Diradical Character View of Singlet Fission

The feasibility conditions of singlet fission on the excitation energy differences are revealed as functions of the multiple diradical characters <i>y</i>_<i>i</i> [defined by the occupation numbers of the LUNO (= Lowest Unoccupied Natural Orbital) +<i> i</i> (<i>i</i> = 0, 1, ...), where 0 ≤ <i>y_i</i> ≤ 1 and <i>y_i</i> ≥ <i>y_j</i> (<i>i</i> > <i>j</i>)] using the linear H₄ full configuration interaction model. The diradical characters suited for singlet fission are found to lie in the region with <i>y</i>₀ > 0.10 except for <i>y</i>₀ ∼ <i>y</i>₁, though its energy efficiency is better in case of smaller <i>y</i>₀, to which diradical and multiradical compounds with low/intermediate diradical characters such as open-shell singlet polycyclic aromatic hydrocarbons belong. These findings indicate that the multiple diradical character is an effective indicator for exploring molecular systems for efficient singlet fission

Theoretical Molecular Design of Heteroacenes for Singlet Fission: Tuning the Diradical Character by Modifying π‑Conjugation Length and Aromaticity

A theoretical molecular design for efficient singlet fission (SF) is performed for several heteroacene models involving nitrogen (N) atoms based on the diradical character criterion of the energy level matching conditions. This criterion is found to be closely related to the relative contributions of diradical and zwitterionic resonance structures of the heteroacenes, i.e., the aromaticity of the central ring(s). From the analysis of the diradical characters of these heteroacene models, the increase in the aromaticity of the central ring(s) is found to prefer the diradical form to the zwitterionic form. From the comparison of the excitation energies evaluated by multireference second-order perturbation theory calculations, two promising candidates, chosen based on the diradical character criterion, are found to satisfy the energy level matching conditions and to possess high triplet energies of ∼1.1 eV, which are suitable for an application in organic photovoltaic cells. The proposed two candidates are shown to have mutually different types of the first excited singlet states, which are distinguished by the primary excitation configurations. These results suggest that the proposed two candidates exhibit different singlet fission dynamics due to the different amplitude of the electronic coupling

Diradical Character View of Singlet Fission

The feasibility conditions of singlet fission on the excitation energy differences are revealed as functions of the multiple diradical characters <i>y</i>_<i>i</i> [defined by the occupation numbers of the LUNO (= Lowest Unoccupied Natural Orbital) +<i> i</i> (<i>i</i> = 0, 1, ...), where 0 ≤ <i>y_i</i> ≤ 1 and <i>y_i</i> ≥ <i>y_j</i> (<i>i</i> > <i>j</i>)] using the linear H₄ full configuration interaction model. The diradical characters suited for singlet fission are found to lie in the region with <i>y</i>₀ > 0.10 except for <i>y</i>₀ ∼ <i>y</i>₁, though its energy efficiency is better in case of smaller <i>y</i>₀, to which diradical and multiradical compounds with low/intermediate diradical characters such as open-shell singlet polycyclic aromatic hydrocarbons belong. These findings indicate that the multiple diradical character is an effective indicator for exploring molecular systems for efficient singlet fission

Theoretical Molecular Design of Heteroacenes for Singlet Fission: Tuning the Diradical Character by Modifying π‑Conjugation Length and Aromaticity

A theoretical molecular design for efficient singlet fission (SF) is performed for several heteroacene models involving nitrogen (N) atoms based on the diradical character criterion of the energy level matching conditions. This criterion is found to be closely related to the relative contributions of diradical and zwitterionic resonance structures of the heteroacenes, i.e., the aromaticity of the central ring(s). From the analysis of the diradical characters of these heteroacene models, the increase in the aromaticity of the central ring(s) is found to prefer the diradical form to the zwitterionic form. From the comparison of the excitation energies evaluated by multireference second-order perturbation theory calculations, two promising candidates, chosen based on the diradical character criterion, are found to satisfy the energy level matching conditions and to possess high triplet energies of ∼1.1 eV, which are suitable for an application in organic photovoltaic cells. The proposed two candidates are shown to have mutually different types of the first excited singlet states, which are distinguished by the primary excitation configurations. These results suggest that the proposed two candidates exhibit different singlet fission dynamics due to the different amplitude of the electronic coupling

