Diradical Molecules Research Articles

Efficient random phase approximation for diradicals.

We apply the analytically solvable model of two electrons in two orbitals to diradical molecules, characterized by two unpaired electrons. The effect of doubly occupied and empty orbitals is taken into account by means of random phase approximation (RPA). We show that in the static limit, the direct RPA leads to the renormalization of the parameters of the two-orbital model. We test our model by comparing its predictions for singlet-triplet splitting with the results of several multi-reference methods for a set of thirteen molecules. We find that for this set, the static RPA results are close to those of the NEVPT2 method with two orbitals and two electrons in the active space.

Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions.

Metal-free diradicals based on polycyclic aromatic hydrocarbons are promising candidates for organic spintronics due to their stable magnetism and tunable spin coupling. However, distinguishing and elucidating the origins of ferromagnetic and antiferromagnetic interactions in these systems remain challenging. Here, we investigate the 2-OS diradical molecule sandwiched between gold electrodes using a combined density functional theory and hierarchical equations of motion approach. We find that the dihedral angle between the radical moieties controls the nature and strength of the intramolecular spin coupling, transitioning smoothly from antiferromagnetic to ferromagnetic as the angle increases. Distinct features in the inelastic electron tunneling spectra are identified that can discern the two coupling regimes, including spin excitation steps whose energies directly reveal the exchange coupling constant. Mechanical stretching of the junction is predicted to modulate the spectral line shapes by adjusting the hybridization of the molecular radicals with the electrodes. Our work elucidates the electronic origin of tunable spin interactions in 2-OS and provides spectroscopic fingerprints for characterizing magnetism in metal-free diradicals.

Diradical-Based Strategy in Designing Narrowband Thermally Activated Delayed Fluorescence Molecules with Tunable Emission Wavelengths.

In the design of thermally activated delayed fluorescence (TADF) materials, narrow-band emission is of particular importance for the development of organic light-emitting diodes (OLEDs). In this work, we proposed a new strategy for designing TADF molecules utilizing degenerate nonbonding (NB) orbitals of diradical parent molecules, and these designed molecules are termed NB-TADF molecules. Based on this strategy, a series of NB-TADF molecules is finely designed and systematically studied by theoretical calculations. Taking advantage of the nonbonding properties, these NB-TADF molecules exhibit desirable narrowband emissions and high quantum yields. More importantly, the emission bands can be easily tuned from blue to near-infrared by changing the conjugate length of the parent group in the NB-TADF molecules. We hope that this new strategy can open a new door for the design of novel TADF materials.

A donor–acceptor coupling unit modulates the spin coupling effect of a stable diradical

This study presents the synthesis and characterization of a highly conjugated stable diradical molecule composed of a donor–acceptor coupling unit.

Excited states with pair coupled cluster doubles tailored coupled cluster theory.

It is known that some non-dynamic effects of electron correlation can be included in coupled cluster theory using a tailoring technique that separates the effects of non-dynamic and dynamic correlations. Recently, the simple pCCD (pair coupled cluster doubles) wavefunction was shown to provide good results for some non-dynamic correlation problems, such as bond-breaking, in a spin-adapted way with no active space selection. In this paper, we report a study of excited states using "tailored coupled cluster singles and doubles," to attempt to use pCCD as a kernel for more complete coupled-cluster singles and doubles (CCSD) results for excited states. Several excited states are explored from those primarily due to single excitations to those dominated by doubly excited states and from singlet-triplet splittings for some diradical states. For the first two situations, tailored pCCD-TCCSD offers no improvement over equation of motion-CCSD. However, when we explore the singlet-triplet gap of diradical molecules that are manifestly multi-reference, a pCCD kernel provides improved results, particularly with generalized valence bond orbitals.

Open-Shell Diradical-Sensitized Electron Transport Layer for High-Performance Colloidal Quantum Dot Solar Cells.

