Absorption and Emission Spectral Shapes of a Prototype Dye in Water by Combining Classical/Dynamical and Quantum/Static Approaches

A Cost-Effective Computational Strategy for the Electronic Layout Characterization of a Second Generation Light-Driven Molecular Rotary Motor in Solution

Light-driven molecular rotary motors are nanometric machines able to convert light into unidirectional motions. Several types of molecular motors have been developed to better respond to light stimuli, opening new avenues for developing smart materials ranging from nanomedicine to robotics. They have great importance in the scientific research across various disciplines, but a detailed comprehension of the underlying ultrafast photophysics immediately after photo-excitation, that is, Franck-Condon region characterization, is not fully achieved yet. For this aim, it is first required to rely on an accurate description at ab initio level of the system in this potential energy region before performing any further step, that is, dynamics. Thus, we present an extensive investigation aimed at accurately describing the electronic structure of low-lying electronic states (electronic layout) of a molecular rotor in the Franck-Condon region, belonging to the class of overcrowded alkenes: 9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene. This system was chosen since its photophysics is very interesting for a more general understanding of similar compounds used as molecular rotors, where low-lying electronic states can be found (whose energetic interplay is crucial in the dynamics) and where the presence of different substituents can tune the HOMO-LUMO gap. For this scope, we employed different theory levels within the time-dependent density functional theory framework, presenting also a careful comparison adopting very accurate post Hartree-Fock methods and characterizing also the different conformations involved in the photocycle. Effects on the electronic layout of different functionals, basis sets, environment descriptions, and the role of the dispersion correction were all analyzed in detail. In particular, a careful treatment of the solvent effects was here considered in depth, showing how the implicit solvent description can be accurate for excited states in the Franck-Condon region by testing both linear-response and state-specific formalisms. As main results, we chose two cost-effective (accurate but relatively cheap) theory levels for the ground and excited state descriptions, and we also verified how choosing these different levels of theory can influence the curvature of the potential via a frequency analysis of the normal modes of vibrations active in the Raman spectrum. This theoretical survey is a crucial step towards a feasible characterization of the early stage of excited states in solution during photoisomerization processes wherein multiple electronic states might be populated upon the light radiation, leading to a future molecular-level interpretation of time-resolved spectroscopies.

The role of microenvironments on computed vibrationally-resolved emission spectra: The case of oxazines

Oxazine dyes act as reporters of their near environment by the response of their fluorescence spectra. At the same time, their fluorescence spectra exhibit a pronounced vibrational progression. In this work, we computationally investigate the impact of near-environment models consisting of aggregated water as well as betaine molecules on the vibrational profile of fluorescence spectra of different oxazine derivatives. For aggregated betaine and a water molecule located above the plane of the dyes, we observe a distinct modification of the vibrational profile, which is more pronounced than the effect of a continuum description of a solvent environment. Our analysis shows that this effect cannot be explained by a pure change in the electronic structure, but that also vibrational degrees of freedom of the environment can be decisive for the vibrational profile and should, hence, not generally be neglected.

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

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

First-Principles Modeling of the Absorption Spectrum of Crystal Violet in Solution: The Importance of Environmentally Driven Symmetry Breaking

