Theoretical Study on Singlet Fission in Aromatic Diaza s-Indacene Dimers.

We theoretically show that diaza (N2)-substitution to s-indacene with 4n π-electrons, by which the number of π-electrons in N2-s-indacene amounts to 4n+2, is a new strategy to design efficient singlet fission (SF) molecules. By N2-substitution, the diradical character and the exchange integral are found to be tuned moderately, leading to satisfying the excitation energy level matching condition for SF with a large triplet excitation energy. On the basis of the effective electronic coupling related to the SF rate, we explore the optimal slip-stack dimer packings for fast SF. Their underlying mechanisms are well understood from the odd-electron density, resonance structure, and frontier orbital distribution, as the functions of the N2-substituted positions. Furthermore, aromaticities of N2-s-indacenes are evaluated explicitly on the basis of the magnetically induced current. Although N2-s-indacenes display strengths of aromaticities similar to that of anthracene, a local decrease in aromaticity is found to correlate to the spatial feature of diradical character, i.e., odd-electron density. The present findings not only newly propose N2-s-indacenes as feasible SF molecules but also contribute to comprehending the interplay between aromaticity and diradical electronic structures contributing to SF.

Vibronic coupling density analysis and quantum dynamics simulation for singlet fission in pentacene and its halogenated derivatives.

We theoretically investigate microscopic origins of vibronic coupling (VC) contributing to singlet fission (SF) dynamics in pentacene and its halogenated derivatives. The features of VCs related to diabatic exciton states and interstate electronic couplings (Holstein and Peierls couplings, respectively) are interpreted by the VC density (VCD) analysis, which allows one to clarify the relationship between the chemical structure and VC as spatial contribution. It is found for the pentacene dimer face-to-edge configuration in a herringbone crystal that characteristic intermolecular vibrations with low frequencies exhibit strong Holstein couplings for the intermediate charge-transfer (CT) exciton states as well as Peierls couplings. From VCD analysis, the comprising density of the intermolecular CT and that of the intermolecular vibration are found to be constructively mixed in the intermolecular space, leading to the enhancement of VC. Moreover, in order to assess the chemical modification manner for controlling VC, we design several halogenated pentacene derivatives with slip-stack configurations. Our strategy to enhance VCD by halogenation is found to be rational, whereas the peaks of VC spectra for the CT states in the slip-stack packings are observed in high frequency regions. We compare their SF dynamics based on the quantum master equation explicitly including the exciton state-dependent VCs. From the analysis on relative relaxation factors between the adiabatic exciton states, their difference in the SF rate is highlighted by exciton configurations in addition to VCs. The present study is expected to be a first step toward efficient SF based on the design of VC in terms of both the chemical structure and intermolecular packing.

Quantum design for singlet-fission-induced nonlinear optical systems: Effects of π-conjugation length and molecular packing of butterfly-shaped acenes.

Theoretical molecular design of efficient nonlinear optical (NLO) systems using singlet fission (SF) is performed for butterfly-shaped acenes with/without nitrogen and sulfur substitutions using quantum chemical calculations, exciton dynamics simulations, and Marcus theory. It is found that these large systems meet the energy level matching conditions of efficient SF and exhibit superior third-order NLO properties (second hyperpolarizability γ at the molecular scale) to a typical SF molecule, pentacene. In addition, we investigate SF rates and γ in the correlated triplet pair [1(TT)] state generated by SF for various slip-stacked dimer models of these systems. For molecular packing with relatively large 1(TT) yields, a significant increase in γ/monomer in the 1(TT) state is observed, which is in good agreement with the electronic-coupling-based design guidelines obtained from our previous study. In particular, the butterfly-shaped acenes involving heteroatoms are found to exhibit a significant increase in γ/monomer as compared to the other systems. By analyzing the excitation properties in the 1(TT) state and intermolecular orbital interactions, we clarify the origin of such γ enhancement. The obtained results contribute to the construction of design guidelines for efficient SF-induced-NLO materials and demonstrate that butterfly-shaped acenes have the potential to surpass conventional NLO systems.

