Effects of spiroconjugation on the calculated singlet-triplet energy gap in 2,2-dialkoxycyclopentane-1,3-diyls and on the experimental electronic absorption spectra of singlet 1,3-diphenyl derivatives. Assignment of the lowest-energy electronic transition of singlet cyclopentane-1,3-diyls

The effect of a 2,2-ethylene-ketal functionality on the singlet-triplet energy gap (Delta E(ST)) and on the first electronic transition in singlet cyclopentane-1,3-diyls (1) has been investigated. UDFT calculations predict a significant increase in the preference for a singlet ground state in the diradical with the cyclic ketal at C2 (1g; Delta E(ST) = -6.6 kcal/mol in C(2) symmetry and -7.6 kcal/mol in C(2v) symmetry), compared to the 2,2-dihydroxy- and 2,2-dimethoxy-disubstituted diradicals (1d, Delta E(ST) = -3.6 kcal/mol in C(2) symmetry, and 1e, Delta E(ST) = -3.4 kcal/mol in C(2) symmetry). Spiroconjugation is shown to be responsible for the larger calculated value of absolute value Delta E(ST) in 1g, relative to 1d and 1e. A strong correlation between the calculated values of Delta E(ST) and the computed electronic excitation energies of the singlet diradicals is found for diradicals 1d, 1e, and 1g and for 2,2-difluorocyclopentane-1,3-diyl (1c). A similar correlation between Delta E(ST) and lambda(calcd) is predicted for the corresponding 1,3-diphenylcyclopentane-1,3-diyls 3, and the predicted blue shift in the spectrum of 3g, relative to 3e, has been confirmed by experimental comparisons of the electronic absorption spectra of the annelated derivatives 2c, 2e, and 2g in a glass at 77 K. The wavelength of the first absorption band in the singlet diradicals decreases in the order 2e (lambda(onset) = 650 nm) > 2g (lambda(onset) = 590 nm) > 2c (lambda(onset) = 580 nm). The combination of these computational and experimental results provides a sound basis for reassignment of the first electronic absorption band in singlet diradicals 2c, 2e, and 2g to the excitation of an electron from the HOMO to the LUMO of these 2,2-disubstituted derivatives of cyclopentane-1,3-diyl.     

On the electronic character of localized singlet 2,2-dimethoxycyclopentane-1,3-diyl diradicals: substituent effects on the lifetime

Photodenitrogenation of the diazenes 4 affords exclusively the housanes 5 through intramolecular cyclization of the spectrally detected and characterized singlet diradicals 3. The lifetime of singlet diradical 3, determined by transient absorption measurements, depends on the Y and Z substituents at the para position of the phenyl ring and has the following order: Y, Z = OMe, OMe > OMe, CN > CN, CN > OMe, H > Cl, Cl approximately CN, H approximately Me, Me > H, H. This unprecedented substituent effect reveals stabilization of the singlet 2,2-dimethoxycyclopentane-1,3-diyl diradicals 3 through radical, zwitterionic, pi-bonding, and hyperconjugative structures.     

Bulky Substituent Effect on Reactivity of Localized Singlet Cyclopentane‐1,3‐diyls with π‐Single Bonding (C‐π‐C) Character

Thorough investigation of key intermediates, such as long‐lived singlet diradicals, is essential to understand the homolytic bond cleavage reactions. In this study, we evaluate the effect of bulky substituents at the meta‐position of the phenyl ring on the bond formation process in singlet 2,2‐diethoxy‐1,3‐diarylcyclopentane‐1,3‐diyls. The bulky groups have significant influence on the diradical lifetime, as such, when the triisopropylphenyl group was used, the lifetime was 45 times longer than that of the parent diradical in benzene at 293 K.     

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.     