Theoretical spectroscopy plays a crucial role in understanding the properties of the materials and molecules. One of the most promising methods for computing optical spectra of chromophores embedded in complex environments from the first principles is the cumulant approach, where both (generally anharmonic) vibrational degrees of freedom and environmental interactions are explicitly accounted for. In this work, we verify the capabilities of the cumulant approach in describing the effect of complex environmental interactions on linear absorption spectra by studying Crystal Violet (CV) in different solvents. The experimental absorption spectrum of CV strongly depends on the nature of the solvent, indicating strong coupling to the condensed-phase environment. We demonstrate that these changes in absorption line shape are driven by an increased splitting between absorption bands of two low-lying excited states that is caused by a breaking of the D3 symmetry of the molecule and that in polar solvents, this symmetry breaking is mainly driven by electrostatic interactions with the condensed-phase environment rather than distortion of the structure of the molecule, in contrast with conclusions reached in a number of previous studies. Our results reveal the importance of explicitly including a counterion in the calculations in nonpolar solvents due to electrostatic interactions between CV and the ion. In polar solvents, these interactions are strongly reduced due to solvent screening effects, thus minimizing the symmetry breaking. Computed spectra in methanol are found to be in reasonable agreement with the experiment, demonstrating the strengths of the outlined approach in modeling strong environmental interactions.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Photophysics of a nucleic acid-protein crosslinking model strongly depends on solvation dynamics: an experimental and theoretical study

We present a combined experimental and theoretical study of the photophysics of 5-benzyluracil (5BU) in methanol, which is a model system for interactions between nucleic acids and proteins. A molecular dynamics study of 5BU in solution through efficient DFT-based hybrid ab initio potentials revealed a remarkable conformational flexibility - allowing the population of two main conformers - as well as specific solute-solvent interactions, which both appear as relevant factors for the observed 5BU optical absorption properties. The simulated absorption spectrum, calculated on such an ensemble, enabled a molecular interpretation of the experimental UV-Vis lowest energy band, which is also involved in the induced photo-reactivity upon irradiation. In particular, the first two excited states (mainly involving the uracil moiety) both contribute to the 5BU lowest energy absorption. Moreover, as a key finding, the nature and brightness of such electronic transitions are strongly influenced by 5BU conformation and the microsolvation of its heteroatoms.

How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability

As an important quantity in atomic and molecular spectroscopy, oscillator strength should be mentioned. Oscillator strength is linked to the transition dipole moment and consequently to the transition probability between two states, where its magnitude is directly connected to the intensity of the peaks in ultraviolet-visible spectra. However, accurately accounting for oscillator strengths still remains one of the greatest challenges in theory and experiment. Given previous efforts in the context of investigations into oscillator strengths, the related theoretical treatments are relatively limited and have proven to be challenging. In this work, the oscillator strengths in the electronic spectra of organic compounds have thoroughly been investigated with the help of optimally tuned range-separated hybrids (OT-RSHs). In particular, variants of the OT-RSHs combined with the polarizable continuum model (PCM), OT-RSHs-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the dielectric constant, OT-SRSHs-PCM, are proposed for reliable prediction of the oscillator strengths. The role of the involved ingredients in the proposed methods, namely the underlying density functional approximations, short-range and long-range Hartree-Fock (HF) exchange, as well as the range-separation parameter, has been examined in detail. It is shown that any combination of the parameters in the proposed approximations does not render the reliable oscillator strengths, but a particular compromise among them is needed to describe the experimental data well. Perusing all the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM, coupled with the linear response theory in the non-equilibrium solvation regime, with the correct asymptotic behavior and incorporating no (low) HF exchange contributions in the short-range part. The best proposed approximations also reveal superior performances not only with respect to their standard counterparts with the default parameters but also as compared to earlier range-separated functionals. Finally, the applicability of the best approximation is also put into broader perspective, where it is used for predicting the oscillator strengths in other sets of compounds not included in the process of developing the approximations. Hopefully, our proposed method can function as an affordable alternative to the expensive wave function-based methods for both theoretical modeling and confirming the experimental observations in the field of electronic spectroscopy.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

An Expedited Route to Optical and Electronic Properties at Finite Temperature via Unsupervised Learning

