Electronic Absorption Spectra and Solvatochromic Shifts by the Vertical Excitation Model: Solvated Clusters and Molecular Dynamics Sampling

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.

Computational Exploration of 1,2-Carboamine Carbonylation Catalyzed by Nickel

Nickel-catalyzed carbonylation of alkenes is a stereoselective and regioselective method for the synthesis of amide compounds. Theoretical predictions with density functional theory calculations revealed the mechanism and origin of stereoselectivity and regioselectivity for the nickel-catalyzed carbonylation of norbornene. The carbonylation reaction proceeds through oxidative addition, migration insertion of alkenes, and subsequent reduction elimination to afford cis-carbonylation product. The C-N bond activation of amides is unfavorable because the oxidative addition ability of the C-C bond is stronger than that of the C-N bond. The determining step of stereoselectivity is the migratory insertion of the strained olefin. The structural analysis shows that steroselectivity is controlled by the steric hindrance of methyl groups to olefins and substituents to IMes in ligands.

Absorption spectra of p-nitroaniline derivatives: charge transfer effects and the role of substituents

CONTEXT

Push-pull compounds are model systems and have numerous applications. By changing their substituents, properties are modified and new molecules for different applications can be designed. The work investigates the gas-phase electronic absorption spectra of 15 derivatives of push-pull para-nitroaniline (pNA). This molecule has applications in pharmaceuticals, azo dyes, corrosion inhibitors, and optoelectronics. Both electron-donor and electron-withdrawing groups were investigated. Employing machine learning-derived Hammett's constants σm, σm0, σR, and σI, correlations between substituents and electronic properties were obtained. Overall, the σm0 constants presented the best correlation with HOMO and LUMO energies, whereas the σR constants best agreed with the transition energy of the first band and HOMO-LUMO energy gap. Electron-donors, which have lower σR values, redshift the absorption spectrum and reduce the HOMO-LUMO energy gap. Conversely, electron-withdrawing groups (higher σR's) blueshift the spectrum and increase the energy gap. The second band maximum energies, studied here for the first time, showed no correlation with σ but tended to increase with σ. A comprehensive charge transfer (CT) analysis of the main transition of all systems was also carried out. We found that donors (lower σ's) slightly enhance the CT character of the unsubstituted pNA, whereas acceptors (higher σ's) decrease it, leading to increased local excitations within the aromatic ring. The overall CT variation is not large, except for pNA-SO2H, which considerably decreases the total CT value. We found that the strong electron donors pNA-OH, pNA-OCH3, and pNA-NH2, which have the smallest HOMO-LUMO energy gaps and lowest σ's, have potential for optoelectronic applications. The results show that none of the studied molecules is fluorescent in the gas phase. However, pNA-NH2 and pNA-COOH in cyclohexane and water reveal fluorescence upon solvation.

METHODS

We investigated theoretically employing the second-order algebraic diagrammatic construction (ADC(2)) ab initio wave function and time-dependent density functional theory (TDDFT) the gas-phase electronic absorption spectra of 15 derivatives of p-nitroaniline (pNA). The investigated substituents include both electron-donor (C6H5, CCH, CH3, NH2, OCH3, and OH,) and electron-withdrawing (Br, CCl3, CF3, Cl, CN, COOH, F, NO2, and SO2H) substituents.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Solute - solvent repulsion effects on the absorption spectra of anthracene in n-hexane investigated under high pressure

The band positions in the UV-VIS absorption spectra of compressed solution of anthracene in n-hexane significantly depend not only on the dispersive but also on the repulsive solute-solvent interactions, what has so far been omitted. Their strength is determined not only by the solvent polarity but also by Onsager cavity radius changing with pressure. The results obtained for anthracene show that repulsive interactions should be included in the interpretation of barochromic and solvatochromic results of aromatic compounds. We show that the barochromic studies in the liquid solvent can be an alternative to solvatochromic studies, e.g. to determine the polarizability of organic molecules in the electronic excited state. The pressure-induced polarity change in n-hexane exceeds that induced by the exchange of n-alkane solvents between n-pentane and n-hexadecane.

