Free radical inactivation of trypsin

Reactivities of free radical oxidants, ^.OH, Br^-·₂ and Cl₃COO^. and a reductant, CO^-·₂, with trypsin and reactive protein components were determined by pulse radiolysis of aqueous solutions at pH 7, 20°C. Highly reactive free radicals, ^.OH, Br^-·₂ and CO^-·₂, react with trypsin at diffusion controlled rates, k(^.OH + trypsin) = 8.2 × 10¹⁰ M^-1 s^-1, k(Br^-·₂ + trypsin) = 2.55 × 10⁹ M^-1 s^-1 and k(CO^-·₂ + trypsin) = 2.6 × 10⁹ M^-1 s^-1. Moderately reactive trichloroperoxy radical, k(Cl₃COO^. + trypsin) = 3 × 10⁸ M^-1 s^-1, preferentially oxidizes histidine residues. The efficiency of inactivation of trypsin by free radicals is inversely proportional to their reactivity. The yields of inactivation of trypsin by ^.OH, Br^-·₂ and CO^-·₂ are low, G(inactivation) = 0.6-0.8, which corresponds to ∾ 10% of the initially produced radicals. In contrast, Cl₃COO^. inactivates trypsin with ∾ 50% efficiency, i.e. G(inactivation) = 3.2.     

The antioxidant reactivity of sorbitylfurfural towards potential harmful radicals,studied by radiation chemistry techniques

Ionising radiations, employed in a broad range of dose-rate, together with a complex non-linear computation of reaction mechanisms, allow the determination of boundary values of rate constants concerning sorbitylfurfural (SF) reactivity towards a wide series of oxidant and/or virtually harmful radicals. SF reacts with some radicals (H, SO₄^-˙, CO₃^-˙, Br₂^-˙, CH₃˙), produced with both pulse and stationary radiolysis in neutral aqueous solution, having electrophilic and/or oxidative behaviour. The rate constants range from diffusional (k = (7-9) × 10⁹ M^-1 s^-1) to relatively low values (k = 2 × 10⁵ M^-1 s^-1). The possibility to observe these reactions, by means of radiolytical techniques, is heavily influenced by dose-rate. A relation between the radical E⁰_NHE and their reactivity with SF is hinted.     

Kinetics of one-electron oxidation by the ClO radical

Pulse radiolysis studies were carried out to determine the rate constants for reactions of ClO radicals in aqueous solution. These radicals were produced by the reaction of OH with hypochlorite ions in N₂O saturated solutions. The rate constants for their reactions with several compounds were determined by following the build up of the product radical absorption and in several cases by competition kinetics. ClO was found to be a powerful oxidant which reacts very rapidly with phenoxide ions to form phenoxyl radicals and with dimethoxybenzenes to form the cation radicals (k = 7 × 10⁸ −2 × 10⁹ M^-1 s^-1). ClO also oxidizes ClO^-₂ and N^-₃ ions rapidly (9.4 × 10⁸ and 2.5 × 10⁸ M^-1 s^-1, respectively), but its reactions with formate and benzoate ions were too slow to measure. ClO does not oxidize carbonate but the CO^-₃ radical reacts with ClO^- slowly (k = 5.1 × 10⁵ M^-1 s^-1).     

Absolute rate constants for the reactions between amino and alkyl radicals at 298 K

The absolute rate constants for the reactions of NH₂ radicals with ethyl, isopropyl, and t-butyl radicals have been measured at 298 K, using a flash photolysis–laser resonance absorption method. Radicals were generated by flashing ammonia in the presence of an olefin. A new measurement of the NH₂ extinction coefficient and oscillator strength at 597.73 nm was performed. The decay curves were simulated by adjusting the rate constants of both the reaction of NH₂ with the alkyl radical and the mutual interactions of alkyl radicals. The results are k(NH₂ + alkyl) = 2.5 (±0.5), 2.0 (±0.4), and 2.5 (±0.5) × 10¹⁰ M^?1·s^?1 for ethyl, isopropyl, and t-butyl radicals, respectively. The best simulations were obtained when taking k(alkyl + alkyl) = 1.2, 0.6, and 0.65 × 10¹⁰M^?1·s^?1 for ethyl, isopropyl, and t-butyl radicals, respectively, in good agreement with literature values.     