Electronic properties and absorption spectra are the grounds to investigate molecular electronic states and their interactions with the environment. Modeling and computations are required for the molecular understanding and design strategies of photo-active materials and sensors. However, the interpretation of such properties demands expensive computations and dealing with the interplay of electronic excited states with the conformational freedom of the chromophores in complex matrices (i.e., solvents, biomolecules, crystals) at finite temperature. Computational protocols combining time dependent density functional theory and ab initio molecular dynamics (MD) have become very powerful in this field, although they require still a large number of computations for a detailed reproduction of electronic properties, such as band shapes. Besides the ongoing research in more traditional computational chemistry fields, data analysis and machine learning methods have been increasingly employed as complementary approaches for efficient data exploration, prediction and model development, starting from the data resulting from MD simulations and electronic structure calculations. In this work, dataset reduction capabilities by unsupervised clustering techniques applied to MD trajectories are proposed and tested for the ab initio modeling of electronic absorption spectra of two challenging case studies: a non-covalent charge-transfer dimer and a ruthenium complex in solution at room temperature. The K-medoids clustering technique is applied and is proven to be able to reduce by ∼100 times the total cost of excited state calculations on an MD sampling with no loss in the accuracy and it also provides an easier understanding of the representative structures (medoids) to be analyzed on the molecular scale.

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

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

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

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

Unraveling the contributions to the spectral shape of flexible dyes in solution: insights on the absorption spectrum of an oxyluciferin analogue

We present a computational investigation of the absorption spectrum in water of 5,5-spirocyclopropyl-oxyluciferin (5,5-CprOxyLH), an analogue of the emitter compound responsible for the bioluminescence in fireflies. Several factors participate in determining the 5,5-CprOxyLH's spectral shape: (i) the contribution of the four close-energy excited states, which show significant non-adiabatic couplings, (ii) the flexible molecular structure and (iii) the specific interactions established with the surrounding environment, which strongly couple the protic solvent dynamics with the dye's spectral response. To tackle the challenge to capture and dissect the role of all these effects we preliminarily investigate the role of non-adiabatic couplings with quantum dynamics simulations and a linear vibronic coupling model in the gas phase. Then, we account for both the molecular flexibility and solvent interactions by resorting to a mixed quantum classical protocol, named Adiabatic Molecular Dynamics generalized Vertical Gradient (Ad-MD|gVG), which is built on a method recently proposed by some of us. It is rooted in the partition between stiff degrees of freedom of the dye, accounted for at the vibronic level within the harmonic approximation, and flexible degrees of freedom of the solute (and of the solvent), described classically through a sampling based on Molecular Dynamics (MD). Ad-MD|gVG avoids spurious effects arising in the excited state Hessians due to non-adiabatic couplings, and can therefore be applied to account for the contributions of the first four excited states to the 5,5-CprOxyLH absorption spectrum. The final simulated spectrum is in very good agreement with the experiment, especially when the MD is driven by a refined quantum-mechanically derived force-field. More importantly, the origin of each separate contribution to the spectral shape is appropriately accounted for, paving the way to future applications of the method to more complex systems or alternative spectroscopies, as emission or circular dichroism.

Cyclo[18]carbon including zero-point motion: ground state, first singlet and triplet excitations, and hole transfer

Recent synthesis of cyclo[18]carbon has spurred increasing interest in carbon rings. We focus on a comparative inspection of ground and excited states, as well as of hole transfer properties of cumulenic and polyynic cyclo[18]carbon via Density Functional Theory (DFT), time-dependent DFT (TD-DFT) and real-time time-dependent DFT (RT-TDDFT). Zero-point vibrations are also accounted for, using a Monte Carlo sampling technique and a less exact, yet mode-resolved, quadratic approximation. The inclusion of zero-point vibrations leads to a red-shift on the HOMO-LUMO gap and the first singlet and triplet excitation energies of both conformations, correcting the values of the 'static' configurations by 9% to 24%. Next, we oxidize the molecule, creating a hole at one carbon atom. Hole transfer along polyynic cyclo[18]carbon is decreased in magnitude compared to its cumulenic counterpart and lacks the symmetric features the latter displays. Contributions by each mode to energy changes and hole transfer between diametrically opposed atoms vary, with specific bond-stretching modes being dominant.