Spatial Decay and Limits of Quantum Solute-Solvent Interactions

Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy decays with increasing intermolecular distance and vanishes at ∼9 Å, and this pattern is independent of the type of solvent environment. The 9 Å cutoff defines an effective interacting volume within which the ionization energy shift per solvent molecule is proportional to the macroscopic solvent polarizability. Finally, we propose a simple model for computing the ionization energies of molecules in an arbitrary solvent environment.

Predicting the Electronic Absorption Band Shape of Azobenzene Photoswitches

Simulations based on molecular dynamics coupled to excitation energy calculations were used to generate simulated absorption spectra for a family of halide derivatives of azobenzene, a family of photoswitch molecules with a weak absorption band around 400-600 nm and potential uses in living tissue. This is a case where using the conventional approach in theoretical spectroscopy (estimation of absorption maxima based on the vertical transition from the potential energy minimum on the ground electronic state) does not provide valid results that explain how the observed band shape extends towards the low energy region of the spectrum. The method affords a reasonable description of the main features of the low-energy UV-Vis spectra of these compounds. A bathochromic trend was detected linked to the size of the halide atom. Analysis of the excitation reveals a correlation between the energy of the molecular orbital where excitation starts and the energy of the highest occupied atomic orbital of the free halide atom. This was put to the test with a new brominated compound with good results. The energy level of the highest occupied orbital on the free halide was identified as a key factor that strongly affects the energy gap in the photoswitch. This opens the way for the design of bathochromically shifted variants of the photoswitch with possible applications.

A Simplified Treatment for Efficiently Modeling the Spectral Signal of Vibronic Transitions: Application to Aqueous Indole

In this paper, we introduce specific approximations to simplify the vibronic treatment in modeling absorption and emission spectra, allowing us to include a huge number of vibronic transitions in the calculations. Implementation of such a simplified vibronic treatment within our general approach for modelling vibronic spectra, based on molecular dynamics simulations and the perturbed matrix method, provided a quantitative reproduction of the absorption and emission spectra of aqueous indole with higher accuracy than the one obtained when using the existing vibronic treatment. Such results, showing the reliability of the approximations employed, indicate that the proposed method can be a very efficient and accurate tool for computational spectroscopy.

Substituent effects on the UV-visible spectrum and excited electronic states of dithiocarboxylates

The absorption spectra of a series of dithiocarboxylates were investigated in the ultraviolet-visible region. Two questions that this study aimed to address were as follows: (1) What transitions give rise to the features in the electronic spectra? And (2) what are the long- and short-range substituent effects on the absorption spectra? A series of 11 dithiocarboxylates were prepared as organic soluble salts. Time-dependent density functional theory (TDDFT) was used to calculate excited state energies and oscillator strengths of electronic transitions. TDDFT at the CAM-B3LYP/def2-TZVPD level of theory predicts two low-energy n → π* transitions and two π → π* transitions at higher energy, consistent with the experimental spectra. This state ordering and density is in contrast to the better studied thiocarbonyls for which only two transitions within the singlet manifold appear in the UV-visible region. For derivatives of dithiobenzoate, the energy of the three lowest energy states are insensitive to changes to substituents para to the dithiocarboxylate group. In contrast, the energy of the highest ππ* state varies by 0.78 eV. This work shows that the results of TDDFT calculations can be used to predict the electronic absorption spectra of dithiocarboxylates, providing a useful tool for designing dithiocarboxylate light absorbers.

