Symmetric Radical Research Articles

Allyl Radical Nature of a Phenylcyclopentadienyl Radical Annelated with Two Homoadamantene Frameworks

1-Phenylcyclopentadiene fused with two homoadamantene units at the 2,3- and 4,5-positions (4) was deprotonated with KH to lead to the quantitative formation of the corresponding cyclopentadienyl (Cp) anion 3(-). This anion was oxidized by AgCl to afford an orange crystalline solid consisting of Cp radical 3(•) and cyclopentadiene 4. The ESR spectrum in hexane exhibited approximately 15 lines, demonstrating that the two homoadamantene frameworks were equivalent and that the C1-C2(Ph)-C3 moiety of the five-membered ring formed a symmetrical allyl-like radical in agreement with the prediction by DFT calculation. The reaction of the Cp radical 3(•) with an oxygen molecule in the presence of Ag(+)SbF(6)(-) afforded the SbF(6)(-) salt of a phenylpyrylium ion annelated with two homoadamantene frameworks (8(+)SbF(6)(-)).

Radical cube zero weakly symmetric algebras and support varieties

One of our main results is a classification of all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. In the process we give a characterization of when a finite dimensional Koszul algebra has such a theory of support in terms of the graded centre of the Koszul dual.

Infrared spectroscopic detection of the methylgermyl (H 2GeCH 3) radical and its perdeuterated counterpart in low temperature matrices

The C s symmetric methylgermyl radical, H 2GeCH 3(X 2A′), and its D5-isotopomer were detected via infrared spectroscopy in electron-irradiated methane – germane matrices via the ν 6 mode at 839 cm −1 and the ν 12 absorption at 1406 cm −1. Experiments with D4-germane – D4-methane matrices also detected absorptions from the D5-methylgermyl species upon electron exposure at 624 cm −1 ( ν 7) and 1406 cm −1 ( ν 3) originating from the CD 3 and GeD 2 groups of the D5-methylgermyl radical. Kinetic fits suggest that methylgermyl is formed via a unimolecular decomposition of methylgermane molecules (H 3GeCH 3), which in turn were synthesized via recombination of germyl (GeH 3) and methyl (CH 3) in the matrix.

Long-range corrected double-hybrid density functionals

We extend the range of applicability of our previous long-range corrected (LC) hybrid functional, omegaB97X [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Moller-Plesset (many-body) perturbation theory. This LC "double-hybrid" density functional, denoted as omegaB97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calculations (as well as training set results), omegaB97X-2 yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree-Fock exchange, omegaB97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.

A Density Functional Theory for Symmetric Radical Cations from Bonding to Dissociation

It has been known for quite some time that approximate density functional (ADF) theories fail disastrously when describing the dissociative symmetric radical cations R(2)(+). By considering this dissociation limit, previous work has shown that Hartree-Fock (HF) theory favors the R(+1)-R(0) charge distribution, whereas DF approximations favor the R(+0.5)-R(+0.5). Yet, general quantum mechanical principles indicate that both these (as well as all intermediate) average charge distributions are asymptotically energy degenerate. Thus, HF and ADF theories mistakenly break the symmetry but in a contradicting way. In this letter, we show how to construct system-dependent long-range corrected (LC) density functionals that can successfully treat this class of molecules, avoiding the spurious symmetry breaking. Examples and comparisons to experimental data is given for R = H, He, and Ne, and it is shown that the new LC theory improves considerably the theoretical description of the R(2)(+) bond properties, the long-range form of the asymptotic potential curve, and the atomic polarizability. The broader impact of this finding is discussed as well, and it is argued that the widespread semiempirical approach which advocates treating the LC parameter as a system-independent parameter is in fact inappropriate under general circumstances.