Contributions of higher-order proximal distribution functions to solvent structure around proteins

The proximal distribution function (pDF) quantifies the probability of finding a solvent molecule in the vicinity of solutes. The approach constitutes a hierarchically organized theory for constructing approximate solvation structures around solutes. Given the assumption of universality of atom cluster-specific solvation, reconstruction of the solvent distribution around arbitrary molecules provides a computationally convenient route to solvation thermodynamics. Previously, such solvent reconstructions usually considered the contribution of the nearest-neighbor distribution only. We extend the pDF reconstruction algorithm to terms including next-nearest-neighbor contribution. As a test, small molecules (alanine and butane) are examined. The analysis is then extended to include the protein myoglobin in the P6 crystal unit cell. Molecular dynamics simulations are performed, and solvent density distributions around the solute molecules are compared with the results from different pDF reconstruction models. It is shown that the next-nearest-neighbor modification significantly improves the reconstruction of the solvent number density distribution in concave regions and between solute molecules. The probability densities are then used to calculate the solute-solvent non-bonded interaction energies including van der Waals and electrostatic, which are found to be in good agreement with the simulated values.

Multiconfigurational Quantum Chemistry Determinations of Absorption Cross Sections (σ) in the Gas Phase and Molar Extinction Coefficients (ε) in Aqueous Solution and Air-Water Interface

Theoretical determinations of absorption cross sections (σ) in the gas phase and molar extinction coefficients (ε) in condensed phases (water solution, interfaces or surfaces, protein or nucleic acids embeddings, etc.) are of interest when rates of photochemical processes, J = ∫ ϕ(λ) σ(λ) I(λ) dλ, are needed, where ϕ(λ) and I(λ) are the quantum yield of the process and the irradiance of the light source, respectively, as functions of the wavelength λ. Efficient computational strategies based on single-reference quantum-chemistry methods have been developed enabling determinations of line shapes or, in some cases, achieving rovibrational resolution. Developments are however lacking for strongly correlated problems, with many excited states, high-order excitations, and/or near degeneracies between states of the same and different spin multiplicities. In this work, we define and compare the performance of distinct computational strategies using multiconfigurational quantum chemistry, nuclear sampling of the chromophore (by means of molecular dynamics, ab initio molecular dynamics, or Wigner sampling), and conformational and statistical sampling of the environment (by means of molecular dynamics). A new mathematical approach revisiting previous absolute orientation algorithms is also developed to improve alignments of geometries. These approaches are benchmarked through the nπ* band of acrolein not only in the gas phase and water solution but also in a gas-phase/water interface, a common situation for instance in atmospheric chemistry. Subsequently, the best strategy is used to compute the absorption band for the adduct formed upon addition of an OH radical to the C6 position of uracil and compared with the available experimental data. Overall, quantum Wigner sampling of the chromophore with molecular dynamics sampling of the environment with CASPT2 electronic-structure determinations arise as a powerful methodology to predict meaningful σ(λ) and ε(λ) band line shapes with accurate absolute intensities.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Multiresolution continuous wavelet transform for studying coupled solute-solvent vibrations via ab initio molecular dynamics

