0-0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds

The 0-0 energies of 80 medium and large molecules have been computed with a large panel of theoretical formalisms. We have used an approach computationally tractable for large molecules, that is, the structural and vibrational parameters are obtained with TD-DFT, the solvent effects are accounted for with the PCM model, whereas the total and transition energies have been determined with TD-DFT and with five wave function approaches accounting for contributions from double excitations, namely, CIS(D), ADC(2), CC2, SCS-CC2, and SOS-CC2, as well as Green's function based BSE/GW approach. Atomic basis sets including diffuse functions have been systematically applied, and several variations of the PCM have been evaluated. Using solvent corrections obtained with corrected linear-response approach, we found that three schemes, namely, ADC(2), CC2, and BSE/GW allow one to reach a mean absolute deviation smaller than 0.15 eV compared to the measurements, the two former yielding slightly better correlation with experiments than the latter. CIS(D), SCS-CC2, and SOS-CC2 provide significantly larger deviations, though the latter approach delivers highly consistent transition energies. In addition, we show that (i) ADC(2) and CC2 values are extremely close to each other but for systems absorbing at low energies; (ii) the linear-response PCM scheme tends to overestimate solvation effects; and that (iii) the average impact of nonequilibrium correction on 0-0 energies is negligible.

Toward the design of alkynylimidazole fluorophores: computational and experimental characterization of spectroscopic features in solution and in poly(methyl methacrylate)

The possibilities offered by organic fluorophores in the preparation of advanced plastic materials have been increased by designing novel alkynylimidazole dyes, featuring different push and pull groups. This new family of fluorescent dyes was synthesized by means of a one-pot sequential bromination-alkynylation of the heteroaromatic core, and their optical properties were investigated in tetrahydrofuran and in poly(methyl methacrylate). An efficient in silico pre-screening scheme was devised as consisting of a step-by-step procedure employing computational methodologies by simulation of electronic spectra within simple vertical energy and more sophisticated vibronic approaches. Such an approach was also extended to efficiently simulate one-photon absorption and emission spectra of the dyes in the polymer environment for their potential application in luminescent solar concentrators. Besides the specific applications of this novel material, the integration of computational and experimental techniques reported here provides an efficient protocol that can be applied to make a selection among similar dye candidates, which constitute the essential responsive part of those fluorescent plastic materials.

Critical analysis of spectral solvent shifts calculated by the contemporary PCM approaches of a representative series of charge-transfer complexes between tetracyanoethylene and methylated benzenes

Applications of contemporary polarisable continuum model (PCM) quantum chemical approaches to account for the solvent shifts of UV-Vis absorption charge transfer (CT) transitions in electron donor-acceptor (EDA) complexes (as well as to account for their stability and other properties in solvents) have been rather rare until now. In this study, we systematically applied different - mainly state-specific - PCM approaches to examine excited state properties, namely, solvatochromic excitation energy shifts in a series of EDA complexes of a tetracyanoethylene (TCNE) acceptor with methyl substituted benzenes with different degrees of methylation N (NMB). For these complexes, representative and reliable experimental data exist both for the gas phase and in solution (dichloromethane). We have found that the linear response (LR) solvent shifts are too small compared to the experimental values, while self-consistent SS approaches give values that are too large. The best agreement with experimental values was obtained by corrected LR (cLR). The transition energies were calculated by means of TD-DFT methodology with PBE0, CAM-B3LYP and M06-2X functionals as well as the wave function CC2 method for the gas phase, and the PCM solvent shifts were added to account for the solvent effects. The best results for transition energies in solvents were obtained using the CC2 method complemented by CAM-B3LYP/cLR for the gas phase transition energy red solvent shift, while all three TD-DFT approaches used gave insufficient values (ca. 50%) of the slope of the dependence of the transition energies on N compared to experimental values.

