Functionality optimization for effective singlet fission coupling screening in the full-dimensional molecular and intermolecular coordinate space

In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening of the structural space employing a "functionality optimization" technique, in which a chosen descriptor, constrained by the ground state energy expression, is optimized. The chosen algorithmic differentiation (AD) framework allows one to automatically obtain gradients without its tedious implementation. We demonstrate the effectiveness of the approach by identifying perylene bisimide (PBI) dimer motifs with enhanced effective SF coupling. Our findings reveal that certain structural modifications of the PBI monomer, such as helical twisting and bending as well as slipped-rotated packing arrangements, can significantly increase the effective SF coupling.

Room Temperature Phosphorescence in Crystalline Iodinated Eumelanin Monomer

We report the room temperature phosphorescence upon iodination on a crystalline eumelanin monomer with shielded hydroxyl moieties, ethyl 5,6-dimethoxyindole-2-carboxylate (DMICE). Ultrafast intersystem crossing (ISC) is observed in the iodinated (IDMICE) as well as brominated (BDMICE) analogues of the eumelanin monomer derivative in solution. The triplet quantum yields (φT) and intersystem crossing rates (kISC) of the halogenated eumelanin derivatives areφ T B D M I C E ${{\phi{} }_{T}^{BDMICE}}$ =25.4±1.1 %;k I S C B D M I C E ${{k}_{ISC}^{BDMICE}}$ =1.95×109 s-1 andφ T I D M I C E ${{\phi{} }_{T}^{IDMICE}}$ =59.1±1.6 %;k I S C I D M I C E = ${{k}_{ISC}^{IDMICE}=}$ 1.36×1010 s-1, as monitored using transient absorption spectroscopy. Theoretical calculations based on nuclear ensemble method reveal that computed kISC and spin-orbit coupling matrix elements for eumelanin derivatives are larger for IDMICE relative to BDMICE. The halogen and π-π interactions, with distinct excitonic coupling and higher ISC rate promote phosphorescence in IDMICE molecular crystals. Accessing triplet excited states and resultant photoluminescence through structural modification of eumelanin scaffolds paves way for exploring the versatility of eumelanin-inspired molecules as bio-functional materials.

Modulating singlet fission through interchromophoric rotation

Singlet fission (SF) is a spin-allowed, exciton-multiplying phenomenon that can be utilized to improve the efficiency of organic solar cells. It is well-understood that SF is sensitive to the local crystal morphology and an appropriately balanced coupling is essential to facilitate efficient SF. In this study, we show how the interchromophoric rotation selectively modulates the interaction between the monomer frontier molecular orbitals, promoting both fast and exothermal SF. We evaluate the effective electronic coupling for SF (V_SF), the square of which is proportional to the SF rate, and the effective energies of the Frenkel exciton (FE/S₁S₀) and triplet pair exciton (TT) in a terrylene dimer model. Optimal interplanar rotation of the chromophoric moieties in slip-stacked arrangements pulls the effective energy of the TT state below that of the FE state. Consequently, SF is favored over competing pathways such as excimer formation, thereby enhancing the overall triplet yield. This work represents a step towards improvising the molecular design guidelines for SF and understanding the importance of interchromophoric rotation over the conventional slip-stacked arrangements for achieving favorable intermolecular electronic coupling towards efficient SF.

Rational design of organic semiconductors with low internal reorganization energies for hole and electron transport: position effect of aza-substitution in phenalenyl derivatives

Amphoteric-redox phenalenyl radical (PLY) is a suitable candidate used to design ambipolar organic materials. Because the singly occupied nonbonding molecular orbital (NBMO) of PLY has a perfect local nonbonding character, its internal reorganization energy (λ) for transporting holes (λ⁺) or electrons (λ^-) is known to be small. Herein, PLY is employed to study the position effect of the aza group on the λ. By adding or extracting an electron from the NBMO, the bond length alterations can be minute. Therefore, the PLY derivatives are also an excellent candidate to study the contributions from the bond angle alterations to the λ. Substituting the aza groups at the β- or α-positions of PLY shows two different trends. When consecutively substituting the aza group at the three β-positions of PLY, the λs are consistently decreased. Contrarily, a series of double functionalization of aza groups at the four α-positions of PLY, the λs are increased. It is because the local bonding or antibonding character in frontier orbitals (FMO) is observed in α2N-PLY and α4N-PLY. As the FMOs of the three β-substituted PLYs and α6N-PLY have perfect local nonbonding character, we found the bond angle alterations are the main contributors of λ. The λs for most aza-PLYs were smaller than 100 meV. Thus, we propose a design rule for substituting aza groups on the parent molecules with strong local nonbonding character in their FMOs. Based on the adiabatic ionization potential and electron affinity, two π-extended PLY derivatives with small λ were recommended for fabricating air-stable ambipolar OFET.