Theoretical Molecular Design of Phenanthrenes for Singlet Fission by Diazadibora-Substitution.

Based on the valence configuration interaction (VCI) model and quantum chemical calculations, we theoretically investigate the potential of diazadibora-substituted phenanthrenes [(BN)2-phenanthrenes] as novel singlet fission (SF) chromophores. (BN)2-substitution to phenanthrene is performed to exhibit a captodative effect, which is found to enhance both diradical character and exchange integral. These enhanced parameters induced by (BN)2-substitution are shown to bring energetically favorable SF with high triplet excitation energies. In order to reveal the relationship between diradical character and positions replaced by (BN)2, analyses based on the VCI model, odd-electron density, and resonance structures are conducted. Accordingly, a concrete design principle, which is inherent in and is understandable from the topology of (BN)2-phenanthrene, is presented. Furthermore, design strategies to fine-tuning of the diradical character are newly demonstrated based on the additional introduction of π-donor and π-acceptor. The present results provide feasible candidate molecules and novel design strategies toward the discovery of bright SF chromophores for the application to efficient organic solar cells.

Singlet-Fission-Induced Enhancement of Third-Order Nonlinear Optical Properties of Pentacene Dimers.

Using quantum chemical calculations and exciton dynamics simulations, we investigate the static second hyperpolarizability γ [the third-order nonlinear optical (NLO) property at the molecular scale] of slip-stacked pentacene dimer models in the correlated-triplet-pair [1(TT)] state created from the singlet excited state in the singlet fission (SF) process. It is found that the SF induces significant (∼20 times at maximum) enhancement of γ/monomer in the 1(TT) state as compared to that in the singlet ground state. The origin of the remarkable enhancement of γ/monomer is revealed by analyzing the γ density distribution and the intermolecular orbital interaction. Furthermore, we clarify molecular packings suitable for highly efficient SF and largely enhanced γ values of a novel class of SF-induced NLO systems, which have promising potential to surpass the conventional NLO systems.

Monte Carlo Wavefunction Approach to Singlet Fission Dynamics of Molecular Aggregates.

We have developed a Monte Carlo wavefunction (MCWF) approach to the singlet fission (SF) dynamics of linear aggregate models composed of monomers with weak diradical character. As an example, the SF dynamics for a pentacene dimer model is investigated by considering the intermolecular electronic coupling and the vibronic coupling. By comparing with the results by the quantum master equation (QME) approach, we clarify the dependences of the MCWF results on the time step (Δt) and the number of MC trajectories (MC). The SF dynamics by the MCWF approach is found to quantitatively (within an error of 0.02% for SF rate and of 0.005% for double-triplet (TT) yield) reproduce that by the QME approach when using a sufficiently small Δt (~0.03 fs) and a sufficiently large MC (~105). The computational time (treq) in the MCWF approach also exhibits dramatic reduction with increasing the size of aggregates (N-mers) as compared to that in the QME approach, e.g., ~34 times faster at the 20-mer, and the size-dependence of treq shows significant reduction from N5.15 (QME) to N3.09 (MCWF). These results demonstrate the promising high performance of the MCWF approach to the SF dynamics in extended multiradical molecular aggregates including a large number of quantum dissipation, e.g., vibronic coupling, modes.

Quantum Master Equation Approach to Singlet Fission Dynamics in Pentacene Linear Aggregate Models: Size Dependences of Excitonic Coupling Effects.

The singlet fission (SF) dynamics of pentacene linear aggregate models are investigated using the quantum master equation method by focusing on the Frenkel excitonic (FE) coupling effects on the SF rate and double triplet (TT) yield as well as on their aggregate size dependences. It is found that for the dimer model, unrealistically large FE couplings are needed to provide significant effects on the SF dynamics, while for the larger aggregate models a realistic FE coupling causes significant variations in the SF dynamics: as increasing the aggregate size, the SF rate rapidly increases, attains the maximum at 8-mer (~3 times enhancement as compared to the non-FE-coupling case) and then decreases, approaching a stationary value after 12-mer, although the stationary TT yield at 20-mer remains slightly smaller than that in the non-FE-coupling case. These features are explained based on the relative relaxation factors between the adiabatic exciton states. The present results contribute to constructing the design guidelines for highly efficient SF aggregates. © 2018 Wiley Periodicals, Inc.

