Theoretical Study on Thermal Structural Fluctuation Effects of Intermolecular Configurations on Singlet Fission in Pentacene Crystal Models.

Singlet fission (SF) occurs as a result of complex excited state relaxation dynamics in molecular aggregates, where a singlet exciton (FE) state is converted into a double-triplet exciton (TT) state through the interactions with several other degrees of freedom, such as nuclear motions. In this study, we combined quantum dynamics simulation based on the quantum master equation approach with all-atom-based classical molecular mechanics/molecular dynamics to examine the thermal structural fluctuation (i.e., static disorder) effects of intermolecular configuration on SF in pentacene crystal models. In particular, we considered two types of static-disordered models, in which excited states are assumed to interact with nuclear motions of intermolecular modes in the classical mechanical/statistical manner. We found that the introduction of static disorder effects leads to a faster decay of coherence between the FE and charge transfer (CT) states in the early stage of SF, contributing to the accelerations of several FE → TT relaxation pathways. Such acceleration in these models is shown to be attributed to fluctuations in the energies and electronic coupling of the CT states based on relative relaxation factor analysis. The present study is expected to contribute to further development of bottom-up materials design for efficient SF in condensed phases where the exitonic system interacts with nuclear motions in various coupling strengths.

Theoretical study on the effect of applying an external static electric field on the singlet fission dynamics of pentacene dimer models.

We investigate the effect of applying an external static electric field on the singlet fission (SF) dynamics of pentacene dimer models using quantum chemical calculations and exciton dynamics simulations. It is found that the excitation energies of anion-cation (AC) and cation-anion (CA) pair exciton states in the SF process are significantly stabilized and destabilized, respectively, by applying an external static electric field (F) in the intermolecular direction. As a result, this change of excitation energies is found to accelerate the SF dynamics in pentacene dimer models. In particular, in the tilted- and parallel-type pentacene dimer models, SF rates at F = 0.001 a.u. are predicted to be about 2.3 and 3.0 times as large as those at F = 0.0 a.u. while keeping the TT yields large. The present result contributes to paving the way for novel physical and chemical controls, that is, an external static electric field application and donor/acceptor substitution on SF molecules, of SF dynamics.

Theoretical Study on Third-Order Nonlinear Optical Properties for One-Hole-Doped Diradicaloids.

We investigate the relationships between open-shell character and longitudinal static second hyperpolarizabilities γ for one-hole-doped diradicaloids using the strong-correlated ab initio molecular orbital methods and simple one-dimensional (1D) three-site two-electron (3s-2e) models. As examples of one-hole-doped diradicaloids, we examine H3 +, methyl radical trimer cation ((CH3)3 +), silyl radical trimer cation ((SiH3)3 +), and 1,2,3,5-dithiadizolyl trimer cation (DTDA3 +). For H3 +, the static γ exhibits negative values and shows a monotonic increase in amplitude with an increase in the open-shell character defined by a neighbor-site interaction (y S). On the other hand, it is found for (CH3)3 +, (SiH3)3 +, and DTDA3 + that the static γ value exhibits similar behavior to that for H3 + up to an intermediate y S value, while it takes the negative maximum at a large y S value, followed by a decrease in γ amplitude, and subsequently, γ changes to positive values with a drastic increase for larger y S values. For example, in DTDA3 +, the negative/positive γ values, -69 × 105/700 × 105 au at y S = 0.75/0.87, exhibit significant enhancements in amplitude, 2.4/24 times as large as that (-29 × 105 au) at intermediate y S = 0.59 as is often the case in DTDA2. Using the 1D 3s-2e valence-bond configuration interaction model, these sign inversions and drastic increase in the amplitude of γ are found to originate in the differences in Coulomb interactions between valence electrons, between valence and core electrons, and between valence electrons and nuclei. These results contribute to pave the way for the construction of novel control guidelines for the amplitude and sign of γ for one-hole-doped diradicaloids.

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.

Theoretical Study on Open-Shell Singlet Character and Second Hyperpolarizabilities in Cofacial π-Stacked Dimers Composed of Weak Open-Shell Antiaromatic Porphyrins.