Bimolecular self-reactions of ketyl radicals of acetophenone and diphenylaminyl radicals

The rate constants of self-reactions of ketyl radicals of acetophenone in n-heptane [2k = (3.2 ± 0.5) × 10⁹ M^?1 s^?1] and diphenylaminyl radicals in toluene [2k = (3.3 ± 0.5) × 10⁷ M^?1 s^?1] have been determined at 298 K using the flash photolysis technique. The rate constant of ketyl radicals is equal to the calculated diffusion constant and, therefore, this reaction is diffusion-controlled. The aminyl radical recombination rate is independent of the viscosity of the toluene/vaseline oil binary mixture (0.55 ? η ? 12 cP) and this reaction is activation-controlled. Reactivity anisotropy averaging due to the cage effect has been considered for ketyl and some other radicals. On the basis of the analysis it has been proposed that ketyl recombination involves formation of not only pinacol, but also iso-pinacols.     

The fluorescence quenching of 1,4-bis[2-(5-phenyl-oxazolyl)]-benzene by bromomethanes

The interaction between the ground and excited states of 1,4-bis[2-(5-phenyloxazolyl)]-benzene and bromomethanes such as CBr₄, CHBr₃ and CH₂Br₂ were investigated in benzene. Distinct complex formation was not observed either in the ground state or in the excited states. The excited singlet and triplet states are deactivated by these bromomethanes. The triplet yield is increased on the addition of CHBr₃ or CH₂Br₂, whereas it is decreased on the addition of CBr₄. The fluorescence quenching rate constants k_q at 23 °C were determined to be 1.6 × 10¹⁰ M⁻¹ s⁻¹, 3.6 × 10⁸M⁻¹s⁻¹ and 2.4 × 10⁷M⁻¹s⁻¹ for CBr₄, CHBr₃ and CH₂Br₂ respectively. The rate constants k_ST′ of the enhanced intersystem crossing associated with the fluorescence quenching were evaluated from emission—absorption flash photolysis experiments as 3.0 × 10⁸ M⁻¹s⁻¹, 1.9 × 10⁸ M⁻¹s⁻¹ and 5.1 × 10⁷ M⁻¹s⁻¹ for CBr₄, CHBr₃ and CH₂Br₂ respectively. k_ST′ increases with increasing number of bromine atoms contained in the quencher, so that the enhanced intersystem crossing is due to the external heavy-atom effect of the quencher. The apparent triplet yield for the quenching system depends not only on k_ST′ but also on the rates of the other non-radiative processes. This is the reason why the apparent triplet yield does not necessarily increase on fluorescence quenching by bromomethanes.     

Hydroxyl radical reactions with halogenated ethanols in aqueous solution: Kinetics and thermochemistry

Laser flash photolysis combined with competition kinetics with SCN^? as the reference substance has been used to determine the rate constants of OH radicals with three fluorinated and three chlorinated ethanols in water as a function of temperature. The following Arrhenius expressions have been obtained for the reactions of OH radicals with (1) 2‐fluoroethanol, k₁(T) = (5.7 ± 0.8) × 10¹¹ exp((?2047 ± 1202)/T) M^?1 s^?1, (2) 2,2‐difluoroethanol, k₂(T) = (4.5 ± 0.5) × 10⁹ exp((?855 ± 796)/T) M^?1 s^?1, (3) 2,2,2‐trifluoroethanol, k₃(T) = (2.0 ± 0.1) × 10¹¹ exp((?2400 ± 790)/T) M^?1 s^?1, (4) 2‐chloroethanol, k₄(T) = (3.0 ± 0.2) × 10¹⁰ exp((?1067 ± 440)/T) M^?1 s^?1, (5) 2, 2‐dichloroethanol, k₅(T) = (2.1 ± 0.2) × 10¹⁰ exp((?1179 ± 517)/T) M^?1 s^?1, and (6) 2,2,2‐trichloroethanol, k₆(T) = (1.6 ± 0.1) × 10¹⁰ exp((?1237 ± 550)/T) M^?1 s^?1. All experiments were carried out at temperatures between 288 and 328 K and at pH = 5.5–6.5. This set of compounds has been chosen for a detailed study because of their possible environmental impact as alternatives to chlorofluorocarbon and hydrogen‐containing chlorofluorocarbon compounds in the case of the fluorinated alcohols and due to the demonstrated toxicity when chlorinated alcohols are considered. The observed rate constants and derived activation energies of the reactions are correlated with the corresponding bond dissociation energy (BDE) and ionization potential (IP), where the BDEs and IPs of the chlorinated ethanols have been calculated using quantum mechanical calculations. The errors stated in this study are statistical errors for a confidence interval of 95%. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 174–188, 2008     