The zinc oxide (ZnO) nanoparticles (NPs) are well-documented as an excellent electron transport layer (ETL) in optoelectronic devices. However, the intrinsic surface flaw of the ZnO NPs can easily result in serious surface recombination of carriers. Exploring effective passivation methods of ZnO NPs is essential to maximize the device's performance. Herein, a hybrid strategy is explored for the first time to improve the quality of ZnO ETL by incorporating stable organic open-shell donor-acceptor type diradicaloids. The high electron-donating feature of the diradical molecules can efficiently passivate the deep-level trap states and improve the conductivity of ZnO NP film. The unique advantage of the radical strategy is that its passivation effectiveness is highly correlated with the electron-donating ability of radical molecules, which can be precisely controlled by the rational design of molecular chemical structures. The well-passivated ZnO ETL is applied in lead sulfide (PbS) colloidal quantum dot solar cells, delivering a power conversion efficiency of 13.54%. More importantly, as a proof-of-concept study, this work will inspire the exploration of general strategies using radical molecules to construct high-efficiency solution-processed optoelectronic devices.

Closed-shell and open-shell dual nature of singlet diradical compounds

Abstract Unlike triplet diradicals, singlet diradicals can vary in diradical character from 0 % to 100 % depending on linker units that allow two formally unpaired electrons to couple covalently. In principle, the electronic structure of singlet diradicals can be described as a quantum superposition of closed-shell and open-shell structures. This means that, depending on the external environment, singlet diradicals can behave as either closed-shell or open-shell species. This paper summarizes our progress in understanding the electronic structure of π-conjugated singlet diradical molecules in terms of closed-shell and open-shell dual nature. We first discuss the coexistence of intra- and intermolecular covalent bonding interactions in the π-dimer of a singlet diradical molecule. The intra- and intermolecular coupling of two formally unpaired electrons are related to closed-shell and open-shell nature of singlet diradical, respectively. Then we demonstrate the coexistence of the covalent bonding interactions in the one-dimensional stack of singlet diradical molecules having different diradical character. The relative strength of the interactions is varied with the magnitude of singlet diradical index y 0. Finally, we show the dual reactivity of a singlet diradical molecule, which undergoes rapid [4 + 2] and [4 + 4] cycloaddition reactions in the dark at room temperature. Closed-shell and open-shell nature endow the singlet diradical molecule with the reaction manner as diene and diradical species, respectively.

Issues on DFT+U calculations of organic diradicals.

The diradical state is an important electronic state for understanding molecular functions and should be elucidated for the in silico design of functional molecules and their application to molecular devices. The density functional theory calculation with plane-wave basis and correction of the on-site Coulomb parameter U (DFT+U/plane-wave calculation) is a good candidate of high-throughput calculations of diradical-band interactions. However, it has not been investigated in detail to what extent the DFT+U/plane-wave calculation can be used to calculate organic diradicals with a high degree of accuracy. In the present study, using typical organic diradical molecules (bisphenalenyl molecules) as model systems, the discrepancy in the optimum U values between the two electronic states (open-shell singlet and triplet) that compose the diradical state is detected. The calculated results show that the reason for this U value discrepancy is the difference in electronic delocalisation due to π-conjugation between the open-shell singlet and triplet states, and that the effect of U discrepancy becomes large as diradical character decreases. This indicates that it is necessary to investigate the U value discrepancy with reference to the calculated results by more accurate methods or to experimental values when calculating organic diradicals with low diradical character. For this investigation, the local magnetic moments, unpaired beta electron numbers, and effective magnetic exchange integral values can be used as reference values. For the effective magnetic exchange integral values, the effects of U discrepancy are partially cancelled out. However, because the effects may not be completely offset, care should be taken when using the effective magnetic exchange integral value as a reference. Furthermore, a comparison of DFT+U and hybrid-DFT calculations shows that the DFT+U underestimates the HOMO-LUMO gap of bisphenalenyls, although a qualitative discussion of the gap is possible.

Theoretical Simulation on Regulating the Magnetic Coupling Properties of Diradical Artificial Bases.

