Comparative assessment of density functional methods for evaluating essential parameters to simulate SERS spectra within the excited state energy gradient approximation

How is the Observation of High-Order Overtones and Combinations Elucidated by the Charge-Transfer Mechanism in SERS?

The charge-transfer chemical mechanism is responsible for altering the molecular spectral pattern and providing valuable insights into the properties of adsorbates. The impact of charge transfer becomes more pronounced in SERS spectra when CT states can gain intensity through vibronic coupling with high-intensity excitations. Experimental SERS spectra of diamino molecules, such as 4,4'-diaminostilbene (DAS) and 4,4'-diaminotolane (DAT), featuring bright CT transitions, have been compared to dipyridyl compounds, such as 1,2-bis(4-pyridyl) ethylene (BPE) and 1,2-di(4-pyridyl) acetylene (DPA), characterized by nearly dark CT excitations. This comparison aims to elucidate the effect of CT transitions on the presence of overtones and combination bands. We explain this distinction using Albrecht's formalism for resonance Raman spectroscopy within the framework of path integral time-dependent density functional theory considering the Herzberg-Teller corrections. It is worth noting that the energy gap between the highest occupied metallic orbital and the lowest unoccupied molecular orbital in diamino derivatives is noticeably smaller than in compounds featuring two pyridyl rings. The high-intensity SERS-CT spectra for diamino derivatives, primarily driven by the Albrecht A term, were acquired and used to elucidate the experimental observation of high-order modes with a significant Huang-Rhys factor. Conversely, the absolute intensity of SERS-CT for dipyridyl compounds is at least 106 times smaller than that for diamines, and the C term makes a significant contribution, explaining the silent overtones.

Resonance Raman spectra and excited state properties of methyl viologen and its radical cation from time-dependent density functional theory

Time-dependent density functional theory (TDDFT) was applied to gain insights into the electronic and vibrational spectroscopic properties of an important electron transport mediator, methyl viologen (MV2+ ). An organic dication, MV2+ has numerous applications in electrochemistry that include energy conversion and storage, environmental remediation, and chemical sensing and electrosynthesis. MV2+ is easily reduced by a single electron transfer to form a radical cation species (MV•+ ), which has an intense UV-visible absorption near 600 nm. The redox properties of the MV2+ /MV•+ couple and light-sensitivity of MV•+ have made the system appealing for photo-electrochemical energy conversion (e.g., solar hydrogen generation from water) and the study of photo-induced charge transfer processes through electronic absorption and resonance Raman spectroscopic measurements. The reported work applies leading TDDFT approaches to investigate the electronic and vibrational spectroscopic properties of MV2+ and MV•+ . Using a conventional hybrid exchange functional (B3-LYP) and a long-range corrected hybrid exchange functional (ωB97X-D3), including with a conductor-like polarizable continuum model to account for solvation, the electronic absorption and resonance Raman spectra predicted are in good agreement with experiment. Also analyzed are the charge transfer character and natural transition orbitals derived from the TDDFT vertical excitations calculated. The findings and models developed further the understanding of the electronic properties of viologens and related organic redox mediators important in renewable energy applications and serve as a reference for guiding the interpretation of electronic absorption and Raman spectra of the ions.

Efficient simulation of resonance Raman spectra with tight-binding approximations to Density Functional Theory

Resonance Raman spectroscopy has long been established as one of the most sensitive techniques for detection, structure characterization and probing the excited-state dynamics of biochemical systems. However, the analysis of resonance Raman spectra is much facilitated when measurements are accompanied by Density Functional Theory (DFT) calculations which are expensive for large biomolecules. In this work, resonance Raman spectra are therefore computed with the Density Functional Tight-Binding (DFTB) method in the time-dependent excited-state gradient approximation. To test the accuracy of the tight-binding approximations, this method is first applied to typical resonance Raman benchmark molecules like β-carotene and compared to results obtained with pure and range-separated exchange-correlation (xc) functionals. We then demonstrate the efficiency of the approach by considering a computationally challenging heme variation. Overall, we find that the vibrational frequencies and excited-state properties (energies and gradients) which are needed to simulate the spectra are reasonably accurate and suitable for interpretation of experiments. We can therefore recommend DFTB as a fast computational method to interpret resonance Raman spectra.

