Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character

Optoelectronic properties of diketopyrrolopyrrole homopolymers compared to donor-acceptor copolymers

Diketopyrrolopyrrole (DPP) is a component of a large number of materials used for optoelectronic applications. As it is exclusively used in combination with aromatic donors, the properties of its homopolymers are unknown. Because donor-acceptor character has been shown for other systems to reduce bandwidths, DPP homopolymers should have even larger conduction bands and better n-type conductivity than the thiophene-flanked systems, which have exceptional n-type conductivity and ambipolar character. Therefore, a theoretical study was carried out to elucidate the properties of the unknown DPP homopolymer. Calculations were done with density functional theory and with the complete active space self-consistent field method plus n-electron valence state perturbation theory for the dynamic correlation. Poly-DPP is predicted to have radical character and an extremely wide low-lying conduction band. If it were possible to produce this material, it should have unprecedented n-type conductivity and might be a synthetic metal. A comparison with various unknown donor-acceptor systems containing vinyl groups and thienyl rings with a higher concentration of DPP than the known copolymers reveals how donor-acceptor substitution reduces bandwidths and decreases electron affinities.

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.

Diradicalar Character and Ring Stability of Mesoionic Heterocyclic Oxazoles and Thiazoles by Ab Initio Mono and Multi-Reference Methods

Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y₀, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.

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.

Improvement of the electrochemical and singlet fission properties of anthraquinones by modification of the diradical character

Quantum chemistry is employed to estimate the effects that the structural modification of 1,5- and 9,10-anthraquinones produces in their electronic structure, in the pursuit of a common strategy to improve the electrochemical and singlet fission features on conjugated quinones.

Molecular Engineering and Structure-Related Properties of Squaraine Dyes Based on the Core and Wings Concept

Three new squaraine-based functional π-conjugated molecules were synthesized considering the core and wings concept. The molecules, SQ-DICN, SQ-DIEt-RH, and SQ-DICN-RH, were end-capped with three different wings, such as malononitrile, 2-(3-hexyl-4-oxothiazolidin-2-ylidene)malononitrile, and 3-ethyl-2-thioxothiazolidin-4-one. Among the three dyes, SQ-DICN-RH showed the highest molar extinction coefficient. The photoluminescence of all the dyes showed an opposite trend to that of the absorption maximum. The electrochemical results showed that the lowest unoccupied molecular orbital level of all the dyes ranged from -3.72 to -3.82 eV, whereas the highest occupied molecular orbital ranged from -4.89 to -4.94 eV. Solvatochromism was carried out to observe the effects of the solvent containing the dyes. The electronic structure of the dyes was examined using ab initio simulations. The dyes were characterized theoretically, and the red-shifted absorption of SQ-DICN-RH was explained and correlated with its biradicaloid character and singlet-triplet energy gap.

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 Ni^II 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.

Potential Use of Squarates and Croconates as Singlet Fission Sensitizers

The geometrical and electronic structures of 44 squarate and croconate derivatives are computationally studied by quantum chemistry methods, in the pursuit of new singlet fission sensitizers. A non-negligible singlet open-shell diradical character is observed for most of the studied molecules, which can be controlled through chemical substitution as well as by the size of the central ring. Such a diradical character is related to small singlet-triplet energy gaps, facilitating the accomplishment of the singlet fission energetic requirements. In general, the present results indicate that squarates hold superior singlet fission capabilities than croconates, although we have identified several derivatives within both families as promising singlet fission sensitizers.

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.

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 design of conjugated diradicaloids as singlet fission sensitizers: quinones and methylene derivatives

New conjugated diradicaloids as potential candidates for singlet fission sensitizers.

Role of a singlet diradical character in carbon nanomaterials: a novel hot spot for efficient nonlinear optical materials

