Effective Time-Independent Calculations of Vibrational Resonance Raman Spectra of Isolated and Solvated Molecules Including Duschinsky and Herzberg–Teller Effects

Aggregation of N-Heteropolycyclic Aromatic Molecules: The Acridine Dimer and Trimer

Polycyclic aromatic hydrocarbons and their nitrogen-substituted analogues are of great interest for various applications in organic electronics. The performance of such devices is determined not only by the properties of the single molecules, but also by the structure of their aggregates, which often form via self-aggregation. Gaining insight into such aggregation processes is a challenging task, but crucial for a fine-tuning of the materials properties. In this work, an efficient approach for the generation and characterisation of aggregates is described, based on matrix-isolation experiments and quantum-chemical calculations. This approach is exemplified for aggregation of acridine. The acridine dimer and trimer are thoroughly analysed on the basis of experimental and calculated UV and IR absorption spectra, which agree well with each other. Thereby a novel structure of the acridine dimer is found, which disagrees with a previously reported one. The calculations also show the changes from excitonic coupling towards orbital interactions between two molecules with decreasing distance to each other. In addition, a structure of the trimer is determined. Finally, an outlook is given on how even higher aggregates can be made accessible through experiment.

Calculating absorption and fluorescence spectra for chromophores in solution with ensemble Franck-Condon methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.

The Role of Hydrogen Bonding in the Raman Spectral Signals of Caffeine in Aqueous Solution

The identification and quantification of caffeine is a common need in the food and pharmaceutical industries and lately also in the field of environmental science. For that purpose, Raman spectroscopy has been used as an analytical technique, but the interpretation of the spectra requires reliable and accurate computational protocols, especially as regards the Resonance Raman (RR) variant. Herein, caffeine solutions are sampled using Molecular Dynamics simulations. Upon quantification of the strength of the non-covalent intermolecular interactions such as hydrogen bonding between caffeine and water, UV-Vis, Raman, and RR spectra are computed. The results provide general insights into the hydrogen bonding role in mediating the Raman spectral signals of caffeine in aqueous solution. Also, by analyzing the dependence of RR enhancement on the absorption spectrum of caffeine, it is proposed that the sensitivity of the RR technique could be exploited at excitation wavelengths moderately far from 266 nm, yet achieving very low detection limits in the quantification caffeine content.

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.

Isolated Dimers Versus Solid-State Dimers of N-Heteropolycycles: Matrix-Isolation Spectroscopy in Concert with Quantum Chemistry

In this work, matrix-isolation spectroscopy and quantum-chemical calculations are used together to analyse the structure and properties of weakly bound dimers of the two isomers benzo[a]acridine and benzo[c]acridine. Our measured experimental electronic absorbance spectra agree with simulated spectra calculated for the equilibrium structures of the dimers in gas-phase, but in contrast, disagree with the simulated spectra calculated for the structures obtained by optimising the experimental solid-state structures. This highlights the sensitivity of the electronic excitations with respect to the dimer structures. The comparison between the solid-state and gas-phase dimers shows how far the intermolecular interactions could change the geometric and electronic structure in a disordered bulk material or at device interfaces, imposing consequences for exciton and charge mobility and other material properties.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

The Resonance Raman Spectrum of Cytosine in Water: Analysis of the Effect of Specific Solute-Solvent Interactions and Non-Adiabatic Couplings

In this contribution, we report a computational study of the vibrational Resonance Raman (vRR) spectra of cytosine in water, on the grounds of potential energy surfaces (PES) computed by time-dependent density functional theory (TD-DFT) and CAM-B3LYP and PBE0 functionals. Cytosine is interesting because it is characterized by several close-lying and coupled electronic states, challenging the approach commonly used to compute the vRR for systems where the excitation frequency is in quasi-resonance with a single state. We adopt two recently developed time-dependent approaches, based either on quantum dynamical numerical propagations of vibronic wavepackets on coupled PES or on analytical correlation functions for cases in which inter-state couplings were neglected. In this way, we compute the vRR spectra, considering the quasi-resonance with the eight lowest-energy excited states, disentangling the role of their inter-state couplings from the mere interference of their different contributions to the transition polarizability. We show that these effects are only moderate in the excitation energy range explored by experiments, where the spectral patterns can be rationalized from the simple analysis of displacements of the equilibrium positions along the different states. Conversely, at higher energies, interference and inter-state couplings play a major role, and the adoption of a fully non-adiabatic approach is strongly recommended. We also investigate the effect of specific solute-solvent interactions on the vRR spectra, by considering a cluster of cytosine, hydrogen-bonded by six water molecules, and embedded in a polarizable continuum. We show that their inclusion remarkably improves the agreement with the experiments, mainly altering the composition of the normal modes, in terms of internal valence coordinates. We also document cases, mostly for low-frequency modes, in which a cluster model is not sufficient, and more elaborate mixed quantum classical approaches, in explicit solvent models, need to be applied.