Charge transport properties of open-shell graphene fragments: a computational study of the phenalenyl tilings

Thinking outside the box of the phenalenyl radical: a systematic structure design strategy, phenalenyl tiling, is found to benefit the electron transport properties of open-shell graphene fragments with one free radical. Compared with the closed-shell species, phenalenyl-based π-radicals exhibit smaller intramolecular reorganization energies and larger intermolecular electronic couplings. However, the on-site Coulomb repulsion can be too strong and impedes the charge transport efficiency of such materials. The repulsion can be weakened in radical species by spin delocalization. In this paper, the extended π-radicals we studied are categorized into three types of open-shell structures: the zigzag, the armchair and the discotic odd alternant hydrocarbons. The latter two belong to phenalenyl tilings. We found that the phenalenyl tilings fully inherit the desirable features of the singly occupied molecular orbital of the phenalenyl radical in a predictable and delocalized fashion, and their on-site Coulomb repulsion is effectively reduced. The zigzag π-radicals are less satisfactory. Therefore, the phenalenyl tilings are favorable candidates for charge transporting materials.

Unconventional singlet fission materials

Singlet fission (SF) is a photophysical downconversion pathway, in which a singlet excitation transforms into two triplet excited states. As such, it constitutes an exciton multiplication generation process, which is currently at the focal point for future integration into solar energy conversion devices. Beyond this, various other exciting applications were proposed, including quantum cryptography or organic light emitting diodes. Also, the mechanistic understanding evolved rapidly during the last year. Unfortunately, the number of suitable SF-chromophores is still limited. This is per se problematic, considering the wide range of envisaged applicability. With that in mind, we emphasize uncommon SF-scaffolds and outline requirements as well as strategies to expand the chromophore pool of SF-materials.

Lessons from intramolecular singlet fission with covalently bound chromophores

Molecular dimers, oligomers, and polymers are versatile components in photophysical and optoelectronic architectures that could impact a variety of applications. We present a perspective on such systems in the field of singlet fission, which effectively multiplies excitons and produces a unique excited state species, the triplet pair. The choice of chromophore and the nature of the attachment between units, both geometrical and chemical, play a defining role in the dynamical scheme that evolves upon photoexcitation. Specific final outcomes (e.g., separated and uncorrelated triplet pairs) are being sought through rational design of covalently bound chromophore architectures built with guidance from recent fundamental studies that correlate structure with excited state population flow kinetics.

Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model

A procedure is described for unbiased identification of all π-electron chromophore pair geometry choices that locally maximize the rate of conversion of a singlet exciton into a singlet biexciton (triplet pair), using a simplified version of the diabatic frontier orbital model of singlet fission (SF). The resulting approximate optimal geometries provide insight and are expected to represent useful starting points for searches by more advanced methods. The general procedure is illustrated on a pair of ethylenes as the simplest model of a π-electron system, but it is applicable to pairs of much larger molecules, with dozens of non-hydrogen atoms, and not necessarily planar. We first examine the value of |T^A|², the square of the electronic matrix element for SF with initial excitation fully localized on partner A, on a grid of several billion geometries within the six-dimensional space of physically realizable possibilities. Several of the optimized pair geometries are somewhat unexpected, but all are found to follow the qualitative guidance proposed earlier. In the neighborhood of each local maximum of |T^A|², consideration of mixing with charge-transfer configurations and of excitonic interaction between partners A and B determines the SF energy balance and yields squared matrix elements |T*|² and |T**|² for the lower and upper excitonic states S* and S**, respectively. Assuming Boltzmann populations of these states, the geometry is further optimized to maximize k, the sum of the SF rates obtained from Marcus theory, and this reorders the suitable geometries substantially. At 87 pair geometries, the |T*|² and |T**|² values are compared with those obtained from high-level ab initio nonorthogonal configuration interaction calculations and found to follow the same trend. Finally, the biexciton binding energy at the optimized geometries is calculated. Altogether, 13 significant local maxima of SF rate for a pair of ethylenes are identified in the physically relevant part of space that avoids molecular interpenetration in the hard-sphere approximation. The three best geometries are twist-stacked, slip-stacked, and L-shaped. The maxima occur at the (five-dimensional) surfaces of seven six-dimensional "parent" regions of space centered at physically inaccessible geometries at which the calculated SF rate is very large but the two ethylenes interpenetrate. The results are displayed in interactive graphics. The computer code ("Simple") written for these calculations is flexible in that it permits a choice of performing the search for local maxima in six dimensions on |T^A|², |T*|², or k. It is available as freeware at https://cloud.uochb.cas.cz/simple .