Dye chemistry with time-dependent density functional theory

In this perspective, we present an overview of the determination of excited-state properties of "real-life" dyes, and notably of their optical absorption and emission spectra, performed during the last decade with time-dependent density functional theory (TD-DFT). We discuss the results obtained with both vertical and adiabatic (vibronic) approximations, choosing relevant examples for several series of dyes. These examples include reproducing absorption wavelengths of numerous families of coloured molecules, understanding the specific band shape of amino-anthraquinones, optimising the properties of dyes used in solar cells, mimicking the fluorescence wavelengths of fluorescent brighteners and BODIPY dyes, studying optically active biomolecules and photo-induced proton transfer, as well as improving the properties of photochromes.

Theoretical description of efficiency enhancement in DSSCs sensitized by newly synthesized heteroleptic Ru complexes

Recently, some new series of heteroleptic ruthenium-based dyes, the so-called RD dyes, were designed and synthesized showing better performances compared to the well-known homoleptic N719.

Quantum mechanical molecular interactions for calculating the excitation energy in molecular environments: a first-order interacting space approach

Intermolecular interactions regulate the molecular properties in proteins and solutions such as solvatochromic systems. Some of the interactions have to be described at an electronic-structure level. In this study, a commutator for calculating the excitation energy is used for deriving a first-order interacting space (FOIS) to describe the environmental response to solute excitation. The FOIS wave function for a solute-in-solvent cluster is solved by second-order perturbation theory. The contributions to the excitation energy are decomposed into each interaction and for each solvent.

High efficiency light harvesting by carotenoids in the LH2 complex from photosynthetic bacteria: unique adaptation to growth under low-light conditions

Rhodopin, rhodopinal, and their glucoside derivatives are carotenoids that accumulate in different amounts in the photosynthetic bacterium, Rhodoblastus (Rbl.) acidophilus strain 7050, depending on the intensity of the light under which the organism is grown. The different growth conditions also have a profound effect on the spectra of the bacteriochlorophyll (BChl) pigments that assemble in the major LH2 light-harvesting pigment-protein complex. Under high-light conditions the well-characterized B800-850 LH2 complex is formed and accumulates rhodopin and rhodopin glucoside as the primary carotenoids. Under low-light conditions, a variant LH2, denoted B800-820, is formed, and rhodopinal and rhodopinal glucoside are the most abundant carotenoids. The present investigation compares and contrasts the spectral properties and dynamics of the excited states of rhodopin and rhodopinal in solution. In addition, the systematic differences in pigment composition and structure of the chromophores in the LH2 complexes provide an opportunity to explore the effect of these factors on the rate and efficiency of carotenoid-to-BChl energy transfer. It is found that the enzymatic conversion of rhodopin to rhodopinal by Rbl. acidophilus 7050 grown under low-light conditions results in nearly 100% carotenoid-to-BChl energy transfer efficiency in the LH2 complex. This comparative analysis provides insight into how photosynthetic systems are able to adapt and survive under challenging environmental conditions.

Unveiling solvents effect on excited-state polarizabilities with the corrected linear-response model

Aiming to assess the environmental effects on the dipole moments and polarizabilities of electronically excited-states, we have applied a combined Polarizable Continuum Model/Time-Dependent Density Functional Theory (PCM/TD-DFT) approach on six representative chromophores. For the first time, we compare polarizabilities obtained with gas phase, linear-response and corrected linear response continuum models and we also investigate the relative importance of direct (electronic) and indirect (geometric) environmental contributions for these properties. It is shown that the solvent effects on excited-state polarizabilities tend to be large and can often, but not always, be captured with the computationally efficient linear-response formalism.

