A general time-dependent route to resonance-Raman spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects

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.

Computational Design of Molecular Probes for Electronic Preresonance Raman Scattering Microscopy

Recently developed electronic preresonance stimulated Raman scattering (epr-SRS) microscopy, in which the Raman signal of a dye is significantly boosted by setting the incident laser frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow line-width of epr-SRS also offers high multiplexity that breaks the "color barrier" in optical microscopy. However, detailed understanding of the fundamental mechanism in these epr-SRS dyes still remains elusive. Here, we combine experiments with theoretical modeling to investigate the structure-function relationship, aiming to facilitate the design of new probes and expanding epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO) model provides a consistent agreement between simulated and experimental SRS intensities of various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and compare them to the DHO model. Overall, the theory allows us to illustrate how the observed intensity differences between molecular scaffolds stem from the coupling strength between the electronic excitation and the targeted vibrational mode, leading to a general design strategy for highly sensitive next-generation vibrational imaging probes.

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.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S₁) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

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.

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.

Efficient and Automated Quantum Chemical Calculation of Rovibrational Nonresonant Raman Spectra

An outline of a newly developed program for the simulation of rovibrational nonresonant Raman spectra is presented. This program is an extension of our recently developed code for rovibrational infrared spectra [J. Chem Phys. 152 (2020) 244104] and relies on vibrational wavefunctions from variational configuration interaction theory to allow for an almost fully automated calculation of such spectra in pure ab initio fashion. Due to efficient contraction schemes this program requires modest computational resources and it can be controlled by only a few lines of input. As the required polarizability surfaces are also computed in an automated fashion, this implementation enables the routine application to small molecules. For demonstrating its capabilities, benchmark calculations for water H216O are compared to reference data and spectra for the beryllium dihydride dimer, Be2H4 (D2h), are predicted. The inversion symmetry of the D2h systems lead to complementary infrared and Raman spectra, which are needed both for a comprehensive investigation of this system.

Time-Resolved Raman Spectroscopy of Polaron Formation in a Polymer Photocatalyst

Polymer photocatalysts are a synthetically diverse class of materials that can be used for the production of solar fuels such as H₂, but the underlying mechanisms by which they operate are poorly understood. Time-resolved vibrational spectroscopy provides a powerful structure-specific probe of photogenerated species. Here we report the use of time-resolved resonance Raman (TR³) spectroscopy to study the formation of polaron pairs and electron polarons in one of the most active linear polymer photocatalysts for H₂ production, poly(dibenzo[b,d]thiophene sulfone), P10. We identify that polaron-pair formation prior to thermalization of the initially generated excited states is an important pathway for the generation of long-lived photoelectrons.

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.

Interplay of stereo-electronic, vibronic and environmental effects in tuning the chiroptical properties of an Ir(III) cyclometalated N-heterocyclic carbene

Chiroptical spectra are among the most suitable techniques for investigating the ground and excited electronic states of chiral systems, but their interpretation is not straightforward and strongly benefits from quantum chemical simulations, provided that the employed computational model is sufficiently accurate and deals properly with stereo-electronic, vibrational averaging and environmental effects. Since the synergy among all these effects is only rarely accounted for, especially for large and flexible organometallic systems, the main aim of this contribution is to illustrate the latest developments of computational approaches rooted into the density functional theory for describing stereo-electronic effects and complemented by effective techniques to deal with vibrational modulation effects and solvatochromic shifts. In this connection, chiral iridium complexes offer an especially suitable case study in view of their bright phosphorescence, which is particularly significant for building effective light emitting diodes (OLEDs) and biomarkers and can be finely tuned by the nature of the metal ligands. For instance, a recently synthesized family of cycloiridiated complexes, KC and KD, bearing a pentahelicenic N-heterocyclic carbene (KB), has shown an enhanced long-lasting, bright phosphorescence. Deeper insights into the still unclear nature and origin of the enhancement could be gained by the interpretation of the chiroptical spectra, which is quite challenging in view of the presence of two sources of chirality, the chiral center on Ir and the chiral axis related to the helicene ligand, in addition to the relativistic effects related to the presence of the Ir center. At the same time, the large dimensions of KC and KD hamper the use of the most sophisticated (but prohibitively expensive) computational models, so that more approximate approaches must be validated on a suitable model compound. To this end, after optimizing the computational scheme on a model system devoid of the helicene moiety (KA), we have performed a comprehensive investigation of the KC and KD spectra, whose interpretation is further aided by novel graphical tools. The discussion and analysis of the results will not be focused on the theoretical background, but, rather, on practical details (specific functional, basis set, vibronic model, solvent regime) with the aim of providing general guidelines for the use of last-generation computational spectroscopy tools also by non-specialists.