Vibrational analysis in solution and the theoretical determination of infrared and Raman spectra are of key importance in many fields of chemical interest. Vibrational band dynamics of molecules and their sensitivity to the environment can also be captured by these spectroscopies in their time dependent version. However, it is often difficult to provide an interpretation of the experimental data at the molecular scale, such as molecular mechanisms or the processes hidden behind them. In this work, we present a theoretical-computational protocol based on ab initio molecular dynamics simulations and a combination of normal-like (generalized) mode analysis of solute-solvent clusters with a wavelet transform, for the first time. The case study is the vibrational dynamics of N-methyl-acetamide (NMA) in water solution, a well-known model of hydration of peptides and proteins. Amide modes are typical bands of peptide and protein backbone, and their couplings with the environment are very challenging in terms of the accurate prediction of solvent induced intensity and frequency shifts. The contribution of water molecules surrounding NMA to the composition of generalized and time resolved modes is introduced in our vibrational analysis, showing unequivocally its influence on the amide mode spectra. It is also shown that such mode compositions need the inclusion of the first shell solvent molecules to be accurately described. The wavelet analysis is proven to be strongly recommended to follow the time evolution of the spectra, and to capture vibrational band couplings and frequency shifts over time, preserving at the same time a well-balanced time-frequency resolution. This peculiar feature also allows one to perform a combined structural-vibrational analysis, where the different strengths of hydrogen bond interactions can quantitatively affect the amide bands over time at finite temperature. The proposed method allows for the direct connection between vibrational modes and local structural changes, providing a link from the spectroscopic observable to the structure, in this case the peptide backbone, and its hydration layouts.

Insights for vibronic effects on spectral shapes of electronic circular dichroism and circularly polarized luminescence of aza[7]helicene

We present a systematic study of vibrationally resolved absorption (ABS), electronic circular dichroism (ECD), emission (EMI), and circularly polarized luminescence (CPL) of aza[7]helicene. Because of the rare experience of theoretical CPL calculation, a variety of harmonic models have been employed to compute the vibronic structures. To fully understand the vibronic effects on the spectral shapes, Franck-Condon (FC) and Herzberg-Teller (HT) contributions, Duschinsky mixings and temperature effect have all been taken into consideration. The performance of different alternative approximate methods has been carefully compared and discussed in detail. The results show that Vertical Hessian (VH) model has a slight better performance on the spectral shapes than Adiabatic Hessian (AH), especially for CPL spectrum. The thermal excitation effect has led to a reduced resolution and a broader spectral width. The moderate HT effects on the different spectral shapes have been addressed. The dissymmetry factors have been correctly reproduced and the main vibronic features of the four different spectral shapes have been successfully captured. A good estimation of the overall spectral width, relative position and relative height of different spectral bands has been presented. The nice agreement with the experiment allows us to present a detailed interpretation of the spectral shapes.

Ab-initio molecular dynamics and hybrid explicit-implicit solvation model for aqueous and nonaqueous solvents: GFP chromophore in water and methanol solution as case study

Solute-solvent interactions are proxies for understanding how the electronic density of a chromophore interacts with the environment in a more exhaustive way. The subtle balance between polarization, electrostatic, and non-bonded interactions need to be accurately described to obtain good agreement between simulations and experiments. First principles approaches providing accurate configurational sampling through molecular dynamics may be a suitable choice to describe solvent effects on solute chemical-physical properties and spectroscopic features, such as optical absorption of dyes. In this context, accurate energy potentials, obtained by hybrid implicit/explicit solvation methods along with employing nonperiodic boundary conditions, are required to represent bulk solvent around a large solute-solvent cluster. In this work, a novel strategy to simulate methanol solutions is proposed combining ab initio molecular dynamics, a hybrid implicit/explicit flexible solvent model, nonperiodic boundary conditions, and time dependent density functional theory. As case study, the robustness of the proposed protocol has been gauged by investigating the microsolvation and electronic absorption of the anionic green fluorescent protein chromophore in methanol and aqueous solution. Satisfactory results are obtained, reproducing the microsolvation layout of the chromophore and, as a consequence, the experimental trends shown by the optical absorption in different solvents.