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.

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

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.

Nonadiabatic Vibrational Resonance Raman Spectra from Quantum Dynamics Propagations with LVC Models. Application to Thymine

We present a viable protocol to compute vibrational resonance Raman (vRR) spectra for systems with several close-lying and potentially coupled electronic states. It is based on the parametrization of linear vibronic coupling (LVC) models from time-dependent density functional theory (TD-DFT) calculations and quantum dynamics propagations of vibronic wavepackets with the multilayer version of the multiconfiguration time-dependent Hartree (ML-MCTDH) method. Our approach is applied to thymine considering seven coupled electronic states, comprising the three lowest bright states, and all vibrational coordinates. Computed vRR at different excitation wavelengths are in good agreement with the available experimental data. Up to 250 nm the signal is dominated by the lowest HOMO → LUMO transition, whereas at 233 nm, in the valley between the two lowest energy absorption bands, the contributions of all the three bright states, and their interferences and couplings, are important. Inclusion of solvent (water) effects improves the agreement with experiment, reproducing the coalescence of vibrational bands due to CC and C═O stretchings. With our approach we disentangle and assess the effect of interferences between the contribution of different quasi-resonant states to the transition polarizability and the effect of interstate couplings. Our findings strongly suggest that in cases of close-lying and potentially coupled states a simple inclusion of interference effects is not sufficient, and a fully nonadiabatic computation should instead be performed. We also document that for systems with strong couplings and quasi-degenerate states, the use of HT perturbative approach, not designed for these cases, may lead to large artifacts.

Computational Model for Electrochemical Surface-Enhanced Raman Scattering: Key Role of the Surface Charges and Synergy between Electromagnetic and Charge-Transfer Enhancement Mechanisms

We present a computational model for electrochemical surface-enhanced Raman scattering (EC-SERS). The surface excess of charge induced by the electrode potential (V_el) was introduced by applying an external electric field to a set of clusters [Ag_n]^q with (n, q) of (19, ±1) or (20, 0) on which a molecule adsorbs. Using DFT/TD-DFT calculations, these metal-molecule complexes were classified by the adsorbate partial charge, and the main V_el-dependent properties were simultaneously studied with the aid of vibronic resonance Raman computations, namely, changes on the vibrational wavenumbers, relative intensities, and enhancement factors (EFs) for all SERS mechanisms: chemical or nonresonant, and resonance Raman with bright states of the adsorbate, charge-transfer (CT) states, and plasmon-like excitations on the metal cluster. We selected two molecules to test our model, pyridine, for which V_el has a remarkable effect, and 9,10-bis((E)-2-(pyridin-4-yl)vinyl)anthracene, which is almost insensitive to the applied bias. The results nicely reproduced most of the experimental observations, while the limitations of our approach were critically evaluated. We detected that accounting explicitly for the surface charges is key for EC-SERS models and that the highest calculated EFs, up to 10⁷ to 10⁸, are obtained by interstate coupling of bright local excitations of the metal cluster and CT states. These results highlight the importance of nonadiabatic effects in SERS and the capabilities of EC-SERS as a technique with potential to study excited-state coupling by tuning the CT and plasmon-like states by manipulating V_el.