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.

Single-molecule resonance Raman effect in a plasmonic nanocavity

Tip-enhanced Raman spectroscopy (TERS) is a versatile tool for chemical analysis at the nanoscale. In earlier TERS experiments, Raman modes with components parallel to the tip were studied based on the strong electric field enhancement along the tip. Perpendicular modes were usually neglected. Here, we investigate an isolated copper naphthalocyanine molecule adsorbed on a triple-layer NaCl on Ag(111) using scanning tunnelling microscope TERS imaging. For flat-lying molecules on NaCl, the Raman images present different patterns depending on the symmetry of the vibrational mode. Our results reveal that components of the electric field perpendicular to the tip should be considered aside from the parallel components. Moreover, under resonance excitation conditions, the perpendicular components can play a substantial role in the enhancement. This single-molecule study in a well-defined environment provides insights into the Raman process at the plasmonic nanocavity, which may be useful in the nanoscale metrology of various molecular systems.

Role of Explicit Solvation in the Simulation of Resonance Raman Spectra within Short-Time Dynamics Approximation

In short-time dynamics approximation, relative resonance Raman (RR) intensity of a vibrational mode primarily depends on the magnitude of square of the excited-state gradient along the corresponding normal coordinate, ground-state normal mode eigenvector, and harmonic vibrational wavenumbers. In this study, through simulation of RR spectra of guanosine-5'-monophosphate (GMP) in two ππ* singlet excited states, we analyze how the explicitly hydrogen-bonded local solvation structure of the chromophore dictates intensities of the RR active modes in an unprecedented manner. We show that the accuracy of the structural model of solvated chromophore plays a decisive role in determining an optimal theoretical method for prediction of the Franck-Condon region of the ππ* excited states. 9-Methylguanine (9-meG) in complex with six water molecules (9-meG·6H₂O) is found out to be the most accurate one for describing GMP in two different bright electronic states. We find that explicit hydrogen-bonded water molecules strongly influence computed RR intensities of GMP by modulating both the ground-state normal mode vectors and the excited-state energy gradients. We find that simultaneous inclusion of six explicit waters to describe the solute-solvent interaction near all hydration sites is essential for reliable prediction of the features of RR spectra in L_b and B_b electronic states of GMP.

Roles of silver nanoclusters in surface-enhanced Raman spectroscopy

The cause for the huge enhancement factors of surface-enhanced Raman spectroscopy (SERS) by the addition of small silver nanoclusters is theoretically investigated by focusing on the difference between resonance Raman activity and surface plasmon effects. First, the resonance and off-resonance Raman spectra are calculated using the incident light wavenumbers of the low-lying charge transfer excitations for the surface (S) and vertex (V) complexes of the pyridine molecule attaching to three small silver nanoclusters: Ag₅, Ag₁₀, and Ag₂₀. As a result, it is found that the incident radiation dramatically increases the resonance Raman activities with the enhancement factors up to 10¹². This indicates that the resonance Raman effects are dominant in the enhancement factors of SERS, at least when to use small silver clusters. It is also found that the resonance Raman spectra significantly depend on the adsorption sites given in S or V complexes, and on the inclusion or exclusion of the long-range correction for density functional theory, irrespective of the size of the silver clusters. The electromagnetic field enhancement effects called "surface plasmon effects" are also examined for the Ag₂₀ cluster to confirm this conclusion. Consequently, the enhancement in the electric field is roughly evaluated as less than one for the static polarizability of this small cluster. It is, therefore, concluded that the resonance Raman activity effect is dominant in the huge SERS enhancement factors for, at least, small silver nanoclusters.

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.