Vibrationally resolved electronic circular dichroism and circularly polarized luminescence spectra of a boron-fused double helicene: A theoretical study

In this work, we present the theoretical study of the vibrationally resolved absorption (ABS), electronic circular dichroism (ECD), emission (EMI), and circularly polarized luminescence (CPL) spectra of a boron-fused double helicene, with a detailed and complete discussion of the alternative possible approximate methods. Given the fact that few examples of CPL calculations exist, the potential energy surfaces (PESs) have been constructed and compared with Adiabatic (AH) and Vertical Hessian (VH) models. All the vibronic calculations have accounted for Duschinsky mixings, Franck-Condon (FC) effect and Herzberg-Teller (HT) contribution. Moreover, different HT expansions have been checked and compared, by computing the derivatives of the electric and magnetic dipole transition moments around the equilibrium geometries of the initial and final states. Our results show that both AH and VH models have well reproduced the experimental vibronic structures and VH model shows a better performance in the simulation of spectral lineshapes. They also show that HT effects dominate the shapes of EMI and CPL, tuning the relative heights of the different vibronic peaks, improving the agreement with the experiment for EMI. Moreover, HT effects are the main reason for the mirror-symmetry breaking between ECD and CPL spectra. Furthermore, interesting interference effects between FC and HT contributions have also been addressed.

Vibrations of the guanine-cytosine pair in chloroform: an anharmonic computational study

We compute at the anharmonic level the vibrational spectra of the Watson-Crick dimer formed by guanosine (G) and cytidine (C) in chloroform, together with those of G, C and the most populated GG dimer. The spectra for deuterated and partially deuterated GC are also computed. We use DFT calculations, with B3LYP and CAM-B3LYP as reference functionals. Solvent effects from chloroform are included via the Polarizable Continuum Model (PCM), and by performing tests on models including up two chloroform molecules. Both B3LYP and CAM-B3LYP calculations reproduce the shape of the experimental spectra well in the fingerprint region (1500-1700 cm-1) and in the N-H stretching region (2800-3600 cm-1), with B3LYP providing better quantitative agreement with experiments. According to our calculations, the N-H amido streching mode of G falls at ∼2900 cm-1, while the N-H amino of G and C falls at ∼3100 cm-1 when hydrogen-bonded, or ∼3500 cm-1 when free. Overtone and combination bands strongly contribute to the absorption band at ∼3300 cm-1. Inclusion of bulk solvent effects significantly increases the accuracy of the computed spectra, while solute-solvent interactions have a smaller, though still noticeable, effect. Some key aspects of the anharmonic treatment of strongly vibrationally coupled supermolecular systems and the related methodological issues are also discussed.

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.

Role of specific solute–solvent interactions on the photophysical properties of distyryl substituted BODIPY derivatives

The role played by specific solute–solvent interactions on the spectroscopic properties of experimentally available BODIPY derivatives has been investigated.

Unveiling anharmonic coupling by means of excited state ab initio dynamics: application to diarylethene photoreactivity

In this work, excited state ab initio molecular dynamics together with a time resolved vibrational analysis is employed to shed light on the vibrational photoinduced dynamics of a well-known diarylethene molecule experiencing a ring opening reaction upon electronic excitation. The photoreactivity of diarylethenes is recognized to be controlled by a non-adiabatic intersection point between the ground and the first excited state surfaces. The computation of an energy scan, along a suitable reaction coordinate, allows us to identify the region of potential energy surfaces in which the ground (S0) and the first excited (S1) state are well separated. The adiabatic sampling of that region in S1 shows that in the first 3 picoseconds, the central CC bond, which is subject to break, oscillates in an antiphase with respect to the energy gap ΔE(S1 - S0). A multiresolution analysis based on the wavelet transform was then applied to the structural parameters extracted from the excited state dynamics. The wavelet maps show characteristic oscillations of the frequencies, mainly CC stretching and CCC bending localized on the central 4-ring moiety. Moreover, we have identified the main frequency (methyl wagging motion) involved in the modulation of these oscillations. The anharmonic coupling within a group of vibrational modes was therefore highlighted, in good agreement with experimental evidence. For the first time, a quantitative analysis of time resolved signals from a wavelet transform/ab initio molecular dynamics approach was performed.

Evaluating excited state atomic polarizabilities of chromophores

Ground and excited state atomic polarizabilities of the chromophores N-methyl-6-oxyquinolinium betaine and coumarin 153 have been evaluated via quantum mechanics.

