Single Elementary Step Research Articles

Kinetic description of site ensembles on catalytic surfaces

We demonstrate that the Langmuir-Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A2 The Hinshelwood assumption results in miscounting of site pairs (e.g., A*-A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir-Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method-with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir-Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step-including adsorbate diffusion-traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

Brønsted-Acid-Catalyzed Intramolecular Carbonyl-Olefin Reactions: Interrupted Metathesis vs Carbonyl-Ene Reaction.

Lewis acid catalysts have been shown to promote carbonyl-olefin metathesis through a critical four-membered-ring oxetane intermediate. Recently, Brønsted-acid catalysis of related substrates was similarly proposed to result in a transient oxetane, which fragments within a single elementary step via a postulated oxygen-atom transfer mechanism. Herein, careful quantum chemical investigations show that Brønsted acid (triflic acid, TfOH) instead invokes a mechanistic switch to a carbonyl-ene reaction, and oxygen-atom transfer is uncompetitive. TfOH's conjugate base is also found to rearrange H atoms and allow isomerization of the carbocations that appear after the carbonyl-ene reaction. The mechanism explains available experimental information, including the skipped diene species that appear transiently before product formation. The present study clarifies the mechanism for activation of intramolecular carbonyl-olefin substrates by Brønsted acids and provides important insights that will help develop this exciting class of catalysts.

Activated complex theory is a classical theory suitable for food science with appropriate use.

Activated complex theory (ACT), apart from Van 't Hoff equation, has long been applying as an alternative tool to connect the kinetics (reaction rate constant, k) and thermodynamics parameters (including standard enthalpy of activation, △H++; standard entropy of activation, △S++; standard Gibbs free energy of activation, △G++). The study mainly focuses on ACT application in food systems, especially oil and fruit juice processing. Considering there are several improper calculations or mistakes often found in papers published recently in 2014-2019, three considerations are presented when applying the ACT, including 1) Understand that the reaction should be a single chemical elementary step; 2) Ensure that the units used should be consistent; 3) Effectively analyze the kinetics and thermodynamic parameters by choosing proper temperatures. This study is expected to further improve the understanding and correct application of this well-known theory in future work.

Rate-Driving Force Relationships in the Multisite Proton-Coupled Electron Transfer Activation of Ketones.

Here we present a detailed kinetic study of the multisite proton-coupled electron transfer (MS-PCET) activations of aryl ketones using a variety of Brønsted acids and excited-state Ir(III)-based electron donors. A simple method is described for simultaneously extracting both the hydrogen-bonding equilibrium constants and the rate constants for the PCET event from deconvolution of the luminescence quenching data. These experiments confirm that these activations occur in a concerted fashion, wherein the proton and electron are transferred to the ketone substrate in a single elementary step. The rates constants for the PCET events were linearly correlated with their driving forces over a range of nearly 19 kcal/mol. However, the slope of the rate-driving force relationship deviated significantly from expectations based on Marcus theory. A rationalization for this observation is proposed based on the principle of non-perfect synchronization, wherein factors that serve to stabilize the product are only partially realized at the transition state. A discussion of the relevance of these findings to the applications of MS-PCET in organic synthesis is also presented.

On the Carbene‐Like Reactions of Imidazolium Acetate Ionic Liquids: Can Theory and Experiments Agree?

The N‐heterocyclic carbene organocatalytic reactivity of the 1‐ethyl‐3‐methylimidazolium acetate ionic liquid was investigated on the model reaction between this solvent and anisaldehyde. The formation of carbenes by a proton transfer from the cation to the anion was compared to a direct reaction mechanism, in which the proton transfer and the C–C bond formation between catalyst and substrate occurs in a single elementary step. Interestingly, the two reaction mechanisms show a much smaller difference in activation energies than those observed for analogous catalytic systems with neutral bases, showing that the mechanism might switch from one to the other at different temperatures or with different substrates. In this particular case, however, the direct reaction mechanism, avoiding free carbenes in the solution, is apparently more feasible. Based on the detailed analysis of this reaction path, the earlier contradictions between theory and experiments can be resolved, resulting in a consistent mechanistic picture for the related processes. Additionally, we show on the example of a platinum surface that introducing metal probes into the liquid may induce carbene‐like reactions, as the formation of a strong coordinative bond between the carbene and a platinum atom at the surface is highly exothermic, shifting the acid‐base equilibrium considerably.

