Diradical character dependences of the first and second hyperpolarizabilities of asymmetric open-shell singlet systems

Tuning the Diradical Character of Indolocarbazoles: Impact of Structural Isomerism and Substitution Position

In this study, a set of 10 positional indolocarbazole (ICz) isomers substituted with dicyanomethylene groups connected via para or meta positions are computationally investigated with the aim of exploring the efficiency of structural isomerism and substitution position in controlling their optical and electronic properties. Unrestricted density functional theory (DFT), a spin-flip time-dependent DFT approach, and the multireference CASSCF/NEVPT2 method have been applied to correlate the diradical character with the energetic trends (i.e., singlet-triplet energy gaps). In addition, the nucleus-independent chemical shift together with ACID plots and Raman intensity calculations were used to strengthen the relationship between the diradical character and (anti)aromaticity. Our study reveals that the substitution pattern and structural isomerism represent a very effective way to tune the diradical properties in ICz-based systems with meta-substituted systems with a V-shaped structure displaying the largest diradical character. Thus, this work contributes to the elucidation of the challenging chemical reactivity and physical properties of diradicaloid systems, guiding experimental chemists to produce new molecules with desirable properties.

Single-Crystal Investigation, Hirshfeld Surface Analysis, and DFT Study of Third-Order NLO Properties of Unsymmetrical Acyl Thiourea Derivatives

In the current research work, unsymmetrical acyl thiourea derivatives, 4-((3-benzoylthioureido)methyl)cyclohexane-1-carboxylic acid (BTCC) and methyl 2-(3-benzoylthioureido)benzoate (MBTB), have been synthesized efficiently. The structures of these crystalline thioureas were unambiguously confirmed by single-crystal diffractional analysis. The crystallographic investigation showed that the molecular configuration of both compounds is stabilized by intramolecular N-H···O bonding. The crystal packing of BTCC is stabilized by strong N-H···O bonding and comparatively weak O-H···S, C-H···O, C-H···π, and C-O···π interactions, whereas strong N-H···O bonding and comparatively weak C-H···O, C-H···S, and C-H···π interactions are responsible for the crystal packing of MBTB. The noncovalent interactions that are responsible for the crystal packing are explored by the Hirshfeld surface analysis for both compounds. The void analysis is performed to find the quantitative strength of crystal packing in both compounds. Additionally, state-of-the-art applied quantum chemical techniques are used to further explore the structure-property relationship in the above-entitled molecules. The optimization of molecular geometries showed a reasonably good correlation with their respective experimental structures. Third-order nonlinear optical (NLO) polarizability calculations were performed to see the advanced functional application of entitled compounds as efficient NLO materials. The average static γ amplitudes are found to be 27.30 × 10^-36 and 102.91 × 10^-36 esu for the compounds BTCC and MBTB, respectively. The γ amplitude of MBTB is calculated to be 3.77 times larger, which is probably due to better charge-transfer characteristics in MBTB. The quantum chemical analysis in the form of 3-D plots was also performed for their frontier molecular orbitals and molecular electrostatic potentials for understanding charge-transfer characteristics. We believe that the current investigation will not only report the new BTCC and MBTB compounds but also evoke the interest of the materials science community in their potential use in NLO applications.

The Interplay between Diradical Character and Stability in Organic Molecules

The number of scientific papers on the unique properties and the potential for various applications of compounds with a diradical character is growing constantly. The diradical character enhances and even engenders certain desired optical properties and its modulation is a modern molecular design strategy. Nowadays, molecules with a non-zero diradical character are regarded as promising materials for new-generation and highly efficient solar cells and photonics devices. What is the price, however, of the unique properties of open-shell compounds? Alongside all the benefits, the diradical character is usually associated with low stability and high reactivity—unwanted molecular qualities for practical purposes. Thus, from a fundamental and applied point of view, it is important to investigate the correlation between the diradical character and laboratory stability, which is the goal of the present paper. Here, we report a combined quantum–chemical study (conceptual DFT and spin-projected HF theory) and multivariate analysis of the diradical character of a series of o- and p-quinomethides, for the stability of which experimental data are available. Our results reveal that a compromise between the diradical character and laboratory stability of a molecule is feasible and that the relationship between these two quantities can be understood in the framework of Clar’s sextet theory.