Nonpolar Dihydrogen Bonds—On a Gliding Scale from Weak Dihydrogen Interaction to Covalent HH in Symmetric Radical Cations [HnE‐H‐H‐EHn]+

The electronic structures and bonding patterns for a new class of radical cations, [HnE-H-H-EHn]+ (EHn=element hydride, E=element of Groups 15-18), have been investigated by applying quantum-chemical methods. All structures investigated give rise to symmetric potential energy minimum structures. We envisage clear periodic trends. The H--H bond length is shorter for elements toward the bottom of the periodic table of elements, and a short H--H bond corresponds to accumulation of electron density in the central H--H region. All [HnE-H-H-EHn]+ of Groups 15-17 are thermodynamically unstable towards loss of either H2 or H. The barriers for these dissociations are rather low. The Group 18 congeners, except E=Xe, appear to be global minima of the respective potential energy surfaces. The findings are discussed in terms of H2 bond activation, and a general mechanistic scheme for the standard reduction process 2H+ + 2e(-) --> H2 is given. Finally, it is proposed that some of the symmetric radical cations are likely to be observed in mass spectrometric or matrix isolation experiments.

Systematic optimization of long-range corrected hybrid density functionals

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.

EXTENDING TORSION RADICALS

Over an arbitrary ring R, a symmetric radical is shown to be strongly normalizing. For a fully semiprimary Noetherian ring R, a symmetric radical is normalizing if and only if the class of torsion factor rings of R is closed under ring isomorphisms. In case S is a strongly normalizing or normalizing extension ring of R, a symmetric radical for S is constructed as an extension of a symmetric radical for R. Applications address questions concerning the behavior of Krull dimension and linked prime ideals of S.

Substitution Effect on Electronic Transition of Bi-substituted Benzyl-type Radicals: Symmetric Substitution

A substitution effect on the electronic transition of bi-substituted benzyl-type radicals was discovered. The origin of the electronic D 1 → Do transition of benzyl-type radicals was red-shifted upon substitution to the benzene ring. For symmetric bi-substituted benzyl-type radicals, it was found that the predicted shift obtained from mono-substituted benzyl-type radicals agreed well with the observation. The reason for this agreement is believed that the substituent contributes independently to the electronic energy. The substitution effect was applied to the symmetric bi-substituted difluoro-, dichloro- and dimethylbenzyl radicals.

Local hybrid functionals based on density matrix products.

We present a novel similarity metric comparing exact and semilocal density functional theory (DFT) exchange holes in real space. This metric is obtained from the product of the one-particle density matrix and the uniform electron gas model density matrix. The metric is bound between 0 and 1, 1 in the uniform electron gas, 0 in regions asymptotically far from finite systems, and can detect delocalization of the exact exchange hole and effective fractional occupations. We also present a parameter-free local hybrid functional that uses this similarity metric to locally mix exact and semilocal DFT exchange energy densities. The resulting functional gives better thermochemistry and reaction barrier heights than our original local hybrids [Jaramillo et al., J. Chem. Phys. 118, 1068 (2003)], while retaining moderate accuracy for symmetric radical cation dimers.

Use of the neighboring orbital model for analysis of electronic coupling in Class III intervalence compounds

Symmetrical charge-delocalized intervalence radical ions should not be described by the traditional two-state model that has been so successful for their localized counterparts. If they lack direct overlap between their charge-bearing units ( M), their diabatic orbitals have an equal energy pair of symmetrized M-centered combination orbitals that are symmetric ( S) or antisymmetric ( A) with respect to a symmetry element at the center of the molecule. The M combination orbitals will mix separately with bridge orbitals of the same symmetry. We call the simplest useful model for this situation the neighboring orbital model, which uses the S and A bridge orbitals of high overlap that lie closest in energy to the M orbital pair, resulting in two two-state models that have a common energy for one pair. This model is developed quantitatively, and examples having 1, 3, 5, and 7 electrons in the neighboring orbitals are illustrated.