Computational study of the 1,3-dipolar cycloaddition between methyl 2-trifluorobutynoate and substituted azides in terms of reactivity indices and activation parameters

The 1,3-dipolar cycloaddition of methyl 2-trifluorobutynoate with various azides has been studied in terms of several theoretical approaches at DFT/B3LYP/6-311++G(d,p) level of theory. The mechanism of regioselectivity of these reactions was investigated through the evaluation of the potential energy surface of the cycloaddition process calculations and density DFT-based reactivity indices. These approaches were successfully applied to prediction of preferable regio-isomers for various reactions of 1,3-dipolar cycloadditions. The reactions were followed by performing transition state optimization, calculation of Intrinsic Reaction Coordinate and activation energies. Analysis of the geometries of the corresponding transition structures shows that the cycloaddition takes place along a single elementary step (one-step mechanism) but asynchronous mechanism. The calculation of the activation energies and reaction energies show that the 1,5-regioisomer for substituted phenyl azides as dipoles and the 1,4-regioisomer for substituted benzyl azides as dipoles are thermodynamically in all the cycloadditions reactions. The solvent effect was also studied in the solvent tert-butyl alcohol using self-consistent reaction field model. The observed regioselectivity was explained by using developed DFT-based reactivity descriptors, such as Fukui and Parr functions. The results were compared with experimental data to find a good agreement.

Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)

AbstractThe transfer coefficientαis a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3rdedition of the IUPAC Green Book, the cathodic transfer coefficientαcis defined as –(RT/nF)(dlnkc/dE), wherekcis the electroreduction rate constant,Eis the applied potential, andR, T, andFhave their usual significance. This definition is equivalent to the other, -(RT/nF)(dln|jc|/dE), wherejcis the cathodic current density corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value. The anodic transfer coefficientαais defined similarly, by simply replacingjcwith the anodic current densityjaand the minus sign with the plus sign. It is shown that this definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake ofnelectrons from the electrode in the case ofαc, or their release to the electrode in the case ofαa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the absolute rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event are examined. Moreover, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncritical application of the above definitions ofαcandαahas led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity isdln|j|/dE, which can be made dimensionless upon multiplication byRT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this experimental quantity equal toαn, according to the above definition of the transfer coefficient, and in trying to estimatenfromαn, upon ascribing an arbitrary value toα, often close to 0.5. The resultingnvalue is then identified with the number of electrons involved in a hypothetical rate-determining step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coefficients by the quantitiesαc= –(RT/F)(dln|jc|/dE) andαa= (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.

Atomic-Scale Picture of the Ion Conduction Mechanism in a Tetrahedral Network of Lanthanum Barium Gallate

Combined experimental study of impedance spectroscopy, neutron powder diffraction, and quasielastic neutron scattering was performed to shed light onto the atomic-scale ion migration processes of protons and oxide ions in La0.8Ba1.2GaO3.9. This material consists of tetrahedral GaO4units, which are rather flexible, and rocking motion of these units promotes the ionic migration process. The oxide ion (vacancy) conduction takes place on channels along the c axis, involving a single elementary step, which occurs between adjacent tetrahedra (intertetrahedra jump). The proton conduction mechanism consists of intratetrahedron and intertetrahedra elementary processes. The intratetrahedron proton transport along the c axis is the rate-limiting process, with activation energy of 0.44 eV. The intertetrahedra proton transport has the activation energy of 0.068 eV.