Relative contributions of Franck-Condon to Herzberg-Teller terms in charge transfer surface-enhanced Raman scattering spectroscopy

We have theoretically modeled charge transfer (CT) surface enhanced raman scattering (SERS) spectroscopy using pyridine bound to a planar Ag₆ metal nanocluster. CT states were determined by natural transition orbital hole-particle plots and CT distance D_CT and the amount of charge transferred q_CT indices. We first consider a resonance Raman (RR) model based on the Albrecht approach and calculate the ratio of the Herzberg-Teller (HT) B or C term to the Franck-Condon (FC) A term for a totally symmetric a₁ vibrational mode exciting in the lowest energy CT state. Using a dimensionless upper limit to the displacement factor ∆ = 0.05 in the FC term based on the examination of overtones in experimental spectra and a calculated HT coupling constant h_CT = 0.439 eV/Å(amu)^1/2 in the HT term, we calculated the scattering ratio of the HT to FC intensities as 147. This example indicated that for totally symmetric modes, the scattering intensity would all come from HT scattering. To further verify this result, we used the general time-dependent-RR formulation of Baiardi, Bloino, and Barone with the adiabatic Hessian model to calculate the FC, the Frank-Condon and Herzberg-Teller (FCHT), and the HT terms for pyridine in the C_2v Ag₆-pyridine complexes. For all cases we studied with pyridine in two orientations either parallel or perpendicular to the planar Ag₆ cluster, the HT terms, FCHT + HT, dominate the FC term in the CT RR spectrum. These results indicate that for CT SERS, the intensity of all the totally and non-totally symmetric vibrational modes should come from the HT effect.

Charge-transfer surface-enhanced resonance Raman spectra of benzene-like derivative compounds under the effect of an external electric field

Since the discovery of surface-enhanced resonance Raman scattering (SERS), elucidating the charge-transfer (CT) mechanism has been a challenging and controversial process. Different theoretical models have been proposed to explain the effect of applied electrode potential on SERS-CT, but achieving a high-quality conserved trend of experimental observations and explaining the nature of the selective enhancement of the signals is not a trivial task and the results and conclusions are still in dispute. We investigated recently the performance of time-dependent excited-state gradient approximation under the effects of a uniform finite electric field in a simulation of the experimental spectra of pyridine on an Ag electrode. The singular patterns of the experimental spectra for symmetric and non-symmetric benzene-like derivative compounds and the consistent trends of enhancements of their signals under various electrode potentials motivated us to extend our simulation studies to 4-methylpyridine, pyrazine and pyrimidine molecules on silver metal clusters. For these molecules, selective enhancement and de-enhancement of totally symmetric (υ_6a, υ_9a and υ_8a) and non-totally symmetric (υ_6b and υ_8b) modes upon changing the field were obtained and matched well with experimental observations. The selective enhancement of each signal in a zero field was explained by means of excited-state vector gradients and excited-state charge density difference for the S₀→ S_CT transition. On-field calculations showed slight perturbations of the geometries and electronic structures of the molecules. These on-field calculations also directly affected the magnitude of specific excited-state vector gradients and dimensionless displacements, and moreover the patterns of the spectra. The results of this investigation provided insight into the nature of the selective enhancements of signals and may help researchers propose the selection rules of SERS-CT.

Elucidation of charge-transfer SERS selection rules by considering the excited state properties and the role of electrode potential

The goal of this study is to shed light on the charge-transfer (CT) mechanism of surface-enhanced Raman scattering (SERS) by considering the properties of CT excited states. The calculations have been done by means of an excited-state gradient approximation for a pyridine molecule interacting with a silver cluster, and provided a satisfactory improvement in comparison to previous work. The effect of electrode potential on the SERS-CT spectra has been modelled theoretically by applying an external electric field for selected CT transitions and the enhancement of the ν_6a and ν_9a modes and a decline in the intensity of the ν_8a mode under a negative electric field (which is directed toward the cluster) have been observed. These results match well with the experimental studies and also explain the effect of electrode potentials on the patterns of spectra, as experimental evidence of the CT mechanism. Finally, this study demonstrated that the excited state vector gradient can be used as a distinguishing factor to explain the SERS selection rules.

Reply to the 'Comment on "Elucidation of charge-transfer SERS selection rules by considering the excited state properties and the role of electrode potential"' by M. Mohammadpour, M. H. Khodabandeh, L. Visscher and Z. Jamshidi, Phys. Chem. Chem. Phys., 2017, 19, 7833

We appreciate Aranda's comments on our recent work entitled ''Elucidation of charge-transfer SERS selection rules by considering the excited state properties and the role of electrode potential''. We would also like to thank the editor of Physical Chemistry Chemical Physics for giving us an opportunity to specify more details of our work in this reply. An important part of our article concerns the role of the electrode potential in charge-transfer SERS spectra and we would like to first address the questions that Aranda et al. posed about our labeling.

Comment on “Elucidation of charge-transfer SERS selection rules by considering the excited state properties and the role of electrode potential” by M. Mohammadpour, M. H. Khodabandeh, L. Visscher and Z. Jamshidi, Phys. Chem. Chem. Phys., 2017, 19, 7833

Different theoretical tools for modelling the complex role of the electrode potential in SERS are highlighted.