Binding Energy Curves from Nonempirical Density Functionals. I. Covalent Bonds in Closed-Shell and Radical Molecules

Binding or potential energy curves have been calculated for the ground-state diatomics H(2)(+), He(2)(+), LiH(+), H(2), N(2), and C(2), for the transition state H(3), and for the triplet first excited state of H(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA. Good binding energy curves in agreement with coupled cluster or configuration interaction calculations are found from the PBE GGA and especially from the TPSS meta GGA. Expected exceptions are the symmetric radicals H(2)(+) and He(2)(+), where the functionals suffer from self-interaction error, and the exotically bonded C(2). Although the energy barrier for the reaction H(2) + H --> H + H(2) is better in PBE than in TPSS, the transition state H(3) is a more properly positioned and curved saddle point of the energy surface in TPSS. The triplet first excited state of H(2) obeys the Aufbau principle and thus is one of the exceptional excited states that are computable in principle from the ground-state functional. The PBE GGA and TPSS meta GGA are useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals that can further improve the binding energy curves.

Electron Paramagnetic Resonance Spectroscopy of gamma-Radiation-Induced Paramagnetic Centers in Titania-Bearing Sodium Silicate Glasses

The electron paramagnetic resonance (EPR) spectra of gamma-irradiated titania-bearing sodium silicate glasses were quantitatively analyzed by using the spectral decomposition of the EPR spectra and categorizing it into two types of randomly oriented paramagnetic centers: the orthorhombic (HC1) center and the axially symmetric (HC2) center. The orthorhombic HC1 center was assigned to the Q2 structural unit (the term Qi represents a SiO4 tetrahedron with i bridging oxygens), whereas the generation of the axially symmetric HC2 radical was expected in the case of the Q3 unit. The relative amounts x(HC1) and x(HC2) of HC1 and HC2 radicals were evaluated using the obtained data of the measured EPR spectra for five gamma-irradiated glasses with titania contents in the range of 0-10 mol%. The strong increase of the HC1 relative abundance, from a value of 26% (for titania-free glass) to a value of 89% (obtained for glass with 1 mol% of titania) confirmed the preferred sensitivity of Q2 units at low titania contents. Thus, titanium, which has a great absorption cross section, preferably entered the positions in the neighborhood of the Q2 units. The semi-empirical linear combination of atomic orbitals to form molecular orbitals by a self-consistent field (LCAO-MO-SCF) quasi-relativistic intermediate neglect of differential overlap (INDO) method was used to confirm this effect. For titania contents of >1 mol%, the above-mentioned effect was overwhelmed by the structural changes induced by titania in the silicate network, namely the diminishing of the Q2 content. Only the axially symmetric HC2 centers were present in the glasses with titania contents of >5 mol%.

A matrix isolation study of the Cs symmetric OCNO(X 2A″) radical

Here we report the first experimental detection of the C(s) symmetric nitroformyl radical, OCNO(X 2A'') in a nitrogen-carbon dioxide matrix at 10 K using a Fourier transform infrared spectrometer (FTIR). The nu1 vibrational frequency was observed at 2113 cm(-1). This assignment was confirmed by follow-up experiments using isotopically labeled reactant molecules (15N, 18O, 13C). To synthesize this radical, we irradiated solid nitrogen-carbon dioxide ice mixtures with energetic electrons at 10 K. Suprathermal nitrogen atoms in their electronic ground and/or first electronically excited state were generated via the radiation induced degradation of molecular nitrogen; these atoms could then react with carbon dioxide to eventually yield the nitroformyl radical. We also investigated the kinetics of the formation of the nitroformyl radical and support the arguments with computations on the doublet and quartet OCNO potential energy surfaces (PESs).

Suicide inactivation of dioldehydratase by glycolaldehyde and chloroacetaldehyde: an examination of the reaction mechanism.

High-level ab initio calculations have been used to study the mechanism for the inactivation of diol dehydratase (DDH) by glycolaldehyde or 2-chloroacetaldehyde. As in the case of the catalytic substrates of DDH, e.g., ethane-1,2-diol, the 5'-deoxyadenosyl radical (Ado*) is able to abstract a hydrogen atom from both substrate analogues in the initial step on the reaction pathway, as evidenced by comparable energy barriers. However, in subsequent step(s), each substrate analogue produces the highly stable glycolaldehyde radical. The barrier for hydrogen atom reabstraction by the glycolaldehyde radical is calculated to be too high ( approximately 110 kJ mol-1) to allow Ado* to be regenerated and recombine with the cob(II)alamin radical, the latter therefore remaining tightly bound to DDH. As a consequence, the catalytic pathway is disrupted, and DDH becomes an impotent enzyme. Interconversion of equivalent structures of the glycolaldehyde radical via the symmetrical cis-ethanesemidione radical is calculated to require 38 kJ mol-1. EPR indications of a symmetrical cis-ethanesemidione structure are likely to be the result of formation of an equilibrium mixture of glycolaldehyde radical structures, this equilibration being facilitated by partial deprotonation of the glycolaldehyde radical by the carboxylate of an amino acid residue within the active site of DDH.