Flash photolysis of SiBr4: the UV spectrum of SiBr2

In the flash photolysis of SiBr₄ both the absorption and the emission spectra corresponding to the B̃²Σ−X̃²Π transition of SiBr have been observed. A broad, structureless absorption band has also been detected in the 340–400 nm region which could be assigned to the hitherto unreported à ¹B₁−x̃ ¹A₁ transition of SiBr₂. The decay of both absorption spectra followed first-order kinetics yielding the pseudo-first-order rate constants: k(SiBr)=2.6 × 10⁴s⁻¹ and k(SiBr₂) = 8.9 × 10³⁻¹. Assuming that the principal reactions consuming these intermediates are SiBr+SiBr₄→Si₂Br₅ and SiBr₂+SiBr₄→ Si₂Br₆, the second-order rate constants have the values k(SiBr)= 9.7×10⁹ M⁻¹s⁻¹ and k(SiBr₂)= 3.3×10⁸M⁻¹s⁻¹.     

Fluorescence quenching in molecular recognition by hydrogen bonding

Steady-state fluorescence and single photon timing have been used to study the effect of the presence of hydrogen bonding on the intermolecular quenching of pyrene covalently linked to a guanine-like receptor I by an aliphatic amine (N,N-dimethylpropylamine) covalently linked to cytosine derivative II. By comparing the fluorescence quenching of I by II with that of 10methylpyrene (1-MP) by triethylamine (TEA), as a model system in which no hydrogen bonding can occur, one could possibly analyze the effect of the hydrogen bonding between receptor and substrate as a quenching as it leads to a higher local concentration of donor and acceptor. While the quenching of I by II was observed with an apparent rate constant k_q of (1.78 ± 0.10) × 10⁹ M⁻¹ s⁻¹ and (8.72 ± 0.42) × 10⁸ M⁻¹ s⁻¹ in toluene and acetonitrile, respectively, no quenching could be observed in methanol. Upon excitation of 1-MP, no quenching by II could be detected in the same concentration range as used in the quenching of I. Quenching of I and of 1-MP by TEA (⩾ 10⁻² M) in toluene leads to exciplex formation with maxima centred at 540 and 514 nm, respectively. The rate constants of exciplex formation and dissociation of I with TEA were analyzed using a global compartmental analysis. The following values were obtained for the rate constants: k₀₁ = (9.70 ± 0.01) × 10⁶ s⁻¹, k₂₁ = (1.12 ± 0.003) × 10⁹ M⁻¹ s⁻¹, k₀₂ = (5.24 ± 0.01) × 10⁷ s⁻¹ and k₁₂ = (7.74 ± 0.08) × 10⁶ s⁻¹. Quenching of I by TEA in the presence of III, a hydrogen-bonding system without an alkyl amine substituent, leads to exciplex formation centred at 538 nm. The rate constant values for the exciplex formation and dissociation of I with TEA in the presence of III were: k₀₁ = (9.32 ± 0.08) × 10⁶ s⁻¹, k₂₁ = (9.32 ± 0.003) × 10⁸ M⁻¹ s⁻¹, k₀₂ = (6.16 ± 0.03) × 10⁷ s⁻¹ and k₁₂ = (21.90 ± 0.3) × 10⁶ s⁻¹. The apparent rate constants k_q for this system was (7.26 ± 0.56) × 10⁶ M⁻¹ s⁻¹. The observed decrease in the rate of exciplex formation of I with TEA in the presence of III could suggest that the guanine-like moiety in I forms hydrogen bonds with the cytosine-like moiety and this could decrease the electron affinity of I. The rate constant of exciplex dissociation increased, indicating that the exciplex is less stable in the presence of III. Because of the single exponential decay of I in the presence and absence of II and of the agreement between steady-state and transient fluorescence measurements, the information available for quantitative analysis of the association between I and II is limited.     

