Comparison of simplified sum-over-state expressions to calculate resonance Raman intensities including Franck-Condon and Herzberg-Teller effects

Coherent Electron-Vibron Interactions in Surface-Enhanced Raman Scattering (SERS)

In this Letter we identify coherent electron-vibron interactions between near-resonant and nonresonant electronic levels that contribute beyond standard optomechanical models for off-resonant or resonance surface-enhanced Raman scattering (SERS). By developing an open-system quantum model using first molecular interaction principles, we show how the Raman interference of both resonant and nonresonant contributions can provide several orders of magnitude modifications of the SERS peaks with respect to former optomechanical models and over the fluorescence backgrounds. This cooperative optomechanical mechanism allows for generating an enhancement of nonclassical photon pair correlations between Stokes and anti-Stokes photons, which can be detected by photon-counting measurements. Our results demonstrate Raman enhancements and suppressions of coherent nature that significantly impact the standard estimations of the optomechanical contribution from SERS spectra and their quantum mechanical observable effects.

A Full Quantum Mechanical Approach Assessing the Chemical and Electromagnetic Effect in TERS

Tip-enhanced Raman spectroscopy (TERS) is a valuable method for surface analysis with nanometer to angstrom-scale resolution; however, the accurate simulation of particular TERS signals remains a computational challenge. We approach this challenge by combining the two main contributors to plasmon-enhanced Raman spectroscopy and to the high resolution in TERS, in particular, the electromagnetic and the chemical effect, into one quantum mechanical simulation. The electromagnetic effect describes the sample's interaction with the strong, highly localized, and inhomogeneous electric fields associated with the plasmonic tip and is typically the thematic focus for most mechanistic studies. On the other hand, the chemical effect covers the different responses to the extremely close-range and highly position-sensitive chemical interaction between the apex tip atom(s) and the sample, and, as we could show in previous works, plays an often underestimated role. Starting from a (time-dependent) density functional theory description of the chemical model system, comprised of a tin(II) phthalocyanine sample molecule and a single silver atom as the tip, we introduce the electromagnetic effect through a series of static point charges that recreate the electric field in the vicinity of the plasmonic Ag nanoparticle. By scanning the tip over the molecule along a 3D grid, we can investigate the system's Raman response on each position for nonresonant and resonant illumination. Simulating both effects on their own already hints at the achievable signal enhancement and resolution, but the combination of both creates even stronger evidence that TERS is capable of resolving submolecular features.

UV-Resonance Raman Spectra of Systems in Complex Environments: A Multiscale Modeling Applied to Doxorubicin Intercalated into DNA

UV-Resonance Raman (RR) spectroscopy is a valuable tool to study the binding of drugs to biomolecular receptors. The extraction of information at the molecular level from experimental RR spectra is made much easier and more complete thanks to the use of computational approaches, specifically tuned to deal with the complexity of the supramolecular system. In this paper, we propose a protocol to simulate RR spectra of complex systems at different levels of sophistication, by exploiting a quantum mechanics/molecular mechanics (QM/MM) approach. The approach is challenged to investigate RR spectra of a widely used chemotherapy drug, doxorubicin (DOX) intercalated into a DNA double strand. The computed results show good agreement with experimental data, thus confirming the reliability of the computational protocol.

Time Resolved Raman Scattering of Molecules: A Quantum Mechanics Approach with Stochastic Schroedinger Equation

Raman scattering is a very powerful tool employed to characterize molecular systems. Here we propose a novel theoretical strategy to calculate the Raman cross-section in time domain, by computing the cumulative Raman signal emitted during the molecular evolution in time. Our model is based on a numerical propagation of the vibronic wave function under the effect of a light pulse of arbitrary shape. This approach can therefore tackle a variety of experimental setups. Both resonance and nonresonance Raman scattering can be retrieved, and also the time-dependent fluorescence emission is computed. The model has been applied to porphyrin considering both resonance and nonresonance conditions and varying the incident field duration. Moreover the effect of the vibrational relaxation, which should be taken into account when its time scale is similar to that of the Raman emission, has been included through the stochastic Schroedinger equation approach.