Carbon atoms have the potential to produce a variety of fascinating all-carbon structures with amazing electronic and mechanical properties. Over the last few decades, several efforts have been made using experimental and computational techniques to functionalize graphene, carbon nanotubes and fullerenes for potential use in modern hi-tech electronic, medicinal, optical and nonlinear optical (NLO) applications. Since photons replaced electrons as a carrier of information, the field of NLO material design has drawn immense interest in contemporary materials science. There have been several reports of bridging the gap between the exciting fields of carbon nanomaterials and NLO materials by functionalizing carbon nanomaterials for potential NLO applications. In contrast to previous reports of the design of third-order NLO materials using conventional closed-shell materials, a novel strategy using open-shell diradical molecular systems has recently been proposed. Quantum chemically, diradical character is explained in terms of the instability of the chemical bonds in open-shell molecular systems. Interestingly, several carbon nanomaterials, which naturally possess open-shell singlet configurations, have recently gained momentum in the design of these classes of open-shell NLO materials with excellent NLO properties, stability and diversity. The present review establishes a systematic sequence of different studies (spanning over two decades of intense research efforts), starting from the simplest theoretical two-site diradical model, continuing to its experimental and theoretical realization in actual chemical systems, and finally applying the abovementioned model/rule to novel carbon nanomaterials to tune their NLO properties, particularly their second hyperpolarizability (γ). In the present report, we highlight several recent efforts to functionalize carbon nanomaterials by exploiting their open-shell diradical character to achieve efficient third-order NLO properties. Several issues and opportunities are discussed, including the inherited disadvantages of both experimental (the high reactivity and short life of diradical compounds) and quantum (need for multi-reference methodology) techniques when dealing with carbon nanomaterials. A comparative analysis of several quantum chemical investigations, along with contemporary experimental results, will be performed to emphasize the core issues and opportunities related to carbon nanomaterials with singlet open-shell diradical character. Thus, the present review will highlight carbon nanomaterials with diradical/biradical character for their prospective applications in the NLO field.

Benzo-thia-fused [n]thienoacenequinodimethanes with small to moderate diradical characters: the role of pro-aromaticity versus anti-aromaticity

Open-shell singlet diradicaloids have recently received much attention due to their unique optical, electronic and magnetic properties and promising applications in materials science. Among various diradicaloids, quinoidal π-conjugated molecules have become the prevailing design. However, the need for a fundamental understanding on how the fusion mode and pro-aromaticity/anti-aromaticity affect their diradical character and physical properties remains unaddressed. In this work, a series of pro-aromatic benzo-thia-fused [n]thienoacenequinodimethanes (Thn-TIPS (n = 1-3) and BDTh-TIPS) were synthesized and compared with the previously reported anti-aromatic bisindeno-[n]thienoacenes (Sn-TIPS, n = 1-4). The ground-state geometric and electronic structures of these new quinoidal molecules were systematically investigated by X-ray crystallographic analysis, variable temperature NMR, ESR, SQUID, Raman, and electronic absorption spectroscopy, assisted by DFT calculations. It was found that the diradical character index (y0) increased from nearly zero for Th1-TIPS to 2.4% for Th2-TIPS, 18.2% for Th3-TIPS, and 38.2% for BDTh-TIPS, due to the enhanced aromatic stabilization. Consequently, with the extension of molecular size, the one-photon absorption spectra are gradually red-shifted, the two-photon absorption (TPA) cross section values increase, and the singlet excited state lifetimes decrease. By comparison with the corresponding anti-aromatic analogues Sn-TIPS (n = 1-3), the pro-aromatic Thn-TIPS (n = 1-3) exhibit larger diradical character, longer singlet excited state lifetime and larger TPA cross section value. At the same time, they display distinctively different electronic absorption spectra and improved electrochemical amphotericity. Spectroelectrochemical studies revealed a good linear relationship between the optical energy gaps and the molecular length in the neutral, radical cationic and dicationic forms. Our research work discloses a significant difference between the pro-aromatic and anti-aromatic quinoidal compounds and provides guidance for the design of new diradicaloids with desirable properties.

Diradical character and nonlinear optical properties of buckyferrocenes: focusing on the use of suitably modified fullerene fragments

Buckyferrocenes, made up of suitably modified fullerenes fragments having an uninterrupted π-electron network, show intermediate diradical character and robustly large third-order nonlinear optical responses.

Linear and nonlinear optical properties of indeno[2,1-b]fluorene and its structural isomers

The DMRG method reveals that third harmonic generation coefficients (γ) of indeno[2,1-b]fluorene and its structural isomers correlate with their diradical character.

Computational investigation on redox-switchable nonlinear optical properties of a series of polycyclic p-quinodimethane molecules

The polycyclic p-quinodimethanes are proposed to be the novel candidates of the high-performance nonlinear optical (NLO) materials because of their large third order polarizabilities (γ). We investigate the switchable NLO responses of a series of polycyclic p-quinodimethanes with redox properties by employing the density functional theory (DFT). The polycyclic p-quinodimethanes are forecasted to exhibit obvious pure diradical characters because of their large y 0 index (the y 0 index is a value between 0 [closed-shell state] and 1 [pure biradical state]). The γ values of these polycyclic p-quinodimethanes and their corresponding one-electron and two-electron reduced/oxidized species are calculated by the (U)BHandHLYP method. The γ values of polycyclic p-quinodimethanes and their corresponding one-electron reduced species are all positive and significantly different. The large differences of the γ values are due to a change in the transition energy and are related to the different delocalization of the spin density, which demonstrates that the NLO switching is more effective on one-electron reduction reactions. Therefore, the study on these polycyclic p-quinodimethanes provides a guideline for a molecular design of highly efficient NLO switching.