Reaction of •OH with CHCl=CH-CHF2 and its atmospheric implication for future environmental-friendly refrigerant

In order to understand the atmospheric implication of the chlorinated hydrofluoroolefin (HFO), the geometrical structures and the IR absorption cross sections of the stereoisomers 1-chloro-3,3-difluoropropene were studied using the B3LYP/6-31G(3df) and M06-2X/6-31G(3df) methods in the gas phase. The cis-trans isomerization was assessed using the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method. The latter method was also employed for thermochemistry and the rate coefficients of the reactions of •OH with the cis- and trans-isomers in the temperature ranging from 200 to 400 K. The computational method CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) was used to benchmark the rate coefficients. It turns out that, the trans-isomer is more stable than cis-isomer and the trans- to cis-isomerization is thermodynamically unfavorable. The rate coefficient follows the Gaussian law with respect to the inverse of temperature. At the global temperature of stratosphere, the calculated rate coefficients served to estimate the atmospheric lifetime along with the photochemical ozone creation potential (POCP). This yielded lifetimes of 4.31 and 7.31 days and POCPs of 3.80 and 2.23 for the cis- and trans-isomer, respectively. The radiative forcing efficiencies gave 0.0082 and 0.0152 W m−2 ppb−1 for the cis- and trans-isomer, respectively. The global warming potential approached zero for both stereoisomers at 20, 100, and 500 years time horizons.

Quantum Mechanics/Fluctuating Charge Protocol to Compute Solvatochromic Shifts

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

Multiscale Modeling of Electronic Spectra Including Nuclear Quantum Effects

Theoretical prediction of electronic absorption spectra without input from experiments is no easy feat, as it requires addressing all of the factors that affect line shapes. In practice, however, the methodologies are limited to treat these ingredients only to a certain extent. Here, we present a multiscale protocol that addresses the temperature, solvent, and nuclear quantum effects as well as anharmonicity and the reconstruction of the final spectra from individual transitions. First, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is conducted to obtain trajectories of solute-solvent configurations, from which the corresponding quantum-corrected ensembles are generated through the generalized smoothed trajectory analysis (GSTA). The optical spectra of the ensembles are then produced by calculating vertical transitions using time-dependent density-functional theory (TDDFT) with implicit solvation. To obtain the final spectral shapes, the stick spectra from TDDFT are convoluted with Gaussian kernels where the half-widths are determined by a statistically motivated strategy. We have tested our method by calculating the UV-vis spectra of a recently discovered acridine photocatalyst in two redox states. Vibronic progressions and broadenings due to the finite lifetime of the excited states are not included in the methodology yet. Nuclear quantization affects the relative peak intensities and widths, which is necessary to reproduce the experimental spectrum. We have also found that using only the optimized geometry of each molecule works surprisingly well if a proper empirical broadening factor is applied. This is explained by the rigidity of the conjugated chromophore moieties of the selected molecules, which are mainly responsible for the excitations in the spectra. In contrast, we have also shown that other parts of the molecules are flexible enough to feature anharmonicities that impair the use of other techniques such as Wigner sampling.

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.

Thermally activated delayed fluorescence: A critical assessment of environmental effects on the singlet-triplet energy gap

The effective design of dyes optimized for thermally activated delayed fluorescence (TADF) requires the precise control of two tiny energies: the singlet-triplet gap, which has to be maintained within thermal energy, and the strength of spin-orbit coupling. A subtle interplay among low-energy excited states having dominant charge-transfer and local character then governs TADF efficiency, making models for environmental effects both crucial and challenging. The main message of this paper is a warning to the community of chemists, physicists, and material scientists working in the field: the adiabatic approximation implicitly imposed to the treatment of fast environmental degrees of freedom in quantum-classical and continuum solvation models leads to uncontrolled results. Several approximation schemes were proposed to mitigate the issue, but we underline that the adiabatic approximation to fast solvation is inadequate and cannot be improved; rather, it must be abandoned in favor of an antiadiabatic approach.

Explicit environmental and vibronic effects in simulations of linear and nonlinear optical spectroscopy

Accurately simulating the linear and nonlinear electronic spectra of condensed phase systems and accounting for all physical phenomena contributing to spectral line shapes presents a significant challenge. Vibronic transitions can be captured through a harmonic model generated from the normal modes of a chromophore, but it is challenging to also include the effects of specific chromophore-environment interactions within such a model. We work to overcome this limitation by combining approaches to account for both explicit environment interactions and vibronic couplings for simulating both linear and nonlinear optical spectra. We present and show results for three approaches of varying computational cost for combining ensemble sampling of chromophore-environment configurations with Franck-Condon line shapes for simulating linear spectra. We present two analogous approaches for nonlinear spectra. Simulated absorption spectra and two-dimensional electronic spectra (2DES) are presented for the Nile red chromophore in different solvent environments. Employing an average Franck-Condon or 2DES line shape appears to be a promising method for simulating linear and nonlinear spectroscopy for a chromophore in the condensed phase.