Hydroxo-bridged dicopper(II,III) and -(III,III) complexes: models for putative intermediates in oxidation catalysis

A macrocyclic ligand (L(4-)) comprising two pyridine(dicarboxamide) donors was used to target reactive copper species relevant to proposed intermediates in catalytic hydrocarbon oxidations by particulate methane monooxygenase and heterogeneous zeolite systems. Treatment of LH4 with base and Cu(OAc)2·H2O yielded (Me4N)2[L2Cu4(μ4-O)] (1) or (Me4N)[LCu2(μ-OH)] (2), depending on conditions. Complex 2 was found to undergo two reversible 1-electron oxidations via cyclic voltammetry and low-temperature chemical reactions. On the basis of spectroscopy and theory, the oxidation products were identified as novel hydroxo-bridged mixed-valent Cu(II)Cu(III) and symmetric Cu(III)2 species, respectively, that provide the first precedence for such moieties as oxidation catalysis intermediates.

QM/MM-MD simulations of conjugated polyelectrolytes: a study of luminescent conjugated oligothiophenes for use as biophysical probes

A methodological development is reported for the study of luminescence properties of conjugated polyelectrolytes, encompassing systems in which dihedral rotational barriers are easily overcome at room temperature. The components of the model include (i) a molecular mechanics (MM) force field description of the solvent in its electronic ground state as well as the chromophore in its electronic ground and excited states, (ii) a conformational sampling by means of classical molecular dynamics (MD) in the respective electronic states, and (iii) spectral response calculations by means of the quantum mechanics/molecular mechanics QM/MM approach. A detailed analysis of the combined polarization effects of the ionic moiety and the polar water solvent is presented. At an increased computational cost of 30% compared to a calculation excluding the solvent, the error in the transition wavelength of the dominant absorption band is kept as small as 1 nm as compared to the high-quality benchmark result, based largely on a QM description of the solvent. At a reduced computational cost the error of the same quantity is kept as small as 6 nm, with the cost reduction being the result of an effective description of the effects of the solvent by means of replacing the carboxylate ions with neutral hydrogens. In absorption spectroscopy, the obtained best theoretical results are in excellent agreement with the experimental benchmark measurement, regarding excitation energies as well as band intensities and profiles. In fluorescence spectroscopy, the experimental spectrum shows a vibrational progression that is not addressed by theory, but the theoretical band position is in excellent agreement with experiment, with a highly accurate description of the Stokes shift as a result.

Environmental and complexation effects on the structures and spectroscopic signatures of organic pigments relevant to cultural heritage: the case of alizarin and alizarin-Mg(II)/Al(III) complexes

An integrated computational approach allowed an unbiased analysis of optical and structural properties of alizarin-based pigments, which can be directly compared with experimental results. Madder lake pigments have been modeled by Mg(II)- and Al(III)-coordinated alizarin taking into account solvation and metal-linkage effects, responsible for colour modifications. Moreover, different environmental conditions have been analyzed for free alizarin, showing in all cases semi-quantitative agreement with experimental spectroscopic data (UV-VIS). Our results point out the ability of in silico approaches to unravel the subtle interplay of stereo-electronic, dynamic, and environmental effects in tuning the physico-chemical properties of pigments relevant to cultural heritage.

Modeling opto-electronic properties of a dye molecule in proximity of a semiconductor nanoparticle

A general methodology is presented to model the opto-electronic properties of a dye molecule in the presence of a semiconductor nanoparticle (NP), a model system for the architecture of dye-sensitized solar cells. The method is applied to the L0 organic dye solvated with acetonitrile in the neighborhood of a TiO2 NP. The total reaction potential due to the polarization of the solvent and the metal oxide is calculated by extending the polarizable continuum model integral equation formalism. The ground state energy is computed by using density functional theory (DFT) while the vertical electronic excitations are obtained by time-dependent DFT in a state-specific corrected linear response scheme. We calculate the excited state oxidation potential (ESOP) for the protonated and deprotonated forms of the L0 dye at different distances and configurations with respect to the NP surface. The stronger renormalizations of the ESOP values due to the presence of the TiO2 nanostructure are found for the protonated dye, reaching a maximum of about -0.15 eV. The role of protonation effect is discussed in terms of the atomic Löwdin charges of the oxidized and reduced species. On the other hand, we observed a weak effect on the L0 optical excitation gap due to the polarization response of the NP.

