Accurate Simulation of Resonance-Raman Spectra of Flexible Molecules: An Internal Coordinates Approach

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.

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/.

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates

The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.

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.

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.

Photophysics and Excited State Dynamics of Cyclometalated [M(Phbpy)(CN)] (M = Ni, Pd, Pt) Complexes: A Theoretical and Experimental Study

Cyclometalated complexes [M(Phbpy)(CN)] (HPhbpy = 6-phenyl-2,2'-bipyridine) of the group 10 metals (Ni, Pd, and Pt) bearing a carbanionic ^-C^∧N^∧N pincer ligand were synthesized and studied in a combined experimental and computational DFT approach. All three complexes were crystallographically characterized showing closely packed dimers with head-to-tail stacking and short metal-metal contacts in the solid state. The computational models for geometries, excited states, and electronic transitions addressed both monomeric (Ni-mono, Pd-mono, and Pt-mono) and dimeric (Ni-dim, Pd-dim, and Pt-dim) entities. Photophysical properties and excited state dynamics of all title complexes were investigated in solution and in the solid at 298 and 77 K. [Ni(Phbpy)(CN)] and [Pd(Phbpy)(CN)] are virtually nonemissive in solution at 298 K, whereas [Pt(Phbpy)(CN)] shows phosphorescence in CH₂Cl₂ (DCM) solution (λ_em = 562 nm) stemming from a mixed ³MLCT/ILCT (metal-to-ligand charge transfer/intraligand charge transfer) state. At 77 K in a glassy frozen DCM:MeOH matrix, [Pd(Phbpy)(CN)] shows a remarkable emission (λ_em = 571 nm) with a photoluminescence quantum yield reaching almost unity, whereas [Ni(Phbpy)(CN)] is again nonemissive. Calculations on the monomeric models M-mono show that low-lying metal-centered states (MC, i.e., d-d* configuration) with dissociative character quench the photoluminescence. In the solid state, the complexes [M(Phbpy)(CN)] show defined photoluminescence bands (λ_em = 561 nm for Pd and 701 nm for Pt). Calculations on the dimeric models M-dim shows that the axial M···M interactions alter the photophysical properties of Pd-dim and Pt-dim toward MMLCT (metal-metal-to-ligand charge transfer) excited states with Pd-dim showing temperature-dependent emission lifetimes, suggesting thermally activated delayed fluorescence, whereas Pt-dim displayed phosphorescence with excimeric character. The metal-metal interactions were analyzed in detail with the quantum theory of atoms in molecules approach.

Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG

In this work, we propose a new method to calculate molecular nonradiative electronic relaxation rates based on the numerically exact time-dependent density matrix renormalization group theory. This method could go beyond the existing frameworks under the harmonic approximation (HA) of the potential energy surface (PES) so that the anharmonic effect could be considered, which is of vital importance when the electronic energy gap is much larger than the vibrational frequency. We calculate the internal conversion (IC) rates in a two-mode model with Morse potential to investigate the validity of HA. We find that HA is unsatisfactory unless only the lowest several vibrational states of the lower electronic state are involved in the transition process when the adiabatic excitation energy is relatively low. As the excitation energy increases, HA first underestimates and then overestimates the IC rates when the excited state PES shifts toward the dissociative side of the ground state PES. On the contrary, HA slightly overestimates the IC rates when the excited state PES shifts toward the repulsive side. In both cases, a higher temperature enlarges the error of HA. As a real example to demonstrate the effectiveness and scalability of the method, we calculate the IC rates of azulene from S₁ to S₀ on the ab initio anharmonic PES approximated by the one-mode representation. The calculated IC rates of azulene under HA are consistent with the analytically exact results. The rates on the anharmonic PES are 30%-40% higher than the rates under HA.

Looking for the bricks of the life in the interstellar medium: The fascinating world of astrochemistry

The discovery in the interstellar medium of molecules showing a certain degree of complexity, and in particular those with a prebiotic character, has attracted great interest. A complex chemistry takes place in space, but the processes that lead to the production of molecular species are a matter of intense discussion, the knowledge still being at a rather primitive stage. Debate on the origins of interstellar molecules has been further stimulated by the identification of biomolecular building blocks, such as nucleobases and amino acids, in meteorites and comets. Since many of the molecules found in space play a role in the chemistry of life, the issue of their molecular genesis and evolution might be related to the profound question of the origin of life itself. Understanding the underlying chemical processes, including the production, reactions and destruction of compounds, requires the concomitant study of spectroscopy, gas-phase reactivity, and heterogeneous processes on dust-grains. The aim of this contribution is to provide a general view of a complex and multifaceted challenge, while focusing on the role played by molecular spectroscopy and quantum-chemical computations. In particular, the derivation of the molecular spectroscopic features and the investigation of gas-phase formation routes of prebiotic species in the interstellar medium are addressed from a computational point of view.

Interplay of Stereoelectronic and Vibrational Modulation Effects in Tuning the UPS Spectra of Unsaturated Hydrocarbon Cage Compounds

The UPS spectra of six hydrocarbon cage compounds have been investigated by a Green-function approach in conjunction with a full harmonic treatment of vibrational modulation effects. The remarkable agreement with experimental results points out the reliability of the proposed computational approach and the strong interplay of stereoelectronic and vibrational effects in tuning the overall spectra.