Ground and excited state dipoles and polarizabilities of the chromophores N-methyl-6-oxyquinolinium betaine (MQ) and coumarin 153 (C153) in solution have been evaluated using time-dependent density functional theory (TD-DFT). A method for determining the atomic polarizabilities has been developed; the molecular dipole has been decomposed into atomic charge transfer and polarizability terms, and variation in the presence of an electric field has been used to evaluate atomic polarizabilities. On excitation, MQ undergoes very site-specific changes in polarizability while C153 shows significantly less variation. We also conclude that MQ cannot be adequately described by standard atomic polarizabilities based on atomic number and hybridization state. Changes in the molecular polarizability of MQ (on excitation) are not representative of the local site-specific changes in atomic polarizability, thus the overall molecular polarizability ratio does not provide a good approximation for local atom-specific polarizability changes on excitation. Accurate excited state force fields are needed for computer simulation of solvation dynamics. The chromophores considered in this study are often used as molecular probes. The methods and data reported here can be used for the construction of polarizable ground and excited state force fields. Atomic and molecular polarizabilities (ground and excited states) have been evaluated over a range of functionals and basis sets. Different mechanisms for including solvation effects have been examined; using a polarizable continuum model, explicit solvation and via sampling of clusters extracted from a MD simulation. A range of different solvents have also been considered.

The modeling of the absorption lineshape for embedded molecules through a polarizable QM/MM approach

We present a polarizable QM/MM strategy to simulate the absorption line shape of chromophores embedded in complex matrices, including both homogeneous and inhomogeneous broadening.

Photoactivated proton coupled electron transfer in DNA: insights from quantum mechanical calculations

The energetics of the two main proton coupled electron transfer processes that could occur in DNA are determined by means of time dependent-DFT calculations, using the M052X functional and the polarizable continuum model to include solvent effect.

Combined UMC- DFT prediction of electron-hole coupling in unit cells of pentacene crystals

Pentacene is an organic semiconductor that draws special attention from the scientific community due to the high mobility of its charge carriers. As electron-hole interactions are important aspects in the regard of such property, a computationally inexpensive method to predict the coupling between these quasi-particles is highly desired. In this work, we propose a hybrid methodology of combining Uncoupled Monte Carlo Simulations (UMC) and Density functional Theory (DFT) methodologies to obtain a good compromise between computational feasibility and accuracy. As a first step in considering a Pentacene crystal, we describe its unit cell: the Pentacene Dimer. Because many conformations can be encountered for the dimer and considering the complexity of the system, we make use of UMC in order to find the most probable structures and relative orientations for the Pentacene-Pentacene complex. Following, we carry out electronic structure calculations in the scope of DFT with the goal of describing the electron-hole coupling on the most probable configurations obtained by UMC. The comparison of our results with previously reported data on the literature suggests that the methodology is well suited for describing transfer integrals of organic semiconductors. The observed accuracy together with the smaller computational cost required by our approach allows us to conclude that such methodology might be an important tool towards the description of systems with higher complexity.

Quantum-Classical Calculation of Vibronic Spectra along a Reaction Path: The Case of the ECD of Easily Interconvertible Conformers with Opposite Chiral Responses

We present a novel mixed method suitable for computing the low-to-middle resolution spectra of systems characterized by a large-amplitude motion s (defined by either a reaction or an internal path) coupled to a bath of harmonic oscillators r, which change with s. The method is based on an adiabatic approximation whereby s is considered much slower than r degrees of freedom and is treated classically. We show that the spectrum can be obtained by a suitable average of quantum vibronic spectra of the fast coordinates computed at representative values of the slow coordinate along the path. By our method we calculate the electronic circular dichroism (ECD) of 2,2,2-trifluoro-anthryl-ethanol, which possesses two conformers with opposite chirality separated by a low-energy barrier. Path-averaged spectra are significantly different from those obtained only at the stable minima: Agreement with experiment is improved. The method represents a generalization of those currently based on harmonic approximation.