Substituent effects on singlet-triplet gaps and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidenes to 1,3-oxazoles

Electronic structures, partial atomic charges, singlet-triplet gaps (Delta E ST), substituent effects, and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidene ( 5) and 4,5-dimethyl- ( 6), 4,5-difluoro- ( 7), 4,5-dichloro- ( 8), 4,5-dibromo- ( 9), and 3-methyl-1,3-oxazol-2-ylidene ( 10) to the corresponding 1,3-oxazoles have been studied using complete-basis-set methods (CBS-QB3, CBS-Q, CBS-4M), second-order M?ller-Plesset perturbation method (MP2), hybrid density functionals (B3LYP, B3PW91), coupled-cluster theory with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)], and the quadratic configuration interaction method including single and double excitations (QCISD) and QCISD plus perturbative triple excitations [QCISD(T)]. The 6-311G(d,p), 6-31+G(d,p), 6-311+G(d,p), and correlation-consistent polarized valence double-xi (cc-pVDZ) basis sets were employed. The carbenes have singlet ground states, and the CBS-QB3 and CBS-Q methods predict Delta E ST values for 5- 8 and 10 of 79.9, 79.8, 74.7, 77.0, and 82.0 kcal/mol, respectively. CCSD(T), QCISD(T), B3LYP, and B3PW91 predict smaller Delta E ST values than CBS-QB3 and CBS-Q, with the hybrid density functionals predicting the smallest values. The concerted unimolecular exothermic out-of-plane 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes to their respective 1,3-oxazoles proceed via cyclic three-center transition states. The CBS-predicted barriers to the 1,2-rearrangements of singlet carbenes 5- 9 to their respective 1,3-oxazoles are 41.4, 40.4, 37.8, 40.4, and 40.5 kcal/mol, respectively. During the 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes 5- 9, there is a decrease in electron density at oxygen, N3 (the migration origin), and C5 and an increase in electron density at C2 (the migration terminus), C4, and the partially positive migrating hydrogen.     

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.     

The diradical mechanism for 1,3-dipolar cycloadditions and related thermal pericyclic reactions

A critical comparison is given of the diradical and concerted mechanisms for 1,3-dipolar cycloadditions, with references also to the Diels-Alder reaction and Cope rearrangement. The experimental facts for the field as a whole favor the diradical mechanism. Among the topics considered are stereospecificity, solvent effects, energetics, penselectivity, substituent effects, acetylenic dipolarophiles, U-shaped Hammett plots, orientation, steric effects, partial charges, conformation and scission of diradicals, hydrogen transfer in extended diradicals and cycloadditions of fluorinated olefins.     

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 -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 -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.     

1,3-Diborata-2,4-diphosphoniocyclobutane-1,3-diyls communicate through a para-phenylene linker

The presence of a second 1,3-diborata-2,4-diphosphoniocyclobutane-1,3-diyl in the para-position of a phenylene linker favors the diradical form over the 1,3-diborata-2,4-diphosphoniobicyclo[1.1.0]butane bond stretch isomer, as long as the two planar diradical units are coplanar with the linker. This demonstrates that two BPBP diradicals communicate through the phenyl ring.     

Steric influence of E- or Z-monosubstituted and terminally disubstituted vinyl groups in matrix-isolated cyclopentane-1,3-diyl triplet diradicals as probed by the zero-field EPR D parameter

The zero-field D parameter of the localized E, Z, and disubstituted vinyl cyclopentane-1,3-diyl triplet diradicals V was determined at 77 K in a 2-methyltetrahydrofuran (2-MTHF) matrix. Good linear correlations were obtained with the semiempirically (PM3; r(2) = 0. 991, n = 19) and DFT (B3LYP; r(2) = 0.998, n = 7) calculated spin densities of the triplet diradicals. The D values for the disubstituted triplet diradicals V are generally larger than the corresponding monosubstituted ones and, thus, the former are less well-delocalized and thereby more poorly stabilized. For the E- and Z-diastereomeric pairs V, only marginal changes in the theoretical assessed spin densities as well as in the D values have been found. Steric effects operate and distort the conformation of the vinyl substituent in the triplet diradical V. This is adequately reproduced by theoretical calculations. For the diphenyl-substituted triplet diradical Vl, for example, they show a more or less planar alignment of the E-phenyl group and the allylic pi system (torsion angle 12 degrees ) and thus optimal delocalization of spin, whereas the Z-phenyl group is twisted about 78 degrees out of plane and therefore is not involved in the delocalization and stabilization of spin. This results in a slightly higher D value (0.0368 cm(-)(1)), and the spin is delocalized less than in the monosubstituted E-Vm one (0.0357 cm(-)(1)).     

