Probing the Influence of Alkyne Substitution on the Electronic and Magnetic Properties of Diindeno[1,2-b;1',2'-i]anthracenes

To further the ability to manipulate the properties of open-shell molecules, logical and incremental modifications to molecular structure are key steps that provide fine-tuning of established diradicaloid scaffolds. We report the synthesis of an electronically "pure" diradicaloid based on a 2,6-anthroquinoidal core where the once necessary ethynyl "wings" are removed. Through the simplification of the overall electronic structure, the singlet-triplet energy gap increases by 0.3-0.4 kcal mol-1 in the reported diradicaloids while avoiding significant disruption to their optoelectronic properties.

Theoretical Study on the Correlation between Open-Shell Electronic Structures and Third-Order Nonlinear Optical Properties in One-Dimensional Chains of π-Radicals

This paper theoretically investigated the correlation between the open-shell electronic structure and third-order nonlinear optical (NLO) properties of one-dimensional (1D) stacked chains of π-radicals. By employing the finite N-mer models consisting of methyl or phenalenyl radicals with different stacking distances, we evaluated the average and standard deviation of diradical characters yi for N-mer models of π-radicals (yav and ySD). Then, we estimated these diradical characters at the limit of N → ∞. These y-based indices were helpful in discussing the correlation between the open-shell electronic structures and the second hyperpolarizability per dimer at the limit N → ∞, γ∞ for the 1D chains with stacking distance alternation (SDA). The calculated γ∞ values and the polymer/dimer ratio γ∞/γ(N = 2) were enhanced significantly when both the stacking distance and SDA are small. We also found that the spin-unrestricted long-range-corrected (LC-)UBLYP method with the range-separating parameter μ = 0.47 bohr-1 well reproduced the trend of γ∞ of this type of 1D chain estimated at the spin-unrestricted coupled-cluster levels. The present study is expected to contribute to establishing the design guidelines for future high-performance open-shell molecular NLO materials.

Doublet Open-Shell Graphene Fragments

The recent advances on neutral delocalized radical species based on polycyclic aromatic hydrocarbons with fused hexagonal rings, herein defined as doublet open-shell graphene fragments, are summarized in this review. A few simple yet useful theoretical approaches for structural analysis and molecular design were introduced at first. Then, based on the number of fused hexagonal rings, molecular systems with different size, symmetry and edge structure were discussed with emphasis on those isolated in the crystalline form. Their unique self-association behavior, chemical reactivity and physical properties were summarized and discussed, and insights on their functions and potential applications were provided.

Periodic B- and N-doped phenalenyl π-aggregates: unexpected nonlinear optical properties by tuning pancake π-π bonding

Phenalenyl (PLY) and its derivatives could form one-dimensional π-aggregates through pancake π-π bonding, which would lead to exotic optoelectronic properties. We will highlight the key aspects of the PLY derivatives from the design strategies to exploration of the electronic properties. Here, we primarily construct alternating boron (B)- and nitrogen (N)-doped PLY π-aggregates: dimer[12], trimer[12-1], trimer[12-2], tetramer[12]₂, pentamer[12]₂-1, pentamer[12]₂-2, and hexamer[12]₃. The geometric and electronic structures show that the short intermolecular distances of the π-aggregates drive the formation of pancake π-π bonding. Significantly, the molecular structures show periodic changes in the π-aggregates, but the first hyperpolarizabilities (β_tot) present unexpected changes, which are found to increase sharply with increasing even layer thickness due to intermolecular charge transfer. The β_tot value of hexamer[12]₃ (5.72 × 10⁴ a.u.) is 6.4 times that of tetramer[12]₂ (8.95 × 10³ a.u.), and is 22.4 times that of dimer[12] (2.55 × 10³ a.u.). Thus, constructing π-aggregates can significantly improve the second-order NLO response, which is mainly due to intermolecular charge transfer through pancake π-π bonding of the interlayers.

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.

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.

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.

Structural diradical character

A reliable first-principles description of singlet diradical character is essential for predicting nonlinear optical and magnetic properties of molecules. As diradical and closed-shell electronic structures differ in their distribution of single, double, triple, and aromatic bonds, modeling electronic diradical character requires accurate bond-length patterns, in addition to accurate absolute bond lengths. We therefore introduce structural diradical character, which we suggest as an additional measure for comparing first-principles calculations with experimental data. We employ this measure to identify suitable exchange-correlation functionals for predicting the bond length patterns and electronic diradical character of a biscobaltocene with the potential for photoswitchable nonlinear optical activity. Out of four popular approximate exchange-correlation functionals with different exact-exchange admixtures (BP86, TPSS, B3LYP, TPSSh), the two hybrid functionals TPSSh and B3LYP perform best for diradical bond length patterns, with TPSSh being best for the organometallic validation systems and B3LYP for the organic ones (for which the D3 dispersion correction was included). Still, none of the functionals is suitable for correctly describing relative bond lengths across the range of molecules studied, so that none can be recommended for predictive studies of (potential) diradicals without reservation. © 2018 Wiley Periodicals, Inc.

