Spin–orbit coupling in oxygen containing diradicals

Intermediate diradicals which occur in the Paterno–Büchi photocycloaddition and in the Norrish type I photoreactions have been calculated taking into account the spin–orbit coupling (SOC) between the singlet (S) and triplet (T) states. Reaction paths for the photocycloaddition of formaldehyde to ethene and the diradical products of the α-cleavage of cyclohexanone have been optimized by the MNDO CI method for a number of different singlet and triplet states. SOC integrals are calculated by an effective one-electron approximation. Intermediate diradicals in the Paterno–Büchi reaction and the SOC effects are also studied ab initio with CAS SCF geometry optimization in a TZV basis set. Both methods predict a large SOC matrix element between the S and T states in the course of the C–C attack, while the SOC integral is two orders of magnitude smaller for the diradical produced in the C–O attack. In the Norrish type I photoreaction the oxygen atom also produces some nonzero contribution to the SOC integral which governs intersystem crossing in a ·C–C· diradical. For the diradicals produced by the α-cleavage of cyclohexanone a vibronic interaction is responsible for the SOC mixing between the lowest S and T states. The importance of one-center versus two-center SOC contributions in diradicals is briefly discussed.     

The Electronic Properties of Diradicals

A review of the various possible definitions of diradicals leads the authors to describe these systems as having two odd electrons in degenerate or nearly-degenerate molecular orbitals. A study of the wave-function for the two odd electrons shows that its form depends entirely on whether the diradical is homo- or heterosymmetric. Energy schemes are given in these two cases, as well as in the intermediate “non-symmetric” case. The extent of zwitterionic character in diradical states is also investigated. This is followed by a discussion of intersystem crossing between singlet and triplet diradical states via spin-orbit coupling and other mechanisms. The electronic matrix elements for spin-orbit coupling are calculated and evaluated numerically for various model cases. It is then possible to establish general rules for favorable (electronic) intersystem crossing. In 1,3 or 1,4 diradicals its efficiency is estimated to be comparable with that in aromatics. The role of the electron-nuclear hyperfine interaction in mixing singlet and triplet states, particularly in CIDNP, is explained. Finally the question of whether diradicals actually occur as secondary minima on potential energy surfaces is examined. Recent quantum-mechanical calculations, in contradiction to some thermochemical and kinetic evidence, lead to flat singlet surfaces without significant minima.     

Reversible Self-Assembling of Boryl Radical Anions to Their Diradicals with Tunable Singlet Ground States

Two novel boron-centered diradicals based on dimesitylpyridine borane ( 1 ) were synthesized by the self-assembling of the corresponding radical sodium and potassium salts, respectively. The sodium diradical was obtained by re-dissolving the crystals of the radical salt 1Na in toluene, while the potassium diradical was directly obtained by the reduction of 1 with potassium in THF. The diradicals could be converted back to their radical anions in THF solution, forming a reversible process. EPR spectroscopy and SQUID measurements, together with theoretical calculations, show that the diradicals have singlet ground states with excited triplet states. Their singlet–triplet energy gaps are tunable with metals.     

A stable triplet diradical emitter

Molecules with luminescence have been extensively investigated, but the luminescence of a stable molecule with a triplet ground state has not been observed. Synthesis of boron-containing radicals has attracted lots of interest because of their unique electronic structures and potential applications in organic semiconductors. Though some boron-based diradicals have been reported, neutral boron-containing diradicals with triplet ground states are rare. Herein two borocyclic diradicals with different substituents (3 and 4) have been isolated. Their electronic structures were investigated by EPR and UV spectroscopy, and SQUID magnetometry, in conjunction with DFT calculations. Both experiment and calculation suggest that 3 is an open shell singlet diradical while 4 is a triplet ground state diradical with a large singlet–triplet gap (0.25 kcal mol⁻¹). Both diradicals show multi fluorescence peaks (3: 414, 431, and 470 nm; 4: 420, 433, and 495 nm). 3 displays multiple redox steps and is a potential material towards the design of high-density memory devices. 4 represents the first example of a neutral triplet boron-containing diradical with a strong ferromagnetic interaction, and also is the first stable triplet diradical emitter.

Stable borocyclic diradical emitters with a tunable ground state.     

DFT calculations on the effects of para substituents on the energy differences between singlet and triplet states of 2,2-difluoro-1,3-diphenylcyclopentane-1,3-diyls

UB3LYP/6-31g* calculations have been performed on a series of para-substituted 2,2-difluoro-1,3-diphenylcyclopentane-1,3-diyls (4). The singlet is computed to be the ground state for each of the diradicals, regardless of the nature of the para substituents, which range from strongly pi-electron-donating (amino) to strongly pi-electron-withdrawing (nitro). In the symmetrically para-disubstituted diradicals, the size of the singlet-triplet energy gap (Delta E(ST)) increases with the pi-electron-donating ability of the substituents, but in the unsymmetrically substituted diradicals, large values of Delta E(ST) are calculated even when one of the substituents is a pi electron acceptor. The origins of the competitive and cooperative substituent effects, predicted for diradical 4, are discussed in light of the calculated effects of the same substituents on the singlet and triplet states of diradical 6, which lacks the geminal fluorines at C-2 that are present in 4.     