Does the radical Me 3O [rad] exist in the gas phase? A joint experimental and theoretical study

A combination of experiment and theory indicate that when Me 3O + undergoes vertical Franck–Condon one-electron reduction, it does not produce a stable Me 3O species, but decomposes to give MeOMe and Me . Theoretical calculations at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d) level of theory indicate that the symmetrical radical Me 3O is not a stable species. However, there is a stable doublet neutral corresponding to a van der Waals complex MeOMe⋯Me, a species which requires only 4.5 kJ mol −1 of excess energy to cause decomposition to MeOMe and Me .

ON SYMMETRIC RADICALS OVER FULLY SEMIPRIMARY NOETHERIAN RINGS

Symmetric radicals over a fully semiprimary Noetherian ring R are characterized in terms of stability on bimodules and link closure of special classes of prime ideals. The notion of subdirect irreduciblity with respect to a torsion radical is introduced and is shown to be invariant under internal bonds between prime ideals. An analog of the Jacobson radical is produced which is properly larger than the Jacobson radical, yet satisfies the conclusion of Jacobson's conjecture for right fully semiprimary Noetherian rings.

Local hybrid functionals

We present a novel approach for constructing hybrid functionals by using a local mix of regular density functional theory (DFT) exchange and exact Hartree–Fock (HF) exchange. This local hybrid approach is computationally feasible for a wide range of molecules. In this work, the local mix of HF and DFT exchange is driven by the ratio of τW=|∇ρ|2/8ρ, the Weizsäcker kinetic energy density, with τ, the exact kinetic energy density. This particular choice of local mix yields 100% of exact exchange in one-electron regions. Dissociation energy curves, binding energies, and equilibrium geometries for two-center, three-electron symmetric radical cations can be modeled accurately using this scheme. We also report encouraging results for reaction energy barriers, and somewhat disappointing atomization energies for the small G2 set.

D 2–D 0 Fluorescence of pseudo-D 3h symmetric radical cations in solution and their `invisible' D 1 state as a route to non-radiative decay

Photophysical properties of three radical cations with a pseudo-D 3h electronic structure in acetonitrile were studied by laser flash photolysis and their tandem excitation to their D 2 state. The theoretical calculations of their electronic levels by the INDO/1 method have indicated that their D 1 and D 0 states deviate from the degenerate state and D 1←D 0 transition has excitation energies of 0.5–1.1 eV with oscillator strengths of nearly zero. The rate constants for their non-radiative decays from the D 2 state increased exponentially with the decrease of the calculated D 2–D 1 energy gap obeying the energy gap law.

Symmetry, Radical Ions, and Butadienes: Exploring the Limits of Density Functional Theory

Pure and hybrid density functional theory (DFT) methods are evaluated regarding their ability to correctly describe asymmetric transition structures for symmetric butadiene radical cations. The study covers unsubstituted butadiene radical cation as well as (2,3-X,X)-disubstituted butadiene radical cations, where X is -CH3, -OH, -F, or -SiH3. The DFT methods either converge toward an erroneous symmetric solution or describe the asymmetric transition structure qualitatively correctly. Whether or not the asymmetric transition structure is found depends on the amount of Hartree−Fock density exchange included in the method, as well as on the electronic characteristics of the substituents, as described by their σ+ values. The disparate behaviors encountered are rationalized by a two-state model. It is also shown that molecular symmetry does not automatically induce errors, as reported by earlier studies. Instead, electronic symmetry is introduced as a factor to observe when organic radical cations are studied c...