Raman Activities of Cyano-Ester Quinoidal Oligothiophenes Reveal Their Diradical Character and the Proximity of the Low-Lying Double Exciton State

Quinoidal oligothiophenes have received considerable attention as interesting platforms with remarkable amphoteric redox behavior associated with their diradical character increasing with the conjugation lengths. In this work, we considered a family of quinoidal oligothiophenes bearing cyano-ester terminal groups and characterized them by UV-Vis-NIR absorption and Raman spectroscopy measurements at different excitation wavelengths. The experimental investigation is complemented by quantum-chemical studies to assess the quality of computed density functional theory (DFT) ground state structures and their influence on predicted Raman intensities. In addition, resonance conditions with the optically active HOMO→LUMO transition as well as with the more elusive state dominated by the doubly excited HOMO,HOMO→LUMO,LUMO configuration, are determined with DFT-MRCI calculations and their contributions to Raman activity enhancement are discussed in terms of computed vibrational Huang–Rhys (HR) factors.

Radiative lifetime of a BODIPY dye as calculated by TDDFT and EOM-CCSD methods: solvent and vibronic effects

The radiative emission lifetime and associated S₁ excited state properties of a BODIPY dye are investigated with TDDFT and EOM-CCSD calculations. The effects of a solvent are described with the polarizable continuum model using the linear response (LR) approach as well as state-specific methods. The Franck-Condon (FC), Herzberg-Teller (HT) and Duschinsky vibronic effects are evaluated for the absorption and emission spectra, and for the radiative lifetime. The transition energies, spectra shapes and radiative lifetime are assessed with respect to experimental results. It is found that the TDDFT transition energies are overestimated by about 0.4-0.5 eV, whereas EOM-CCSD improves the vertical emission energy by about 0.1 eV in comparison to TDDFT. The solvatochromic and Stokes shifts are better reproduced by the state-specific solvation methods, which show that these methods are more suited than the LR model to describe the solvent effects on the BODIPY dye. The vibronic effects lead to an increase of the radiative lifetime of about 0.4 to 1.0 ns depending on the theoretical approach, which highlights the importance of such effects. Moreover, the HT effects are negligible on both the spectra and lifetime, which demonstrates that the FC approximation is accurate for the BODIPY dye. Finally, the comparison with experimental data shows that the radiative lifetimes predicted by EOM-CCSD and TDDFT have comparable accuracy.

Sum-over-state expressions including second-order Herzberg-Teller effects for the calculation of absorption and resonance Raman intensities

The sum-over-state expressions are derived to calculate the second-order Herzberg-Teller (HT) effects in absorption and resonance Raman spectroscopies. These effects depend on the second derivatives of the transition dipole moment with respect to the vibrational coordinates. The method is applied to the molecule of 1,3-butadiene using density functional theory calculations. It is found that the second-order HT effects are significant for both absorption and resonance Raman intensities, and that the calculated spectra are in good agreement with the experimental data. The second-order HT effects originate from diagonal elements of the second derivatives matrix, whereas non-diagonal elements have a negligible impact on the intensities of 1,3-butadiene.

Classical Correlation Model of Resonance Raman Spectroscopy

A classical correlation model (CCM), based on forces instead of potentials, is developed and applied to resonance Raman scattering to provide a foundation for further advances in understanding the effects of fields and vibronic perturbations on the optical properties of materials by a simple, yet versatile, description. The model consists of a charge connected by a classical spring to a surface and driven by an external electric field. The spring represents the charge cloud of the electrons and the transition strength, and the surface represents the nucleus or molecule. Molecular vibrations are assumed to be many-body effects that change the configuration and hence modify the spring constant directly, as opposed to all previous classical models of Raman scattering, and opposed to the anisotropic bond model (ABM) of nonlinear optics, by adding anharmonic terms to the potential. The resulting expression agrees exactly with quantum mechanical models of resonance Raman scattering in the limit of weak electron-phonon coupling, and it agrees well when the coupling becomes strong. The result is a classical derivation of Kramers-Heisenberg-Dirac scattering theory. We show that the difference between classical and quantum approaches lies only in the interpretation of the prefactor. In particular, the Raman excitation profile shows excellent agreement with all other methods of calculation. By comparing complementary classical and quantum solutions of the same complex system, understanding of both is enhanced.