Computational evidence for self-initiation in spontaneous high-temperature polymerization of methyl methacrylate

This paper presents computational evidence for the occurrence of diradical mechanism of self-initiation in thermal polymerization of methyl methacrylate. Two self-initiation mechanisms of interest were explored with first-principles density functional theory calculations. Singlet and triplet potential energy surfaces were constructed. The formation of two Diels-Alder adducts, cis- and trans-dimethyl 1,2-dimethylcyclobutane-1,2-dicarboxylate and dimethyl 2-methyl-5-methylidene-hexanedioate, on the singlet surface was identified. Transition states were calculated using B3LYP/6-31G* and assessed using MP2/6-31G*. The calculated energy barriers and rate constants with different levels of theory were found to show good agreement to corresponding data obtained from laboratory experiments. The presence of a diradical intermediate on the triplet surface was identified. When MCSCF/6-31G* was used, the spin-orbit coupling constant for the singlet to triplet crossover was calculated to be 2.5 cm(-1). The mechanism of monoradical generation via a hydrogen abstraction by both triplet and singlet diradicals from a third monomer was identified to be the most likely mechanism of initiation in spontaneous polymerization of methyl methacrylate.     

C3H4: Theoretical study of structures and stabilities of isomers

The various isomers including stable structures, carbenes, and diradicals on the C₃H₄ surface have been investigated. The two carbenes propenylidene and cyclopropylidene have been found to have singlet ground states. Vinylmethylene is predicted to have a triplet ground state with a planar diradical type of structure. The syn and anti forms of this state are degenerate. This is in agreement with the observation of two triplet states in the electron spin resonance (ESR ) spectra. The π electrons are found to be delocalized over the three carbons. The singlet diradical structures are found to be more stable than the carbene structures, which retain the CH₂ (DOUBLE BOND) CH allylic structures. The orbital compositions of the frontier orbitals of all systems have been determined to examine the nature of these orbitals. © 1996 John Wiley & Sons, Inc.     

DFT study on singlet diradical character of zethrenes

The diradical character of zethrenes was investigated using a symmetry-broken UB3LYP/6-311G(d,p) method. The number of hexagons in the investigated molecules ranges from 6 to 12. It was found that all zethrenes are singlet diradicals, whose diradical character increases with the increasing size of the molecules. A singlet diradical structure provides a possibility for an electron pair to occupy different parts of space, and allows for achieving aromatic stabilization. It can be predicted, on the basis of the singlet-triplet values, that even higher zethrenes will be singlet, but not triplet molecules.     

A Highly Stable Organic Luminescent Diradical

It is very challenging to obtain stable room-temperature luminescent open-shell singlet diradicals. Herein we report the first stable Müller's hydrocarbon TTM-PhTTM with luminescent properties. Variable-temperature electron paramagnetic resonance spectroscopy measurements and theoretical calculations show that TTM-PhTTM has an open-shell singlet ground state with a diradical character of 90 %. Because of a small singlet-triplet energy gap, the open-shell singlet ground state can be thermally excited to a triplet state. TTM-PhTTM shows room-temperature deep-red emission in various solutions. Unusually high stability of TTM-PhTTM was also observed owing to effective steric hindrance and spin delocalization. Our results are beneficial to the rational design and discovery of more stable luminescent diradical materials.     

Direct Detection of a Chemical Equilibrium between a Localized Singlet Diradical and Its σ‐Bonded Species by Time‐Resolved UV/Vis and IR Spectroscopy

Localized singlet diradicals are key intermediates in bond homolyses. The singlet diradicals are energetically much less stable than the σ‐bonded species. In general, only one‐way reactions from diradicals to σ‐bonded species are observed. In this study, a thermal equilibrium between a singlet 1,2‐diazacyclopentane‐3,5‐diyl diradical and the corresponding σ‐bonded species was directly observed. The singlet diradical was more stable than the σ‐bonded species. The solvent effect clarified key features, such as the zwitterionic character of the singlet diradical. The effect of the nitrogen atoms is discussed in detail.     