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.

Elucidating the Mechanism of Zn(2+) Sensing by a Bipyridine Probe Based on Two-Photon Absorption

In this work, we examine, by means of computational methods, the mechanism of Zn(2+) sensing by a bipyridine-centered, D-π-A-π-D-type ratiometric molecular probe. According to recently published experimental data [Divya, K. P.; Sreejith, S.; Ashokkumar, P.; Yuzhan, K.; Peng, Q.; Maji, S. K.; Tong, Y.; Yu, H.; Zhao, Y.; Ramamurthy, P.; Ajayaghosh, A. A ratiometric fluorescent molecular probe with enhanced two-photon response upon Zn(2+) binding for in vitro and in vivo bioimaging. Chem. Sci. 2014, 5, 3469-3474], after coordination to zinc ions the probe exhibits a large enhancement of the two-photon absorption cross section. The goal of our investigation was to elucidate the mechanism behind this phenomenon. For this purpose, linear and nonlinear optical properties of the unbound (cation-free) and bound probe were calculated, including the influence of solute-solvent interactions, implicitly using a polarizable continuum model and explicitely employing the QM/MM approach. Because the results of the calculations indicate that many conformers of the probe are energetically accessible at room temperature in solution and hence contribute to the signal, structure-property relationships were also taken into account. Results of our simulations demonstrate that the one-photon absorption bands for both the unbound and bound forms correspond to the bright π → π* transition to the first excited state, which, on the other hand, exhibits negligible two-photon activity. On the basis of the results of the quadratic response calculations, we put forward a notion that it is the second excited state that gives the strong signal in the experimental nonlinear spectrum. To explain the differences in the two-photon absorption activity for the two lowest-lying excited states and nonlinear response enhancement upon binding, we employed the generalized few-state model including the ground, first, and second excited states. The analysis of the optical channel suggests that the large two-photon response is due to the coordination-induced increase of the transition moment from the first to the second excited state.

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and Experiment

Natural anthocyanin pigments/dyes and phenolic copigments/co-dyes form noncovalent complexes, which stabilize and modulate (in particular blue, violet, and red) colors in flowers, berries, and food products derived from them (including wines, jams, purees, and syrups). This noncovalent association and their electronic and optical implications constitute the copigmentation phenomenon. Over the past decade, experimental and theoretical studies have enabled a molecular understanding of copigmentation. This review revisits this phenomenon to provide a comprehensive description of the nature of binding (the dispersion and electrostatic components of π-π stacking, the hydrophobic effect, and possible hydrogen-bonding between pigment and copigment) and of spectral modifications occurring in copigmentation complexes, in which charge transfer plays an important role. Particular attention is paid to applications of copigmentation in food chemistry.

Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases

The photophysics and photochemistry of DNA is of great importance due to the potential damage of the genetic code by UV light. Quantum mechanical studies have played a key role in interpretating the results of modern time-resolved pump-probe spectroscopy, and in elucidating the main photoactivated reactive paths. This review provides a concise, complete picture of the computational studies carried out, approximately, in the past decade. We start with an overview of the photophysics of the nucleobases in the gas phase and in solution. We discuss the proposed mechanisms for ultrafast decay to the ground state, that involve conical intersections, consider the role of triplet states, and analyze how the solvent modulates the photophysics. Then we move to larger systems, from dinucleotides to single- and double-stranded oligonucleotides. We focus on the possible role of charge transfer and delocalized or excitonic states in the photophysics of these systems and discuss the main photochemical paths. We finish with an outlook on the current challenges in the field and future directions of research.

Disentangling vibronic and solvent broadening effects in the absorption spectra of coumarin derivatives for dye sensitized solar cells

Individuation of vibronic and solvent contributions to the spectra of a family of coumarin dyes helps to understand the main differences in their lineshapes.