Evaluation of Aromaticity for Open-Shell Singlet Dicyclopenta-Fused Acenes and Polyacenes Based on a Magnetically Induced Current.

The aromaticity of dicyclopenta-fused acenes (DPAs) and polyacenes (PAs) of increasing size has been studied by evaluation with the GIMIC method at the DFT level of the magnetically-induced currents (MICs), and by analyzing their spatial distributions. For these open-shell singlet molecules, spin-restricted and -unrestricted treatments provide very different MICs, the latter ones providing the most reliable solution. These MICs and the differences between spin-restricted and -unrestricted treatments are interpreted in terms of the bond current strengths and the current gradients, which indicate the bond aromaticity and enable the spatial distributions of the diatropic and paratropic currents to be analyzed, respectively. In particular, they allow the rationalization of the MICs in correlation with the odd-electron density distributions and their diradical characters. These calculations demonstrate that 1) in increasingly large PAs the bond current strengths get smaller and smaller than in benzene and get almost similar in the central and terminal rings, 2) for DPAs the MICs increase from dominant paratropic currents and antiaromaticity in the small compounds to diatropic currents and aromaticity in the larger ones, and 3) in the largest DPAs, the central rings are characterized by large diatropic currents and the terminal five-membered rings, for which the odd-electron densities are localized by weak ones.

Third-Order Nonlinear Optical Properties of One-Dimensional Quinoidal Oligothiophene Derivatives Involving Phenoxyl Groups.

The diradical characters (y) and third-order nonlinear optical (NLO) properties of open-shell quinoidal oligothiophene derivatives with phenoxyl groups, and the corresponding reduced (hydrogenated)-state oligomers, are investigated by using the broken-symmetry density functional theory method. The oxidized (dehydrogenated) states are predicted to have an open-shell singlet ground state and their y values increase with the number of units. Static second hyperpolarizabilities (γ) of the open-shell oligomers with intermediate y are shown to be enhanced significantly compared with those of the closed-shell analogues. Furthermore, owing to the effective diradical distances, the γ values of open-shell oligomers are found to exceed that of s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene, which is known as an organic molecule with the largest two-photon absorption cross-section in this size of the pure hydrocarbons. This feature extends the range of efficient open-shell third-order NLO materials to a novel class of one-dimensional conjugated oligomers with redox-based high tunability of third-order NLO properties.

Theoretical Study on the Open-Shell Singlet Nature and the Second Hyperpolarizabilities of Corannulene Derivatives with Two Phenoxyl Radicals.

Using the spin-unrestricted density functional theory method, we investigate the interplay between the diradical character y and second hyperpolarizabilities γ (the third-order nonlinear optical (NLO) properties at the molecular scale) of corannulene derivatives with two phenoxyl radicals. This molecule in the singlet state exhibits intermediate y and thus displays a significantly larger γ value than the triplet state and the closed-shell bis-phenol analogue. We also examine the planar molecules involving a coronene moiety in place of the curved corannulene. The intermediate y and large γ values of the corannulene systems are found to originate not from their curved skeleton but from the equilibrium between benzenoid/quinoid resonance forms due to delocalization of the radical electrons of the terminal phenoxyl rings. The longitudinal γ value of the singlet state is found to be comparable to that of s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene, which is known to be one of the organic molecules with the largest two-photon absorption cross section in this size of pure hydrocarbons. The present system is thus expected to be a promising candidate for highly efficient open-shell NLO molecules.

Diradical and Ionic Characters of Open-Shell Singlet Molecular Systems.