Sub-50 fs excited state dynamics of 6-chloroguanine upon deep ultraviolet excitation

The photophysical properties of natural nucleobases and their respective nucleotides are ascribed to the sub-picosecond lifetime of their first singlet states in the UV-B region (260-350 nm). Electronic transitions of the ππ* type, which are stronger than those in the UV-B region, lie at the red edge of the UV-C range (100-260 nm) in all isolated nucleobases. The lowest energetic excited states in the UV-B region of nucleobases have been investigated using a plethora of experimental and theoretical methods in gas and solution phases. The sub-picosecond lifetime of these molecules is not a general attribute of all nucleobases but specific to the five primary nucleobases and a few xanthine and methylated derivatives. To determine the overall UV photostability, we aim to understand the effect of more energetic photons lying in the UV-C region on nucleobases. To determine the UV-C initiated photophysics of a nucleobase system, we chose a halogen substituted purine, 6-chloroguanine (6-ClG), that we had investigated previously using resonance Raman spectroscopy. We have performed quantitative measurements of the resonance Raman cross-section across the Bb absorption band (210-230 nm) and constructed the Raman excitation profiles. We modeled the excitation profiles using Lee and Heller's time-dependent theory of resonance Raman intensities to extract the initial excited state dynamics of 6-ClG within 30-50 fs after photoexcitation. We found that imidazole and pyrimidine rings of 6-ClG undergo expansion and contraction, respectively, following photoexcitation to the Bb state. The amount of distortions of the excited state structure from that of the ground state structure is reflected by the total internal reorganization energy that is determined at 112 cm(-1). The contribution of the inertial component of the solvent response towards the total reorganization energy was obtained at 1220 cm(-1). In addition, our simulation also yields an instantaneous response of the first solvation shell within an ultrafast timescale of less than 30 fs following photoexcitation.

Assessment of Electron Propagator Methods for the Simulation of Vibrationally Resolved Valence and Core Photoionization Spectra

The analysis of photoelectron spectra is usually facilitated by quantum mechanical simulations. Because of the recent improvement of experimental techniques, the resolution of experimental spectra is rapidly increasing, and the inclusion of vibrational effects is usually mandatory to obtain a reliable reproduction of the spectra. With the aim of defining a robust computational protocol, a general time-independent formulation to compute different kinds of vibrationally resolved electronic spectra has been generalized to also support photoelectron spectroscopy. The electronic structure data underlying the simulation are computed using different electron propagator approaches. In addition to the more standard approaches, a new and robust implementation of the second-order self-energy approximation of the electron propagator based on a transition operator reference (TOEP2) is presented. To validate our implementation, a series of molecules has been used as test cases. The result of the simulations shows that, for ultraviolet photoionization spectra, the more accurate nondiagonal approaches are needed to obtain a reliable reproduction of vertical ionization energies but that diagonal approaches are sufficient for energy gradients and pole strengths. For X-ray photoelectron spectroscopy, the TOEP2 approach, besides being more efficient, is also the most accurate in the reproduction of both vertical ionization energies and vibrationally resolved bandshapes.

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Our general framework for the simulation of vibrational signatures in electronic spectra has been extended to treat one large-amplitude motion (LAM) at the anharmonic level, coupled to the other small-amplitude motions (SAM) treated as harmonic. The coupling between LAM and SAM is minimized thanks to the use of delocalized internal coordinates, which are built automatically from the molecular topology. General LAMs can be employed, ranging from intrinsic reaction coordinates to rigid or flexible paths based on the distinguished coordinate approach. The anharmonic model is based on a fully numerical method based on the discrete variable representation (DVR) theory, supporting different types of boundary conditions. The inclusion of this model in a general-purpose electronic structure code makes available to the user a large panel of quantum chemistry models, for both isolated and condensed phases. The flexibility and reliability of the new framework are illustrated by some case studies, covering various types of LAMs, ranging from a small test case, the photoelectron spectrum of ammonia, to larger systems, such as phenylanthracene and cyclobutanone.

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.

Understanding the interplay between the solvent and nuclear rearrangements in the negative solvatochromism of a push–pull flexible quinolinium cation

The main effects (solvation, vibronic progression) affecting the band position and shape of a push–pull flexible quinolinium cation OPA are highlighted.

General formulation of vibronic spectroscopy in internal coordinates

Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.