Full cLR-PCM calculations of the solvatochromic effects on emission energies

Are cLR-PCM excited-state geometries providing more accurate solvatochromic shifts?

Ultrafast resonance energy transfer in the umbelliferone–alizarin bichromophore

Fast and efficient intramolecular energy transfer takes place in the umbelliferone–alizarin bichromophore; the process is well described by the Förster mechanism.

Efficiency enhancement of black dye-sensitized solar cells by newly synthesized D–π–A coadsorbents: a theoretical study

The electronic structure, optical properties, and adsorption geometry of two novel D–π–A coadsorbents are studied, using density functional theory and time-dependent density functional theory.

Absorption and fluorescence signatures of 1,2,3-triazole based regioisomers: challenging compounds for TD-DFT

Photophysical signatures of 1,2,3-triazole regioisomers: a surprisingly challenging problem for TD-DFT.

On the optical absorption of the anionic GFP chromophore in vacuum, solution, and protein

In spite of the large number of experimental and theoretical studies, the optical absorption trend of the green fluorescent protein (GFP) chromophore in several environments has not been fully understood. We calculated at the same level of time dependent density functional theory the vertical excitation energy of the anionic GFP chromophore in the protein and in ethanol, dioxane, methanol and water solutions. As result, we reproduced for the first time the experimental trend of the absorption peaks with 0.015 eV as the standard deviation of the accuracy. This systematic error allowed us to analyze with confidence the relative weight of several solvation effects on the vertical excitation energy. Experimental trends not correlated with the solvent polarity were therefore explained with a fine balance of different steric and electronic effects on the photophysics of the chromophore. As an indirect and remarkable result, the present analysis confirms that the optical absorption of the chromophore in the gas phase is close to the value of 2.84 eV extrapolated by Dong et al. (J. Am. Chem. Soc., 2006, 128, 12038), and, as a consequence, that the protein environment induces a red shift of 0.23 eV.

Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model

The accurate calculation of electronic transition energies and properties of isolated chromophores is not sufficient to provide a realistic simulation of their excited states in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields. Therefore, a proper description of the solvent effect is fundamental. This can be achieved by combining polarizable explicit and implicit representations of the solvent. The former provides a realistic description of solvent molecules around the solute, while the latter introduces the electrostatic effect of the bulk solution and reduces the need of too large a number of explicit solvent molecules. This strategy is particularly appealing when an accurate method such as equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed for the treatment of the chromophore. In this contribution, we present the coupling of EOM-CCSD with a fluctuating charges (FQ) model and polarizable continuum model (PCM) of solvation for vertical excitations in a state-specific framework. The theory, implementation, and prototypical applications of the method are presented. Numerical tests on small solute-water clusters show very good agreement between full EOM-CCSD and EOM-CCSD-FQ calculations, with and without PCM, with differences ≤ 0.1 eV. Additionally, approximated schemes that further reduce the computational cost of the method are introduced and showed to perform well compared to the full method (errors ≤ 0.1 eV).

Circular dichroism and optical rotation of lactamide and 2-aminopropanol in aqueous solution

The performance of implicit and explicit solvent models (polarizable continuum model (PCM) and microsolvation with positions of water molecules obtained either from molecular dynamics (MD) simulations or quantum mechanical geometry optimization) for calculations of electronic circular dichroism (CD) and optical rotation (OR) is examined for two polar and flexible molecules: lactamide and 2-aminopropanol. The vibrational structure of the CD spectrum is modeled for lactamide. The results are compared with the newly obtained experimental data. The signs of the bands are correctly reproduced using all three methods under investigation and the CAM-B3LYP functional for the CD spectrum of lactamide, but not for 2-aminopropanol. The sign of the calculated optical rotation is correctly predicted by means of PCM, but its magnitude is somewhat underestimated in comparison with experiment for lactamide and overestimated for 2-aminopropanol. To some extent it is rectified by employing explicit hydration. Overall, microsolvation with geometry optimization seems more cost-effective than classical MD, but this is likely to be a consequence of inadequate classical potential and electronic structure model.