The diradical and ionic natures of open-shell singlet systems have been investigated using new definitions of the diradical and ionic characters as well as of their densities within the valence configuration interaction (VCI) model with two electrons in two active orbitals. The two-site symmetric and asymmetric diradical models are examined by using these diradical/ionic characters. For realistic compounds, we investigate a diradicaloid diphenalenyl and a rectangular graphene nanoflake in the presence of an external static electric field, as well as π-stacked phenalenyl-derivative dimers with varying the intermonomer distance, where the central carbon atoms in the phenalenyl rings are substituted by boron (B) and nitrogen (N) atoms, respectively. It is found that the increase of charge asymmetricity induced by the static electric field decreases the diradical character and finally induces an ionic character in the ground state, while the first excited state is changed from pure ionic to diradical-dominant as the field amplitude increases. On the other hand, when increasing the intermonomer distance, the B/N substitution in the phenalenyl dimer changes the electronic state from open-shell singlet with small diradical character to closed-shell with large ionic character. These results indicate that the application of a static electric field to diradicaloids and the asymmetric substitution of a pancake bonded π-dimer combined with the variation of intermonomer distance could tune the diradical/ionic characters and therefore control the nonlinear optical responses.

Intermolecular Packing Effects on Singlet Fission in Oligorylene Dimers.

Using the density functional theory method, the crystalline packing effect on the singlet fission (SF) rate of oligorylenes, some of which are found to exhibit SF in crystal forms, is revealed by evaluating the effective electronic coupling (|Veff|), the square of which is proportional to the SF rate. The |Veff| values for terrylene and quaterrylene dimer models are investigated for a variety of slip-stacked forms. It is found that these values show similar dependences on the intermolecular packing as a function of lateral and longitudinal displacements of monomer frameworks, and that they are maximized in several configurations of one monomer slipped from another along the longitudinal axis. The present estimation method of the SF rate is also found to qualitatively explain the experimental SF rate difference between terrylene derivatives with different packing forms. Furthermore, by analyzing the effect of electronic couplings on the adiabatic electronic states related to SF, we predict several favorable molecular packings leading to a fast SF with a high triplet yield.

Tuning Nonlinear Optical Properties by Altering the Diradical and Charge-Transfer Characteristics of Chichibabin's Hydrocarbon Derivatives.

Heteroatomic derivatives of Chichibabin's hydrocarbon are explored theoretically to highlight the relationship between the electronic structure and nonlinear optical (NLO) properties. The results show that the systems are divided into two classes: one that has intermediate electronic structure between two main contributing resonance structures, and a second with an electronic structure that is approximated by only one resonance structure. It is found that the former class of derivatives exhibits approximately one-order larger static second hyperpolarizability (γ) than the latter class, because of either their intermediate diradical or charge-transfer (CT) characteristics. The asymmetric systems are further scrutinized by using the static electric field model, which shows that the intermediate CT character is essential for the very large enhancement of γ in the asymmetric systems. These results not only clarify the structure-property relationships of open-shell singlet NLO compounds with redox switching properties, but also shed light on a new and unexplored class of closed-shell NLO systems generated by the introduction of intermediate CT nature into open-shell singlet systems.

Theoretical Study on the Second Hyperpolarizailities of Oligomeric Systems Composed of Carbon and Silicon π-Structures.

To explore the prospect of molecules involving silicon-silicon multiple bonds as nonlinear optical molecular systems, the relationship between the structure and the second hyperpolarizabilities γ of the oligomeric systems composed of carbon and silicon π-structures is investigated using the density functional theory method. It is found that these compounds indicate intramolecular charge transfer (ICT) from the silicon units to the carbon units together with nonzero diradical characters. The γ values of these compounds are shown to be 2-13 times as large as those of the carbon analogs. Although asymmetric carbon and silicon π-systems exhibit comparable enhancement to the corresponding symmetric systems, donor-π-donor structures exhibit remarkable enhancement of γ despite of their both-end short silicon π-chain moieties (donor units). Further analysis using the odd electron and γ densities clarifies that the intermediate diradical character also contributes to the enhancement of γ. These results predict that even short π-conjugated silicone moieties can cause remarkable enhancement of γ by introducing them into π-conjugated hydrocarbon structures.