Substituent Effect on Vibrationally Resolved Absorption Spectra and Exciton Dynamics of Dipyrrolonaphthyridinedione Aggregates

Dipyrrolonaphthyridinedione (DPND) thin films exhibit interesting photophysical properties and singlet fission (SF) processes. A recent experimental work found that the alkyl substitution in the DPND skeleton has the remarkable influence on the characteristics of electronic absorption spectra and SF rates. Here, we theoretically elucidate the microscopic mechanism of the substituent effect on the optical properties and exciton dynamics of materials by combining the electronic structure calculations and the quantum dynamics simulations. The results show that the alkyl substituent has a minor effect on the single molecular properties but dramatically changes those of DPND aggregates via varying the intermolecular interactions. The aggregates of DPND with and without alkyl side chains exhibit the more likely characters of H-type aggregations. In the former (DPND6), the weak degree of mixing of intramolecular localized excited (LE) states and intermolecular charge transfer (CT) states makes the low-energy absorption band possess the predominant optical absorption, while in the latter (DPND), the CT and LE states are close in energy, together with their strong interaction, resulting in the substantial state-mixing, so that its two low-energy absorption bands have nearly equal oscillator strengths and a wide energy spacing of more than 0.5 eV. The simulation of exciton dynamics elucidates that the photoinitiated states in both aggregates cannot generate the free charge carrier because of the lack of enough driving forces. However, the population exchanges between LE and CT states in DPND aggregates are much faster than in DPND6 aggregates, indicating the different SF behaviors, consistent with the experimental observation.

Amide Spectral Fingerprints are Hydrogen Bonding-Mediated

The origin of the peculiar amide spectral features of proteins in aqueous solution is investigated, by exploiting a combined theoretical and experimental approach to study UV Resonance Raman (RR) spectra of peptide molecular models, namely N-acetylglycine-N-methylamide (NAGMA) and N-acetylalanine-N-methylamide (NALMA). UVRR spectra are recorded by tuning Synchrotron Radiation at several excitation wavelengths and modeled by using a recently developed multiscale protocol based on a polarizable QM/MM approach. Thanks to the unparalleled agreement between theory and experiment, we demonstrate that specific hydrogen bond interactions, which dominate hydration dynamics around these solutes, play a crucial role in the selective enhancement of amide signals. These results further argue the capability of vibrational spectroscopy methods as valuable tools for refined structural analysis of peptides and proteins in aqueous solution.

Vibronic Coupling Effect on the Vibrationally Resolved Electronic Spectra and Intersystem Crossing Rates of a TADF Emitter: 7-PhQAD

Assessing and improving the performance of organic light-emitting diode (OLED) materials require quantitative prediction of rate coefficients for the intersystem crossing (ISC) and reverse ISC (RISC) processes, which are determined not only by the energy gap and the direct spin-orbit coupling (SOC) between the first singlet and triplet excited-states at a thermal equilibrium position of the initial electronic state but also by the non-Condon effects such as the Herzberg-Teller-like vibronic coupling (HTVC) and the spin-vibronic coupling (SVC). Here we apply the time-dependent correlation function approaches to quantitatively calculate the vibrationally resolved absorption and fluorescence spectra and ISC/RISC rates of a newly synthesized multiple-resonance-type (MR-type) thermally activated delayed fluorescence (TADF) emitter, 7-phenylquinolino[3,2,1-de]acridine-5,9-dione (7-PhQAD), with the inclusion of the Franck-Condon (FC), HTVC, and Duschinsky rotation (DR) effects. The SVC effect on the rates has also been approximately evaluated. We find that the experimentally measured ISC rates of 7-PhQAD originate predominantly from the vibronic coupling, consistent with the previous reports on other MR-type TADF emitters. The SVC effect on ISC rates is about 10 times larger than the HTVC effect, and the latter increases the ISC rates by more than 1 order of magnitude while it slightly affects the vibrationally resolved absorption and fluorescence spectra. The discrepancy between the theoretical and experimental results is attributed to inaccurately describing excited-states calculated by the time-dependent density functional theory as well as to not fully accounting for the complex experimental conditions. This work provides a demonstration of what proportion of ISC and RISC rate coefficients of a MR-type TADF emitter can be covered by the HTVC effect, and it opens design routes that go beyond the FC approximation for the future development of high-performance OLED devices.

Ring Vibrations to Sense Anionic Ibuprofen in Aqueous Solution as Revealed by Resonance Raman

We unravel the potentialities of resonance Raman spectroscopy to detect ibuprofen in diluted aqueous solutions. In particular, we exploit a fully polarizable quantum mechanics/molecular mechanics (QM/MM) methodology based on fluctuating charges coupled to molecular dynamics (MD) in order to take into account the dynamical aspects of the solvation phenomenon. Our findings, which are discussed in light of a natural bond orbital (NBO) analysis, reveal that a selective enhancement of the Raman signal due to the normal mode associated with the C-C stretching in the ring, νC=C, can be achieved by properly tuning the incident wavelength, thus facilitating the recognition of ibuprofen in water samples.