High magnetic exchange coupling constants: a density functional theory based study of substituted schlenk diradicals

The Schlenk diradical has been known since 1915. After a detailed experimental work by Rajca, its magnetic nature has remained more or less unexplored. We have investigated by quantum chemical calculations the nature of magnetic coupling in 11 substituted Schlenk diradicals. Substitution has been considered at the fifth carbon atom of the meta-phenylene moiety. The UB3LYP method has been used to study 12 diradicals including the original one. The 6-311G(d,p) basis set has been employed for optimization of molecular geometry in both singlet and triplet states for each species. The singlet optimization has led to the optimization of the broken-symmetry structure for 10 species including the unsubstituted one. This development makes it possible to carry out further broken symmetry calculations in two ways. The triplet calculation has been done using 6-311++G(d,p) basis set and the optimized triplet geometry in both procedures. The broken symmetry calculations have used the optimized geometries of either the triplet states or the broken symmetry solutions. The first method leads to the prediction of electron paramagnetic resonance (EPR) compatible magnetic exchange coupling constant (J) in the range 517-617 cm(-1). A direct optimization of the broken symmetry geometry gives rise to a lower estimate of J, in the range of 411-525 cm(-1) and compatible with macroscopic Curie studies. The calculated J for the unsubstituted Schlenk diradical is 512 cm(-1) that can be compared with 455 cm(-1) estimated by Rajca. In both cases, introduction of groups with +M and +I effects (Ingold's notation) decreases the J value from that for the unsubstituted Schlenk diradical while -I and -M groups at the same position increases J. These trends have been explained in terms of Hammett constants, atomic spin densities, and dihedral angles.     

Crystalline Diradical Dianions of Pyrene-Fused Azaacenes

Although diradicals and azaacenes have been greatly attractive in fundamental chemistry and functional materials, the isolable diradical dianions of azaacenes are still unknown. Herein, we describe the first isolation of pyrene-fused azaacene diradical dianion salts [(18-c-6)K(THF)₂]⁺[(18-c-6)K]⁺⋅ 1 ^2−.. and [(18-c-6)K(THF)]²⁺⋅ 2 ^2−.. by reduction of the neutral pyrene-fused azaacene derivatives 1 and 2 with excess potassium graphite in THF in the presence of 18-crown-6. Their electronic structures were investigated by various experiments, in conjunction with theoretical calculations. It was found that both dianions are open-shell singlets in the ground state and their triplet states are thermally readily accessible owing to the small singlet–triplet energy gap. This work provides the first examples of crystalline diradical dianions of azaacenes with considerable diradical character.     

TTF+1-π共轭桥-6-氧四联氮阳离子双自由基NLO性质的理论研究

采用量子化学UPBE1PBE结合有限场(FF)方法,对系列TTF+?-π共轭桥-6-氧四联氮阳离子双自由基体系的稳定性,极化率αs和第一超极化率βtot进行研究.结果表明,TTF+?-6-氧四联氮阳离子双自由基引入共轭桥后,随体系共轭性增强,αs和βtot值均增大(体系2S的βtot值除外).自旋多重度和构象对双自由基体系的极化率和第一超极化率都有影响,双自由基体系由单重态转变为三重态时,极化率减小,而第一超极化率明显增大.以体系2为例,在单重态时αs和βtot值随构象变化较小,而三重态时αs和βtot值随二面角θ1和θ2的增加而减小.     

The chemistry of localized singlet 1,3-diradicals (biradicals): from putative intermediates to persistent species and unusual molecules with a π-single bonded character

Localized singlet diradicals (biradicals) are key intermediates in chemical reactions involving homolytic bond-cleavage and formation processes. The molecular structure and electronic structure had been historically elusive due to the short-lived character of the reactive intermediates. In the last 15 years, a significant development of singlet diradical chemistry was achieved after the pioneering findings of long-lived singlet diradicals. In this tutorial review, the recent development of localized singlet diradical chemistry is summarized and discussed. The following subjects are included (a) the mechanism by which the ground state spin-multiplicity of localized 1,3-diradicals is controlled; (b) the substituent and heteroatom effect on the most stable electronic configuration of the singlet 1,3-diradicals, type-1 versus type-2; (c) the molecular design for the long-lived singlet ground state diradicals; (d) the generation and characterization of the singlet diradicals; and (e) the future prospects.     

Conformationally constrained, stable, triplet ground state (S = 1) nitroxide diradicals. Antiferromagnetic chains of S = 1 diradicals