Electron transfer,equilibrium, and protonation in the system of cis- and trans-stilbene in 2-propanol

Spectrophotometric pulse radiolysis experiments with cis- and trans-stilbene (S_c and S_t) in 2-propanol show that both isomers react with the solvated electron with a rate constant of 4.5 × 10⁹ M^?1 s^?1. The absorption spectra of the two anion radicals have maxima at 496 and 486 nm, respectively. The absorbances at 400–550 nm disappear exponentially corresponding to a pseudo first order protonation of the anion radicals. The rate constants for the protonation of the cis isomer is 6.4 × 10⁵ and of the trans isomer 0.7 × 10⁵ s^?1. In mixtures of cis- and trans-stilbene the electron transfer

has a forward rate constant of 9 × 10⁷ M^?1 s^?1 while the back reaction has a rate constant of 2.15 × 10⁷ M^?1 s^?1. An equilibrium constant K = 4.2 is calculated.     

Absolute rate constants for the reaction of O(3P) aroms with n-butane and NO(M  Ar) over the temperature range 298–439 K

Absolute rate constants for the reaction of O(³P) atoms with n-butane (k₂) and NO(M  Ar)(k₃) have been determined over the temperature range 298–439 K using a flash photolysis-NO₂ chemiluminescence technique. The Arrhenius expressions obtained were k₂ = 2.5 × 10^?11exp[-(4170 ± 300)/RT] cm³ molecule^?1 s^?1, k₃ = 1.46 × 10^?32 exp[940 ± 200)/ RT] cm⁶ molecule^?2 s^?1, with rate constants at room temperature of k₂ = (2.2 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 and k₃ = (7.04 ± 0.70)×10^?32 cm⁶ molecule^?2 s^?1. These rate constants are compared and discussed with literature values.     

Kinetic study of the reaction of meso-tetrakis (p-trimethylammoniumphenyl)porphinatodiaquorhodate(II) with chloride,bromide, iodide,hexacyanocobaltate(III) and thiocyanate ions in aqueous solution

The reaction of Cl^?, Br^?, I^?, Co(CN)₆^3? and NCS^? with meso-tetrakis (p-trimethylammoniumphenyl)porphinatodiaquorhodate(III), [RhTAPP(H₂O)₂]⁵⁺, has been studied at 15, 25 and 35°C in 0.1 M [H⁺] with μ = 1.00 M (NaNO₃). The value of the acidity constant, K_al, at 25°C is 4.39 × 10^?9 M. The reactions are first order in anion concentration up to 0.9 M. The values of the stability constants, K₁, and the second order rate constants, k₁, for the reaction with Cl^?, Br^?, I^?, Co(CN)₆^3? and NCS^? are respectively 0.23 M^?1 and 2.5 × 10^?3 M^?1 s^?1, 1.1 M^?1 and 6.92 × 10^?3 M^?1 s^?1, 40.0 M^?1 and 17.0 × 10^?3 M^?1 s^?1, 550 M^?1 and 20.0 × 10^?3 M^?1 s^?1, 3400 M^?1 and 20.9 × 10^?3 M^?1 s^?1. The porphine greatly labilizes the Rh(III). There has been about a 500-fold increase in the rate constant for substitution compared to that of [Rh(NH₃)₅H₂O]³⁺. The substitution rates are however about the same as for [Rh(TPPS)(H₂O)₂]^3?, indicating that the overall charge on the complex plays only a minor role. The kinetic results indicate that dissociative activation is occurring in these reactions.     

The Role of Solvation in the Kinetics and the Mechanism of Hydroperoxide Radicals Addition to π‐Bonds of 1,2‐Diphenylethylene and 1,4‐Diphenylbutadiene‐1,3

