Experimental and Theoretical Study for Core Excitation of Firefly Luciferin in Carbon K-Edge Spectra.

Carbon (C) K-edge X-ray absorption spectra for firefly luciferin were measured and assigned using time-dependent density functional theoretical calculations for luciferin anion and dianion to elucidate the effect of hydroxy-group deprotonation. It was found that the C K-edge spectra for luciferin had four characteristic peaks. The effect of deprotonation of the hydroxy group appears in the energy difference of the first and second peaks of these spectra. This energy difference is 1.0 eV at pH 7 and 2.3 eV at pH 10. The deprotonation of the hydroxy group can be distinguished based on the soft X-ray absorption spectra.

Significant contributions of second-order exchange terms in GW electron-hole interaction kernel for charge-transfer excitations.

The GW electron-hole interaction kernel, which includes two second-order exchange terms in addition to the first-order direct and exchange terms considered in the conventional GW + Bethe-Salpeter method, is applied to 10 two-molecular systems and six thermally activated delayed fluorescence (TADF) molecules in which inter- and intramolecular charge transfer excitations are expected to occur. The contributions of the two second-order exchange terms are almost zero for intermolecular charge transfer excitations and ∼0.75 eV for intramolecular charge transfer excitations according to our exciton analysis method with exciton wave functions. For TADF molecules, we found that the second-order exchange terms are more significant than the first-order exchange terms, and the contributions-even for local-type and delocalized-type excitations-are not negligibly small. We revealed that the two second-order exchange terms are proportional to the molecular size, the exciton binding energy, and the electron-hole overlap strength for intramolecular charge-transfer excitations. We believe that our findings are indispensable for further considerations of the GW method in the future.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation.

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Exciton maps for thermally activated delayed fluorescence active/inactive carbazole benzonitrile derivatives.

The all-electron first-principles GW+Bethe-Salpeter method was applied to six carbazole benzonitrile (CzBN) derivatives, which were recently reported to be both thermally activated delayed fluorescence (TADF) active and inactive despite their singlet-triplet splittings being commonly around 0.2 eV. The present method successfully reproduced very similar photoabsorption spectra as experiments from the viewpoint of the peak positions and relative peak heights. We also performed exciton analysis with the exciton wave functions for several lowest singlet and triplet exciton states to reveal the details of the optical properties. We applied this to not only the present six CzBN derivatives but also 18 other TADF molecules and proposed a new exciton map to classify the molecules as the TADF active/inactive by using the exciton binding energy in the vertical axis and the ratio of electron and hole delocalization in the horizontal axis. Our results suggest two possible TADF mechanisms: spatially less localized hole states than the electron states where the exciton binding energy is proportional to the ratio of hole and electron delocalization and spatially more localized hole states than the electron states where the exciton binding energy should be large.

Absorption Spectra for Firefly Bioluminescence Substrate Analog: TokeOni in Various pH Solutions.

AkaLumine hydrochloride, named TokeOni, is one of the firefly luciferin analogs, and its reaction with firefly luciferase produces near-infrared (NIR) bioluminescence. Prior to studying the bioluminescence mechanism, basic knowledge about the chemical structures, electronic states, and absorption properties of TokeOni at various pH values of solution has to be acquired. In this paper, the absorption spectra for TokeOni and AkaLumine at pH 2-10 were measured. Density functional theory (DFT) calculations, time-dependent DFT calculations, and the vibrational analyses were carried out. The absorption spectra indicate that the chemical forms of TokeOni in solutions are same as those of AkaLumine. The peaks at pH 7-10 in the absorption spectra correspond to the excitation from the ground state of a carboxylate anion of AkaLumine, the peak at pH 2 corresponds to the excitation from the ground state of a carboxylate anion with an N-protonated thiazoline ring and N-protonated dimethylamino group of AkaLumine, and the peak at pH 4 corresponds to the excitation from the ground state of a carboxylate anion with an N-protonated thiazoline ring of AkaLumine.

Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states.

Stabilizing mechanisms of three possible isomers (phenolate-keto, phenolate-enol, and phenol-enolate) of the oxyluciferin anion hydrated with quantum explicit water molecules in the first singlet excited state were investigated using first-principles Born-Oppenheimer molecular dynamics simulations for up to 1.8 ns (or 3.7 × 106 MD steps), revealing that the surrounding water molecules were distributed to form clear single-layered structures for phenolate-keto and multi-layered structures for phenolate-enol and phenol-enolate isomers. The isomers employed different stabilizing mechanisms compared to the ground state. Only the phenolate-keto isomer became attracted to the water molecules in its excited state and was stabilized by increasing the number of hydrogen bonds with nearby water molecules. The most stable isomer in the excited state was the phenolate-keto, and the phenolate-enol and phenol-enolate isomers were higher in energy by ∼0.38 eV and 0.57 eV, respectively, than the phenolate-keto. This was in contrast to the case of ground state in which the phenolate-enol was the most stable isomer.