Automated discovery of chemically reasonable elementary reaction steps

Due to the significant human effort and chemical intuition required to locate chemical reaction pathways with quantum chemical modeling, only a small subspace of possible reactions is usually investigated for any given system. Herein, a systematic approach is proposed for locating reaction paths that bypasses the required human effort and expands the reactive search space, all while maintaining low computational cost. To achieve this, a range of intermediates are generated that represent potential single elementary steps away from a starting structure. These structures are then screened to identify those that are thermodynamically accessible, and then feasible reaction paths to the remaining structures are located. This strategy for elementary reaction path finding is independent of atomistic model whenever bond breaking and forming are properly described. The approach is demonstrated to work well for upper main group elements, but this limitation can easily be surpassed. Further extension will allow discovery of multistep reaction mechanisms in a single computation. The method is highly parallel, allowing for effective use of modern large-scale computational clusters.

Mechanism of the irreversible inhibition of human cyclooxygenase-1 by aspirin as predicted by QM/MM calculations

Acetylsalicylic acid (aspirin) suppresses the generation of prostaglandin H2, which is the precursor of thromboxane A2. Aspirin acts as an acetylating agent in which its acetyl group is covalently attached to a serine residue (S530) in the active site of the cyclooxygenase-1 enzyme. The exact reaction mechanism has not been revealed by experimental methods.In this study the putative structure of human cyclooxygenase-1 was constructed from ovine cyclooxygenase-1 by homology modeling, and the acetylsalicylic acid was docked into the arachidonic acid binding cavity of the enzyme. To characterize the shape of the potential energy surface of the acetylating reaction and to determine the relative energies of the stationary points on the surface, a series of ONIOM-type quantum mechanical/molecular mechanical (QM/MM) calculations were carried out at different QM levels of theories applying electronic embedding approximations. The acetylsalicylic acid and the surrounding amino acids were included in these calculations. Frequency analyses were performed to prove the existence of first order saddle points (representing transition states) and local minima on the potential energy surface.It was found that all levels of theories predicted similar transition state geometries. The activation energy values, however, demonstrated significant dependence on the methods that were applied. All the applied “dependable” ab initio and DFT methods predicted that the breakage of the S530 OγHγ and formation of the OγC(acetylsalicylic acid carbonyl) bonds occur in a single elementary step.

A density-functional-theory study of atomic nitrogen abstraction from Si(100)-(2×1) by a gaseous O(P3) atom

We have employed density-functional theory (DFT) to investigate the abstraction of a nitrogen atom from the Si(100)-(2 x 1) surface by a gas-phase O(3P) atom for different initial bonding configurations of nitrogen at the surface. For the N-Si(100) structures investigated, nitrogen abstraction by an O(3P) atom is predicted to be exothermic by at least 1.9 eV. Abstraction in a single elementary step is found only for the interaction of an O(3P) atom with nitrogen bound in a coordinatively saturated configuration, and an energy barrier of 0.20 eV is computed for this reaction. For nitrogen bound in coordinatively unsaturated configurations, abstraction is predicted to occur by precursor-mediated pathways in which the initial O-surface collision results in the formation of a N-O bond and the concomitant release of between 2.7 and 4.8 eV of energy into the surface, depending on the initial N-Si(100) structure. This initial step produces different surface structures containing an adsorbed NO species, which can then undergo a series of elementary steps leading to NO desorption. Since the barriers for these steps are found to be less than 1 eV in all cases, a significant excess of energy is available from initial N-O bond formation that could activate NO desorption within no more than a few vibrational periods after the initial gas-surface collision. Nitrogen abstraction by such a pathway is essentially an Eley-Rideal process since NO desorption occurs rapidly after the initial gas-surface collision, without the reactants thermally accommodating with the surface. These computational results indicate that nitrogen abstraction by gaseous O(3P) atoms should be facile, even at low surface temperatures, if nitrogen is bound to the Si(100) surface in coordinatively unsaturated configurations.

