The geometry of 21 valence electron radicals

A semi-empirical LCAO-MO-SCAF theory has been applied to Cl₃ and CIF₂, the only 21 valence electron triatomic radicals known, and equilibrium geometries have been calculated. The results of these calculations are in reasonable agreement with existing experimental data. The predictions of several well known quantitative models for geometry correlation are also discussed.     

Computational studies on acyclic amidyl radicals: Π and Σ states and conformations

Restricted open and unrestricted Becke3LYP/6-31+G(d) calculations on Π and Σ states as well as equilibrium geometries of the formamidyl radical (1) and four of its dialkyl substituted derivatives 2–5 have been carried out. While all radicals studied are significantly twisted about the RN–C(O) bond and show a Π-type total spin density, the calculations confirm the special status of N-tert-butyl acetamidyl (4) that was found with EPR spectroscopy. Each of the torsional double-minimum potentials of N-methyl and N-isopropyl radicals 2, 3, and 5 shows a low barrier to interconversion for two equivalent conformers whereas 4 is situated in a steeper well with a larger twist angle which explains reported EPR ¹³C hyperfine splittings.     

Theoretical calculations of hyperfine coupling constants for muoniated butyl radicals

The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al. J. Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C-Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the β-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C-Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near 0 K, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.     

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.     

Jet spectroscopy of arylmethyl radicals in the visible region: assignment of low-frequency vibrational modes in diphenylmethyl and chlorodiphenylmethyl radicals

The D(1)-D(0) transitions of diphenylmethyl (DPM) and chlorodiphenylmethyl (CDPM) radicals were studied by laser induced fluorescence (LIF) spectroscopy in a supersonic jet. Laser induced fluorescence excitation and dispersed fluorescence (DF) spectra were obtained for DPM and CDPM radicals produced by ArF excimer laser (193 nm) photolyses of their chlorides. With the aid of the density functional theory (DFT) calculation, vibronic bands are assigned by comparing the observed LIF excitation spectra of the jet-cooled radicals with the single vibronic level DF spectra. Low-frequency vibrations of 55 and 53 cm(-1) in the ground and excited states, respectively, are assigned to the symmetric phenyl torsional mode of the DPM radical. The geometries of DPM in the ground and excited states are discussed with regards to observed spectra and DFT calculations. Similarly for the CDPM radical, symmetric phenyl torsional and Ph-C-Ph bending modes are assigned and the halogen-substitution effect in equilibrium geometry is discussed.     

Beyond vinyl: electronic structure of unsaturated propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl hydrocarbon radicals

Vertical excitation energies and oscillator strengths for several valence and Rydberg electronic states of vinyl, propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl radicals are calculated using the equation-of-motion coupled cluster methods with single and double substitutions (EOM-CCSD). The ground and the lowest excited state (n <-- pi) equilibrium geometries are calculated using the CCSD(T) and EOM-SF-CCSD methods, respectively, and adiabatic excitation energies for the n <-- pi state are reported. Systematic changes in the geometries, excitation energies, and Rydberg state quantum defects within this group of radicals are discussed.     

Substituent Effects in the Absorption Spectra of Phenol Radical Species: Origin of the Redshift Caused by 3,5‐Dimethoxyl Substitution

The ground‐state equilibrium geometries, electronic structures and vertical excitation energies of methyl‐ and methoxyl‐substituted phenol radical cations and phenoxyl radicals have been investigated using time‐dependent density‐functional theory (namely TD‐B3LYP) and complete‐active‐space second‐order perturbation theory (CASPT2). The “anomalous” large redshifts of the absorption maxima of the phenol radical species observed in the ultraviolet–visible spectral region upon di‐meta‐methoxyl substitution are reproduced by the calculations. Furthermore, these “anomalous” shifts which were unexplained to date can be rationalized on the basis of a qualitative molecular orbital perturbation analysis.     