CPL Spectra of Camphor Derivatives in Solution by an Integrated QM/MD Approach

We extend a recently proposed computational strategy for the simulation of absorption spectra of semi-rigid molecular systems in condensed phases to the emission spectra of flexible chromophores. As a case study, we have chosen the CPL spectrum of camphor in methanol solution, which shows a well-defined bisignate shape. The first step of our approach is the quantum mechanical computation of reference spectra including vibrational averaging effects and taking bulk solvent effects into account by means of the polarizable continuum model. In the present case, the large amplitude inversion mode is explicitly treated by a numerical approach, whereas the other small-amplitude vibrational modes are taken into account within the harmonic approximation. Next, the snapshots of classical molecular dynamics computations are clusterized and one representative configuration from each cluster is used to compute a reference spectrum. In the present case, different clusters correspond to the two stable conformers of camphor in the S1 excited electronic state and, for each of them, to different numbers of strong solute-solvent hydrogen bonds. Finally, local fluctuation effects within each cluster are taken into account by means of the perturbed matrix model. The overall procedure leads to good agreement with experiment for absorption and emission spectra together with their chiral counterparts, thus allowing to analyze the role of different effects (stereo-electronic, vibrational, environmental) in tuning the overall experimental spectra.

Adiabatic-Molecular Dynamics Generalized Vertical Hessian Approach: A Mixed Quantum Classical Method To Compute Electronic Spectra of Flexible Molecules in the Condensed Phase

We present a general mixed quantum classical method that couples classical molecular dynamics (MD) and vibronic models to compute the shape of electronic spectra of flexible molecules in the condensed phase without, in principle, any phenomenological broadening. It is based on a partition of the nuclear motions of the solute + solvent system in "soft" and "stiff" vibrational modes and an adiabatic hypothesis that assumes that stiff modes are much faster than soft ones. In this framework, the spectrum is rigorously expressed as a conformational integral of quantum vibronic spectra along the stiff coordinates only. Soft modes enter at the classical level through the conformational distribution that is sampled with classical MD runs. In each configuration, reduced-dimensionality quadratic Hamiltonians are built in the space of the stiff coordinates only, thanks to a generalization of the Vertical Hessian harmonic model and an iterative application of projectors in internal coordinates to remove soft modes. Quantum vibronic spectra, specific for each sampled configuration of the soft coordinates, are then computed at the desired temperature with efficient time-dependent techniques, and the global spectrum simply arises from their average. For consistency of the whole procedure, classical MD runs are performed with quantum-mechanically derived force fields, parameterized at the same level of theory selected for generating the quadratic Hamiltonians along the stiff coordinates. Application to N-methyl-6-oxyquinolinium betaine in water, dithiophene in ethanol, and cyanidine in water is presented to show the performance of the method.

Unbiased Determination of Absolute Configurations by vis-à-vis Comparison of Experimental and Simulated Spectra: The Challenging Case of Diplopyrone

A new experimental-computational strategy for the determination of the absolute configuration (AC) of complex chiral molecules is proposed by combining diverse experimental spectroscopies with quantum-mechanical simulations well beyond the current computational practice. Key features are the conformer search and relative stability evaluation performed by a new stochastic two-level tool followed by a vis-à-vis comparison of experimental and computed spectra without any ad hoc adjustment. The entire computational procedure is embedded in the user-friendly VMS software, and its reliability is granted by the inclusion of mechanic/electric/magnetic anharmonicity as well as ro-vibrational and vibronic couplings by means of generalized perturbation theory in conjunction with double-hybrid functionals combined with empirical dispersion contributions and suitable basis sets. To test and validate the new approach, the puzzling case of diplopyrone, a fungal phytotoxic metabolite, has been chosen: the close match between new experimental and simulated infrared absorption and vibrational circular dichroism spectra has led to the unbiased evaluation of its AC.

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.

On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction

By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.

Challenges in spectroscopy: accuracy versus interpretation from isolated molecules to condensed phases

This themed issue includes a collection of articles on Challenges in spectroscopy: accuracy versus interpretation from isolated molecules to condensed phases.

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.

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

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

Computational simulation of vibrationally resolved spectra for spin-forbidden transitions

In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck-Condon and Herzberg-Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode-mixing effects into account when evaluating Franck-Condon integrals. Spin-orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two-component time-dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

Towards the SMART workflow system for computational spectroscopy

Is it possible to convert highly specialized research in the field of computational spectroscopy into robust and user-friendly aids to experiments and industrial applications?

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.

Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route

We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.

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.

Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates

Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q₁-frame, where Q₁ are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q₁-frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal modes of initial and final states in adiabatic approaches. We highlight that such a dependence of G on s is also an issue in vertical models, due to the necessity to approximate the kinetic term in the Hamiltonian when setting up the so-called GF problem. When large structural differences exist between the initial and the final-state minima, the changes in the G matrix can become too large to be disregarded.

Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate

A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski equations by a robust numerical approach rooted in the discrete variable representation (DVR). Application to a number of case studies shows that the results issuing from our approach are identical to those delivered by previous software (in particular DiTe) for rigid scans along a dihedral angle, but can be improved by employing relaxed scans (i.e., constrained geometry optimizations) or even more general large amplitude paths. The theoretical and numerical background is robust and general enough to allow quite straightforward extensions in several directions (e.g., inclusion of reactive paths, solution of Fokker-Planck or stochastic Liouville equations, multidimensional problems, free-energy rather than electronic-energy driven processes).

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.

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.

Theoretical investigation of the broad one-photon absorption line-shape of a flexible symmetric carbazole derivative

The one-photon absorption spectrum of a carbazole derivative has been studied by employing density functional response theory combined with a mixed quantum/classical approach to simulate the spectral shape.

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.