Optimal arrangements of 1,3-diphenylisobenzofuran molecule pairs for fast singlet fission

A simplified version of the frontier orbital model has been applied to pairs of C₂, C_2v, C_s, and C₁ symmetry 1,3-diphenylisobenzofuran rotamers to determine their best packing for fast singlet fission (SF). For each rotamer the square of the electronic matrix element for SF was calculated at 2.2 × 10⁹ pair geometries and a few thousand most significant physically accessible local maxima were identified in the six-dimensional space of mutual arrangements. At these pair geometries, SF energy balance was evaluated, relative SF rate constants were approximated using Marcus theory, and the SF rate constant k_SF was maximized by further optimization of the geometry of the molecular pair. The process resulted in 142, 67, 214, and 291 unique geometries for the C₂, C_2v, C_s, and C₁ symmetry molecular pairs, respectively, predicted to be superior to the C₂ symmetrized known crystal pair structure. These optimized pair geometries and their triplet biexciton binding energies are reported as targets for crystal engineering and/or covalent dimer synthesis, and as possible starting points for high-level pair geometry optimizations.

Striking the right balance of intermolecular coupling for high-efficiency singlet fission

Singlet fission is a process that splits collective excitations, or excitons, into two with unity efficiency. This exciton splitting process, unique to molecular photophysics, has the potential to considerably improve the efficiency of optoelectronic devices through more efficient light harvesting. While the first step of singlet fission has been characterized in great detail, subsequent steps critical to achieving overall highly-efficient singlet-to-triplet conversion are only just beginning to become well understood. One of the most elementary suggestions, which has yet to be tested, is that an appropriately balanced coupling is necessary to ensure overall highly efficient singlet fission; that is, the coupling needs to be strong enough so that the first step is fast and efficient, yet weak enough to ensure the independent behavior of the resultant triplets. In this work, we show how high overall singlet-to-triplet conversion efficiencies can be achieved in singlet fission by ensuring that the triplets comprising the triplet pair behave as independently as possible. We show that side chain sterics govern local packing in amorphous pentacene derivative nanoparticles, and that this in turn controls both the rate at which triplet pairs form and the rate at which they decay. We show how compact side chains and stronger couplings promote a triplet pair that effectively couples to the ground state, whereas bulkier side chains promote a triplet pair that appears more like two independent and long-lived triplet excitations. Our results show that the triplet pair is not emissive, that its decay is best viewed as internal conversion rather than triplet-triplet annihilation, and perhaps most critically that, in contrast to a number of recent suggestions, the triplets comprising the initially formed triplet pair cannot be considered independently. This work represents a significant step toward better understanding intermediates in singlet fission, and how molecular packing and couplings govern overall triplet yields.

Theoretical Studies of Singlet Fission: Searching for Materials and Exploring Mechanisms

In this Review article, a survey is given for theoretical studies in the subject of singlet fission. Singlet fission converts one singlet exciton to two triplet excitons. With the doubled number of excitons and the longer lifetime of the triplets, singlet fission provides an avenue to improve the photoelectric conversion efficiency in organic photovoltaic devices. It has been a subject of intense research in the past decade. Theoretical studies play an essential role in understanding singlet fission. This article presents a Review of theoretical studies in singlet fission since 2006, the year when the research interest in this subject was reignited. Both electronic structure and dynamics studies are covered. Electronic structure studies provide guidelines for designing singlet fission chromophores and insights into the couplings between single- and multi-excitonic states. The latter provides fundamental knowledge for engineering interchromophore conformations to enhance the fission efficiency. Dynamics studies reveal the importance of vibronic couplings in singlet fission.

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, γ_yyyy , 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 γ_yyyy 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.

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 (|V_eff|), the square of which is proportional to the SF rate. The |V_eff| 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.

Rational design of doubly-bridged chromophores for singlet fission and triplet–triplet annihilation

A novel multiple-bridging realizes rational molecular design for efficient singlet fission and triplet–triplet annihilation.