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.

Insight of UV-vis spectra and atmospheric implication for the reaction of ˙OH radical towards glyphosate herbicide and its hydrates

The rate constant of the reactions of ˙OH radicals with glyphosate (GPS) and its hydrates (GPS(H₂O)_n=1–3) were evaluated using the dual method M06-2X/6-311++G(df,p)//6-31+G(df,p) over the temperature range of 200–400 K. The results served to estimate the atmospheric lifetime along with the photochemical ozone creation potential (POCP). The calculations yielded an atmospheric lifetime of 2.34 hours and a POCP of 24.7 for GPS. Upon addition of water molecules, there is an increase of lifetime and decrease of POCP for water monomer and water dimer. The POCP for water trimer is slightly above the gaseous GPS. However, the POCPs of GPS and its hydrates are comparable to that of alkanes. The GPS and its hydrates were found to be a potential reservoir of CO₂. The acidification potential (AP) of GPS was found to be 0.189 and decreases upon addition of water molecules. This shows negligible contribution to rain acidification as the AP is less than that of SO₂. The UV-vis spectra were attained using the M06-L/6-311++G(3df,3pd) method and cover the range 160–260 nm which fits well with experiment.

The rate constant of the reactions of ˙OH radical with glyphosate (GPS) and its hydrates (GPS(H₂O)_n=1–3) were evaluated using the dual method M06-2X/6-311++G(df,p)//6-31+G(df,p) over the temperature range of 200–400 K.

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.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

Chirality of a rhodamine heterodimer linked to a DNA scaffold: an experimental and computational study

The chiroptical properties of multi-chromophoric systems are governed by the intermolecular arrangement of the monomeric units. We report on a computational and experimental study of the linear optical properties and supramolecular structure of a rhodamine heterodimer assembled on a DNA scaffold. The experimental absorption and circular dichroism (CD) profiles confirm the dimer formation. Computationally, starting from low-cost DFT/TDDFT simulations of the bare dimer we attribute the measured -/+ CD sign sequence of the S1/S2 bands to a specific chiral conformation of the heterodimer. In the monomers, as typical for rhodamine dyes, the electric transition dipole of the lowest π-π* transition is parallel to the long axis of the xanthene planes. We show that in the heterodimer the sign sequence of the two CD bands is related to the orientation of these long axes. To account explicitly for environment effects, we use molecular dynamics (MD) simulations for characterizing the supramolecular structure of the two optical isomers tethered on DNA. Average absorption and CD-profiles were modeled using ab initio TDDFT calculations at the geometries sampled along a few nanosecond MD run. The absorption profiles computed for both optical isomers are in good agreement with the experimental absorption spectrum and do not allow one to discriminate between them. The computed averaged CD profiles provide the orientation of monomers in the enantiomer that is dominant under the experimental conditions.

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.

DFT Study of Photochemical Properties and Radiative Forcing Efficiency Features of the Stereoisomers cis- and trans-CHCl═CH-CF3