From the analysis based on the broken-symmetry density functional theory (DFT) calculations, we in this study propose a strategy to enhance the open-shell characters and third-order nonlinear optical (NLO) properties of π-stacked dimers composed of antiaromatic molecules with weak open-shell characters. For this purpose, we here constructed cofacial π-stacked dimer models composed of aromatic and antiaromatic NiII porphyrins in order to examine the π-π stacking distance (R) dependence of the diradical characters (y) and static second hyperpolarizabilities (γ). The antiaromatic porphyrin dimers are found to have intermediate y around R∼3.3 Å, the result of which originates in the unique intermolecular interactions between the antiaromatic monomers. Static γ along the stacking direction of such antiaromatic porphyrin dimers with intermediate diradical characters are shown to be enhanced significantly as compared to those of the isolated monomers and the aromatic porphyrin dimers.

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.

Exploring the novel donor-nanotube archetype as an efficient third-order nonlinear optical material: asymmetric open-shell carbon nanotubes.

Contrary to the enormous number of previous studies on carbon nanotubes (CNTs), herein, we realized the origin of the intrinsic open-shell diradical character and second hyperpolarizability γ using a broken symmetry approach. This study was inspired by our recent findings (S. Muhammad, et al., Nanoscale, 2016, 8, 17998 and Nakano, et al., J. Phys. Chem. C, 2016, 120, 1193). We performed structural modifications through a unique asymmetric donor-nanotube framework, which led to a novel paradigm of modified CNTs with tunable open-shell diradical character and remarkably superior NLO response properties. Interestingly, asymmetry and diradical character were found to be the crucial factors to modulate the second hyperpolarizability γ. We initially performed a comparative analysis of the diradical characters and γ amplitudes of boron nitride nanotubes (BNNTs) and CNTs possessing significant ionic characters and covalent characters, respectively. The basic findings for these simple configurations were further extended to the donor-acceptor CNT paradigm, which finally led to excellent asymmetric donor-CNT configurations with remarkably larger γ amplitudes. Furthermore, among the CNTs, finite length zigzag CNT(6,0)3 were modified with different donor-acceptor configurations. Interestingly, for the first time, unique donor-nanotube configurations [1,4-(NH2)2CNT-(6,0)3 and 1,4-(NH2)2CNT-(6,0)5] were found; they showed significantly robust γ amplitudes as large as 2519 × 103 and 4090 × 103 a.u. at the LC-UBLYP(µ = 0.33)/6-31G* level of theory. Additionally, several molecular level insights have been obtained for these novel donor-nanotube configurations using their odd electron densities, molecular electrostatic maps, densities of states and γ density analyses to highlight the realization of these novel materials for highly efficient optical and NLO applications.

Tunability of Open-Shell Character, Charge Asymmetry, and Third-Order Nonlinear Optical Properties of Covalently Linked (Hetero)Phenalenyl Dimers.

Tunability of the open-shell character, charge asymmetry, and third-order nonlinear optical (NLO) properties of covalently linked (hetero)phenalenyl dimers are investigated by using the density functional theory method. By changing the molecular species X and substitution position (i, j) for the linker part, a variety of intermonomer distances R and relative alignments between the phenalenyl dimers can be realized from the geometry optimizations, resulting in a wide-range tuning of diradical character y and charge asymmetry. It is found that the static second hyperpolarizabilities along the stacking direction, γyyyy , are one-order enhanced for phenalenyl dimer systems exhibiting intermediate y, a feature that is in good agreement with the "y-γ correlation". By replacing the central carbon atoms of the phenalenyl rings with a boron or a nitrogen, we have also designed covalently linked heterophenalenyl dimers. The introduction of such a charge asymmetry to the open-shell systems, which leads to closed-shell ionic ground states, is found to further enhance the γyyyy values of the systems having longer intermonomer distance R with intermediate ionic character, that is, charge asymmetry. The present results demonstrate a promising potential of covalently linked NLO dimers with intermediate open-shell/ionic characters as a new building block of highly efficient NLO systems.