Quantum Mechanics/Fluctuating Charge Protocol to Compute Solvatochromic Shifts

Despite the potentialities of the quantum mechanics (QM)/fluctuating charge (FQ) approach to model the spectral properties of solvated systems, its extensive use has been hampered by the lack of reliable parametrizations of solvents other than water. In this paper, we substantially extend the applicability of QM/FQ to solvating environments of different polarities and hydrogen-bonding capabilities. The reliability and robustness of the approach are demonstrated by challenging the model to simulate solvatochromic shifts of four organic chromophores, which display large shifts when dissolved in apolar, aprotic or polar, protic solvents.

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.

Theoretical method for near-field Raman spectroscopy with multipolar Hamiltonian and real-time-TDDFT: Application to on- and off-resonance tip-enhanced Raman spectroscopy

Tip-enhanced Raman spectroscopy in combination with scanning tunneling microscopy could produce ultrahigh-resolution Raman spectra and images for single-molecule vibrations. Furthermore, a recent experimental study successfully decoupled the interaction between the molecule and the substrate/tip to investigate the intrinsic properties of molecules and their near-field interactions by Raman spectroscopy. In such a circumstance, more explicit treatments of the near field and molecular interactions beyond the dipole approximation would be desirable. Here, we propose a theoretical method based on the multipolar Hamiltonian that considers full spatial distribution of the electric field under the framework of real-time time-dependent density functional theory. This approach allows us to treat the on- and off-resonance Raman phenomena on the same footing. For demonstration, a model for the on- and off-resonance tip-enhanced Raman process in benzene was constructed. The obtained Raman spectra are well understood by considering both the spatial structure of the near field and the molecular vibration in the off-resonance condition. For the on-resonance condition, the Raman spectra are governed by the transition moment, in addition to the selection rule of off-resonance Raman. Interestingly, on-resonance Raman can be activated even when the near field forbids the π-π^* transition at equilibrium geometry due to vibronic couplings originating from structural distortions.

Accurate Computation of the Absorption Spectrum of Chlorophyll a with Pair Natural Orbital Coupled Cluster Methods

The ability to accurately compute low-energy excited states of chlorophylls is critically important for understanding the vital roles they play in light harvesting, energy transfer, and photosynthetic charge separation. The challenge for quantum chemical methods arises both from the intrinsic complexity of the electronic structure problem and, in the case of biological models, from the need to account for protein–pigment interactions. In this work, we report electronic structure calculations of unprecedented accuracy for the low-energy excited states in the Q and B bands of chlorophyll a. This is achieved by using the newly developed domain-based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD) in combination with sufficiently large and flexible basis sets. The results of our DLPNO–STEOM-CCSD calculations are compared with more approximate approaches. The results demonstrate that, in contrast to time-dependent density functional theory, the DLPNO–STEOM-CCSD method provides a balanced performance for both absorption bands. In addition to vertical excitation energies, we have calculated the vibronic spectrum for the Q and B bands through a combination of DLPNO–STEOM-CCSD and ground-state density functional theory frequency calculations. These results serve as a basis for comparison with gas-phase experiments.

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.

Theoretical insights into UV-Vis absorption spectra of difluoroboron β-diketonates with an extended π system: An analysis based on DFT and TD-DFT calculations

The UV-Vis absorption spectra of difluoroboron β-diketonates with aromatic substituents at the β-carbon are studied thoroughly using DFT and TD-DFT with the CAM-B3LYP functional. The complicated experimental spectra of these dyes can be correctly interpreted by considering their structural features. A closer look at the calculated data shows that the conformational flexibility of these compounds markedly influences their spectral shape. For the complexes with an extended π system, several conformers with significantly different absorption spectra are present in the equilibrium mixture in solution. Introducing a donor group alters the electronic structure of the complexes, so the charge distribution asymmetry in the molecules increases and the nature of the electronic transitions changes. Thus, both types of substituents, aromatic and donor ones, affect the spectral shape. Understanding their roles may help one to explain the absorption spectra of these and similar compounds and predict their response to analytes and other factors.

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.