The accurate assessment of radiative forcing efficiency (RFE) of a greenhouse gas is based on the precise knowledge of its structure and infrared absorption spectrum. The present work investigates the UV-vis absorption spectra and IR absorption spectra that are used for the determination of RFE of the short-lived compounds, cis- and trans-CHCl═CHCF₃ (CTFP). These investigations were carried out with six different density functional theory (DFT) methods B3LYP, CAM-B3LYP, M06, M06-2X, TPSS0, and ωB97X-D associated to the basis set 6-31G(3df). Therefrom, the relative populations of the two states cis and trans for temperatures over the range 220-370 K at 1 atm and along the atmospheric altitude were assessed. It turns out that trans-CTFP is the abundant component between the two states. This review reveals that B3LYP and M06 reproduce well the experimental results of UV-vis spectra of trans-CTFP. As for cis-CTFP, EOM-CCSD is not well fitted by DFT methods. The cis- to trans-CTFP isomerization leads to the red shift for DFT methods and to the blue shift in regard to EOM-CCSD and experimental results. The IR absorption spectra are well fitted by B3LYP over the range 500-1600 cm^-1 and TPSS0 over 1300-2000 cm^-1 for both stereoisomers. Moreover, the root-mean-square errors (RMSEs) of frequencies from experimental data are lower for B3LYP and TPSS0 for both systems. The computed IR absorption band strengths over 500-2000 cm^-1 for cis- and over 600-1800 cm^-1 for trans-CTFP are consistent with the experiment. The relevant descriptor RFEs of the climate effect were calculated using a narrow band model for a constant vertical profile and then corrected with a lifetime factor for different computational methods. The computed values correlate well with the experimental results for both stereoisomers except M06-2X and TPSS0. It is worth noting that, for both systems, the intense radiative forcing spectra are located at frequencies ranging in 1000-1200 cm^-1. The lower forcings of trans-CTFP lying in the atmospheric window region 800-1000 cm^-1 are greater than those of cis-CTFP. Therefore, RFE(trans-CTFP) = 1.127 RFE(cis-CTFP).

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

Quantum Confinement Effects on Solvatochromic Shifts of Molecular Solutes

We demonstrate the pivotal role of quantum mechanics density confinement effects on solvatochromic shifts. In particular, by resorting to a quantum mechanics/molecular mechanics (QM/MM) approach capable of accounting for confinement effects we successfully reproduce vacuo-to-water solvatochromic shifts for dark n → π* and bright π → π* transitions of acrolein and dark n → π* transitions of pyridine and pyrimidine without the need of including explicit water molecules in the QM portion. Remarkably, our approach is also able to dissect the effects of the single forces acting on the solute-solvent couple and allows for a rationalization of the experimental findings in terms of physicochemical quantities.

Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches

Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.

Unraveling electronic absorption spectra using nuclear quantum effects: Photoactive yellow protein and green fluorescent protein chromophores in water

Many physical phenomena must be accounted for to accurately model solution-phase optical spectral line shapes, from the sampling of chromophore-solvent configurations to the electronic-vibrational transitions leading to vibronic fine structure. Here we thoroughly explore the role of nuclear quantum effects, direct and indirect solvent effects, and vibronic effects in the computation of the optical spectrum of the aqueously solvated anionic chromophores of green fluorescent protein and photoactive yellow protein. By analyzing the chromophore and solvent configurations, the distributions of vertical excitation energies, the absorption spectra computed within the ensemble approach, and the absorption spectra computed within the ensemble plus zero-temperature Franck-Condon approach, we show how solvent, nuclear quantum effects, and vibronic transitions alter the optical absorption spectra. We find that including nuclear quantum effects in the sampling of chromophore-solvent configurations using ab initio path integral molecular dynamics simulations leads to improved spectral shapes through three mechanisms. The three mechanisms that lead to line shape broadening and a better description of the high-energy tail are softening of heavy atom bonds in the chromophore that couple to the optically bright state, widening the distribution of vertical excitation energies from more diverse solvation environments, and redistributing spectral weight from the 0-0 vibronic transition to higher energy vibronic transitions when computing the Franck-Condon spectrum in a frozen solvent pocket. The absorption spectra computed using the combined ensemble plus zero-temperature Franck-Condon approach yield significant improvements in spectral shape and width compared to the spectra computed with the ensemble approach. Using the combined approach with configurations sampled from path integral molecular dynamics trajectories presents a significant step forward in accurately modeling the absorption spectra of aqueously solvated chromophores.