Computational study on the formation of five-membered rings in pah through reaction with O 2

The oxidation reactions of phenyl and 1-naphthyl radicals through reaction with O 2 were investigated through a quantum chemical molecular orbital method as potential sources of PAH species containing 5-membered rings in hydrocarbon flames. The reaction between phenyl radical and O 2 was seen to produce phenoxy radical in a single elementary step. The same mechanism was followed in the reaction between 1-naphthyl radical and O 2 with formation of naphthoxy radical in a single step. In both phenyl and 1-naphthyl oxidation reactions, the variation of energy and atomic arrangement with the reaction coordinate was found to be similar and their rate coefficients, evaluated through transition state theory, to agree with each other. Thus, because the oxidation reaction of a species composed of one aromatic ring (phenyl radical) and that of a species composed of two aromatic rings (1-naphthyl radical) proceed through the same mechanism and have similar rate coefficients, the oxidation of species composed of an arbitrary number of aromatic rings can be supposed to proceed through that mechanism and have the same rate coefficient. The mechanism of the subsequent decomposition of phenoxy radical into cyclopentadienyl radical and CO agreed with the mechanism reported in the literature, and the decomposition of naphthoxy radical was found to be similar to that of phenoxy radical. In summary, the routes C 6 H 5+ O 2→ C 6 H 5 O+ O→ C 5 H 5+ CO+ O C 10 H 7+ O 2→ C 10 H 7 O+ O→ C 9 H 7+ CO+ O, where C 5H 5 and C 9H 7 are, respectively, cyclopentadienyl radical and indenyl radical, proceed through the same mechanism. From these results it is suggested that the formation of species containing a peripheral 5-membered ring (aryl-5) through partial oxidation of a peripheral 6-membered ring of arbitrary aryl radicals (aryl-6), described generally as aryl-6+ O 2→ aryl-6- O+ O→ aryl-5+ CO+ O, can be thought to proceed through the same mechanism. The rate coefficients of the first step are the same for any aryl-6 species, but they were found to be much smaller than values reported in the literature for phenyl as aryl-6 species.

Ab Initio Study on the Dynamics of the Oxidation Reaction of Acetylene.

The dynamics of the oxidation reaction of an acetylene molecule with an oxygen atom was investigated through an ab initio molecular orbital method. The three reactions (1) C2H2+O→HCCO+H, (2) HCCO+CH2+CO and (3)C2H2+O→CH2+CO, reported in reaction schemes, were confirmed as being the main elementary steps related to the acetylene oxidation but were found to be not single elementary steps, with each one forming intermediary spacies before the proposed products. These intermediaries are expected to decompose always and much faster than they form, so that those three reactions can be treated as elementary steps without problem. Under ideal conditions, only reaction (3) can be expected to proceed, but vibrations of the atoms in a structure formed during the process can cause its decomposition into HCCO +H, and later the so formed HCCO can meet another H atom and react to CH2+CO. Reactions (1) and (2) are then found to be, respectively, an early and a late step of reaction (3), but each of the three events can occur, depending on how is the collision between the O atom and the vibrating C2H2 molecule. The present results are compared with experimental data reported in the literature, and a qualitative agreement with the data of Miller and Bowman can be seen for reactions (1) and (3), and with the data of Warnatz for reaction (2).

Long Time-Step Particle Pushing in Drift Approximation without Orbit Averaging

An alternative way to utilize the well known drift approximation for particle motion in electromagnetic fields is proposed. Contrary to the traditional approach, in which the motion of the guiding center of a particle is considered, in the suggested algorithm the coordinates and velocities of the particle itself are evaluated. This approach is found to give accurate results provided that the characteristic scales of the change of fields both in time and in space are large compared to the corresponding micro-scales of the particle motion in these fields (e.g., wavelength of radio wave is large compared to the particle gyroradius in the magnetic field of that wave). Under this condition an approximate analytical solution for the Newton–Lorentz Law, accurate within many characteristic micro-timescales of the particle motion, is derived. This approximation is exploited to advance a particle substantially within a single elementary step of the algorithm, which can extend for as long as ∼mi/me≃ 2000 times the traditional one for certain astrophysical plasmas. Utilization of this approach can give a boost of productivity for the existing and new PIC codes, in which substantial computational time is spent solving the Newton–Lorentz Law for superparticles. In the present work the approach is implemented for the ultrarelativistic case, with the magnetic field prevailing over, although being not necessarily much higher than the electric field. The relevant computer code is developed and used to simulate the motion of a particle in an electromagnetic field with a complicated profile. The results exhibit a good agreement with those, obtained by direct integration of the Newton–Lorentz law, using a conventional ODE solver.