Intramolecular Charge Transfer Effects on the Diradical Character and Second Hyperpolarizabilities of Open-Shell Singlet X−π–X (X = Donor/Acceptor) Systems

We investigate the effect of the quadrupole-type intramolecular charge transfer (ICT) in open-shell singlet donor−π–donor (D−π–D) molecules on the singlet open-shell (diradical) character and the longitudinal second hyperpolarizabilities γ (the third-order nonlinear optical (NLO) properties at the molecular scale). For this investigation we used the <i>para</i>-quinodimethane (PQM) with point charges (pc’s) model calculated with the unrestricted coupled cluster method including single and double excitations with a perturbative treatment of the triple excitations (UCCSD­(T)). In this model, the diradical character <i>y</i> and the amount of the ICT, that is, the D−π–D nature, can be varied primarily by changing the exocyclic carbon–carbon bond (C–C) lengths and the external pc's <i>Q</i>, respectively. It turns out that the increase in the D−π–D nature decreases the <i>y</i> values, moves the <i>y</i> values (<i>y</i>_max) giving the maximum γ (γ_max) to the large <i>y</i> region, and enhances the γ_max values, for example, the γ_max of the singlet diradical PQM with <i>Q</i> = −2.8 au reaches twice that of the singlet diradical PQM without any pc's. This result indicates that open-shell singlet D−π–D systems with ICT are promising candidates for a new class of third-order NLO molecules, whose γ values are more enhanced than those of conventional closed-shell D−π–D systems and of symmetric open-shell singlet systems without the ICT. To confirm this tendency, we examine the boron-disubstituted PQM dianion model, which is found to exhibit further enhancement of γ as compared to the PQM model with intermediate diradical character due to the synergy effects of the intermediate open-shell singlet nature and the strong field-induced ICT nature in the dianionic state of the D−π–D system. Further investigation of the acceptor−π–acceptor (A−π–A) type ICT effect in the PQM-pc model shows that both D−π–D and A−π–A type symmetric ICTs give similar effects on the relationship between <i>y</i> and γ, though there are some differences originating in the orbital contraction and extension induced by the pc's. The present results contribute to understanding the third-order NLO properties of open-shell symmetric ICT systems and thus to constructing new design guidelines for highly efficient third-order NLO systems

Theoretical Study of Singlet Fission in Oligorylenes

Using the time-dependent tuned long-range corrected density functional theory method, the feasibility for singlet fission in oligorylenes has been investigated within the scope of the diradical character based guideline and of the energy level matching conditions for the isolated monomers. It is found that the relatively small-size oligorylenes, that is, terrylene and quaterrylene, which present intermediate diradical character without significant tetraradical character, are possible candidates for energetically efficient singlet fission. In relation to this result, we also raise the possibility that the unsettled ultrafast dynamics previously observed on quaterrylene is evidence for singlet fission

Third-Order Nonlinear Optical Properties of Asymmetric Non-Alternant Open-Shell Condensed-Ring Hydrocarbons: Effects of Diradical Character, Asymmetricity, and Exchange Interaction