Ion chemistry of 1H-1,2,3-triazole. 2. Photoelectron spectrum of the iminodiazomethyl anion and collision induced dissociation of the 1,2,3-triazolide ion

The 363.8 nm photoelectron spectrum of the iminodiazomethyl anion has been measured. The anion is synthesized through the reaction of the hydroxide ion (HO-) with 1 H-1,2,3-triazole in helium buffer gas in a flowing afterglow ion source. The observed spectrum exhibits well-resolved vibronic structure of the iminodiazomethyl radical. Electronic structure calculations have been performed at the B3LYP/6-311++G(d,p) level of theory to study the molecular structure of the ion. Equilibrium geometries of four possible conformers of the iminodiazomethyl anion have been obtained from the calculations. Spectral simulations have been performed on the basis of the calculated geometries and normal modes of these conformationally isomeric ions and the corresponding radicals. The spectral analysis suggests that the ions of two conformations are primarily formed in the aforementioned reaction. The relative abundance of the two conformers substantially deviates from the thermal equilibrium populations, and it reflects the potential energy surfaces relevant to conformational isomerization processes. The electron affinities of the ( ZE)- and ( EE)-iminodiazomethyl radicals have been determined to be 2.484 +/- 0.007 and 2.460 +/- 0.007 eV, respectively. The energetics of the iminodiazomethyl anion is compared with that of the most stable structural isomer, the 1,2,3-triazolide ion. Collision-induced dissociation of the 1,2,3-triazolide ion has also been studied in flowing afterglow-selected ion flow tube experiments. Facile fragmentation generating a product ion of m/ z 40 has been observed. DFT calculations suggest that fragmentation of the 1,2,3-triazolide ion to the cyanomethyl anion and N2 is exothermic. The stability of the ion is discussed in comparison with other azolide ions with different numbers of N atoms in the five-membered ring.     

Structure and magnetic properties of some boron containing radicals: A molecular orbital study

Equilibrium geometries, hyperfine coupling constants andg-tensors have been calculated for seven boron containing free radicals using the INDO method.Ab initio calculations are reported for BO and BS.     

The structure and hyperfine splittings of simple phosphoranyl radicals

The ab initio UHF method has been employed to calculate equilibrium geometries and isotopic hyperfine coupling constants for the radicals PH₂, PF₂, PH₄ and PF₄.     

Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.; et al. Nature 1979, 278, 332; Rayez, J. C.; et al., J. Chem. Phys. 1981, 75, 5393] indicated these molecules would have a shallow minimum and adopt symmetrical geometries that accord with the valence shell electron pair repulsion (VSEPR) rules for geometries defined by electron pairs surrounding a central point of attraction. These earlier calculations were all based upon Hartree-Fock (HF) calculations with a fairly small basis of atomic functions, except for the H3(-) ion for which configuration interaction (CI) calculations were carried out. A related paper [Hirao, K.; et al., Chem. Phys. 1983, 80, 237] carried out similar calculations on the same clusters, finding geometries similar to our earlier calculations. However, although that paper argued that the stabilization energy of negative ion clusters H(n)(-) is small, vibration frequencies for the whole set of clusters was not reported, and so a definitive assertion of a true equilibrium was not present. In this paper we recalculate the energetics of the ion induced dipole clusters using density function theory (DFT) B3LYP method calculations in a basis of functions (6-311++G(d,p)). By calculating the vibration frequencies of the VSEPR geometries, we prove that in general they are not true minima because not all the resulting frequencies correspond to real values. By searching the energy surface of the B3LYP calculations, we find the true minimum geometries, which are surprising configurations and are perhaps counterintuitive. We calculate the total energy and binding energy of the new geometries. We also calculate the bond paths associated with the quantum theory of atoms in molecules (QTAIM). The B3LYP/6-311++G(d,p) results, for each molecule, deliver bond paths that radiate between each polarized H2 molecule and the polarizing H(-) ion.     

Low-energy electronic states of methylene

Ab initio SCF calculations using a slightly extended basis set have been carried out on the low-energy electronic states of methylene. The equilibrium geometries and energies of these states are determined, and potential curves for each state are obtained.     

Are 1,5-disubstituted semibullvalenes that have C2v equilibrium geometries necessarily bishomoaromatic?