Computer modeling of formation of soot precursors in the oxidation of methane

AbstractA previously developed method was extended for computer modeling of chemical processes involving large number of species. Improvements introduced for the combinatorial generation of stoichiometrically possible reaction steps include hierarchical structuring of the chemical system under study, replacing invariant atomic groups by symbols, as well as the combined application of two complexity constraints for the reduction of the set of reactions.Modeling revealed that while in the oxidation of methane the formation of ethynyl benzene (phenylacetylene), 1‐naphtyl radical, diethynyl benzene and ethynyl naphtalene by acetylene addition to the precursor radicals can be accepted to proceed in a single elementary step, this is not valid for anthracyl radical. Formation of acenaphtylene, 12‐biphenyl radical, 3‐phenantryl radical, phenantrene, and pyrene needs further investigation in this respect. Furthermore, formation of benzene, phenyl, and biphenyl by recombination of propargyl or substituted propargyl radicals in a single elementary reaction was not supported by modeling. Results suggest the possibility of not yet identified intermediates participating in these processes.

Computational studies of the potential energy surface for O(3P)+H2S: Characterization of transition states and the enthalpy of formation of HSO and HOS

Structures and vibrational frequencies for minima and 11 transition states on the O(3P)+H2S potential energy surface have been characterized at the MP2=FULL/6-31G(d) level. GAUSSIAN-2 theory was employed to calculate ΔHf,298 for HSO and HOS of −19.9 and −5.5 kJ mol−1, respectively. The kinetics of HSO=HOS isomerization are analyzed by Rice–Ramsperger–Kassel–Marcus theory. Transition state theory analysis for O+H2S suggests OH+HS is the dominant product channel, with a rate constant given by 1.24×10−16 (T/K)1.746 exp(−1457 K/T) cm3 molecule−1 s−1. Kinetic isotope effects and the branching ratio for H+HSO production are also analyzed. The other possible products H2+SO and H2O+S do not appear to be formed in single elementary steps, but low-barrier pathways to these species via secondary reactions are identified. No bound adducts of O+H2S were found, but results for weakly bound triplet HOSH are presented. The likely kinetics for the reactions OH+SH→S(3P)+H2O, OH+SH→cis and trans 3HOSH, cis 3HOSH→HOS+H, and HSO and HOS+H→H2+3SO are discussed.

Activity patterns in some oxidation and reduction reactions on oxides

The literature concerning the activity of the first long period oxides in the oxidation and reduction (oxygen removal) reactions is briefly reviewed and analysed. Essential in the discussion is that in the oxygen 16-oxygen 18 exchange the prevailing mechanism involves dissociation of O 2 by its dissolution in the oxide. Several reactions show the same activity pattern as the just mentioned oxygen exchange reactions and, it is speculated, therefore that a similar mechanism prevails. Another mechanism is the one upon which only a single oxygen atom is transfered between the solid and the gas phase, in one single elementary step. In the same group with such reaction are the reactions in which there is no transfer of oxygen between the phases whatsoever.