Sulfate radical induced degradation of β2-adrenoceptor agonists salbutamol and terbutaline: Phenoxyl radical dependent mechanisms

The present study investigated the reactivity and oxidation mechanisms of salbutamol (SAL) and terbutaline (TBL), two typical β2-adrenoceptor agonists, towards sulfate radical (SO₄^-) by using photo-activated persulfate (PS). The reaction pathways and mechanisms were proposed based on products identification using high resolution HPLC-ESI-MS, laser flash photolysis (LFP) and molecular orbital calculations. The results indicated that SO₄^- was the dominant reactive species in the UV/PS process. The second-order rate constants of sulfate radical reaction with SAL and TBL were measured as (3.7 ± 0.3) × 10⁹ and (4.2 ± 0.3) × 10⁹ M^-1 s^-1 by LFP, respectively. For both SAL and TBL, phenoxyl radicals were found to play key roles in the orientation of the primary pathways. For SAL, a benzophenone derivative was generated by oxidation of the phenoxyl radical. However, in the case of TBL, the transformation of the phenoxyl radical into benzoquinone was impossible. Instead, the addition of OSO₃H on the aromatic ring was the major pathway. The same reactivity pattern was observed in the case of TBL structural analogs resorcinol and 3,5-dihydroxybenzyl alcohol. Our results revealed that basic conditions inhibited the decomposition of SAL and TBL, while, increasing PS dose enhanced the degradation. The present work could help for a better understanding of the difference in oxidation reactivity of substituted phenols widely present in natural waters.

Nonempirical Simulations of Inhomogeneous Broadening of Electronic Transitions in Solution: Predicting Band Shapes in One- and Two-Photon Absorption Spectra of Chalcones

We have examined several approaches relying on the Polarizable Embedding (PE) scheme to predict optical band shapes for two chalcone molecules in methanol solution. The PE-TDDFT and PERI-CC2 methods were combined with molecular dynamics simulations, where the solute geometry was kept either as rigid, flexible or partly-flexible (restrained) body. The first approach, termed RBMD-PE-TDDFT, was employed to estimate the inhomogeneous broadening for subsequent convolution with the vibrationally-resolved spectra of the molecule in solution determined quantum-mechanically (QM). As demonstrated, the RBMD-PE-TDDFT/QM-PCM approach delivers accurate band widths, also reproducing their correct asymmetric shapes. Further refinement can be obtained by the estimation of the inhomogeneous broadening using the RBMD-PERI-CC2 method. On the other hand, the remaining two approaches (FBMD-PE-TDDFT and ResBMD-PE-TDDFT), which lack quantum-mechanical treatment of molecular vibrations, lead to underestimated band widths. In this study, we also proposed a simple strategy regarding the rapid selection of the exchange-correlation functional for the simulations of vibrationally-resolved one- and two-photon absorption spectra based on two easy-to-compute metrics.

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.

Can the Resonance Raman Optical Activity Spectrum Display Sign Alternation?

The monosignate character of resonance Raman optical activity (RROA) spectra has been often taken as granted in experimental and computational approaches, on the basis of basic theoretical approximations only considering resonance with a single electronic state of the molecule and the scattering process to be governed by the Franck-Condon mechanism. We show in this letter for the first time that, by resorting to a fully quantum mechanical (QM) methodology able to take into account all terms entering the general definition of RROA, and which considers excited state interference and Herzberg-Teller effects, sign alternation and at the same time intensity enhancement in RROA spectra is obtained. Such features constitute an important milestone toward the exploration of RROA of a wide range of chiral biological molecules.

Assessment of Franck-Condon Methods for Computing Vibrationally Broadened UV-vis Absorption Spectra of Flavin Derivatives: Riboflavin, Roseoflavin, and 5-Thioflavin

We address the performance of the vertical and adiabatic Franck-Condon (VFC/AFC) approaches combined with time-independent or time-dependent (TI/TD) formalisms in simulating the one-photon absorption spectra of three flavin compounds with distinct structural features. Calculations were done in the gas phase and in two solvents (water, benzene) for which experimental reference measurements are available. We utilized the independent mode displaced harmonic oscillator model without or with frequency alteration (IMDHO/IMDHO-FA) and also accounted for Duschinsky mixing effects. In the initial validation on the first excited singlet state of riboflavin, the range-separated functionals, CAM-B3LYP and ωB97xD, showed the best performance, but B3LYP also gave a good compromise between peak positions and spectral topology. Large basis sets were not mandatory to obtain high-quality spectra for the selected systems. The presence of a symmetry plane facilitated the computation of vibrationally broadened spectra, since different FC variants yield similar results and the harmonic approximation holds rather well. Compared with the AFC approach, the VFC approach performed equally well or even better for all three flavins while offering several advantages, such as avoiding error-prone geometry optimization procedures on excited-state surfaces. We also explored the advantages of curvilinear displacements and of a Duschinsky treatment for the AFC spectra in cases when a rotatable group is present on the chromophore. Taken together, our findings indicate that the combination of the VFC approach with the TD formalism and the IMDHO-FA model offers the best overall performance.

