Biradical Paradox Revisited Quantitatively: A Theoretical Model for Self-Associated Biradical Molecules as Antiferromagnetically Exchange Coupled Spin Chains in Solution

An ESR hyperfine splitting pattern of a biradical in solution depends on the magnitude of the intramolecular exchange interaction <i>J</i>_intra compared with the hyperfine coupling constant <i>A</i>. Some biradicals exhibit their hyperfine splitting patterns characteristic of a monoradical, even though their exchange interaction is strong enough, |<i>J</i>_intra| ≫ |<i>A</i>|. The contradiction in ESR spectroscopy is known as “biradical paradox”, puzzling scientists for a long time. In this study, it is shown from ESR spectral simulations underlain by a theoretical model of a series of spin Hamiltonians that noncovalent aggregation of biradical molecules in solution leads to the appearance of paradoxical ESR spectra. Most of the spins in an aggregate of one dimension lose their contribution to the ESR spectra owing to intermolecular antiferromagnetic interactions <i>J</i>_inter, leaving two outermost spins ESR-active in the aggregate of one dimension. Paradoxical ESR spectra appear only when <i>J</i>_intra and <i>J</i>_inter fall within a particular range of the magnitudes which depends on the number of molecules in the aggregate

Quasi-Restricted Orbital Treatment for the Density Functional Theory Calculations of the Spin–Orbit Term of Zero-Field Splitting Tensors

A quasi-restricted orbital (QRO) approach for the calculation of the spin–orbit term of zero-field splitting tensors (<b>D</b>^SO tensors) by means of density functional theory (DFT) importantly features in the fact that it is free from spin contamination problems because it uses spin eigenfunctions for the zeroth order wave functions. In 2011, however, Schmitt and co-workers pointed out that in the originally proposed QRO working equation some possible excitations were not included in their sum-over-states procedure, which causes spurious <b>D</b>^SO contributions from closed-shell subsystems located far from the magnetic molecule under study. We have revisited the derivation of the QRO working equation and modified it, making it include all possible types of excitations in the sum-over-states procedure. We have found that the spurious <b>D</b>^SO contribution can be eliminated by taking into account contributions from all possible types of singly excited configuration state functions. We have also found that only the SOMO­(α) → SOMO­(β) excited configurations have nonzero contributions to the <b>D</b>^SO tensors as long as α and β spin orbitals have the same spatial distributions and orbital energies. For the <b>D</b>^SO tensor calculations, by using a ground state wave function free from spin contamination, we propose a natural orbital-based Pederson–Khanna (NOB-PK) method, which utilizes the single determinant wave function consisting of natural orbitals in conjunction with the Pederson–Khanna (PK) type perturbation treatment. Some relevant calculations revealed that the NOB-PK method can afford more accurate <b>D</b>^SO tensors than the conventional PK method as well as the QRO approach in Mn^II complexes and Re^IV-based single molecule magnets

Synthesis and Characterization of Dibenzo[<i>a</i>,<i>f</i>]pentalene: Harmonization of the Antiaromatic and Singlet Biradical Character

Mesityl derivatives of the unknown dibenzopentalene isomer dibenzo­[<i>a</i>,<i>f</i>]­pentalene were synthesized. The molecular geometry and physical properties of dibenzo­[<i>a</i>,<i>f</i>]­pentalene were investigated. Dibenzo­[<i>a</i>,<i>f</i>]­pentalene combines a large antiaromatic and appreciable singlet open-shell character, properties not shared by well-known isomer dibenzo­[<i>a</i>,<i>e</i>]­pentalene

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations

An Enantiopair of Organic Ferromagnet Crystals Based on Helical Molecular Packing of Achiral Organic Radicals

We report the ferromagnetic ordering phenomena occurring in organic molecular crystals with structural chirality. Achiral radical <b>1</b> has been found to crystallize in two enantiomorphs with chiral space groups of <i>P</i>4₃ and <i>P</i>4₁. The <i>P</i>4₃ form (<b>1L</b>) has left-handed stacking of the molecules, giving the helical chirality in a crystalline solid. In the other form of <i>P</i>4₁ (<b>1R</b>), the right-handed stacking corresponds to a mirror image of <b>1L</b>. Magnetic susceptibility measurements show that both the crystals undergo a ferromagnetic phase transition at <i>T</i>_C = 1.1 K. The ferromagnetic ordering has been confirmed by heat capacity measurements. The magnetic heat capacity exhibits a λ-shaped peak at <i>T</i>_C = 1.1 K with an entropy change of <i>R </i>ln 2, as expected for <i>S</i> = 1/2 spins. This is the first example of genuinely organic molecule-based ferromagnetism associated with the structural chirality based on the helical molecular packing in the crystalline solid

An Enantiopair of Organic Ferromagnet Crystals Based on Helical Molecular Packing of Achiral Organic Radicals