The orbital picture of the first dipole hyperpolarizability from many-body response theory

We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (β) from correlated many-body electronic structure methods. Ab initio calculations of β rely on quadratic response theory, which recasts the sum-over-all-states expression of β into a closed-form expression by calculating a handful of first- and second-order response states; for resonantly enhanced β, damped response theory is used. These response states are then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visualization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic structure with β. We explain the interpretation of different components of the response 1PDMs and the corresponding NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by deconstructing β for cis-difluoroethene, para-nitroaniline, and hemibonded OH^· + H₂O complex, computed within the framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and NOs for a range of frequencies.

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.

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.

Molecule Isomerism Modulates the Diradical Properties of Stable Singlet Diradicaloids

Inclusion of quinoidal cores in conjugated hydrocarbons is a common strategy to modulate the properties of diradicaloids formed by aromaticity recovery within the quinoidal unit. Here we describe an alternative approach of tuning of diradical properties in indenoindenodibenzothiophenes upon anti → syn isomerism of the benzothiophene motif. This alters the relationship of the S atom with the radical center from linear to cross conjugation yet retains the same 2,6-naphtho conjugation pattern of the rearomatized core. We conduct a full comparison between the anti and syn derivatives based on structural, spectroscopic, theoretical, and magnetic measurements, showing that these systems are stable open-shell singlet diradicaloids that only access their triplet state at elevated temperatures.

A Twist on Nonlinear Optics: Understanding the Unique Response of π-Twisted Chromophores

Materials with large nonlinear optical (NLO) response have the ability to manipulate the frequency and phase of incident light and exhibit phenomena that form the basis of modern telecommunication systems. In molecule-based materials, the second- and third-order NLO performance is related to the hyperpolarizability (β) and second hyperpolarizability (γ) of the constituent molecules. The search for higher β materials is driven by the desire to keep pace with expanding demand for high speed data transmission, while discovery of high γ chromophores is crucial for the development of emergent photonic technologies reliant on manipulation of "light-with-light". For decades, it was believed that for highest performance, organic NLO materials must be composed of planar π-system chromophores, and much exploratory research focused on subtle molecular modifications, which generally yielded incremental increases in μβ, where μ is the molecular dipole moment. The surprising recent discovery that twisted π-system chromophores can exhibit dramatically higher β values than their planar analogues has revealed a new design paradigm and stimulated the development of high performance twisted intramolecular charge transfer (TICT) chromophores, which are composed of electron-donating and electron-accepting π-substituents joined by a sterically constrained twisted biaryl fragment. In such chromophores, the twisting of the π-system enforces charge separation in the electronic ground state, leading to large dipole moments and low-lying charge-transfer excitations. This unique electronic structure forms the basis for enhanced NLO response, with an archetypal TICT chromophore, TMC-2, exhibiting very large second- ( μβ = 24 000 × 10^-48 esu) and third-order (γ = 1.4 × 10^-33 esu) metrics in dilute low-polarity solutions. This Account summarizes several approaches to enhance μβ in various environments, including (1) manipulating the biaryl torsional angle, (2) modifying the electron accepting fragment, (3) extending conjugation, (4) adding multiple twisted fragments, (5) modifying chromophore side chains, and (6) tuning the chromophore environment. Another set of modifications is explored to enhance γ, including (1) coupling to a cyanine dye to hybridize the cyanine and TICT orbitals, (2) manipulating the donor and acceptor group identity. The extensive modifications described above yield a detailed understanding of TICT chromophore molecular NLO response and unambiguous evidence that such chromophores have the potential to revolutionize organic electro-optics.