The importance of nuclear quantum effects in spectral line broadening of optical spectra and electrostatic properties in aromatic chromophores

In this work, we examine the importance of nuclear quantum effects on capturing the line broadening and vibronic structure of optical spectra. We determine the absorption spectra of three aromatic molecules indole, pyridine, and benzene using time dependent density functional theory with several molecular dynamics sampling protocols: force-field based empirical potentials, ab initio simulations, and finally path-integrals for the inclusion of nuclear quantum effects. We show that the absorption spectrum for all these chromophores are similarly broadened in the presence of nuclear quantum effects regardless of the presence of hydrogen bond donor or acceptor groups. We also show that simulations incorporating nuclear quantum effects are able to reproduce the heterogeneous broadening of the absorption spectra even with empirical force fields. The spectral broadening associated with nuclear quantum effects can be accounted for by the broadened distribution of chromophore size as revealed by a particle in the box model. We also highlight the role that nuclear quantum effects have on the underlying electronic structure of aromatic molecules as probed by various electrostatic properties.

Solvent effects for vertical absorption and emission processes in solution using a self-consistent state specific method based on constrained equilibrium thermodynamics

A self-consistent state specific (SS) method in the framework of TDDFT is presented to account for solvent effects on absorption and emission processes for molecules in solution. In these processes, the initial state is an equilibrium state, while the polarization of the solvent is in nonequilibrium with the electron density of the solute in the final state. Nonequilibrium solvation free energy is calculated based on a novel nonequilibrium solvation model with constrained equilibrium manipulation. The bulk solvent effects are considered using the polarizable continuum method (PCM), where the solvent-solute interaction is described with a reaction field. Molecular orbitals and orbital energies in the presence of the reaction field corresponding to the excited state are employed and the response of the solvent is not included in the TDDFT calculations. A self-consistent procedure is designed to obtain the excited state reaction field. The equations based on this new nonequilibrium solvation model in the framework of the self-consistent SS-PCM/TDDFT method for calculation of vertical absorption and emission energies are presented and implemented in the Q-Chem package. Vertical absorption and emission energies for several small molecules in solution using the newly developed code are calculated and compared with available experimental data and the results of other theoretical studies. Solvent shifts of absorption and emission energies are reasonably reproduced with this approach. The new model is a promising approach to study nonequilibrium absorption and emission processes in solution.

Solvent effects on excitation energies obtained using the state-specific TD-DFT method with a polarizable continuum model based on constrained equilibrium thermodynamics

Nonequilibrium solvation effects need to be treated properly in the study of electronic absorption processes of solutes since solvent polarization is not in equilibrium with the excited-state charge density of the solute. In this work, we developed a state specific (SS) method based on the novel nonequilibrium solvation model with constrained equilibrium manipulation to account for solvation effects in electronic absorption processes. Time-dependent density functional theory (TD-DFT) is adopted to calculate electronic excitation energies and a polarizable continuum model is employed in the treatment of bulk solvent effects on both the ground and excited electronic states. The equations based on this novel nonequilibrium solvation model in the framework of TDDFT to calculate vertical excitation energy are presented and implemented in the Q-Chem package. The implementation is validated by comparing reorganization energies for charge transfer excitations between two atoms obtained from Q-Chem and those obtained using a two-sphere model. Solvent effects on electronic transitions of coumarin 153 (C153), acetone, pyridine, (2E)-3-(3,4-dimethoxyphenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (DMHP), and uracil in different solvents are investigated using the newly developed code. Our results show that the obtained vertical excitation energies as well as spectral shifts generally agree better with the available experimental values than those obtained using the traditional nonequlibrium solvation model. This new model is thus appropriate to study nonequilibrium excitation processes in solution.

