Theoretical design of singlet localized σ-diradicals: C(MH2)3C (M = Si, Ge, Sn, Pb)

Some localized singlet 1,3-σ-diradicals, C(MH₂)₃C, (M = Si, Ge, Sn, Pb) were theoretically designed by the orbital phase theory and density functional theory calculations. The bicyclic carbon-centered singlet diradicals were more stable than the lowest triplets. Except for M = C, σ-bonded isomers were not located for 1,3-σ-diradicals. 1,4-σ-diradicals, C(M₂H₄)₃C, also had singlet ground states, but they were less stable than σ-bonded isomers.     

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.     

Stretch Effects Induced by Molecular Strain on Weakening σ-Bonds: Molecular Design of Long-Lived Diradicals (Biradicals)

Stretch effects induced by two types of molecular strain were examined by quantum chemical calculations at the B3LYP/6-31G(d), B3LYP/cc-PVDZ, CCSD/6-31G(d), and CASPT2/ANO-RCC-VTZP level of theory, to design persistent multiradicals such as localized diradicals and oxyallyls. The cooperative molecular strain (Type-1) induced by the spiro[5.5]undecane and bicyclo[2.1.0]cyclopentane structures was found to significantly destabilize in energy the ring-closed compounds of the diradicals, leading to small energy differences between the diradicals and the σ-bonded compounds. Another stretch effect (Type-2) induced by macrocyclic systems was also found to energetically destabilize the corresponding ring-closed structures of the 1,3-diradicals. The computational studies predict that the two types of stretch effects are quite effective in lowering the energy barriers of the bond-breaking reaction of the ring-closed compounds and in generating long-lived localized diradicals and oxyallyl derivatives.     

Properties of stable organic bond-stretched non-Lewis molecules

The conditions required for the existence of a stable bond-stretched singlet isomer of hetero derivatives of bicyclo[2.1.0]pentane (which is a cyclopentane-1,3-diyl derivative) are discussed. Such species are non-Lewis systems with a ruptured C-C bond (formally diradicals), in which two electrons occupy the nonbonding orbital. A high-level calculation shows that in contrast with the carbon substituted compounds, in which the open form is a transition state between two classical-bonded closed bicyclic forms, in the heterosubstituted molecules, the open form is calculated to be a stable minimum. The ionization potentials of the open forms are considerably lower than those of their bicyclic isomers and also of regular organic radicals/diradicals. Nitrogen atoms are found to be more effective than oxygen or sulfur in stabilizing the open isomer. In this case, the open isomer is calculated to be a little more stable than the bicyclic compound, and a barrier of approximately 40 kcal/mol is computed for the ring closing reaction. Thus, the open isomer is both thermodynamically and kinetically stable. This result rationalizes some experimental observations that indicated the existence of non-Lewis singlet species.     

Reactive cross-talk between adjacent tension-trapped transition states

Tension along a polymer chain traps neighboring s-trans/s-trans-1,3-diradicals from the mechanically induced ring opening of gem-difluorocyclopropanes (gDFCs). The diradicals correspond to the transition states of the force-free thermal isomerization reactions of gDFCs, and the tension trapping allows a new disproportionation reaction between two simultaneously trapped diradicals to take place.     

Do deviations from bond enthalpy additivity define the thermodynamic stabilities of diradicals?

Deviations from bond enthalpy additivity (DeltaBEA) are frequently used to assess the thermodyamic stabilities of diradicals. (U)B3LYP/6-31G calculations have been performed in order to determine how well DeltaBEA values actually do reflect the thermodynamic stabilities of the triplet states of diradicals in which one or both nonbonding electrons occupy a delocalized pi orbital. The calculations find that different pathways for forming sigma,pi-diradicals, such as alpha,2- and alpha,4-dehydrotoluene (4 and 6), give DeltaBEA values that differ by ca. 1 kcal/mol. The path dependency of the DeltaBEA values is computed to be one order of magnitude larger for non-Kekulé hydrocarbon diradicals, such as m-benzoquinodimethane (12) and 1,3-dimethylenecyclobutane-2,4-diyl (15), than for sigma,pi-diradicals. Since the DeltaBEA values for forming 4, 6, 12, and 15 are all path dependent, we conclude that DeltaBEA values for diradicals with one or two delocalized, nonbonding pi electrons do not, in general, uniquely define the thermodynamic stabilities of the diradicals. Hence, DeltaBEA values should not be used for this purpose, especially for non-Kekulé hydrocarbon diradicals.     