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.

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, 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.

Second-order NLO responses of two-cavity inorganic electrides Lin@B20H26 (n = 1, 2): evolutions with increasing excess electron number and various B-B connection sites of B20H26

Confining excess electrons in a specific space is an effective strategy to design nonlinear optical (NLO) molecules. The complexants with excess electrons are usually organic compounds, but these compounds are thermally unstable and thus hardly meet the processing requirements of NLO materials. To obtain better thermostability and NLO response molecules, in this work, inorganic compounds of B₂₀H₂₆ isomers containing two cavities were proposed. With the two included cavities, B₂₀H₂₆ can be doped by one or two Li atoms to form electrides of Li@B₂₀H₂₆ and Li₂@B₂₀H₂₆. These electrides show larger NLO responses, with respect to the corresponding undoped complexant of B₂₀H₂₆. Particularly, Li₂@B₂₀H₂₆ has the largest β₀ value of 108 846 a.u. (MP2/6-31+G(d) level) that is 850 times as large as that of corresponding B₂₀H₂₆. Moreover, the change of β₀ values with excess electron number is remarkable for two of the isomers, and differences between the β₀ values among those isomers are also significant owing to various B-B connection sites between the two cavities. Therefore, the present inorganic electrides have not only better performance due to the magnitude of their β₀ values but also better behavior on the molecular-level modulation of NLO.

Theoretical Study on the Second Hyperpolarizailities of Oligomeric Systems Composed of Carbon and Silicon π-Structures

To explore the prospect of molecules involving silicon-silicon multiple bonds as nonlinear optical molecular systems, the relationship between the structure and the second hyperpolarizabilities γ of the oligomeric systems composed of carbon and silicon π-structures is investigated using the density functional theory method. It is found that these compounds indicate intramolecular charge transfer (ICT) from the silicon units to the carbon units together with nonzero diradical characters. The γ values of these compounds are shown to be 2–13 times as large as those of the carbon analogs. Although asymmetric carbon and silicon π-systems exhibit comparable enhancement to the corresponding symmetric systems, donor-π-donor structures exhibit remarkable enhancement of γ despite of their both-end short silicon π-chain moieties (donor units). Further analysis using the odd electron and γ densities clarifies that the intermediate diradical character also contributes to the enhancement of γ. These results predict that even short π-conjugated silicone moieties can cause remarkable enhancement of γ by introducing them into π-conjugated hydrocarbon structures.

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal-Carbon Bonds

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal-carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when the bond length increases, γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems.

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.

Open-Shell Singlet Nature and σ-/π-Conjugation Effects on the Third-Order Nonlinear Optical Properties of Si Chains: Polysilane and Poly(disilene-1,2-diyl)

We theoretically investigate the open-shell singlet nature and σ-/π-conjugation effects on the longitudinal second hyperpolarizabilities (γ) of one-dimensional chains involving silicon-silicon bonds, that is, polysilane and poly(disilene-1,2-diyl), by comparison with their carbon analogues, polyethylene and polyacetylene, respectively. It is found that poly(disilene-1,2-diyl) has less bond length alternation than polyacetylene and that σ-conjugation of polysilane is less effective on the enhancement of γ than π-conjugation of polyacetylene, whereas π-conjugation of poly(disilene-1,2-diyl) indicates a more than 20 times greater enhancement of the γ than that of polyacetylene, which is known to be a typical nonlinear optical molecule with large γ, for one-dimensional chains involving 3-5 double bonds. Further theoretical analyses of poly(disilene-1,2-diyl) reveal the σ- and π-electrons contribute negatively and positively to the γ, respectively. The latter contribution is significantly larger than the former and thus causes the remarkable enhancement of γ amplitudes due to the emerging open-shell singlet nature in the long π-conjugation length.

Structural fluctuation governed dynamic diradical character in pentacene

Energy field-induced structural fluctuation can not only induce potential diradical character but also modulate its dynamical behavior in pentacene.