Nitroxide diradicals, in which nitroxides are annelated to m-phenylene forming tricyclic benzobisoxazine-like structures, have been synthesized and characterized by X-ray crystallography, magnetic resonance (EPR and 1H NMR) spectroscopy, as well as magnetic studies in solution and in solid state. For the octamethyl derivative of benzobisoxazine nitroxide diradical, the conformationally constrained nitroxide moieties are coplanar with the m-phenylene, leading to large values of 2J (2J/k > 200 K in solution and 2J/k > 300 K in the solid state). For the diradical, in which all ortho and para positions of the m-phenylene are sterically shielded, distortion of the nitroxide moieties from coplanarity is moderate, such that the singlet-triplet gaps remain large in both solution (2J/k > 200 K) and the solid state (2J/k approximately 400-800 K), though an onset of thermal depopulation of the triplet ground state is detectable near room temperature. These diradicals have robust triplet ground states with strong ferromagnetic coupling and good stability at ambient conditions. Magnetic behavior of the nitroxide diradicals at low temperature is best fit to the model of one-dimensional S = 1 Heisenberg chains with intrachain antiferromagnetic coupling. The antiferromagnetic coupling between the S = 1 diradicals may be associated with the methyl nitroxide C-H- - -O contacts, including nonclassical hydrogen bonds. These unprecedented organic S = 1 antiferromagnetic chains are highly isotropic, compared to those of the extensively studied Ni(II)-based chains.     

Crystalline Diradical Dianions of Pyrene‐Fused Azaacenes

Although diradicals and azaacenes have been greatly attractive in fundamental chemistry and functional materials, the isolable diradical dianions of azaacenes are still unknown. Herein, we describe the first isolation of pyrene‐fused azaacene diradical dianion salts [(18‐c‐6)K(THF)₂]⁺[(18‐c‐6)K]⁺? 1 ^2?.. and [(18‐c‐6)K(THF)]²⁺? 2 ^2?.. by reduction of the neutral pyrene‐fused azaacene derivatives 1 and 2 with excess potassium graphite in THF in the presence of 18‐crown‐6. Their electronic structures were investigated by various experiments, in conjunction with theoretical calculations. It was found that both dianions are open‐shell singlets in the ground state and their triplet states are thermally readily accessible owing to the small singlet–triplet energy gap. This work provides the first examples of crystalline diradical dianions of azaacenes with considerable diradical character.     

Coupling of Fischer carbene complexes with conjugated enediynes featuring radical traps: Novel structure and reactivity features of chromium complexed arene diradical species

The reaction of Fischer carbene complexes with conjugated enediynes that feature a pendant alkene group has been examined. The reaction proceeds through carbene–alkyne coupling to generate an enyne–ketene intermediate. This intermediate then undergoes Moore cyclization to generate a chromium complexed arene diradical, which then undergoes cyclization with the pendant alkene group. The radical cyclization prefers the 6-endo mode unless radical-stabilizing groups are present to favor the 5-exo mode. The intermediate diradical species were evaluated computationally in both the singlet and triplet configurations. Arene triplet diradicals feature minimal spin density at oxygen and delocalization to chromium. The 6-endo cyclization product was kinetically and thermodynamically favored.     

Conformational analysis of singlet-triplet state mixing in Paternò-Büchi diradicals

Conformational dependence of spin-orbit coupling (SOC) in flexible Paternò-Büchi (PB) diradicals has been studied with high-level ab initio methods using both (i) one-electron spin-orbit Hamiltonian with parametrized (effective) nuclear charges in conjunction with a state-averaged MCSCF wave function as implemented by Robb in Gaussian 98 and (ii) complete one- and two-electron SOC with a fully optimized MCSCF triplet wave function and frozen core singlet as implemented by Furlani in the GAMESS computational package. The ab initio results revealed two distinct areas of elevated SOC values, one corresponding to the region whereby a cisoid conformation in the C-C-O-C fragment brings the two odd-electron orbitals closer to each other, and the other area corresponding to the partially eclipsed conformation lacking direct overlap between the spin centers. In this second region the 1,4-electronic communication is mediated by the oxygen's 2p-lone pair, which is suitably oriented to play the role of a "relay-antenna". The other critical factor affecting the rate of intersystem crossing (ISC)--singlet-triplet energy separation--was computed utilizing a multireference CASSCF-MP2 method to include dynamic correlation effects. The largest singlet-triplet energy gap, approximately 2 kcal/mol, was found for a gauche conformer (also a minimum SOC conformation). Rotation about the central C-O bond either toward the fully eclipsed (0 degrees ) or the partially eclipsed (120 degrees ) conformations decreases the singlet-triplet gap while increasing the value of the SOC matrix element. These computational findings support the Griesbeck model for stereochemistry of triplet PB reactions and provide a rigorous basis for predicting the probability of ISC in diradicals separated by a partially conjugated spacer.     

Theoretical Study on Photoisomerization of 2-Methylfuran to 3-Methylfuran

1 INTRODUCTION 2-Methylfuran belongs to the basic heteroaromatic compounds relevant to many fields of modern che- mistry, ranging from the study of natural products and biologically active substances to the develop- ment of building blocks for organic synthesis and conducting polymers[1]. Since the photochemistry ofR-furan was gradually recognized in 1960s[2～7], lots of interest has been aroused. Herein we only study one branch of photoche- mistry of R-furan: the isomerization of 2-methy…     

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.