The nature of the intramolecular charge transfer state in peridinin

Experimental and theoretical evidence is presented that supports the theory that the intramolecular charge transfer (ICT) state of peridinin is an evolved state formed via excited-state bond-order reversal and solvent reorganization in polar media. The ICT state evolves in <100 fs and is characterized by a large dipole moment (~35 D). The charge transfer character involves a shift of electron density within the polyene chain, and it does not involve participation of molecular orbitals localized in either of the β-rings. Charge is moved from the allenic side of the polyene into the furanic ring region and is accompanied by bond-order reversal in the central portion of the polyene chain. The electronic properties of the ICT state are generated via mixing of the "1(1)Bu(+)" ionic state and the lowest-lying "2(1)Ag(-)" covalent state. The resulting ICT state is primarily (1)Bu(+)-like in character and exhibits not only a large oscillator strength but an unusually large doubly excited character. In most solvents, two populations exist in equilibrium, one with a lowest-lying ICT ionic state and a second with a lowest-lying "2(1)Ag(-)" covalent state. The two populations are separated by a small barrier associated with solvent relaxation and cavity formation.

Theoretical modeling of large molecular systems. Advances in the local self consistent field method for mixed quantum mechanics/molecular mechanics calculations

Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantum mechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantum mechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantum mechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantum mechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of the atom: for an sp(3) carbon atom, we consider the two core 1s electrons and treat that carbon as an atom with three electrons. This results in an LSCF+3 model. Similarly, a nitrogen atom with a lone pair of electrons available for conjugation is treated as an atom with five electrons (LSCF+5). This approach is particularly well suited to splitting peptide bonds and other bonds that include carbon or nitrogen atoms. To embed the induced polarization within the calculation, researchers must use a polarizable force field. However, because the parameters of the usual force fields include an average of the induction effects, researchers typically can obtain satisfactory results without explicitly introducing the polarization. When considering electronic transitions, researchers must take into account the changes in the electronic polarization. One approach is to simulate the electronic cloud of the surroundings by a continuum whose dielectric constant is equal to the square of the refractive index. This Electronic Response of the Surroundings (ERS) methodology allows researchers to model the changes in induced polarization easily. We illustrate this approach by modeling the electronic absorption of tryptophan in human serum albumin (HSA).

Energetics and dynamics of the low-lying electronic states of constrained polyenes: implications for infinite polyenes

Steady-state and ultrafast transient absorption spectra were obtained for a series of conformationally constrained, isomerically pure polyenes with 5-23 conjugated double bonds (N). These data and fluorescence spectra of the shorter polyenes reveal the N dependence of the energies of six (1)B(u)(+) and two (1)A(g)(-) excited states. The (1)B(u)(+) states converge to a common infinite polyene limit of 15,900 ± 100 cm(-1). The two excited (1)A(g)(-) states, however, exhibit a large (~9000 cm(-1)) energy difference in the infinite polyene limit, in contrast to the common value previously predicted by theory. EOM-CCSD ab initio and MNDO-PSDCI semiempirical MO theories account for the experimental transition energies and intensities. The complex, multistep dynamics of the 1(1)B(u)(+) → 2(1)A(g)(-) → 1(1)A(g)(-) excited state decay pathways as a function of N are compared with kinetic data from several natural and synthetic carotenoids. Distinctive transient absorption signals in the visible region, previously identified with S* states in carotenoids, also are observed for the longer polyenes. Analysis of the lifetimes of the 2(1)A(g)(-) states, using the energy gap law for nonradiative decay, reveals remarkable similarities in the N dependence of the 2(1)A(g)(-) decay kinetics of the carotenoid and polyene systems. These findings are important for understanding the mechanisms by which carotenoids carry out their roles as light-harvesting molecules and photoprotective agents in biological systems.