Linear Vibronic Coupling Approach for Surface-Enhanced Raman Scattering: Quantifying the Charge-Transfer Enhancement Mechanism.

The outstanding amplification observed in surface-enhanced Raman scattering (SERS) is due to several enhancement mechanisms, and standing out among them are the plasmonic (PL) and charge-transfer (CT) mechanisms. The theoretical estimation of the enhancement factors of the CT mechanism is challenging because the excited-state coupling between bright plasmons and dark CT states must be properly introduced into the model to obtain reliable intensities. In this work, we aim at simulating electrochemical SERS spectra, considering models of pyridine on silver clusters subjected to an external electric field E⃗ that represents the effect of an electrode potential Vel. The method adopts quantum dynamical propagations of nuclear wavepackets on the coupled PL and CT states described with linear vibronic coupling models parametrized for each E⃗ through a fragment-based maximum-overlap diabatization. By presenting results at different values of E⃗, we show that indeed there is a relation between the population transferred to the CT states and the total scattered intensity. The tuning and detuning processes of the CT states with the bright PLs as a function of the electric field are in good agreement with those observed in experiments. Finally, our estimations for the CT enhancement factors predict values in the order of 105 to 106, meaning that when the CT and PL states are both in resonance with the excitation wavelength, the CT and PL enhancements are comparable, and vibrational bands whose intensity is amplified by different mechanisms can be observed together, in agreement with what was measured by typical experiments on silver electrodes.

A computational study of the vibrationally-resolved electronic circular dichroism spectra of single-chain transoid and cisoid oligothiophenes in chiral conformations.

We simulate the vibronic profile of the electronic circular dichroism (ECD) spectra of oligothiophenes in cisoid and transoid chiral arrangements. We consider oligomers of different lengths, from two to fifteen units, and investigate extensively how the ECD spectral shapes depend on the inter-ring torsions. In general, the molecular structures we consider are not stationary points of the ground state potential energy surface. Therefore, in order to perform vibronic calculations, we present a new computational protocol able to define reduced-dimensionality models where the effect of the off-equilibrium modes is removed. This is done adopting a description of the vibrational motions in curvilinear internal coordinates, and vertical harmonic models coupled with an iterative application of projectors to define energy Hessians, and therefore effective normal modes, in the space complementary to the one of the off-equilibrium coordinates. Although we consider both Franck-Condon and Herzberg-Teller contributions, the results show that transoid twisted ribbons always give rise to monosignated ECD spectra, while bi-signated and multi-signated spectra are expected for cisoid helices. These findings are explained on the basis of the different transition strengths of the lowest electronic states imparted by the different spatial arrangement, that is almost linear for transoid structures and more globular for cisoid ones. We predicted the chiroptical response of a large number of possible molecular arrangements. These data are employed to critically discuss the experimental ECD of polythiophenes in different experimental conditions, forming either aggregates or host-guest complexes. The method here proposed to perform vibronic calculations in reduced-dimensionality models is of general applicability and its potential interest goes beyond the practical application presented here.

Toward a general mixed quantum/classical method for the calculation of the vibronic ECD of a flexible dye molecule with different stable conformers: Revisiting the case of 2,2,2-trifluoro-anthrylethanol.

We extend a recently proposed mixed quantum/classical method for computing the vibronic electronic circular dichroism (ECD) spectrum of molecules with different conformers, to cases where more than one hindered rotation is present. The method generalizes the standard procedure, based on the simple Boltzmann average of the vibronic spectra of the stable conformers, and includes the contribution of structures that sample all the accessible conformational space. It is applied to the simulation of the ECD spectrum of (S)-2,2,2-trifluoroanthrylethanol, a molecule with easily interconvertible conformers, whose spectrum exhibits a pattern of alternating positive and negative vibronic peaks. Results are in very good agreement with experiment and show that spectra averaged over all the sampled conformational space can deviate significantly from the simple average of the contributions of the stable conformers. The present mixed quantum/classical method is able to capture the effect of the nonlinear dependence of the rotatory strength on the molecular structure and of the anharmonic couplings among the modes responsible for molecular flexibility. Despite its computational cost, the procedure is still affordable and promises to be useful in all cases where the ECD shape arises from a subtle balance between vibronic effects and conformational variety.

Modeling Solvent Broadening on the Vibronic Spectra of a Series of Coumarin Dyes. From Implicit to Explicit Solvent Models.

We present a protocol to estimate the solvent-induced broadening of electronic spectra based on a model that explicitly takes into account the environment embedding the solute. Starting from a classical approximation of the solvent contribution to the spectrum, the broadening arises from the spread of the excitation energies due to the fluctuation of the solvent coordinates, and it is represented as a Gaussian line shape that convolutes the vibronic spectrum of the solute. The latter is computed in harmonic approximation at room temperature with a time-dependent approach. The proposed protocol for the computation of spectral broadening exploits molecular dynamics (MD) simulations performed on the solute-solvent system, keeping the solute degrees of freedom frozen, followed by the computation of the excitation properties with a quantum mechanics/molecular mechanics (QM/MM) approach. The factors that might influence each step of the protocol are analyzed in detail, including the selection of the empirical force field (FF) adopted in the MD simulations and the QM/MM partition of the system to compute the excitation energies. The procedure is applied to a family of coumarin dyes, and the results are compared with experiments and with the predictions of a very recent work (Cerezo et al., Phys. Chem. Chem. Phys. 2015, 17, 11401-11411), where an implicit model was adopted for the solvent. The final spectra of the considered coumarins were obtained without including ad hoc phenomenological parameters and indicate that the broadenings computed with explicit and implicit models both follow the experimental trend, increasing as the polarity change from the initial to the final state increases. More in detail, the implicit model provides larger estimations of the broadening that are closer to the experimental evidence, while explicit models appear to better capture relative differences arising from different solvents or different solutes. Possible inaccuracies of the adopted FF that may lead to the observed underestimation are analyzed in detail.