In this work, we computationally designed a series of diradical molecules with obvious magnetic coupling properties based on newly synthesized artificial bases, 6-amino-3-(1'-β-d-2'-deoxyribofuranosyl)-5-nitro-1H-pyridin-2-one (Z), 2-amino-8-(1'-β-d-2'-deoxyribofuranosyl)-imidazo-[1,2a]-1,3,5-triazin-[8H]-4-one (P), 6-amino-9[(1'-β-d-2'-deoxyribofuranosyl)-4-hydroxy-5-(hydroxymethyl)-oxolan-2-yl]-1H-purin-2-one (B), and found two methods (base pairing and nitro group rotation) of regulating the magnetic magnitude, making them become magnetic switches with promising prospects. On one hand, the modified diradical artificial base P3 possesses an excellent magnetic exchange coupling constant due to its spin density concentration on a unique spin polarization path. Because of the serious mismatch between the singly occupied molecular orbital (SOMO) and the lowest unoccupied molecular orbital (LUMO) of Z-P3 base pairing, the magnetic coupling property of the Z-P3 base pair disappears, which indicates that the base pairing can be used as an effective means to regulate the molecular magnetic coupling properties. On the other hand, the investigation shows that the rotation of the nitro group on Z has an influence on the energy gaps between the closed-shell (CS) singlet and triplet (T) states of the base pairs formed by Z-analogues and thereby the expression of magnetic coupling properties. This work can help to develop the modification strategy of the diradical base and provide theoretical guidance for the design and synthesis of magnetic coupling materials with controllable magnetic coupling properties.

Variation in spin contamination and diradical character with distance between a singlet biradical molecule and surface

As diradical molecules are used to perform various unique functions, they are expected to be applied as molecular devices. In addition, theoretical calculations based on density functional theory (DFT) are critical tools in the field of computational material science. In the DFT calculations of a diradical molecule, investigation of the spin contamination error and estimation of the diradical character, which is a feature of diradical molecules, are necessary. However, little is known regarding the variation in the spin contamination error and diradical character with the distance from a surface. These data are essential in the fields of physical chemistry and surface science to enable the study of the effects of surface interactions on strongly correlated electrons. Herein, the variations were clarified by performing approximate spin-projection DFT/plane-wave (AP-DFT/plane-wave) calculations using three reaction model systems: (1) diradical adsorption state → non-diradical molecule, (2) non-diradical adsorption state → diradical molecule, and (3) diradical adsorption state → diradical molecule. Variations in the diradical character were monotonic, whereas the spin contamination error exhibited extreme values and inflections. This was because the interaction with the surface exhibited two opposing effects: (1) the diradical character of the adsorbate increased, which increased the spin contamination error, and (2) the energy difference between the open singlet and high-spin states decreased, which decreased the spin contamination error. When a diradical/non-diradical transformed owing to surface adsorption, the effect of the spin contamination error on the adsorption energy became large. Hence, spin contamination should be analysed when the considered adsorption system features diradical/non-diradical transformations. In addition, the diradical character was affected by a surface even when dispersion forces were the major adsorption stabilisation factor. This indicated that the optimisation of the surface interactions was critical in the immobilisation of diradical molecules.

Donor-Acceptor Conjugated Macrocycles with Polyradical Character and Global Aromaticity.

SummaryPolyradical character and global aromaticity are fundamental concepts that govern the rational design of cyclic conjugated macromolecules for optoelectronic applications. Here, we report donor-acceptor (D−A) conjugated macromolecules with and without π-spacer derivatives to tune the antiferromagnetic couplings between the unpaired electrons. The macromolecules without π-spacer have a closed-shell electronic configuration and show global nonaromatic character in the singlet and lowest triplet states. However, the derivatives with π-spacer develop a nearly pure open-shell diradical and a very high polyradical character, not reported for D−A type macromolecules. Furthermore, the π-spacer derivatives display global nonaromaticity in the singlet ground state, but global aromaticity in the lowest triplet state, according to Baird's rule. The absorption spectra of the open-shell macromolecules calculated with time-dependent density functional theory indicate intensive light absorption in the near-infrared region and broadening to 2,500 nm, making these materials suitable for numerous optoelectronic applications.

Redox-Induced Modulation of Exchange Interaction in a High-Spin Ground-State Diradical/Triradical System.

A triplet ground-state diradical molecule, bis(nitronyl nitroxide)-substituted diphenyldihydrophenazine (1.. ), that can be converted into a one-electron oxidized species, 1…+ , in the quartet ground state has been developed. Surprisingly, these species, 1.. and 1…+ , can be used under ambient conditions because they are reasonably stable under aerobic conditions, even in solution. The temperature-dependent magnetic susceptibilities reveal that 1.. and 1…+ are in the triplet state, with a weak exchange interaction (J1 /kB = +3.1 K) and quartet ground state with a strong exchange interaction (J2 /kB = +160 K), respectively. The interconversion between the neutral and one-electron oxidized species can be realized through electrochemical reactions. Significantly different absorption bands in the near-IR region newly appeared in the electronic spectra acquired during electrochemical oxidation/reduction.