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.     

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.     

Theoretical designs of singlet localized 1,3-diradicals

Spin preference and S-T gaps of localized 1,3-diradicals were studied by an orbital phase theory and theoretical calculations. The orbital phase theory was applied to rationalize thermodynamic and kinetic stabilities of diradicals. We theoretically designed some singlet localized 1,3-diradicals, substituted trimethylenes, which are more stable than the lowest triplets. Some diradicals with the four-membered rings, 2,4-disilacyclobutane-1,3-diyls, were designed and shown to have singlet ground states and to be more stable than the sigma-bonded isomers, 2,4-disilabicyclo[1.1.0]butanes. The ab initio calculations supported predictions of the stable carbon-centered localized singlet 1,3-diradicals.     

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.     

A Puckered Singlet Cyclopentane‐1,3‐diyl: Detection of the Third Isomer in Homolysis

In the photochemical denitrogenation of 1,4‐diaryl‐2,3‐diazabicyclo[2.2.1]heptane ( AZ6 ) bearing sterically hindered substituents, a curious new absorption band at about 450 nm was observed under low‐temperature matrix conditions, together with the previously well‐characterized planar singlet diradical pl‐¹ DR6 with λ_max=≈580 nm. The 450 nm species was electron paramagnetic resonance (EPR)‐silent. Instead of generating the planar diradical pl‐¹ DR6 and the precursor azoalkane AZ6 upon warming, the ring‐closed bicyclo[2.1.0]pentane derivative SB6 , that is, the AZ6 denitrogenation product was identified. Based on product analysis, low‐temperature spectroscopic observations, high‐level quantum‐mechanical computations, viscosity effect, and laser‐flash photolysis, the puckered singlet diradicaloid puc‐¹ DR6 was assigned to the new 450 nm absorption. The latter was detected experimentally at the same time as the planar singlet diradical pl‐¹ DR6 . Sterically demanding substituents as well as viscosity impediments were essential for the detection of the experimentally hitherto unknown puckered singlet cyclopentane‐1,3‐diyl diradicaloid puc‐¹ DR6 , that is, the third isomer in homolysis. The present findings should stimulate future work on the mechanistically fascinating stereoselectivity documented in the formation of bicyclo[2.1.0]pentanes during the 2,3‐diazabicyclo[2.2.1]heptane denitrogenation.     

The D Parameter (EPR Zero-Field Splitting) of Localized 1,3-Cyclopentanediyl Triplet Diradicals as a Measure of Electronic Substituent Effects on the Spin Densities in Para-Substituted Benzyl-Type Radicals

The zero-field splitting parameters D of the symmetrically disubstituted and unsymmetrically monosubstituted 1,3-diaryl-1,3-cyclopentanediyl triplet diradicals 1, 2 (X = p-MeO, p-Me, p-Cl, p-NH(2), p-CO(2)Me, p-CN, p-NO(2)), and 5 were determined in 2-methyltetrahydrofuran glass at 77 K. The linear plot (m = 0.558, r(2) = 0.993) of the experimental D values for the symmetrically disubstituted derivatives versus the corresponding monosubstituted ones reveals that the electronic substituent effects are additive and implies (except for the magnetic dipolar interaction) that each benzyl-type radical site acts independently in the localized diradicals. This additivity permits us to view these triplet diradicals as a composite of the two separate monoradical components and allows us to assess valuable electronic properties of benzyl-type monoradicals from the D parameter of the triplet diradical species. A theoretical analysis shows that the D parameter is a measure of the spin density rho at the benzylic positions and the inter-radical distance d in localized diradicals. A good correlation exists between the D parameter of these triplet diradicals (constant inter-radical distance d) and the EPR hyperfine coupling constants of the corresponding benzyl-type monoradicals, which establishes that the observed electronic substituent effects reflect changes in the spin densities at the radical sites. The novel DeltaD scale allows us to quantify spectroscopically the para substituent effect on the spin delocalization at the benzylic position.     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

