).

It is clear that the enhancement seen at the longer wavelengths is due to the cis isomer, while the enhancement at shorter wavelengths is due to the trans isomer. The simulations of the two isomers show that when scanning through the sample from low energy to high energy, first the S₀ → S₁ transition of the cis isomer is resonantly probed while far from resonance with the trans states. Next, a brief period in wavelengths is scanned where neither S₀ → S₁ of the cis molecule nor S₀ → S₂ of the trans molecule is scanned, leading to no largely enhanced spectral features. Finally, the shorter wavelengths are probed, which are close to resonance with the S₀ → S₂ state of the trans molecule, resulting in an enhancement of the 1550 cm⁻¹ mode. The cis-trans isomer model, however, does not reproduce the vibrational bands below 1450 cm⁻¹. To explain this discrepancy, we revisit the classic theory of DR-IVSFG.

The vibrational bands below 1500 cm⁻¹ in Fig. 2 (assigned to the tertiary amine-carbon stretch and the central azo bond stretch) follow a similar electronic enhancement pattern as the nitrile and the 1600 cm⁻¹ stretch, indicating electronic enhancement due to both S₀ → S₁ and S₀ → S₂ electronic transitions. In the classic treatment of DR-IVSFG, developed by Huang and Shen,⁴² only the ground state dipole moment is considered modulated by a vibration, resonantly driven by IR absorption. The electronic transition dipole moment is then expressed in Condon approximation as a product of the equilibrium configuration term and the Franck-Condon factor. This treatment is sufficient for strong Franck-Condon active modes but apparently becomes deficient when a particular electronic transition is forbidden. In this case, not only the ground state transition dipole moment should be expanded in a power series over the normal coordinates but also the transition dipole moment from the ground vibronic state to an excited vibronic state (both Condon and Herzberg-Teller terms should be taken into account).^13,60 According to Herzberg-Teller approximation, the electronic transition dipole moment weakly depends on nuclear coordinates. The Taylor expansion of the transition dipole moment operator has its zeroth order term as purely electronic at the equilibrium geometry. The first order term includes linear dependence on the normal coordinate: μ = μ₀ + m_αQ_α, where μ is the total transition dipole moment, μ₀ is its value at the equilibrium geometry, and m_α is a vector constant quantifying the transition moment induced by unit nuclear displacement along the normal coordinate Q_α.⁶¹ 

According to Craig and Small,⁶¹ a hot band transition, defined as the symmetry allowed vibronic transition from an excited vibrational state, ν′ = 1, within the ground electronic state manifold [as defined in Eq. (2)], has an interference cross term in the expression for the intensity,

with its sign opposite to that of the interference cross term in the expression for the intensity of transition from the zeroth vibrational level of the electronic ground state, ν′ = 0, to a vibronic excited state. What it means, in practice, is that any strong vibronic transition observed in UV-Vis (like S₀ → S₂ of azobenzene) should have its intensity strongly suppressed in the hot band transition spectrum if a vibration, resonantly driven by IR photon, is strongly coupled to the electron density of the ground electronic state. Such a hot band transition is directly correlated with the DR-IVSFG signal.

On the other hand, for a transition that is electronically forbidden, or at least much weaker, than S₀ → S₂ in the UV-Vis absorption spectrum (like S₀ → S₁ of azobenzene), only the first order term of the expansion of the dipole moment operator survives in the expressions for both zero-point and hot band transition intensities (square of the transition dipole moment). The strength of this term is not large enough to result in any measurable UV-Vis signal but large enough to compete with the interference-suppressed hot band transition strength, and therefore the DR-IVSFG signal, of the electronically allowed S₀ → S₂ transition.

Even though the vibronic coupling strength to non-bonding MO electron density seems to be negligible, a relatively high IR intensity and the weakness of the interference term in the expression for the hot band transition intensity can result in a measurable DR-IVSFG signal. In fact, the coupling of all but one vibration we considered to non-bonding electron density is rather small. The one exclusion is the N=N Azo stretch. It is actually “through bond” interaction that can couple the electron density of, for example, nitrile group to that of Azo motif. According to Hoffmann,⁶² “through bond” interaction may operate over “surprisingly long distances.” In our case, the lone pairs on the Azo motif can interact with π-density on nitrile through, for example, symmetry-matching σ-densities localized on C—C bonds of phenyl. When a vibration shrinks/expands the local π-electron density on the nitrile group, a “chain reaction” occurs, that is, a change in the electron density on nitrile results in a change in the electron density on phenyl which in turn affects the electron density on Azo lone pairs. Such “through bond” coupling must be very weak (it depends on the energy separation between the corresponding molecular orbitals), but it is still non-vanishing and can be more intense than the direct “through space” coupling of nitrile π-electron density with Azo lone pair electron density. In fact, direct “through space” coupling can even be identically zero because of the non-matching symmetry of the corresponding orbitals.

Apart from vibronically coupled SFG, a purely electronic contribution to the SFG signal can be estimated via computing the electronic first hyperpolarizability of a molecule, β, at the sum frequency, ω_Vis + ω_IR. Our DFT calculations predicted a main (z; z, z)-component (where z is the principal axis in the molecular frame xyz) of the first hyperpolarizability tensor. This tensor element computed with Vis frequency corresponding to the S₀ → S₁ transition is more than three times than that computed with the Vis frequency corresponding to the energy of the S₀ → S₂ transition (see Table S1 in the supplementary material). Since electronic structure calculations make use of the adiabatic approximation, internal nuclear motion is not accounted for. This result tells us that part of the observed enhancement can be attributed to purely the electronic effect although the exact percentage of this contribution is somewhat difficult to estimate. The literature provides an excellent analysis of the hyperpolarizability of a similar molecule.²⁵ 

In summary, we studied push-pull substituted azobenzene molecules on a silica surface by means of doubly resonant infrared-visible sum-frequency generation. Our results showed conformational-specific vibronic coupling that identifies two distinct photochromic species coexisting at the interface. The conformation of molecules bound to surfaces has shown to have profound effects in response to electron transport⁶³ and interfacial electric fields.⁶⁴ The conformation-specific detection of surface-bound photoactive molecular probes via the unique DR-IVSFG selection rules has been rarely reported. Excited-state conformational, electronic, and vibrational relationships remain a rich area for gaining new insights into the control of electronic and nuclear degrees of freedom at interfaces. This can have direct implications for implementing novel molecular probes for sensitive detection of interfacial structure and dynamics.

Our computational model predicts that the coupling of the trans isomer azo and nitrile vibrations is more prominent at higher SFG energy through the S₀ → S₂ transition, whereas the coupling of the cis isomer azo and nitrile vibrations predominates at lower energies through the S₀ → S₁ electronic transition. We propose a scenario where symmetry allowed electronic transitions with strong coupling to fundamental vibrations are interference-suppressed in DR-IVSFG, at which point the weak electronic transitions with relatively weak coupling to fundamental normal modes can be efficiently observed. From this perspective, DR-IVSFG is complementary to more traditional resonance Raman spectroscopy.

See supplementary material for detailed information about sample preparation, characterization, computational details, and isomerization considerations.

We thank Natalia Gonzalez for obtaining the absorbance spectrum in Fig. 4. We are grateful to Andrey Kuzmin for help with the Raman spectrum in the supplementary material. M.R. and L.V. thank Jason Benedict for helpful discussions. This work was based upon work supported in part by the National Science Foundation (NSF) under Grant No. CHE- 1753207. J.C.B. and L.J. acknowledge support from NSF Award Nos. CHE-1362825 and NRT-1449785.