Magnetically Tuned Kondo Effect in a Molecular Double Quantum Dot: Role of the Anisotropic Exchange

We investigate theoretically and experimentally the singlet-triplet Kondo effect induced by a magnetic field in a molecular junction. Temperature dependent conductance, $G(T)$, is calculated by the numerical renormalization group, showing a strong imprint of the relevant low energy scales, such as the Kondo temperature, exchange and singlet-triplet splitting. We demonstrate the stability of the singlet-triplet Kondo effect against weak spin anisotropy, modeled by an anisotropic exchange. Moderate spin anisotropy manifests itself by lowering the Kondo plateaus, causing the $G(T)$ to deviate from a standard temperature dependence, expected for a spin-half Kondo effect. We propose this scenario as an explanation for anomalous $G(T)$, measured in an organic diradical molecule coupled to gold contacts. We uncover certain new aspects of the singlet-triplet Kondo effect, such as coexistence of spin-polarization on the molecule with Kondo screening and non-perturbative parametric dependence of an effective magnetic field induced by the leads.

Thermally and Magnetically Robust Triplet Ground State Diradical.

High spin ( S = 1) organic diradicals may offer enhanced properties with respect to several emerging technologies, but typically exhibit low singlet triplet energy gaps and possess limited thermal stability. We report triplet ground state diradical 2 with a large singlet-triplet energy gap, Δ EST ≥ 1.7 kcal mol-1, leading to nearly exclusive population of triplet ground state at room temperature, and good thermal stability with onset of decomposition at ∼160 °C under inert atmosphere. Magnetic properties of 2 and the previously prepared diradical 1 are characterized by SQUID magnetometry of polycrystalline powders, in polystyrene glass, and in other matrices. Polycrystalline diradical 2 forms a novel one-dimensional (1D) spin-1 ( S = 1) chain of organic radicals with intrachain antiferromagnetic coupling of J'/ k = -14 K, which is associated with the N···N and N···O intermolecular contacts. The intrachain antiferromagnetic coupling in 2 is by far strongest among all studied 1D S = 1 chains of organic radicals, which also makes 1D S = 1 chains of 2 most isotropic, and therefore an excellent system for studies of low-dimensional magnetism. In polystyrene glass and in frozen benzene or dibutyl phthalate solution, both 1 and 2 are monomeric. Diradical 2 is thermally robust and is evaporated under ultrahigh vacuum to form thin films of intact diradicals on silicon substrate, as demonstrated by X-ray photoelectron spectroscopy. Based on C-K NEXAFS spectra and AFM images of the ∼1.5 nm thick films, the diradical molecules form islands on the substrate with molecules stacked approximately along the crystallographic a-axis. The films are stable under ultrahigh vacuum for at least 60 h but show signs of decomposition when exposed to ambient conditions for 7 h.

Isomerism, Diradical Signature, and Raman Spectroscopy: Underlying Connections in Diamino Oligophenyl Dications.

A diradical dication of a 4,4'-di(bis(1,4-methylphenyl)amino)-p-terphenyl oligomer has been characterized in solid-state by Raman spectroscopy and thermo-spectroscopy together with quantum chemical calculations. The diradical character has been evaluated on the basis of the Raman spectra and as a function of temperature. A complete understanding of the nature of the changes in solid state has been provided based on a pseudo-Jahn-Teller effect, which is feasible owing to the fine balance between quinoidal/aromatic extension among consecutive rings and steric crowding. This study contributes to the further comprehension of the molecular and electronic structures of these particular diradical molecules with strong implications on the understanding of the nature of chemical bonds in the limits of high electronic correlation or π-conjugation.