Revisiting the Charge-Transfer States at Pentacene/C60 Interfaces with the GW/Bethe-Salpeter Equation Approach.

Molecular orientations and interfacial morphologies have critical effects on the electronic states of donor/acceptor interfaces and thus on the performance of organic photovoltaic devices. In this study, we explore the energy levels and charge-transfer states at the organic donor/acceptor interfaces on the basis of the fragment-based GW and Bethe-Salpeter equation approach. The face-on and edge-on orientations of pentacene/C60 bilayer heterojunctions have employed as model systems. GW+Bethe-Salpeter equation calculations were performed for the local interface structures in the face-on and edge-on bilayer heterojunctions, which contain approximately 2000 atoms. Calculated energy levels and charge-transfer state absorption spectra are in reasonable agreements with those obtained from experimental measurements. We found that the dependence of the energy levels on interfacial morphology is predominantly determined by the electrostatic contribution of polarization energy, while the effects of induction contribution in the edge-on interface are similar to those in the face-on. Moreover, the delocalized charge-transfer states contribute to the main absorption peak in the edge-on interface, while the face-on interface features relatively localized charge-transfer states in the main absorption peak. The impact of the interfacial morphologies on the polarization and charge delocalization effects is analyzed in detail.

Charge-transfer excited states in the donor/acceptor interface from large-scale GW calculations.

Predicting the charge-transfer (CT) excited states across the donor/acceptor (D/A) interface is essential for understanding the charge photogeneration process in an organic solar cell. Here, we present a fragment-based GW implementation that can be applied to a D/A interface structure and thus enables accurate determination of the CT states. The implementation is based on the fragmentation approximation of the polarization function and the combined GW and Coulomb-hole plus screened exchange approximations for self-energies. The fragment-based GW is demonstrated by application to the pentacene/C60 interface structure containing more than 2000 atoms. The CT excitation energies were estimated from the quasiparticle energies and electron-hole screened Coulomb interactions; the computed energies are in reasonable agreement with experimental estimates from the external quantum efficiency measurements. We highlight the impact of the induced polarization effects on the electron-hole energetics. The proposed fragment-based GW method offers a first-principles tool to compute the quasiparticle energies and electronic excitation energies of organic materials.

Photoabsorption Spectra of Aqueous Oxyluciferin Anions Elucidated by Explicit Quantum Solvent.

Experimental photoabsorption spectra of three possible isomers (phenolate-keto, phenolate-enol, and phenol-enolate) of oxyluciferin anions in aqueous solution were reproduced by first-principles time-dependent density functional theory simulations in which the entire system including the oxyluciferin anion and 64 water molecules were modeled by full quantum mechanics (full QM), unlike the conventional hybrid method, where the surrounding water molecules are modeled by molecular mechanics (MM) or a continuum solvent model. The full QM photoabsorption spectra were calculated from 1000 structures that had been obtained using the first-principles Born-Oppenheimer molecular dynamics simulations, which included the van der Waals correction, to take into account the effect of dynamical fluctuations of the hydration structure. The full QM calculation with CAM-B3LYP functional, which is the most elaborate one and is apparently the most consistent with experiment, is compared to others obtained with different levels of the functional and the solvent model. The amount of charge leakage from the oxyluciferin anions to the aqueous solution is found to differ significantly between the ground and excited states and is strongly dependent on the simulation method. The conventional solvent models do not take this into account, but the QM/MM can do it appropriately when including more than 10 water molecules into the QM region.

The effect of dynamical fluctuations of hydration structures on the absorption spectra of oxyluciferin anions in an aqueous solution.

In this study, the effect of hydration on the absorption spectra of oxyluciferin anion isomers in an aqueous solution is investigated for elucidating the influence of characteristic hydration structures. Using a canonical ensemble of hydration structures obtained from first-principles molecular dynamics simulations, the instantaneous absorption spectra of keto-, enol-, and enolate-type aqueous oxyluciferin anions at room temperature are computed from a collection of QM/MM calculations using an explicit solvent. It is demonstrated that the calculations reproduce experimental results concerning spectral shifts and broadening, for which traditional methods based on quantum chemistry and the Franck-Condon approximation fail because of the molecular vibrations of oxyluciferin anions and dynamical fluctuations of their hydration structures. Although the first absorption band associated with the lowest energy excitation corresponds to a π-π* transition for all oxyluciferin anion isomers, the changes in this band upon hydration are different among the isomers. In particular, the bands of enol- and enolate-type of oxyluciferin anions are significantly blue-shifted by hydration, whereas those of the keto-type oxylucifeion anion are shifted relatively less. Thus, the order of the first-peak positions in the aqueous solution changed relative to that in vacuo. We ascribe this to the nature of the oxyluciferin anion being more hydrophobic in the keto form as compared with the enol and enolate isomers.