Unrestricted density functional theory (UB3LYP), CASSCF, and CASPT2 calculations have been employed to compute the relative energies of the C(s) and C(2v) geometries of several 1,5-disubstituted semibullvalenes. Substitution at these positions with R = F, -CH(2)-, or -O- affords semibullvalenes that are predicted to have C(2v) equilibrium geometries. Calculated singlet-triplet energy splittings and the energies of isodesmic reactions are used to assess the amount of bishomoaromatic character at these geometries. The results of these calculations show that employing strain to destabilize the C(s) geometries of semibullvalenes can lead to a significant decrease in the amount of bishomoaromatic stabilization of the C(2v) geometries, due to reduced through-space interaction between the two allyl groups. However, the C(2v) equilibrium geometries of the 1,5-disubstituted semibullvalenes with R = F and -RR- = -O- do benefit from stabilizing through-bond interactions between the two allyl groups. These interactions involve mixing of the bisallyl HOMO with the low-lying C-F or C-O sigma orbital combinations of the same symmetry. In contrast, for -RR- = -CH(2)-, through-bond interactions destabilize the bisallyl HOMO and are predicted to make the ground state of this semibullvalene a triplet.     

Theoretical description of the 2A′' and 2A′ states of the peroxyformyl radical

The equilibrium geometries and spin density distributions for some phosphoranyl radicals and the radical anion PH₃O^? were calculated by the UHF CNDO/2 method. Barriers to permutational isomerization in PF₄ and PH₃OH were estimated.     

Author index

The ring puckering potential energy function relative to cyclopentene is calculated using the standard CNDO/2 method optimizing all geometrical parameters. Ab initio calculations are performed upon selected geometries and the equilibrium conformations are discussed.     

Electrochemical and microsomal production of free radicals from 1,2,5-oxadiazole N-oxide as potential antiprotozoal drugs

The electron spin resonance (ESR) spectra of free radicals obtained by electrolytic or microsomal reduction of several potential antiprotozoal 1,2,5-oxadiazoles were characterized and analyzed. Ab initio molecular orbital calculations were performed to obtain the optimized geometries and the theoretical hyperfine constant was carried out using ZINDO semiempirical methodology. Density functional theory was used to rationalize the reduction potentials of these compounds.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

DFT‐EPR study of radiation‐induced radicals in α‐D‐glucose

The structures of two radiation‐induced radicals in solid‐state α‐D ‐glucose have been identified by means of single‐molecule density function theory (DFT) calculations. Using the original crystalline structure as input, several radical models were created and their geometries optimized. Subsequently, electron paramagnetic resonance (EPR) parameters were calculated. During these calculations, the global orientation of the radical structure was kept fixed with respect to the crystal axes reference frame. This was essential to allow for an easy analysis of the hyperfine tensor principal directions, besides the isotropic and anisotropic coupling constants. By comparing these calculated EPR parameters with their experimentally determined counterparts, a plausible identification of two carbon‐centered glucose radicals was possible. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Theoretical studies of alkyl radicals in the NaY and HY zeolites

Interplay of quantum mechanical calculations and experimental data on hyperfine coupling constants of ethyl radical in zeolites at several temperatures was engaged to study the geometries and binding energies and to predict the temperature dependence of hyperfine splitting of a series of alkyl radicals in zeolites for the first time. The main focus is on the hyperfine interaction of alkyl radicals in the NaY and HY zeolites. The hyperfine splitting for neutral free radicals and free radical cations is predicted for different zeolite environments. This information can be used to establish the nature of the muoniated alkyl radicals in the NaY and HY zeolites via muSR experiments. The muon hyperfine coupling constants of the ethane radical cation in these zeolites are very large with relatively little dependence on temperature. It was found that the intramolecular dynamics of alkyl free radicals are only weakly affected by their strong binding to zeolites. In contrast, the substrate binding has a significant effect on their intermolecular dynamics.     

Electron spin resonance studies and theoretical quantum calculations of free radicals generated from anthracenetrione by electrochemical and microsomal reduction

The ESR spectra of radicals obtained by electrolytic reduction of 4,4-dimethylanthracene-1,9,10 (4H)-trione (1) and the regioisomeric quinones 8-acetyloxymethyl-4,4,5-trimethyl- (2), and 5-acetyloxy-methyl-4,4,8-trimethyl-(4H)-1,9,10-anthracenetrione (3) were measured in DMSO and analyzed by quantum chemical calculations. The electrochemistry of these compounds was characterized using cyclic voltammetry, in DMSO and DMF solvents and compared with nifurtimox. The quinones were also reduced by microsomal NADPH-cytochrome P-450 reductase and the corresponding radicals species were also detected by ESR spectroscopy. AMI, INDO, and ADF calculations were performed to obtain the optimized geometries, theoretical hyperfine constants, and spin distributions, respectively. Density functional theory was used to rationalize the reduction potential of these compounds.