MC-PDFT can calculate singlet–triplet splittings of organic diradicals

The singlet-triplet splittings of a set of diradical organic molecules are calculated using multiconfiguration pair-density functional theory (MC-PDFT), and the results are compared with those obtained by Kohn-Sham density functional theory (KS-DFT) and complete active space second-order perturbation theory (CASPT2) calculations. We found that MC-PDFT, even with small and systematically defined active spaces, is competitive in accuracy with CASPT2, and it yields results with greater accuracy and precision than Kohn-Sham DFT with the parent functional. MC-PDFT also avoids the challenges associated with spin contamination in KS-DFT. It is also shown that MC-PDFT is much less computationally expensive than CASPT2 when applied to larger active spaces, and this illustrates the promise of this method for larger diradical organic systems.

Carbon-Bridged Phenylene-Vinylenes: On the Common Diradicaloid Origin of Their Photonic and Chemical Properties

In this paper, experimental and computational investigations are combined to analyze the impact of the diradical character in the photonic and chemical properties of two tetracyano quinodimethane derivatives of phenylene-vinylenes. The photonic properties are evaluated with high-level quantum-chemical calculations and are rationalized in the context of the four-level model typical of diradical molecules, including one triplet and three singlet states, whereas the diradical extent in the ground electronic state is shown to be the driving force for the dimerization reactions. To this end DFT, CASSCF, and CASPT2//CASSCF calculations are carried out and complemented with experimental UV–vis–NIR absorption and emission measurements, as a function of the temperature along with resonance Raman spectroscopy investigations. The study of diradical molecules with enhanced chemical stability in the framework of organic electronics is an important field of research in organic π-conjugated molecules with direct applica...

Redox-Induced Gating of the Exchange Interactions in a Single Organic Diradical.

Embedding a magnetic electroactive molecule in a three-terminal junction allows for the fast and local electric field control of magnetic properties desirable in spintronic devices and quantum gates. Here, we provide an example of this control through the reversible and stable charging of a single all-organic neutral diradical molecule. By means of inelastic electron tunnel spectroscopy we show that the added electron occupies a molecular orbital distinct from those containing the two radical electrons, forming a spin system with three antiferromagnetically coupled spins. Changing the redox state of the molecule therefore switches on and off a parallel exchange path between the two radical spins through the added electron. This electrically controlled gating of the intramolecular magnetic interactions constitutes an essential ingredient of a single-molecule quantum gate.

A comparative study on seniority-based MO and VB calculations of the singlet and triplet energy gaps of open-shell molecules

The recently proposed truncated configuration interaction (CI) approach based on the seniority number (Ω), which is defined as the number of singly occupied orbitals in a Slater determinant, is applied to study the adiabatic singlet-triplet excitation energies of some open-shell non-Kekulé diradical molecules, including: trimethylenemethane (TMM), tetramethyleneethane (TME) and meta-quinodimethane (m-QDM). Inasmuch as the singlet state exhibits strongly correlated electronic structure but the triplet state does not, adequate evaluation of the excitation energies requires balanced treatment of both states. It is found that within the active space comprised with the π-electrons/orbitals, the seniority-based VB approach is able to describe both the lowest singlet and triplet states in balance, but the MO analogue shows inharmonious convergence behavior toward the CASSCF limit. As a result, the seniority-based VB approach, superior to the MO analogue, can produce good singlet-triplet energy gap even at lower levels.

Assessment of semi-empirical molecular orbital calculations for describing magnetic interactions

We report a thorough comparison between the spin-unrestricted semi-empirical molecular orbital (SE-UMO) and density functional theory (UDFT) calculations for a variety of π-conjugated diradical molecules which exhibit through-bond magnetic exchange interactions. The spin-unrestricted neglect of diatomic differential overlap (NDDO)-based methods (UPM6 and UrPM6) and self-consistent charge density functional tight-biding (UDFTB) are examined. The UCAM-B3LYP method is used as a representative of UDFT. We have found that NDDO-based and UDFTB methods give different performances with respect to the results of UCAM-B3LYP. The degree of diradical character in the target systems decreases in the order of UPM6>UrPM6≈UCAM-B3LYP>UDFTB. The conventional UPM6 and UDFTB calculations tend to overestimate and underestimate the diradical character, respectively, whereas UrPM6 is able to provide much the same results as UCAM-B3LYP. This is convincing evidence that UrPM6 will be useful for in silico screening of materials science at much lower computational cost.