In this work we carefully investigate the relationship between computed data and experimental electronic spectra. To that end, we compare both vertical transition energies, EV, and characteristic frequencies of the spectrum like the maximum, ν(max), and the center of gravity, M(1), taking advantage of an analytical expression of M(1) in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, experimental spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, we simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with experimental data. Our results indicate that the customary comparison of experimental ν(max) and computational EV, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the investigated systems, are on the order of 0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of experimental and computed M(1) and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs are proposed to help rationalize which kind of correction one should expect when comparing EV, M(1), and ν(max).

When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.

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 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 classical level through the conformational distribution that is sampled with classical MD runs. At 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 a flexible cyanidine in water are presented to show the performance of the method.

For the rational design of new fluorophores, reliable predictions of fluorescence quantum yields from first principles would be of great help. However, efficient computational approaches for predicting transition rates usually assume that the vibrational structure is harmonic. While the harmonic approximation has been used successfully to predict vibrationally resolved spectra and radiative rates, its reliability for non-radiative rates is much more questionable. Since non-adiabatic transitions convert large amounts of electronic energy into vibrational energy, the highly excited final vibrational states deviate greatly from harmonic oscillator eigenfunctions. We employ a time-dependent formalism to compute radiative and non-radiative rates for transitions and study the dependence on model parameters. For several coumarin dyes, we compare different adiabatic and vertical harmonic models (AS, ASF, AH, VG, VGF, and VH), in order to dissect the importance of displacements, frequency changes, and Duschinsky rotations. In addition, we analyze the effect of different broadening functions (Gaussian, Lorentzian, or Voigt). Moreover, to assess the qualitative influence of anharmonicity on the internal conversion rate, we develop a simplified anharmonic model. We address the reliability of these models considering the potential errors introduced by the harmonic approximation and the phenomenological width of the broadening function.

The accuracy of molecular mechanics force fields (FF) reveals critical for applications where precise molecular structures along a conformational sampling are required, as in the simulation of electronic spectroscopies. This implies abandoning generalized FFs in favor of specific FFs, with non-transferable parameters able to accurately describe the targeted species. A promising strategy in this direction consists in the so-called quantum mechanically derived FFs, in which the parameters are fitted onto reference data computed through quantum chemistry. However, in order to obtain a global set of parameters able to reliably describe the reference potential energy surface in different regions of the conformational space, the complexity of the analytical expressions of the FF becomes crucial. Regarding intramolecular interactions, the functional form of standard transferable FFs is restricted to terms that depend on only one internal coordinate. It will be shown that such models may reveal insufficient to describe systems as polyenic chains, where complex electronic effects, e.g. conjugation, intrinsically couple different ICs. We propose a functional form for intramolecular FFs, which includes explicit couplings between flexible dihedrals and stiff ICs (bonds and angles), being able to properly describe the geometrical changes arising not only from steric interactions, but also from conjugation effects, i.e. the change of bond orders induced by conformational changes. The parameterization of the coupled FFs is carried out by means of automated and efficient computational

We present a protocol to estimate the solvent-induced broadening of electronic spectra based on a model that explicitly takes into account the environment embedding the solute. Starting from a classical approximation of the solvent contribution to the spectrum, the broadening arises from the spread of the excitation energies due to the fluctuation of the solvent coordinates, and it is represented as a Gaussian line shape that convolutes the vibronic spectrum of the solute. The latter is computed in harmonic approximation at room temperature with a time-dependent approach. The proposed protocol for the computation of spectral broadening exploits molecular dynamics (MD) simulations performed on the solute-solvent system, keeping the solute degrees of freedom frozen, followed by the computation of the excitation properties with a quantum mechanics/molecular mechanics (QM/MM) approach. The factors that might influence each step of the protocol are analyzed in detail, including the selection of the empirical force field (FF) adopted in the MD simulations and the QM/MM partition of the system to compute the excitation energies. The procedure is applied to a family of coumarin dyes, and the results are compared with experiments and with the predictions of a very recent work (Cerezo et al., Phys. Chem. Chem. Phys. 2015, 17, 11401-11411), where an implicit model was adopted for the solvent. The final spectra of the considered coumarins were obtained without including ad hoc phenomenological parameters and indicate that the broadenings computed with explicit and implicit models both follow the experimental trend, increasing as the polarity change from the initial to the final state increases. More in detail, the implicit model provides larger estimations of the broadening that are closer to the experimental evidence, while explicit models appear to better capture relative differences arising from different solvents or different solutes. Possible inaccuracies of the adopted FF that may lead to the observed underestimation are analyzed in detail.

We study the absorption and emission electronic spectra in an aqueous solution of N-methyl-6-oxyquinolinium betaine (MQ), an interesting dye characterized by a large change of polarity and H-bond ability between the ground (S0) and the excited (S1) states. To that end we compare alternative approaches based either on explicit solvent models and density functional theory (DFT)/molecular-mechanics (MM) calculations or on DFT calculations on clusters models embedded in a polarizable continuum (PCM). In the first approach (ClMD), the spectrum is computed according to the classical Franck-Condon principle, from the dispersion of the time-dependent (TD)-DFT vertical transitions at selected snapshots of molecular dynamics (MD) on the initial state. In the cluster model (Qst) the spectrum is simulated by computing the quantum vibronic structure, estimating the inhomogeneous broadening from state-specific TD-DFT/PCM solvent reorganization energies. While both approaches provide absorption and emission spectral shapes in nice agreement with experiment, the Stokes shift is perfectly reproduced by Qst calculations if S0 and S1 clusters are selected on the grounds of the MD trajectory. Furthermore, Qst spectra better fit the experimental line shape, mostly in absorption. Comparison of the predictions of the two approaches is very instructive: the positions of Qst and ClMD spectra are shifted due to the different solvent models and the ClMD spectra are narrower than the Qst ones, because MD underestimates the width of the vibrational density of states of the high-frequency modes coupled to the electronic transition. On the other hand, both Qst and ClMD approaches highlight that the solvent has multiple and potentially opposite effects on the spectral width, so that the broadening due to solute-solvent vibrations and electrostatic interaction with bulk solvent is (partially) counterbalanced by a narrowing of the contribution due to the solute vibrational modes. Qst analysis evidences a pure quantum broadening effect of the spectra in water due to vibronic progressions along the solute/solvent H-bonds.

A complex mechanical-biological waste treatment plant designed for the processing of mixed municipal solid wastes (MSW) and source-selected organic fraction of municipal solid wastes (OFMSW) has been studied by using stability indices related to aerobic (respiration index, RI) and anaerobic conditions (biochemical methane potential, BMP). Several selected stages of the plant have been characterized: waste inputs, mechanically treated wastes, anaerobically digested materials and composted wastes, according to the treatment sequence used in the plant. Results obtained showed that the main stages responsible for waste stabilization were the two first stages: mechanical separation and anaerobic digestion with a diminution of both RI and BMP around 40% and 60%, respectively, whereas the third stage, composting of digested materials, produced lesser biological degradation (20-30%). The results related to waste stabilization were similar in both lines (MSW and OFMSW), although the indices obtained for MSW were significantly lower than those obtained for OFMSW, which demonstrated a high biodegradability of OFMSW. The methodology proposed can be used for the characterization of organic wastes and the determination of the efficiency of operation units used in mechanical-biological waste treatment plants.