Role of MLCT States in the Franck-Condon Region of Neutral, Heteroleptic Cu(I)-4H-imidazolate Complexes: A Spectroscopic and Theoretical Study

The impact of the electronic structure of a series of 4H-imidazolate ligands in neutral, heteroleptic Cu(I) complexes is investigated. Remarkable broad and strong ligand-dependent absorption in the visible range of the electromagnetic spectrum renders the studied complexes promising photosensitizers for photocatalytic applications. The electronic structure of the Cu(I) complexes and the localization of photoexcited states in the Franck-Condon region are unraveled by means of UV-vis absorption and resonance Raman (rR) spectroscopy supported by time-dependent density functional theory (TD-DFT) calculations. The visible absorption bands stem from a superposition of bright metal-to-ligand charge-transfer (MLCT) and π-π* as well as weakly absorbing MLCT states. Additionally, the analysis of involved molecular orbitals and rR spectra upon excitation of MLCT and π-π* states highlights the impact of the electronic structure of the 4H-imidazolate ligands on the properties of the corresponding Cu(I) complexes to avail a toolbox for predictive studies and efficient complex design.

Ab Initio Approach to Femtosecond Stimulated Raman Spectroscopy: Investigating Vibrational Modes Probed in Excited-State Relaxation of Quaterthiophenes

Femtosecond stimulated Raman spectroscopy (FSRS) is an ultrafast pump-probe technique designed to elucidate excited-state molecular dynamics by means of vibrational spectroscopy. We present a first-principles protocol for the simulation of FSRS that integrates ab initio molecular dynamics with computational resonance Raman spectroscopy. Theoretical calculations can monitor the time-dependent evolution of specific vibrational modes and thus provide insight into the nature of the motion responsible for the experimental FSRS signal, and we apply this technique to study quaterthiophene derivatives. The S₁ state of two different quaterthiophene derivatives relaxes via in-phase and out-of-phase stretching modes whose frequencies are coupled to the dihedral backbone angle, such that the spectral evolution reflects the excited-state relaxation toward a planar conformation. The simulated spectra aid in confirming the experimental assignment of the vibrational modes that are probed in the existing FSRS experiments on quaterthiophenes.

The chemical effect goes resonant - a full quantum mechanical approach on TERS

Lately, experimental evidence of unexpectedly extremely high spatial resolution of tip-enhanced Raman scattering (TERS) has been demonstrated. Theoretically, two different contributions are discussed: an electromagnetic effect, leading to a spatially confined near field due to plasmonic excitations; and the so-called chemical effect originating from the locally modified electronic structure of the molecule due to the close proximity of the plasmonic system. Most of the theoretical efforts have concentrated on the electromagnetic contribution or the chemical effect in case of non-resonant excitation. In this work, we present a fully quantum mechanical description including non-resonant and resonant chemical contributions as well as charge-transfer phenomena of these molecular-plasmonic hybrid systems at the density functional and the time-dependent density functional level of theory. We consider a surface-immobilized tin(ii) phthalocyanine molecule as the molecular system, which is minutely scanned by a plasmonic tip, modeled by a single silver atom. These different relative positions of the Ag atom to the molecule lead to pronounced alterations of the Raman spectra. These Raman spectra vary substantially, both in peak positions and several orders of magnitude in the intensity patterns under non-resonant and resonant conditions, and also, depending on, which electronic states are addressed. Our computational approach reveals that unique - non-resonant and resonant - chemical interactions among the tip and the molecule significantly alter the TERS spectra and are mainly responsible for the high, possibly sub-Angstrom spatial resolution.