Synthesis, Physical Properties, and Reactivity of Stable, π-Conjugated, Carbon-Centered Radicals

Recently, long-lived, organic radical species have attracted much attention from chemists and material scientists because of their unique electronic properties derived from their magnetic spin and singly occupied molecular orbitals. Most stable and persistent organic radicals are heteroatom-centered radicals, whereas carbon-centered radicals are generally very reactive and therefore have had limited applications. Because the physical properties of carbon-centered radicals depend predominantly on the topology of the π-electron array, the development of new carbon-centered radicals is key to new basic molecular skeletons that promise novel and diverse applications of spin materials. This account summarizes our recent studies on the development of novel carbon-centered radicals, including phenalenyl, fluorenyl, and triarylmethyl radicals.

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.

Pancake Bonding in π-Stacked Trimers in a Salt of Tetrachloroquinone Anion

The crystal structure of [4-damp])₂ [Cl₄ Q]₃ (4-damp=4-dimethylamino-N-methylpyridinium, Cl₄ Q=tetrachloroquinone) salt is built up from slipped columnar stacks of quinoid rings composed of closely bound trimers with the intra-trimer separation distance of 2.84 Å and total charge of -2 whereas the inter-trimer distance is 3.59 Å. The individual rings exhibit partial negative charges that are distributed unevenly among the three Cl₄ Qs in the trimer. The strong interactions within a trimer (Cl₄ Q)₃^2- have a partially covalent character with two-electron/multicentered bonding, that is extended over three rings, plausibly termed as "pancake bonding". The electron pairing within this multicentre bond leads to the fact that the crystals are diamagnetic and act as insulators. The studies of the structure and nature of bonding are based on X-ray charge density analysis and density functional theory.

Open-Shell Character Dependences of the Second Hyperpolarizability in Two-Dimensional Tetraradicaloids

The open-shell character dependences of the second hyperpolarizability, γ, are investigated for rectangular-shaped tetraradicaloid models, such as diradical dimers, using numerically exact solutions of the extended Hubbard model. The newly defined local diradical characters for intra- and intermolecular interactions (referred to as y_intra and y_inter, respectively) are compared to conventional global ones ( y₀ and y₁) and provide a comprehensive understanding of the electronic structure of the system. The system shows two kinds of enhancements of the γ components, γ_intra and γ_inter (caused, respectively, by intra- and intermolecular diradical interactions): (i) a system with a large y_intra ( y_inter) (>∼0.4) exhibits the enhancement of a single component of γ, γ_inter (γ_intra), at the intermediate y_inter ( y_intra) region (∼0.3-0.4), and (ii) in contrast to conventional diradical systems, the system exhibits a further enhancement of both components of γ (γ_intra and γ_inter) at the region where y_intra ∼ y_inter with small values (≤∼0.3). The obtained relationships are verified by using ab initio quantum chemical calculations of the realistic tertraradical models of a 4,4'-bis(1,2,3,5-dithiazdiazolyl) (BDTDA) dimer and a disilene dimer. The present results are expected to pioneer an alternative class of two-dimensional multiradical NLO systems, which potentially cause further enhancement of γ as compared with conventional intermediate diradical NLO systems.

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.

Intramolecular Pancake Bonding in Helical Structures

We show that diradicaloid helical conjugated molecules can display strong through-space bonding interactions. These interactions are analogous to π-stacking pancake bonding widely observed for dimers and other aggregates of stable π-conjugated radicals. We show that these multicenter interactions can have a significant stabilizing effect, but they depend in subtle ways on the specific overlap and relative orientations of the radical carrying subunits. The specific through-space interactions between the radicaloid units occur at specific size ranges of the helical molecules.

Tuning the inter-molecular charge transfer, second-order nonlinear optical and absorption spectra properties of a π-dimer under an external electric field

Different strengths of external electric fields enhance the stability, control the inter-molecular charge transfer and strengthen the nonlinear optical responses of a π-dimer.

Singlet fission in pancake-bonded systems

Open-shell aggregates with pancake bonding are found to cause highly efficient singlet fission and large charge transport simultaneously.

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.

Nonlinear optical properties in open-shell molecular systems

For more than 30 years, nonlinear optical (NLO) properties of molecular systems have been actively studied both theoretically and experimentally due to their potential applications in photonics and optoelectronics. Most of the NLO molecular systems are closed-shell species, while recently open-shell molecular species have been theoretically proposed as a new class of NLO systems, which exhibit larger NLO properties than the traditional closed-shell NLO systems. In particular, the third-order NLO property, the second hyperpolarizability γ, was found to be strongly correlated to the diradical character y, which is a quantum-chemically defined index of effective bond weakness or of electron correlation: the γ values are enhanced in the intermediate y region as compared to the closed-shell (y = 0) and pure open-shell (y = 1) domains. This principle has been exemplified by accurate quantum-chemical calculations for polycyclic hydrocarbons including graphene nanoflakes, multinuclear transition-metal complexes, main group compounds, and so on. Subsequently, some of these predictions have been substantiated by experiments, including two-photon absorption. The fundamental mechanism of the y-γ correlation has been explained by using a simple two-site model and the valence configuration interaction method. On the basis of this y-γ principle, several molecular design guidelines for controlling γ have been proposed. They consist in tuning the diradical characters through chemical modifications of realistic open-shell singlet molecules. These results open a new path toward understanding the structure-NLO property relationships and toward realizing a new class of highly efficient NLO materials. WIREs Comput Mol Sci 2016, 6:198-210. doi: 10.1002/wcms.1242.

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.