We report the ferromagnetic ordering phenomena occurring in organic molecular crystals with structural chirality. Achiral radical <b>1</b> has been found to crystallize in two enantiomorphs with chiral space groups of <i>P</i>4₃ and <i>P</i>4₁. The <i>P</i>4₃ form (<b>1L</b>) has left-handed stacking of the molecules, giving the helical chirality in a crystalline solid. In the other form of <i>P</i>4₁ (<b>1R</b>), the right-handed stacking corresponds to a mirror image of <b>1L</b>. Magnetic susceptibility measurements show that both the crystals undergo a ferromagnetic phase transition at <i>T</i>_C = 1.1 K. The ferromagnetic ordering has been confirmed by heat capacity measurements. The magnetic heat capacity exhibits a λ-shaped peak at <i>T</i>_C = 1.1 K with an entropy change of <i>R </i>ln 2, as expected for <i>S</i> = 1/2 spins. This is the first example of genuinely organic molecule-based ferromagnetism associated with the structural chirality based on the helical molecular packing in the crystalline solid

ESR and ¹H-,¹⁹F-ENDOR/TRIPLE Study of Fluorinated Diphenylnitroxides as Synthetic Bus Spin-Qubit Radicals with Client Qubits in Solution

Electron and nuclear spins as quantum bits (qubits) have been the focus of current issues in quantum information science/technology and related fields. From the viewpoint of chemistry, synthetic spin qubits are emerging. Diphenylnitroxide (DPNO) and its novel fluorine-substituted radicals are characterized as synthetic electron bus spin-qubits by continuous-wave ESR and ¹H-,¹⁹F-ENDOR/TRIPLE spectroscopy in solution and by DFT calculations. The partially fluorinated DPNOs have been synthesized to illustrate that they are candidates for the synthetic bus spin-qubits with well-defined client qubits. The fluorinated DPNOs undergo spin delocalization, dominating the robust spin polarization in the π-conjugation of phenyl rings, serving to increase the number of distinguishable client qubits from three to six

Time-Resolved Electron Paramagnetic Resonance and Phosphorescence Studies of the Lowest Excited Triplet States of Rh(III) Corrole Complexes

The lowest excited triplet (T₁) ππ* states of gallium (Ga) and various rhodium (Rh) 5,10,15-trispentafluorophenyl corroles (Cors) were studied in the liquid crystal (LC) E-7 and in rigid glasses by time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy. The triplet sublevel energies were experimentally determined by the alignment of the molecules in the LC and by magnetophotoselection in the glass. The sublevel scheme of GaCor was determined by calculating the zero field splitting (ZFS) parameters. Axial ligand effects and quantum chemical calculations were used for the sublevel assignment of RhCors. The anisotropic EPR parameters were used to determine the important higher excited states and the magnitudes of their spin–orbit coupling (SOC) contributions were evaluated. On the basis of these results and analyses, the EPR parameters and triplet lifetime were discussed for each RhCor complex

Time-Resolved Electron Paramagnetic Resonance and Phosphorescence Studies of the Lowest Excited Triplet States of Rh(III) Corrole Complexes

The lowest excited triplet (T₁) ππ* states of gallium (Ga) and various rhodium (Rh) 5,10,15-trispentafluorophenyl corroles (Cors) were studied in the liquid crystal (LC) E-7 and in rigid glasses by time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy. The triplet sublevel energies were experimentally determined by the alignment of the molecules in the LC and by magnetophotoselection in the glass. The sublevel scheme of GaCor was determined by calculating the zero field splitting (ZFS) parameters. Axial ligand effects and quantum chemical calculations were used for the sublevel assignment of RhCors. The anisotropic EPR parameters were used to determine the important higher excited states and the magnitudes of their spin–orbit coupling (SOC) contributions were evaluated. On the basis of these results and analyses, the EPR parameters and triplet lifetime were discussed for each RhCor complex

Time-Resolved Electron Paramagnetic Resonance and Phosphorescence Studies of the Lowest Excited Triplet States of Rh(III) Corrole Complexes

The lowest excited triplet (T₁) ππ* states of gallium (Ga) and various rhodium (Rh) 5,10,15-trispentafluorophenyl corroles (Cors) were studied in the liquid crystal (LC) E-7 and in rigid glasses by time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy. The triplet sublevel energies were experimentally determined by the alignment of the molecules in the LC and by magnetophotoselection in the glass. The sublevel scheme of GaCor was determined by calculating the zero field splitting (ZFS) parameters. Axial ligand effects and quantum chemical calculations were used for the sublevel assignment of RhCors. The anisotropic EPR parameters were used to determine the important higher excited states and the magnitudes of their spin–orbit coupling (SOC) contributions were evaluated. On the basis of these results and analyses, the EPR parameters and triplet lifetime were discussed for each RhCor complex