Ab Initio Investigation of the Resonance Raman Spectrum of the Hydrated Electron

According to the conventional picture, the aqueous or "hydrated" electron, e^-(aq), occupies an excluded volume (cavity) in the structure of liquid water. However, simulations with certain one-electron models predict a more delocalized spin density for the unpaired electron, with no distinct cavity structure. It has been suggested that only the latter (non-cavity) structure can explain the hydrated electron's resonance Raman spectrum, although this suggestion is based on calculations using empirical frequency maps developed for neat liquid water, not for e^-(aq). All-electron ab initio calculations presented here demonstrate that both cavity and non-cavity models of e^-(aq) afford significant red-shifts in the O-H stretching region. This effect is nonspecific and arises due to electron penetration into frontier orbitals of the water molecules. Only the conventional cavity model, however, reproduces the splitting of the H-O-D bend (in isotopically mixed water) that is observed experimentally and arises due to the asymmetric environments of the hydroxyl moieties in the electron's first solvation shell. We conclude that the cavity model of e^-(aq) is more consistent with the measured resonance Raman spectrum than is the delocalized, non-cavity model, despite previous suggestions to the contrary. Furthermore, calculations with hybrid density functionals and with Hartree-Fock theory predict that non-cavity liquid geometries afford only unbound (continuum) states for an extra electron, whereas in reality this energy level should lie more than 3 eV below vacuum level. As such, the non-cavity model of e^-(aq) appears to be inconsistent with available vibrational spectroscopy, photoelectron spectroscopy, and quantum chemistry.

Resonance Raman Spectro-Electrochemistry to Illuminate Photo-Induced Molecular Reaction Pathways

Electron transfer reactions play a key role for artificial solar energy conversion, however, the underlying reaction mechanisms and the interplay with the molecular structure are still poorly understood due to the complexity of the reaction pathways and ultrafast timescales. In order to investigate such light-induced reaction pathways, a new spectroscopic tool has been applied, which combines UV-vis and resonance Raman spectroscopy at multiple excitation wavelengths with electrochemistry in a thin-layer electrochemical cell to study [Ru^II(tbtpy)₂]²⁺ (tbtpy = tri-tert-butyl-2,2':6',2''-terpyridine) as a model compound for the photo-activated electron donor in structurally related molecular and supramolecular assemblies. The new spectroscopic method substantiates previous suggestions regarding the reduction mechanism of this complex by localizing photo-electrons and identifying structural changes of metastable intermediates along the reaction cascade. This has been realized by monitoring selective enhancement of Raman-active vibrations associated with structural changes upon electronic absorption when tuning the excitation wavelength into new UV-vis absorption bands of intermediate structures. Additional interpretation of shifts in Raman band positions upon reduction with the help of quantum chemical calculations provides a consistent picture of the sequential reduction of the individual terpyridine ligands, i.e., the first reduction results in the monocation [(tbtpy)Ru(tbtpy^•)]⁺, while the second reduction generates [(tbtpy^•)Ru(tbtpy^•)]⁰ of triplet multiplicity. Therefore, the combination of this versatile spectro-electrochemical tool allows us to deepen the fundamental understanding of light-induced charge transfer processes in more relevant and complex systems.

Structure of the aqueous electron

A cavity or excluded-volume structure best explains the experimental properties of the aqueous or “hydrated” electron.

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

The role of Herzberg-Teller effects on the resonance Raman spectrum of trans-porphycene investigated by time dependent density functional theory

The S₁ excited state properties as well as the associated absorption and resonance Raman (RR) spectra of trans-porphycene are investigated by means of time dependent density functional theory calculations. The relative magnitude of the Franck-Condon (FC) contribution and of the Herzberg-Teller (HT) effects is evaluated for both the absorption and RR intensities. The accuracy of the calculated spectra is assessed by employing different theoretical approximations and by comparing with experimental data. The obtained results show that Duschinsky effects lead to noticeable modifications in the absorption intensities but are nearly negligible in the RR spectrum. By contrast, the HT effects are stronger for the RR intensities compared to the absorption intensities, and these effects significantly improve the agreement with the experimental RR spectrum. Moreover, the HT effects produce different values of the RR depolarization ratios, which can be used to quantify the relative importance of the FC and HT contributions. Generally, it is found that the HT effects have a significant role on the RR spectrum of trans-porphycene and that their inclusion in the computational scheme is mandatory to accurately predict the RR intensities.