A combination of microcalorimetry, the rotating sector method, and ESR at 323 K in the environment of 10 solvents of different polarities was used to measure rate constants of addition of hydroperoxide radicals () to π bonds of trans‐1,2‐diphenylethylene and trans,trans‐1,4‐diphenylbutadiene‐1,3 (k₂) and disproportionation rate constants of these radicals (k₃). With increasing dielectric constant of the medium, k₂ values increase from 69 to 410 M⁻¹ · s⁻¹, and k₃ values almost do not change and are in the range of (1.0 ± 0.2) × 10⁸ M⁻¹ · s⁻¹. A linear dependence of logarithm values of rate constants from the dielectric constant of the medium in the coordinates of the Kirkwood–Onsager equation was found that allows to make a conclusion about the effect of nonspecific solvation in the studied systems. The quantum‐chemical analysis (NWChem, DFT B3LYP/6‐311G**) of the detailed mechanism for addition shows that the influence of the medium polarity reflects the superposition of the effects of nonspecific and specific solvation. The scale of the polar effect will depend on how different solvation energies of the transition and the initial reaction complexes. If a value of the solvation energy of the transition complex is larger than the solvation energy of the initial reaction complex, then the reaction rate should increase with an increase of the solvent's polarity and decrease otherwise.     

Kinetic studies of the reactions of pentacyanoferrate(III) complexes with L‐ascorbic acid

The reduction of Fe(CN)₅L^2? (L = pyridine, isonicotinamide, 4,4′‐bipyridine) complexes by ascorbic acid has been subjected to a detailed kinetic study in the range of pH 1–7.5. The rate law of the reaction is interpreted as a rate determining reaction between Fe(III) complexes and the ascorbic acid in the form of H₂A(k₀), HA^?(k₁), and A^2? (k₂), depending on the pH of the solution, followed by a rapid scavenge of the ascorbic acid radicals by Fe(III) complex. With given Ka₁ and Ka₂, the rate constants are k₀ = 1.8, 7.0, and 4.4 M^?1 s^?1; k₁ = 2.4 × 10³, 5.8 × 10³, and 5.3 × 10³ M^?1 s^?1; k₂ = 6.5 × 10⁸, 8.8 × 10⁸, and 7.9 × 10⁸ M^?1 s^?1 for L = py, isn, and bpy, respectively, at μ = 0.10 M HClO₄/LiClO₄, T = 25°C. The kinetic results are compatible with the Marcus prediction. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 126–133, 2005     

Flash photolysis study for reactions of NO3· with sulfur compounds in acetonitrile solution

The rate constants for the reaction of NO₃· with sulfur compounds in acetonitrile have been determined by the flash photolysis method. The rate constant for dimethyl sulfone (2.7 × 10⁴ M^?1s^?1 at ?10°C) is larger than that of the deuterium derivative, indicating that NO₃· abstracts the hydrogen atom from dimethyl sulfone. In the case of dimethyl sulfide, the rate constant was evaluated to be 1.5 × 10⁹ M^?1 s^?1 at ?10°C; the transient absorption band attributable to the cation radical was observed after the decay of NO₃·, suggesting the electron transfer reaction from the sulfide to NO₃·. For diphenyl sulfide and dimethyl disulfide, the electron transfer reactions were also confirmed. For dimethyl sulfoxide, the reaction rate constant of 1.2 × 10⁹ M^?1 s^?1 (at ?10°C) was not practically affected by the deuterium substitution, suggesting that NO₃· adds to sulfur atom forming (CH₃)₂?(O)-ONO₂. On the other hand, for diphenyl sulfoxide, the electron transfer reaction occurs. By the comparison of these rate constants in acetonitrile solution with the reported rate constants in the gas phase, the change of the reaction paths was revealed.     

Rate constants for the reaction of OH radicals with 2-methyl-2-butene over the temperature range 297–425 K

Absolute rate constants, k₂, for the reaction of OH radicals with 2-methyl-2-butene have been determined over the temperature range 297–425 K using a flash photolysis-resonance fluorescence technique. The Arrhenius expression obtained was k₂ = 3.6 × 10^?11 exp [(450 ± 400)/RT] cm³ molecule^?1 s^?1.     