With a little help from my friends: forty years of fruitful chemical collaborations

Over the past 40 years, much of the author's research, both computational and experimental, has involved collaborations. This Perspective describes some of the author's collaborative research in eight different areas of organic and theoretical chemistry: (1) hydrocarbons containing unsaturatively, 1,3-bridged cyclobutane rings, (2) the use of orbital topology for predicting the ground states of diradicals, (3) violations of Hund's rule, (4) the chemistry of phenylnitrenes, (5) tunneling by carbon in organic reactions, (6) the Cope rearrangement and the effect of substituents on it, (7) pyramidalized alkenes, dehydrocubanes, cubyl cation, and octanitrocubane, and (8) the effects of geminal fluorine substitution at C-2 of 1,3-diradicals. Highlighted in this Perspective are the synergism between calculations and experiments in the author's research and the many different roles that serendipity has played in the collaborations that are described herein.     

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.     

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.     

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.     

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.     

Photochemical preparation of highly functionalized 1-indanones

A series of o-alkylphenyl alkyl ketones 1 were synthesized by different methods. The presence of a leaving group X adjacent to the carbonyl group is the special peculiarity of these ketones. Upon irradiation the keto carbonyl group of these compounds undergoes an n-pi* excitation followed by a 1,5-hydrogen migration from the o-alkyl substituent to the carbonyl oxygen atom. The thus formed 1,4-diradicals are subject to a very rapid elimination of acid HX, giving 1,5-diradicals. We called this process spin center shift. After intersystem crossing these diradicals cyclize to 1-indanones 20 in good yields. Depending on the solvent and on substituents, o-alkoxyalkyl ketones 22 or benzo[c]furanes 21 are obtained as byproducts. The mechanism of the cyclization was elucidated by quantum chemical calculations and kinetic measurements.     

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.     

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.     

Ab initio multireference investigation of disjoint diradicals: singlet versus triplet ground states

We present improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO‐CASCI) and IVO‐CASCI‐based multireference Møller–Plesset perturbation theory (MRMPPT) calculations with an aim to elucidate the electronic structure of tetramethyleneethane (TME) in its lowest singlet and triplet state and to quantify their order and extent of splitting. The potential surfaces of singlet and triplet states for the twisting of TME are also studied. We found that the triplet state is higher in energy than the singlet one in the whole range of twisting angles with the energy gap minimum at a twisting angle of about 45°. Harmonic vibrational frequencies of TME have also been calculated for both the states. We also report the ground to first excited triplet state transition energies. Our results are analyzed with respect to the results available in the literature to illustrate the efficacy of our methods employed. We also demonstrate that the spin character of the ground state of disjoint, TME‐like diradicals can be manipulated by using appropriate selection of annulenic spacer to separate the allyl groups of TME.     

1,3-Diphosphetane-2,4-diyles--Cryptocarbenes?

1,3-Diphosphetane-2,4-diyles ( A ) possess a diradical molecular structure. Experimental studies reveal interconversions of different valence isomers of the diradicals. As a consequence of the facile thermal ring opening of 1,3-diphosphetane-2.4-diyles A , we obtained crypto-phosphinocarbenes ( B ), confirmed by the results of intramolecular rearrangements as well as reactions with multiple bonded systems. A new range of five- and six-membered phosphorus heterocycles are isolated, including transition-metal complexes. The mechanism for the ring-expansion are predicted by quantum chemical calculations.     

RHF and two-configuration SCF calculations are inappropriate for conjugated diradicals

Restricted Hartee Fock (RHF) and two-configuration self-consistent field (TCSCF) calculations provide qualitatively correct molecular orbitals for the two open-shell electrons in diradicals. Nevertheless, these calculations fail to give correct relative energies and in some cases they even lead to incorrect geometries. Examples of these failures are given for both singlet and triplet states of some conjugated diradicals. In several cases these failures are related to the “doublet instability problem” in RHF calculations on radicals. It is argued that unrestricted Hartee-Fock (UHF) calculations on triplet states are more likely that RHF to provide accurate geometries.     

Ab initio studies on the vibrational spectra and conformational isomerism of 2,4-dimethyl-1,3-pentadiene

Ab initio was used to study the structure of various conformational isomers and their vibrational spectra of 2,4-dimethyl-1,3-pentadiene (2,4-PD) in detail. Two stable conformations, s-trans and s-cis, were found in which s-trans is more stable. The geometry of stable conformations and charge distributions were studied, and the effect of different basis sets on geometry optimization is discussed. The results of complete optimization indicate that molecular skeleton is nearly in a plane, its largest deviation is only 0.3 degrees. Therefore, it is reasonable and available to hypothesis that the molecule has Cs symmetry. The thermal dynamics conformations were calculated and compared with experimental values. DeltaH(o) between two conformations of 2,4-PD measured from experiment is 4.36 kJ/mol, deltaS(o) is 2.56 J/mol K., calculated results are slightly different from experimental ones. Vibrational frequencies of 2,4-PD conformers have been studied by ab initio molecular orbital calculations using different basis set. The calculated vibrational frequencies are analyzed and compared with the experimental spectra.     

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.     

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.