Advances in theory and their application within the field of zeolite chemistry

Zeolites are versatile and fascinating materials which are vital for a wide range of industries, due to their unique structural and chemical properties, which are the basis of applications in gas separation, ion exchange and catalysis. Given their economic impact, there is a powerful incentive for smart design of new materials with enhanced functionalities to obtain the best material for a given application. Over the last decades, theoretical modeling has matured to a level that model guided design has become within reach. Major hurdles have been overcome to reach this point and almost all contemporary methods in computational materials chemistry are actively used in the field of modeling zeolite chemistry and applications. Integration of complementary modeling approaches is necessary to obtain reliable predictions and rationalizations from theory. A close synergy between experimentalists and theoreticians has led to a deep understanding of the complexity of the system at hand, but also allowed the identification of shortcomings in current theoretical approaches. Inspired by the importance of zeolite characterization which can now be performed at the single atom and single molecule level from experiment, computational spectroscopy has grown in importance in the last decade. In this review most of the currently available modeling tools are introduced and illustrated on the most challenging problems in zeolite science. Directions for future model developments will be given.

Exploring the vibrational fingerprint of the electronic excitation energy via molecular dynamics

A Fourier-based method is presented to relate changes of the molecular structure during a molecular dynamics simulation with fluctuations in the electronic excitation energy. The method implies sampling of the ground state potential energy surface. Subsequently, the power spectrum of the velocities is compared with the power spectrum of the excitation energy computed using time-dependent density functional theory. Peaks in both spectra are compared, and motions exhibiting a linear or quadratic behavior can be distinguished. The quadratically active motions are mainly responsible for the changes in the excitation energy and hence cause shifts between the dynamic and static values of the spectral property. Moreover, information about the potential energy surface of various excited states can be obtained. The procedure is illustrated with three case studies. The first electronic excitation is explored in detail and dominant vibrational motions responsible for changes in the excitation energy are identified for ethylene, biphenyl, and hexamethylbenzene. The proposed method is also extended to other low-energy excitations. Finally, the vibrational fingerprint of the excitation energy of a more complex molecule, in particular the azo dye ethyl orange in a water environment, is analyzed.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

The temperature dependence of vibronic lineshapes: linear electron-phonon coupling

We calculate the effect of a linear electron-phonon coupling on vibronic transitions of dye molecules of arbitrary complexity. With the assumption of known vibronic frequencies (for instance from quantum-chemical calculations), we give expressions for the absorption or emission lineshapes in a second-order cumulant expansion. We show that the results coincide with those obtained from generalized Redfield theory if one uses the time-local version of the theory and applies the secular approximation. Furthermore, the theory allows to go beyond the Huang-Rhys approximation and can be used to incorporate Dushinsky effects in the treatment of the temperature dependence of optical spectra. We consider both, a pure electron-phonon coupling independent of the molecular vibrations and a coupling bilinear in the molecular vibrational modes and the phonon coordinates. We discuss the behavior of the vibronic density of states for various models for the spectral density representing the coupling of the vibronic system to the harmonic bath. We recover some of the results that have been derived earlier for the spin-boson model and we show that the behavior of the spectral density at low frequencies determines the dominant features of the spectra. In case of the bilinear coupling between the molecular vibrations and the phonons we give analytical expressions for different spectral densities. The spectra are reminiscent of those obtained from the well known Brownian oscillator model and one finds a zero-phonon line and phonon-side bands located at vibrational frequencies of the dye. The intensity of the phonon-side bands diminishes with increasing vibrational frequencies and with decreasing coupling strength (Huang-Rhys factor). It vanishes completely in the Markovian limit where only a Lorentzian zero-phonon line is observed.