Molecular size insensitivity of optical gap of [n]cycloparaphenylenes (n = 3-16).

The first-principles GW+Bethe-Salpeter method is applied to [n]cycloparaphenylenes ([n]CPPs, n = 3-16) to explain why the experimental UV-vis absorption spectra for n = 7-16 are roughly size-insensitive, unlike the fluorescence spectra. Having confirmed that the calculated absorption spectra consistently exhibit size-insensitivity, the exciton properties are investigated in detail using a novel analysis method based on the two-particle picture. The size-insensitivity of large-sized [n]CPPs (n≥9) is found due to a common spatial distribution of the wave functions involved with the first dark exciton and the first bright exciton, which are characterized primarily by a number of the wave function nodes. The exciton wave function as well as other properties of smaller molecules of n = 7 and 8 is, on the contrary, size-sensitive, although and the peak positions are essentially size-insensitive because of the cancellation of size-dependence of exciton binding energy and orbital energy. Different size-sensitivity between absorption and fluorescence can thus be explained unless such cancellation also occurs for fluorescence.

Quantitative characterization of exciton from GW+Bethe-Salpeter calculation.

We propose a method of classifying excitons into local-, Rydberg-, or charge transfer-type as a step toward enabling a data-driven material design of organic solar cells. The classification method is based on the first-principles many-body theory and improves over the conventional method based on state-by-state visualization of the one-electron wave functions. In our method, the exciton wave function is calculated within the level of the GW+Bethe-Salpeter equation, which is used to obtain two dimensionless parameters for the automatic classification. We construct criteria for exciton classification from experiences with a model molecule, dipeptide. Then we check the validity of our method using a model ß-dipeptide which has a geometry and an excitation spectrum similar to the model dipeptide. In addition, we test the effectiveness of the method using porphyrin molecules, or P1TA and P2TA, for which the conventional method is hampered by the strong state hybridization associated with excitation. We find that our method works successfully for P1TA, but the analysis of P2TA is hindered by its centrosymmetry.

Reverse Stability of Oxyluciferin Isomers in Aqueous Solutions.

We investigated the stability of oxyluciferin anions (keto, enol, and enolate isomers) in aqueous solution at room temperature by performing a nanosecond time scale first-principles molecular dynamics simulation. In contrast to all previous quantum chemistry calculations, which suggested the keto-type to be the most stable, we show that the enol-type is slightly more stable than the keto-type, in agreement with some recent experimental studies. The simulation highlights the remarkable hydrophobicity of the keto-type by the cavity formed at the oxyluciferin-water interface as well as a reduction in hydrophobicity with the number of hydrating water molecules. It is therefore predicted that the isomeric form in a hydrated cluster is size-dependent.

First-Principles Investigation of Strong Excitonic Effects in Oxygen 1s X-ray Absorption Spectra.

We calculated the oxygen 1s X-ray absorption spectra (XAS) of acetone and acetic acid molecules in vacuum by utilizing the first-principles GW+Bethe-Salpeter method with an all-electron mixed basis. The calculated excitation energies show good agreement with the available experimental data without an artificial shift. The remaining error, which is less than 1% or 2-5 eV, is a significant improvement from those of time-dependent (TD) density functional methods (5% error or 27-29 eV for TD-LDA and 2.4-2.8% error or 13-15 eV for TD-B3LYP). Our method reproduces the first and second isolated peaks and broad peaks at higher photon energies, corresponding to Rydberg excitations. We observed a failure of the one-particle picture (or independent particle approximation) from our assignment of the five lowest exciton peaks and significant excitonic or state-hybridization effects inherent in the core electron excitations.

Vibronic Structures in Absorption and Fluorescence Spectra of Firefly Oxyluciferin in Aqueous Solutions.

To elucidate the factors determining the spectral shapes and widths of the absorption and fluorescence spectra for keto and enol oxyluciferin and their conjugate bases in aqueous solutions, the intensities of vibronic transitions between their ground and first electronic excited states were calculated for the first time via estimation of the vibrational Franck-Condon factors. The major normal modes, overtones and combination tones in absorption and fluorescence spectra are similar for all species. The theoretical full widths at half maximum of absorption spectra are 0.4-0.7 eV and those for the fluorescence spectra are 0.4-0.5 eV, except for phenolate-keto that exhibits exceptionally sharp peak widths due to the dominance of the 0-0' or 0'-0 band. These spectral shapes and widths explain many relevant features of the experimentally observed spectra.