Sensitivity analysis based reduction of complex reaction mechanisms in turbulent non-premixed combustion

A turbulent combustion model without simplifying assumptions about the chemical reactions is evaluated by means of a sensitivity analysis. The turbulence model is conventional and based on gradient transport assumptions and an eddy viscosity concept. In addition to the equations of the turbulent flow field the species conservation equations are solved. The chemical reactions are described by a detailed, elementary kinetics reaction mechanism. The source terms in the species conservation equations are treated by means of a presumed-shape pfd-closure relaxing the assumption of statistically independent variables. The sensitivity analysis for the turbulent combustion model is performed in terms of the local first order sensitivity coefficients. The turbulent combustion model and sensitivity analysis are adopted to a turbulent hydrogen air diffusion flame in a simple flow geometry. Temperature, major chemical species and OH radical concentrations are reasonable well predicted. The sensitivity analysis shows the relative importance of single elementary steps of the reaction mechanism compared with turbulent transport. Only few rate coefficients of the entire chemical mechanism influence the main response of the turbulent combustion model, viz. temperature and mass fractions of the major chemical components. From this simplifications of the closure for the mean chemical reaction rates are derived. Furthermore, for the turbulent hydrogen air flame under consideration sensitivity analysis shows control of turbulent transport throughout the largest part of the flame. Therefore, the substantial properties of the flame, viz. temperatures, mass fractions of H2, O2 and H2O are predicted reasonably by any reduced chemical model providing sufficiently large conversion rates of the fuel.

Kinetics and Thermodynamics of the Reaction of Molecular Oxygen with YBa3Cu3Ox

The sensitivity of the properties of RBa2Cu3Ox materials to oxygen stoichiometry has been widely reported.1 This is a serious problem in the synthesis and processing of these compounds since many operations must be carried out at temperatures and oxygen partial pressures where bulk oxygen is in dynamic equilibrium with gas phase molecular oxygen. Therefore it is crucial for the rational design of processing strategies to understand how the equilibria and kinetics of oxygen stoichiometry in this material vary with temperature and pressure. In this paper we report work on two problems in this area: first, we describe the development of accurate methods for the determination of oxygen stoichiometry in experimental samples, and second, the use of these methods to investigate and analyze equilibrium oxygen contents over a range of temperatures and oxygen partial pressures. Equilibrium oxygen contents from 350 – 900°C at oxygen pressures of. 05, .21, and 1.00 atmospheres have been determined. The pressure dependence has also been examined over a wider range at selected temperatures. Most of this data can be adequately fit to a model which assumes that a single chemical equilibrium constant can describe the entire stoichiometry range from x=6 to 7. However, kinetic data suggests that the detailed mechanism must be more complex, and that the overall thermochemistry may reflect contributions from a number of interacting processes rather than any single elementary step. In concurrent work we have used these methods to develop sample series that can be used to examine magnetic properties2 and far IR spectra3 of these materials as a systematic function of oxygen content.

The chemical preparation and electron spin resonance spectra of specific trapped hydrocarbon radicals

The restriction of a free-radical reaction to a single elementary step has been achieved by means of a rotating cryostat. Beams of vapour of halohydrocarbon and sodium are condensed upon opposite sides of the exterior surface of a rapidly rotating stainless-steel drum which contains liquid nitrogen. Each reactant deposits on a freshly formed surface of the other. The halohydrocarbon layer is about nine monolayers thick, but the sodium layer is so thin that it is discontinuous, there being only one atom of sodium to approximately twenty-five surface molecules of the halohydrocarbon. Radicals formed by the reaction RX + Na.→ R .+ Na X are trapped on this surface, surrounded by unreactive neighbours. As deposition continues they are covered over, and a structure like a Swiss roll is built up in which radicals are sandwiched between layers of excess halohydrocarbon. By suitable choice of halohydrocarbon a specific radical may be prepared, and the method has proved to be a general one for the chemical preparation of hydrocarbon radicals. Electron spin resonance spectra of the following radicals have been recorded: propyl, butyl, heptyl, phenylethyl, s-butyl, isobutyl, t-butyl, hept-4-yl, cyclopentyl, cyclohexyl, allyl, phenyl and benzyl. The spectra of the alkyl radicals are discussed in relation to molecular configuration.