Disentangling vibronic and solvent broadening effects in the absorption spectra of coumarin derivatives for dye sensitized solar cells.

We simulate from first-principles the absorption spectra of five structure-related coumarin derivatives utilized in dye sensitized solar cells (DSSCs), investigating the vibronic and solvent contributions to the position and width of the spectra in ethanol. Ground and excited state potential energy surfaces (PESs) are modeled by Density Functional Theory (DFT) and its time-dependent (TD) expression for the excited state (TD-DFT). The solute vibronic structure associated with the spectrum is calculated by a TD formalism, accounting for both Duschinsky and temperature effects, while solvent inhomogeneous broadening is evaluated according to Marcus' theory, computing the solvent reorganization energy by the state-specific implementation of the polarizable continuum model (PCM) within TD-DFT. We adopted both the standard hybrid PBE0 and the range separated CAM-B3LYP functionals showing that the latter performs better both concerning the vibronic and solvent-induced contributions to the absorption lineshape. The different predictions of the two functionals are then rationalized in terms of the charge transfer (CT) character of the transitions showing that, in this class of compounds, it is strongly dependent on the nuclear structure. Such a dependence introduces a bias in the PBE0 PES that has a drastic impact on the vibronic spectra. We show that both the intrinsic vibronic structure and the solvent broadening play a relevant role in differentiating the absorption width of the five dyes. In this sense, our results provide a guide to understand the sources of spectral broadening of this family of dyes, a valuable help for a rational design of new molecules to improve DSSC devices.

The lineshape of the electronic spectrum of the green fluorescent protein chromophore, part II: solution phase.

The vibronic spectra of the green fluorescent protein chromophore analogues p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) and 3,5-tert-butyl-HBDI (35Bu) are similar in the vacuum, but very different in water or ethanol. To understand this difference, we have computed the vibrationally resolved solution spectra of these chromophores, using the polarizable continuum model (PCM) to account for solvent effects on the (harmonic) potential energy surfaces (PES). In agreement with experiment, we found that the vibrational progression increases with the polarity of the solvent, but we could neither reproduce the broadening, nor the large difference between the absorption spectra of HBDI and 35Bu. To account for the inhomogeneous broadening of the solution spectra, we used two approaches. In the first, we estimated the polar broadening from the solvent reorganization energy upon photo-excitation, using the state-specific PCM implementation. In the second, we estimated the broadening from the variance of the vertical excitation energies in molecular dynamics trajectories. Although we found good agreement for the lineshape of 35Bu in ethanol, and to a lesser extent in water, we highly underestimated the broadening for HBDI. To resolve this discrepancy, we explored the PES of HBDI in water and found that in contrast to the PCM result, the ground-state geometry is not planar in explicit solvent. We furthermore found that nonplanar geometries enhance the intramolecular charge transfer upon excitation. Therefore, the solvent reorganization and broadening are much larger and we speculate that the much broader spectrum of HBDI in water is due to the population of nonplanar geometries.

Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures.

When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for ß-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.

Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation.

In this work we carefully investigate the relationship between computed data and experimental electronic spectra. To that end, we compare both vertical transition energies, EV, and characteristic frequencies of the spectrum like the maximum, ν(max), and the center of gravity, M(1), taking advantage of an analytical expression of M(1) in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, experimental spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, we simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with experimental data. Our results indicate that the customary comparison of experimental ν(max) and computational EV, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the investigated systems, are on the order of 0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of experimental and computed M(1) and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs are proposed to help rationalize which kind of correction one should expect when comparing EV, M(1), and ν(max).

Duschinsky, Herzberg-Teller, and Multiple Electronic Resonance Interferential Effects in Resonance Raman Spectra and Excitation Profiles. The Case of Pyrene.

We show that a recently developed time-independent approach for the calculation of vibrational resonance Raman (vRR) spectra is able to describe Duschinsky and Herzberg-Teller (HT) effects acting on a single resonant state, together with interferential contributions arising from multiple electronic resonances, allowing us to investigate in detail how their interplay determines both the vRR spectra at selected wavelengths and the Raman excitation profiles. We apply this methodology to the study of the spectra of pyrene in acetonitrile, an ideal system since it exhibits three close-lying electronic transitions that are bright but also subjected to HT effects. To single out the different contributions to vRR line shapes we adopted two different adiabatic models for resonant-state potential energy surfaces, namely, Adiabatic Shift (only accounting from equilibrium geometry displacements) and Adiabatic Hessian (AH, including also the Duschinsky effects), and Franck-Condon (FC) or HT approximations for the transition dipole. We show that, on balance, FC+HT calculations within the AH model provide the best agreement with experiment. Moreover, our methodology permits to individuate bands in the experimental spectra due to the simultaneous contribution of more than one resonant state and to point out and analyze interferential effects between the FC and HT terms in each resonance Raman process, together with FC-HT and HT-HT interferences between different electronic states.