Theoretical calculations of the effects of 2-heavier group 14 element and substituents on the singlet-triplet energy gap in cyclopentane-1,3-diyls and computational prediction of the reactivity of singlet 2-silacyclopentane-1,3-diyls

UDFT and CASSCF calculations with the 6-31G(d) basis set were performed to investigate the heavier group 14 element (M) effect on the ground-state spin multiplicity of cyclopentane-1,3-diyls and their reactivity. The calculations find that 2-metallacyclopentane-1,3-diyls (M = Si, Ge) that possess a variety of substituents (X = H, Me, F, OR, SiH(3)) at M(2) are singlet ground-state molecules. The energies of the 1,3-diphenyl-substituted singlet 2-silacyclopentane-1,3-diyls are calculated to be ca. 5 kcal/mol lower than those of the intramolecular ring-closure products, i.e., 1,4-diphenyl-5-silabicyclo[2.1.0]pentanes, at the B3LYP/6-31G(d) level of theory. The energy barrier for the disrotatory ring closure of singlet 2,2-dimethyl-1,3-diphenyl-2-silacyclopentane-1,3-diyl (lambda(calcd) = 757 nm, f = 1.01 at RCIS/6-31G(d)) to the corresponding 5-silabicyclo[2.1.0]pentane is computed to be 11.6 kcal/mol, which is 13.1 kcal/mol lower in energy than that for the conrotatory ring-opening to a 3-silapenta-1,4-diene. The computational work predicts that singlet 1,3-diaryl-2-silacyclopentane-1,3-diyls are persistent molecules under conditions without trapping agents.     

2-Silyl group effect on the reactivity of cyclopentane-1,3-diyls. Intramolecular ring-closure versus silyl migration

Generation of singlet and triplet 2-silylcyclopentane-1,3-diyls and their reactivity have been investigated in the thermal and photochemical denitrogenation of 2,3-diaza-7-silylbicyclo[2.2.1]hept-2-ene. 5-Silylcyclopentene (silyl migration product) is quantitatively obtained, while 5-silylbicyclo[2.1.0]pentane (intramolecular ring-closure product) is not detected in the denitrogenation reactions. Deuterium labeling studies clarify that 5-silylcyclopentene is formed by a suprafacial [1,2] silyl migration in singlet 2-silylcyclopentane-1,3-diyl. UDFT calculations closely reproduce the observed reactivity of the singlet diradical: The enthalpic barriers of the intramolecular ring-closure are calculated to be DeltaH++exo468 = 5.8 kcal/mol and DeltaH++endo468 = 6.7 kcal/mol, which are much higher than the energy barrier for the [1,2] silyl migration, DeltaH++468 = 2.7 kcal/mol. The notable effect of the silyl group on raising the energy barrier of the intramolecular cyclization is rationalized by an electronic configuration of the lowest singlet state of 2-silylcyclopentane-1,3-diyls.     

Triplet ground state derivative of aza-m-xylylene diradical with large singlet-triplet energy gap

Organic molecules with a strong preference for triplet ground states, in which the triplet state is below the lowest singlet state by ≥10 kcal/mol, are typically short-lived and mostly detected as reactive intermediates. We now report a triplet ground state derivative of aza-m-xylylene diradical with a large singlet-triplet energy gap (ΔE(ST)) of ～10 kcal/mol, which is comparable to ΔE(ST) for the well-known reactive intermediate m-xylylene diradical. The aminyl diradical persists in solution at room temperature on the time scale of minutes.