Using spin-unrestricted density functional theory, the longitudinal static second hyperpolarizability γ has been investigated for an asymmetric azulene-like open-shell condensed-ring molecule (<b>1)</b> as well as for its symmetric almost closed-shell and open-shell analogues (pentacene (<b>2</b>) and its dicyclopenta- (<b>3</b>) and dicyclohepta-fused (<b>4</b>) analogues). It is found that the symmetric systems, <b>3</b> and <b>4</b>, having intermediate diradical characters show a 6–9 times enhancement of γ as compared to <b>2</b>, but that this enhancement is even larger (by a factor of 30) for the asymmetric diradicaloid, <b>1</b>. Geometrical, electronic, and magnetic descriptors have shown that in <b>1</b> the terminal seven- and five-membered rings display a cooperative push–pull effect, leading to a large dipole moment, that seems to reinforce its aromaticity as well as its ionic character, whereas <b>3</b> and <b>4</b> are mostly neutral diradicaloids and are less aromatic. These features have been rationalized by resorting to an asymmetric two-site model within the valence configuration interaction method. It is found that the diradical character decreases with increasing the asymmetricity and the exchange interaction. Then, an increase in the exchange interaction leads to a decrease of the asymmetricity value defining the critical point (where the diradical and ionic contributions of the ground and first excited states exchange) and increases the amplitudes of the γ extrema. The increase in asymmetricity has been realized in two ways: (i) by applying a static electric field to the symmetric nonalternant condensed-ring diradicaloid (<b>3</b>), and (ii) by designing an asymmetric nonalternant azulene-like condensed-ring conjugated system (<b>1</b>). Scheme ii gives a triplet ground state and it therefore requires large <i>r</i>_<i>K</i>, i.e., small HOMO–LUMO overlap. As a result, such an increase of <i>r</i>_<i>K</i> in scheme ii leads to a new class of asymmetric NLO systems, having a ferromagnetic ground state and a singlet first excited state. The latter has an intermediate or small diradical character <i>y</i> and it exhibits negative γ values with amplitudes larger than those of symmetric diradicaloids with smaller <i>r</i>_<i>K</i>

Thermal Decomposition of Silver Acetate: Physico-Geometrical Kinetic Features and Formation of Silver Nanoparticles

The thermal decomposition of silver acetate (CH₃COOAg) was investigated to reveal the factors controlling the formation of Ag nanoparticles (NPs). The overall kinetic behavior was interpreted as partially overlapping two reaction steps using systematic kinetic and morphological analyses. Although the apparent activation energies were comparable (approximately 75 kJ mol^–1), the initial reaction step was regulated by the first order law because of the consumption of reactive sites on the end surfaces of columnar crystals, whereas the subsequent reaction step advanced by shrinkage of the side surfaces of the crystals with an accelerating linear shrinkage rate, resulting in slimming of the crystals. A large surface area of the reactant crystals was exposed to the reaction atmosphere during the course of the reaction by the self-induced migration of the Ag product to the surfaces of the Ag-NP aggregates formed at certain parts of the reactant surfaces. As a result, the atmospheric water vapor affected the kinetic behavior by significantly lowering the reaction temperature. As a possible explanation for these phenomena, a physical mechanism involving evaporation of the reactant and simultaneous condensation of the product is proposed herein

Fundamental of Diradical-Character-Based Molecular Design for Singlet Fission

The fundamental of diradical-character-based molecular design for singlet fission is clarified through the correlation between the diradical character, the first singlet (S₁) and triplet (T₁) excitation energies, the frontier orbital energy gap, and the energy level matching condition (2<i>E</i>(T₁) – <i>E</i>(S₁) ≈ 0 or < 0) for singlet fission by using the analytical solution of the electronic structure for a model system with two electrons in two orbitals. Moreover, the S₁–T₁ gap is found to be a key factor for governing the amplitude of <i>E</i>(T₁) for 2<i>E</i>(T₁) – <i>E</i>(S₁) ≈ 0. These findings are indeed justified by the spin-flip time-dependent density functional theory calculations for a series of typical alternant/nonalternant hydrocarbons, that is, phenacenes, acenes, and isobenzofulvene. The present results demonstrate that a weak diradical character is the underlying concept for efficient singlet fission molecules

Density Analysis of Intra- and Intermolecular Vibronic Couplings toward Bath Engineering for Singlet Fission

Vibronic coupling plays a crucial role in singlet fission whereby a singlet exciton splits into two triplet excitons. In order to reveal the physicochemical origin of the vibronic coupling associated with singlet fission as well as to clarify its relationship with chemical structure, we evaluate relevant vibronic couplings from the viewpoint of their spatial contributions described by vibronic coupling density. From the analysis using a model tetracene dimer, a typical singlet fission system, the frequency dependence of vibronic couplings in each electronic state is found to be significantly different from that of another depending on the nature of the electronic structure (intra/intermolecular excitation) and the related vibrational motion. These findings contribute not only to the fundamental understanding of the singlet fission mechanism from the viewpoint of vibronic couplings but also to opening a new path to designing highly efficient singlet fission materials through phonon–bath engineering