Optical response of the Cu2 S2 diamond core in Cu2II(NGuaS)2 Cl2

Density functional theory (DFT) and time-dependent DFT calculations are presented for the dicopper thiolate complex Cu2 (NGuaS)2 Cl2 [NGuaS=2-(1,1,3,3-tetramethylguanidino) benzenethiolate] with a special focus on the bonding mechanism of the Cu2 S2 Cl2 core and the spectroscopic response. This complex is relevant for the understanding of dicopper redox centers, for example, the CuA center. Its UV/Vis absorption is theoretically studied and found to be similar to other structural CuA models. The spectrum can be roughly divided in the known regions of metal d-d absorptions and metal to ligand charge transfer regions. Nevertheless the chloride ions play an important role as electron donors, with the thiolate groups as electron acceptors. The bonding mechanism is dissected by means of charge decomposition analysis which reveals the large covalency of the Cu2 S2 diamond core mediated between Cu dz2 and S-S π and π* orbitals forming Cu-S σ bonds. Measured resonant Raman spectra are shown for 360- and 720-nm excitation wavelength and interpreted using the calculated vibrational eigenmodes and frequencies. The calculations help to rationalize the varying resonant behavior at different optical excitations. Especially the phenylene rings are only resonant for 720 nm. © 2016 Wiley Periodicals, Inc.

Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects

Vibrationally resolved one-photon absorption and electronic circular dichroism spectra of (R)-methyl oxirane were calculated with different electronic and vibronic models selecting, through an analysis of the convergence of the results, the best compromise between reliability and computational cost. Linear-response TD-DFT/CAM-B3LYP/SNST electronic computations in conjunction with the simple vertical gradient vibronic model were chosen and employed for systematic comparison with the available experimental data. Remarkable agreement between simulated and experimental spectra was achieved for both one-photon absorption and circular dichroism concerning peak positions, relative intensities, and general spectral shapes considering the computational efficiency of the chosen theoretical approach. The significant improvement of the results with respect to smearing of vertical electronic transitions by phenomenological Gaussian functions and the possible inclusion of solvent effects by polarizable continuum models at a negligible additional cost paves the route toward the simulation and analysis of spectral shapes of complex molecular systems in their natural environment.

The Virtual Multifrequency Spectrometer: a new paradigm for spectroscopy

On going developments of hardware and software are changing computational spectroscopy from a strongly specialized research area to a general tool in the inventory of most researchers. Increased interactions between experimentally-oriented users and theoretically-oriented developers of new methods and models would result in more robust, flexible and reliable tools and studies for the systems of increasing complexity, which are of current scientific and technological interest. This is the philosophy behind this review, which presents the development of a so-called virtual multi-frequency spectrometer (VMS) including state-of-the-art approaches in a user-friendly frame. The current status of the VMS tool will be illustrated by a number of case studies with special reference to infrared and UV-vis regions of the electro-magnetic spectrum including also chiral spectroscopies. Only the basic theoretical background will be provided avoiding explicit equations as far as possible, and pointing out the most recent advancements beyond the standard rigid-rotor harmonic-oscillator model coupled to vertical electronic excitation energies.

Variable-Temperature Tip-Enhanced Raman Spectroscopy of Single-Molecule Fluctuations and Dynamics

Structure, dynamics, and coupling involving single-molecules determine function in catalytic, electronic or biological systems. While vibrational spectroscopy provides insight into molecular structure, rapid fluctuations blur the molecular trajectory even in single-molecule spectroscopy, analogous to spatial averaging in measuring large ensembles. To gain insight into intramolecular coupling, substrate coupling, and dynamic processes, we use tip-enhanced Raman spectroscopy (TERS) at variable and cryogenic temperatures, to slow and control the motion of a single molecule. We resolve intrinsic line widths of individual normal modes, allowing detailed and quantitative investigation of the vibrational modes. From temperature dependent line narrowing and splitting, we quantify ultrafast vibrational dephasing, intramolecular coupling, and conformational heterogeneity. Through statistical correlation analysis of fluctuations of individual modes, we observe rotational motion and spectral fluctuations of the molecule. This work demonstrates single-molecule vibrational spectroscopy beyond chemical identification, opening the possibility for a complete picture of molecular motion ranging from femtoseconds to minutes.

Anharmonic Effects on Vibrational Spectra Intensities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity

The aim of this paper is 2-fold. First, we want to report the extension of our virtual multifrequency spectrometer (VMS) to anharmonic intensities for Raman optical activity (ROA) with the full inclusion of first- and second-order resonances for both frequencies and intensities in the framework of the generalized second-order vibrational perturbation theory (GVPT2) for all kinds of vibrational spectroscopies. Then, from a more general point of view, we want to present and validate the performance of VMS for the parallel analysis of different vibrational spectra for medium-sized molecules (IR, Raman, VCD, ROA) including both mechanical and electric/magnetic anharmonicity. For the well-known methyloxirane benchmark, careful selection of density functional, basis set, and resonance thresholds permitted us to reach qualitative and quantitative agreement between experimental and computed band positions and shapes. Next, the whole series of halogenated azetidinones is analyzed, showing that it is now possible to interpret different spectra in terms of mass, electronegativity, polarizability, and hindrance variation between closely related substituents, chiral spectroscopies being particular effective in this connection.