Determination of the rate constants for the gas-phase reactions of methyl butenol with OH radicals,ozone, NO3 radicals,and Cl atoms

Using a relative rate method, rate constants for the gas-phase reactions of 2-methyl-3-buten-2-ol (MBO) with OH radicals, ozone, NO₃ radicals, and Cl atoms have been investigated using FTIR. The measured values for MBO at 298±2 K and 740±5 torr total pressure are: k_OH=(3.9±1.2)×10⁻¹¹ cm³ molecule⁻¹ s⁻¹, k_O3=(8.6±2.9)×10⁻¹⁸ cm³ molecule⁻¹ s⁻¹, k=(8.6±2.9)×10⁻¹⁵ cm³ molecule⁻¹ s⁻¹, and k_Cl=(4.7±1.0)×10⁻¹⁰ cm³ molecule⁻¹ s⁻¹. Atmospheric lifetimes have been estimated with respect to the reactions with OH, O₃, NO₃, and Cl. The atmospheric relevance of this compound as a precursor for acetone is, also, briefly discussed. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 589–594, 1998     

Pulsed amperometric detection of sulfur compounds: Part II. Dependence of response on adsorption time

A mathematical model is developed for the response of PAD and is applied to data from the study of I_p as a function of t_ads for evaluation of the adsorption rate constants, and the maximum molar surface coverage for thiourea at a Pt electrode. The results are, respectively: k₁ = 4.1 × 10⁴ M⁻¹ s⁻¹, k₋₁ = 1.9 s⁻¹, and Γ₀ = 1.3 × 10⁻¹⁰ mol cm⁻². The calculated adsorption equilibrium constant (k₁/k₋₁) is 2.1 × 10⁴ M⁻¹, compared to 4.9 × 10⁴ M⁻¹ calculated from the plot of 1/I_p vs. 1/c^b for c^b > 1.0 × 10⁻⁴ M and t_ads = 8500 ms. Analytical calibration procedures are examined; linear plots of 1/I_p vs 1/c^b cannot be expected for cases of mixed transport-isotherm control of detector response.     

Couloamperometry. A fast kinetic technique for halogenations. I. Bromination rate constants of highly reactive enol ethers

A new couloamperometric apparatus has been designed to extend the range of this kinetic technique to the measurement of very high rate constants, 10⁸M^?1s^?1, by using TFCR-EXSEL conditions (TFCR—very low reactant concentration; EXSEL—salt excess), which give half-lives of a few seconds for very fast second-order reactions. Very low faradaic currents, in the nanoampere range for halogens, corresponding to very low reactant concentrations of 10^?8–10^?9M, are measured selectively by compensating the eddy currents, principally the residual and the induced currents. When the electroactive species is bromine, the concentration is demonstrated to be linearly related to the limiting reduction current in the very low concentration range. The upper limit of this technique for bromination is at present 3 × 10⁸M^?1s^?1. The method is applied to the kinetic study of highly reactive enol ethers EtO-C(R) = CH-R′, where R and R′ are H or Me. A value of 2.2 × 10⁸M^?1s^?1 is obtained for k, the rate constant for free bromine addition to EtO-CH = CH₂, by extrapolating the kinetic bromide ion effects to [Br^?] = 0. An α-methyl effect (k_α-Me/k_H)_EtO of 15 is found; this is a small decrease in the methyl effect compared to the marked increase in the double bond reactivity. For the enol acetate MeCOO-CH = CH₂, whose rate constant is 6 × 10²M^?1s^?1, (k_α-Me/k_H)_OCOMe is 21. The dependence of substituent effects on reactivity is discussed in terms of the Hammond effect on the transition state position and of charge delocalization by group G of olefins G-CH = CH₂.     

Free-radical chain oxidation of 1,4-dioxane and styrene in the presence of fullerene C60

The antiradical activity of fullerene C₆₀ was studied for the oxidation of 1,4-dioxane and styrene initiated by azobisisobutyronitrile and benzoyl peroxide as model reactions. The effective rate constants of the reaction of peroxyl radicals with fullerene C₆₀ (k ₇) and the stoichiometric inhibition factor (f _eff) were determined in air ( $P_{O_2 }$ = 0.21 atm) and oxygen ( $P_{O_2 }$ = 1.0 atm). The rate of the liquid-phase oxidation of 1,4-dioxane does not depend on $P_{O_2 }$ , and the effective rate constant of inhibition is k ₇ = (2.4 ± 0.2) × 10⁴ L mol^?1 s^?1. Chain termination in the oxidation of styrene occurs when C₆₀ reacts with both the peroxyl radicals (k ₇ = (1.2 ± 0.1) × 10³ L mol^?1 s^?1) and alkyl (k ₈ = 1.07 × 10⁷ L mol^?1 s^?1) radicals.