Symmetry breaking and excitonic effects on optical properties of defective nanographenes.

We investigate optical properties of the nanographene family and predict a defect induced effect by utilizing the all-electron first-principles GW+Bethe-Salpeter equation (BSE) method based on the many-body perturbation theory. As an accuracy check of the GW+BSE, photoabsorption spectra are calculated for a grossly warped nanographene (C80H30), which was very recently synthesized [Kawasumi et al., Nat. Chem. 5, 739-744 (2013)]. The calculated spectra are found to faithfully reproduce the shape, height, and position of the measured peaks. Then the method is applied to the flat nanographene without defect (C24H12 and C38H16), the curved ones with single defect (C20H10, C28H14, and C32H16), and fragments of C80H30 with double defect (C36H16 and C42H20). The existence of the defects significantly changes the optical spectra. In particular, the interaction between the defects is found to break the symmetry of the atomic geometries and enhance the excitonic effect, thereby generating the extra peaks at the lower photon energy side of the main peak. The present results might help explain the origin of the first two peaks experimentally observed for C80H30.

First-principles investigation on Rydberg and resonance excitations: A case study of the firefly luciferin anion.

The optical properties of an isolated firefly luciferin anion are investigated by using first-principles calculations, employing the many-body perturbation theory to take into account the excitonic effect. The calculated photoabsorption spectra are compared with the results obtained using the time-dependent density functional theory (TDDFT) employing the localized atomic orbital (AO) basis sets and a recent experiment in vacuum. The present method well reproduces the line shape at the photon energy corresponding to the Rydberg and resonance excitations but overestimates the peak positions by about 0.5 eV. However, the TDDFT-calculated positions of some peaks are closer to those of the experiment. We also investigate the basis set dependency in describing the free electron states above vacuum level and the excitons involving the transitions to the free electron states and conclude that AO-only basis sets are inaccurate for free electron states and the use of a plane wave basis set is required.

A GW+Bethe-Salpeter calculation on photoabsorption spectra of (CdSe)3 and (CdSe)6 clusters.

Photoabsorption spectra are calculated for the magic number clusters, (CdSe)(3) and (CdSe)(6), using an all-electron mixed basis GW scheme with the excitonic effect incorporated by solving the Bethe-Salpeter equation (BSE). The GW+BSE calculation provided clear size dependence of the optical gap as expected, while magnitude of the gap is overestimated compared to available experimental one. The gap is found very similarly overestimated when using the local density approximation (LDA) within the density functional theory because accidental error cancellation occurs between the significantly underestimated LDA gap and the excitonic effect neglected therein. The excitonic states are described by superposition of many one-particle states that would not be properly described within a one-particle theory, as clearly visualized in the plot of the exciton wavefunctions.

Quasiparticle energy spectra of alkali-metal clusters: all-electron first-principles calculations.

A good approximation to the one-electron self-energy operator in the calculation of quasiparticle energy spectra including the first ionization potential (IP) and electron affinity (EA) is to expand it as a simple product of a one-particle Green's function G and a dynamically screened Coulomb interaction W, namely, GW approximation. We developed a spin-polarized version of the all-electron GW approach and applied it to the first-principles calculation of quasiparticle energy spectra of alkali-metal clusters (Na(n) and K(n), n=1-8). Our all-electron mixed basis approach, in which wave functions are expressed as a linear combination of numerical atomic orbitals and plane waves, enables us to compare the absolute values of the singly (or highest) occupied molecular orbital and the lowest unoccupied molecular orbital levels with available experimental IPs and EAs. The agreements with the corresponding experimental values are fairly good. Comparing with the non-spin-polarized results of Na(2n) and K(2n) (n=1-4), we discuss the effect of spin polarization as well as the cluster size dependence of IPs or EAs.

Dimensional dependence of electronic structure of fullerene polymers.

Fullerene polymers made of C(60) are systematically investigated by means of a first-principles pseudopotential approach within the local density approximation of the density functional theory. We assume 10 different structures of fullerene polymers. The first three are C(60) polymer networks cross-linked by [2+2] cycloadditional four-membered rings, and the other seven are composed of peanut-shaped fused C(60) polymer chains cross-linked by either seven-membered rings or eight-membered rings. Owing to the overlap of wave functions as well as the hybrid networks of sp(2)-like (3-fold coordinated) and sp(3)-like (4-fold coordinated) carbon atoms, the electronic structure is considerably different from each other. We find that the resulting electronic structure is either semiconductor or semimetal depending on the spatial dimensionality of materials.