Theoretical Assessment of Excited State Gradients and Resonance Raman Intensities for the Azobenzene Molecule

The ground state geometries and vibrational frequencies as well as the excitation energies and excited state gradients of the S₁(nπ*) and S₂(ππ*) states of trans- and cis-azobenzene are investigated by several DFT methods, namely B3LYP, PBE, M06-2X, CAM-B3LYP, and ωB97X. Excited state properties and in particular gradients are also assessed using the wave function based methods EOM-CCSD and RASPT2/RASSCF. Comparison with experimental data shows that the B3LYP functional gives the most accurate results for the ground state geometry and vibrational frequencies. The analysis of the vertical excitation energies reveals that the RASPT2 approach provides the most accurate excitation energies with deviations of the order of 0.1 eV. Among the TDDFT methods, the CAM-B3LYP functional shows the best performance on the excitation energies. By assessing the excited state gradients with respect to the reference RASPT2 data, the most accurate gradients are obtained with B3LYP, whereas other functionals as well as the EOM-CCSD and RASSCF calculations give less consistent results. Overall, despite the tendency of B3LYP to underestimate the excitation energies, this functional provides the most balanced description of both ground and excited state properties for both isomers of azobenzene in the Franck-Condon region.

Multiconfigurational Effects in Theoretical Resonance Raman Spectra

We analyze resonance Raman spectra of the nucleobase uracil in the short‐time approximation calculated with multiconfigurational methods. We discuss the importance of static electron correlation by means of density‐matrix renormalization group self‐consistent field (DMRG‐SCF) calculations. Our DMRG‐SCF results reveal that a minimal active orbital space that leads to a qualitatively correct description of the resonance Raman spectrum of uracil should encompass parts of the σ/σ* bonding/anti‐bonding orbitals of the pyrimidine ring. We trace these findings back to the considerable entanglement between the σ/σ* bonding/anti‐bonding as well as valence π/π* orbitals in the excited‐state electronic structure of uracil, which indicates non‐negligible non‐dynamical correlation effects that are less pronounced in the electronic ground state.

Spectroelectrochemical Investigation of the One-Electron Reduction of Nonplanar Nickel(II) Porphyrins

The electrochemical reduction of a series of nickel porphyrins with an increasing number of substituents was investigated in acetonitrile. A one-electron reduction of [5,15-bis(1-ethylpropyl)porphyrinato]nickel(II) leads to π-anion radicals and to efficient formation of phlorin anions, presumably by disproportionation and subsequent protonation of the doubly reduced species. The phlorin anion was identified by using cyclic voltammetry and UV/Vis and resonance Raman spectroelectrochemistry, complemented by quantum-chemical calculations to assign the spectral signatures. The theoretical analysis of the potential-energy landscape of the singly reduced species suggests a thermally activated intersystem crossing that populates the quartet state and thus lowers the energy barrier towards disproportionation channels. Structure-reactivity correlations are investigated by considering different substitution patterns of the investigated nickel(II) porphyrin cores, that is, for the porphyrin with additional β-aryl ([5,15-bis(1-ethylpropyl)-2,8,12,18-tetra(p-tolyl)porphyrinato]nickel(II)) and meso-alkyl substitution ([5,10,15,20-tetrakis(1-ethylpropyl)porphyrinato]nickel(II)), no phlorin anion formation was observed under electrochemical conditions. This observation is correlated either to kinetic inhibition of the disproportionation reaction or to lower reactivity of the subsequently formed doubly reduced species towards protonation.

Dependence of Adenine Raman Spectrum on Excitation Laser Wavelength: Comparison between Experiment and Theoretical Simulations

We acquired the Raman spectra of adenine in powder and aqueous phase using excitation lasers with 532, 633, and 785 nm wavelengths for the region between 300 and 1500 cm^-1. In comparison to the most distinct peak at 722 cm^-1, the peaks between 1200 and 1500 cm^-1 exhibited a characteristic increase in cross-section with decreasing excitation wavelength in both phases. This trend can be reproduced by different density functional theory (DFT) calculations for the adenine molecule in the gas phase as well as in the aqueous phase. Furthermore, from the calculation on the π-stacked dimer, hydrogen-bonded dimer, and trimer, we find that this trend toward excitation laser wavelength is not sensitive to the packing. When comparing the Raman spectra given by different excitation wavelength, one should take care in analyzing the cross-section, and present day DFT calculations are able to capture general trends in the excitation laser wavelength dependence of the Raman activity.

Synthesis and characterization of ruthenium and rhenium dyes with phosphonate anchoring groups

The synthesis and characterization of new Ru and Re complexes with elongated phosphonate substituents are presented, enabling their immobilization on electrode surfaces.