Virtual eyes for technology and cultural heritage: toward computational strategy for new and old indigo-based dyes

A cost-effective, robust, and reliable computational strategy is applied to simulate peak positions and band-shapes of UV-vis spectra together with the dye colours perceived by human eyes. The features of our virtual multifrequency spectrometer (VMS) relevant to this topic are sketched with special focus on the selection of density functional, vibronic model, and solvent description. Furthermore, the new VMS-Draw graphical user interface (GUI) is employed for user-friendly pre- and post-processing of the computed data. The family of indigo dyes is used as case study in view of their continued use in the field of cultural heritage, together with new promising applications for photonics and sustainable energy. After assessment of different simplified models employed in previous studies, the role of several substituents and of dimerization in tuning the colour and spectral features are analyzed in detail by means of both accurate computations and interpretative models. The results are in remarkable agreement with experiment and allow to rationalize the behaviour of this class of dyes.

Vibrationally resolved optical spectra of modified diamondoids obtained from time-dependent correlation function methods

Optical properties of modified diamondoids have been studied theoretically using vibrationally resolved electronic absorption, emission and resonance Raman spectra. A time-dependent correlation function approach has been used for electronic two-state models, comprising a ground state (g) and a bright, excited state (e), the latter determined from linear-response, time-dependent density functional theory (TD-DFT). The harmonic and Condon approximations were adopted. In most cases origin shifts, frequency alteration and Duschinsky rotation in excited states were considered. For other cases where no excited state geometry optimization and normal mode analysis were possible or desired, a short-time approximation was used. The optical properties and spectra have been computed for (i) a set of recently synthesized sp(2)/sp(3) hybrid species with C[double bond, length as m-dash]C double-bond connected saturated diamondoid subunits, (ii) functionalized (mostly by thiol or thione groups) diamondoids and (iii) urotropine and other C-substituted diamondoids. The ultimate goal is to tailor optical and electronic features of diamondoids by electronic blending, functionalization and substitution, based on a molecular-level understanding of the ongoing photophysics.

CC/DFT Route toward Accurate Structures and Spectroscopic Features for Observed and Elusive Conformers of Flexible Molecules: Pyruvic Acid as a Case Study

The structures and relative stabilities as well as the rotational and vibrational spectra of the three low-energy conformers of pyruvic acid (PA) have been characterized using a state-of-the-art quantum-mechanical approach designed for flexible molecules. By making use of the available experimental rotational constants for several isotopologues of the most stable PA conformer, Tc-PA, the semiexperimental equilibrium structure has been derived. The latter provides a reference for the pure theoretical determination of the equilibrium geometries for all conformers, thus confirming for these structures an accuracy of 0.001 Å and 0.1 deg for bond lengths and angles, respectively. Highly accurate relative energies of all conformers (Tc-, Tt-, and Ct-PA) and of the transition states connecting them are provided along with the thermodynamic properties at low and high temperatures, thus leading to conformational enthalpies accurate to 1 kJ mol(-1). Concerning microwave spectroscopy, rotational constants accurate to about 20 MHz are provided for the Tt- and Ct-PA conformers, together with the computed centrifugal-distortion constants and dipole moments required to simulate their rotational spectra. For Ct-PA, vibrational frequencies in the mid-infrared region accurate to 10 cm(-1) are reported along with theoretical estimates for the transitions in the near-infrared range, and the corresponding infrared spectrum including fundamental transitions, overtones, and combination bands has been simulated. In addition to the new data described above, theoretical results for the Tc- and Tt-PA conformers are compared with all available experimental data to further confirm the accuracy of the hybrid coupled-cluster/density functional theory (CC/DFT) protocol applied in the present study. Finally, we discuss in detail the accuracy of computational models fully based on double-hybrid DFT functionals (mainly at the B2PLYP/aug-cc-pVTZ level) that avoid the use of very expensive CC calculations.