Solubility and Preferential Solvation of Piroxicam in Neat Solvents and Binary Systems

The solubilization and solvatochromic behavior of piroxicam (PRX) were analyzed using UV-vis spectroscopy in neat (protic and aprotic) and binary solvent mixtures. The effects of solvent dipolarity/polarizability and solvent–solute hydrogen bonding interactions on the absorption maxima were evaluated by means of the linear solvation energy relationship concept of Kamlet and Taft. This analysis indicated that both interactions play an important role in the position of the absorption maxima in neat solvents. While, the PRX solubility depends on the solute–solvent specific interactions, polarizability and the cohesive forces of the solvent, manifested mainly by means of the Hildebrand’s solubility parameter. Preferential solvation (PS) was studied in 10 binary mixtures. A non-ideal behavior of the wavenumber curve as the function of analytical mole fraction of co-solvent was detected. Index of preferential solvation, as well as the influence of solvent parameters were calculated. The process of dissolution was analyzed in aqueous binary mixtures of ethanol, ethylene glycol and propylene glycol. They were not spontaneous in all proportions, but when water concentration decreases in the mixtures, the process becomes more spontaneous.

Franck-Condon Models for Simulating the Band Shape of Electronic Absorption Spectra

Band shape is an essential ingredient in the simulation of electronic absorption spectra. The excitation of multiple series of vibrational levels during an electronic excitation is a main contributor to band shapes. Here we present two simple models based on the Franck-Condon displaced-harmonic-oscillator model. The models are both derived from the time-dependent formulation of electronic spectroscopy. They assume that the transition dipoles do not depend on geometry and that the potential energy surfaces are locally quadratic; one model is second order in time and is called LQ2, and the other is third order in time and is called LQ3. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many vibrational modes. The models are straightforward and can be easily applied to simulate absorption spectra that are composed of many electronic transitions. As compared to carrying out molecular dynamics simulations, they require relatively few electronic structure calculations, and the additional cost for constructing the spectra is negligible. Therefore, the models are suitable for simulating the spectra of complex systems such as transition-metal complexes.

Electronic absorption spectra of pyridine and nicotine in aqueous solution with a combined molecular dynamics and polarizable QM/MM approach

The electronic absorption spectra of pyridine and nicotine in aqueous solution have been computed using a multistep approach. The computational protocol consists in studying the solute solvation with accurate molecular dynamics simulations, characterizing the hydrogen bond interactions, and calculating electronic transitions for a series of configurations extracted from the molecular dynamics trajectories with a polarizable QM/MM scheme based on the fluctuating charge model. Molecular dynamics simulations and electronic transition calculations have been performed on both pyridine and nicotine. Furthermore, the contributions of solute vibrational effect on electronic absorption spectra have been taken into account in the so called vertical gradient approximation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

The role of hydrogen bonding in the fluorescence quenching of 2,6-bis((E)-2-(benzoxazol-2-yl)vinyl)naphthalene (BBVN) in methanol

The excited state hydrogen bonding dynamics of BBVN in hydrogen donating methanol solvent was explored at the TD-BMK/cc-pVDZ level of theory with accounting for the bulk environment effects at the polarizable continuum model (PCM). The heteroatoms of the BBVN laser dye form hydrogen bonds with four methanol molecules. In the formed BBVN-(MeOH)₄ complex, the A-type hydrogen bond (N…HO), of an average strength of 25kJmol^-1, is twofold stronger than the B-type (O…HO) one. Upon photon absorption, the total HB binding energy increases from 78.5kJmol^-1 in the ground state to 82.6kJmol^-1 in the first singlet (S₁) excited state. In consequence of the hydrogen bonding interaction, the absorption band maximum of the BBVN-(MeOH)₄ complex, which was anticipated at 398nm (exp. 397), is redshifted by 5nm relative to that of the free dye in methanol. The spectral shift of the stretching vibrational mode for the hydrogen bonded hydroxyl groups (with a maximum shift of 285cm^-1) from that of the free methanol indicated the elevated strengthening of hydrogen bonds in the excited state. The vibrational modes associated with hydrogen bonding provide effective accepting modes for the dissipation of the excitation energy, thus, decreasing the fluorescence quantum yield of BBVN in alcohols as compared to that in the polar aprotic solvents. Since there is no sign of photochemistry or phosphorescence, it seems reasonable in view of the outcomes of this study to assign the major decay process of the excited singlet (S₁) of BBVN in alcohols to vibronically induced internal conversion (IC) facilitated by hydrogen bonding.