Diradical Character-Based Design for Singlet Fission of Bisanthene Derivatives: Aromatic-Ring Attachment and π-Plane Twisting.

We demonstrate a diradical character-based molecular design for singlet fission using polycyclic aromatic hydrocarbons, bisanthene derivatives. Two types of chemical modifications-aromatic-ring attachment and π-plane twisting-are examined in order to satisfy the energy level matching condition for singlet fission. Detailed analysis of the electronic structures of the model molecules using nucleus-independent chemical shift, molecular orbitals, and their energies has demonstrated the usefulness of the relationship between the resonance structure and aromaticity and that between nonplanarity of π-conjugated systems and reduction of orbital overlap for tuning the diradical character. This result provides a novel design guideline for polycyclic aromatic hydrocarbons toward efficient singlet fission.

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal-Carbon Bonds.

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal-carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when the bond length increases, γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems.

Design Principles of Electronic Couplings for Intramolecular Singlet Fission in Covalently-Linked Systems.

We theoretically investigate the singlet fission in three types of covalently-linked systems, that is, ortho-, meta- and para-linked pentacene dimers, where these are shown to have significantly different singlet fission rates. Each molecule is composed of two chromophores (pentacenes), which are active sites for singlet fission, and covalent bridges linking them. We clarify the origin of the difference in the electronic couplings in these systems, which are found to well support a recent experimental observation. It is also found that the next-nearest-neighbor interaction is indispensable for intramolecular singlet fission in these systems. On the basis of these results, we present design principles for efficient intramolecular singlet fission in covalently-linked systems and demonstrate the performance by using several novel conjugated linkers.

Open-Shell Singlet Nature and σ-/π-Conjugation Effects on the Third-Order Nonlinear Optical Properties of Si Chains: Polysilane and Poly(disilene-1,2-diyl).

We theoretically investigate the open-shell singlet nature and σ-/π-conjugation effects on the longitudinal second hyperpolarizabilities (γ) of one-dimensional chains involving silicon-silicon bonds, that is, polysilane and poly(disilene-1,2-diyl), by comparison with their carbon analogues, polyethylene and polyacetylene, respectively. It is found that poly(disilene-1,2-diyl) has less bond length alternation than polyacetylene and that σ-conjugation of polysilane is less effective on the enhancement of γ than π-conjugation of polyacetylene, whereas π-conjugation of poly(disilene-1,2-diyl) indicates a more than 20 times greater enhancement of the γ than that of polyacetylene, which is known to be a typical nonlinear optical molecule with large γ, for one-dimensional chains involving 3-5 double bonds. Further theoretical analyses of poly(disilene-1,2-diyl) reveal the σ- and π-electrons contribute negatively and positively to the γ, respectively. The latter contribution is significantly larger than the former and thus causes the remarkable enhancement of γ amplitudes due to the emerging open-shell singlet nature in the long π-conjugation length.

Diradical Character Tuning for the Third-Order Nonlinear Optical Properties of Quinoidal Oligothiophenes by Introducing Thiophene-S,S-dioxide Rings.

To create a design guideline for efficient third-order nonlinear optical (NLO) molecules, the chain-length (n) dependences of the diradical character y and the longitudinal second hyperpolarizability γ of quinoidal oligothiophenes (QTs), from monomers to octamers, involving thiophene-S,S-dioxide rings are investigated by using the density functional theory method. It turns out that the diradical character of the modified QTs is reduced as compared to those of the pristine QTs. By introducing an appropriate number of oxidized rings into the QT framework, intermediate y values can be achieved even in the systems with large values of n, in which the pristine QTs are predicted to have pure diradical character. Such intermediate diradical oligomers are shown to exhibit enhanced γ values as compared to the pristine QTs with the same value for n. From the calculation results, the introduction of the optimal number of thiophene-S,S-dioxide rings is predicted to be an efficient chemical modification for optimizing the third-order NLO properties of open-shell QTs through tuning the diradical characters.