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Evaluation of Reactivity for NitroxideRadical Trapping by CorrelationAnalysis Using Steric Substituent

( )Parameter V s

KEIJI IWAO, KAZUHISA SAKAKIBARA, MINORU HIROTADepartment of Synthetic Chemistry, Faculty of Engineering, Yokohama National University,Hodogaya-ku, Yokohama 240, Japan

Received 31 May 1997; accepted 29 August 1997

Ž .ABSTRACT: The reactivity of nitroxide radical trapping NRT , where stablenitroxide radicals react with transient carbon-centered radicals to formdiamagnetic molecules, was evaluated. This was done with the use of the stericsubstituent parameter of both radicals by correlation analysis on the basis of thereactivity data determined by Ingold’s group. In the case where the transientcarbon-centered radicals were not resonance stabilized, the rate constant couldbe well correlated by using only V parameters of R NO? and U? . If thes 2transient radicals were stabilized by resonance, the parameter to estimate theamount of the resonance stabilization of U? was necessary in the regressionequation to evaluate the reactivity correctly. When the spin density, calculatedby PM3 UHF molecular orbital calculations, was used as the resonancestabilization parameter, the rate constant could be well evaluated by a dual-parameter regression equation. Q 1998 John Wiley & Sons, Inc. J ComputChem 19: 215]221, 1998.

Keywords: nitroxide radical trapping; steric substituent parameter V ;smolecular mechanics; correlation analysis; reactivity

Correspondence to: K. Sakakibara; e-mail: mozart@center3.ipc.ynu.ac.jp

( )Journal of Computational Chemistry, Vol. 19, No. 2, 215]221 1998Q 1998 John Wiley & Sons, Inc. CCC 0192-8651 / 98 / 020215-07

IWAO, SAKAKIBARA, AND HIROTA

Introduction

he radical reactions in which short-lived reac-T tive radical species are involved proceedrapidly and can be monitored only by using so-phisticated laser flash photolysis andror kineticcompetition product studies. Therefore, it is rather

Ž .difficult to determine the rate constants k forTvarious reactions involving transient radicalspecies. In addition, substituent effects for theseradical reactions could not be studied in detailbecause the proper substituent parameters repre-senting the steric and electronic effects were notavailable for the radical species. We have devel-oped a steric substituent parameter, V ,1 based onsthe geometries calculated by molecular mechanicsand extensively studied its applicability to varioustypes of reactions.2 V is defined as the ratio of thesshadow area of the substituent projected on thecircumscribing sphere to the total surface area. It isof interest to determine whether the V parame-sters for radical species can also be applied toevaluate the reactivity of radical reactions. As theMM2rMM3 force field parameters have alreadybeen determined for carbon-centered radicals3 andnitroxide radicals,4 the V values for these radicalsspecies can be calculated by using the OMEGAS90program developed by our group.5 Ingold’s grouphas studied the kinetics of nitroxide radical trap-

Ž . w Ž .xping NRT eq. 1 extensively by using the radi-cal ‘‘clock’’ method and by the laser flash photoly-

Ž .sis LFP technique and reported the structuraleffects6 and solvent effects7 so that:

kT 6 Ž .U? q R NO? U]ONR 12 2

where U? and R NO? are the transient carbon-2centered radicals and persistent nitroxide radicals,respectively.

Ingold concluded from the kinetic results thatŽthe rate constant, k , for this NRT nitroxide radi-T

.cal trapping reaction depends upon the steric hin-drance to coupling and upon the extent of reso-nance stabilization of the carbon radical. It is ofinterest to observe whether the steric effect on kTfor the NRT reaction can be evaluated by usingsteric parameter V for the radical species. If thesvalidity of V for the radical species is verified,sand the k values can be correlated with V , thenT sit provides a way to estimate the reactivity for theother radical reactions by the use of the V param-s

eter. Not only for the NRT reactions, but also forthe other reactions involving the radical species,such as spin trapping reactions, the steric effect onreactivity seems to be evaluated correctly by thecorrelation analysis of use of V parameters.s

In this report, an attempt to evaluate the reac-Ž .tivity k of the NRT reaction by using the corre-T

lation analysis with the aid of steric parameter V sis made and the applicability and the usefulness ofthe kind of correlation analysis is discussed.

Theory

CALCULATION OF V FOR THE TRANSIENTs( )CARBON-CENTERED RADICAL U? AND

( )NITROXIDE RADICAL R NO?2

To calculate the V for the radicals, the loca-stions of the reaction center atoms for the carbon-centered radical and the nitroxide radical must

Ž .first be determined. The reaction center atom X

FIGURE 1. Definition of steric substituent param-eter, V .s

Shadow area of substituentV = .s Total surface area

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REACTIVITY FOR NRT

TABLE I.y7 ( y1 y 1)Rate Constants, 10 k ///// M s , for Nitroxide Radical Trapping at 18 """"" 28C and Steric SubstituentT

Parameter V of Nitroxide and Carbon-Centered Radicals.s

Tempo TMIO DBNO ABNO( ) ( ) ( ) ( )No. Radical U? structure 0.479 0.433 0.501 0.359

?( ) ( ) ( ) ( ) ( ) ( )1. CH CH CH 0.263 123 " 26 116 128 " 31 193 108 " 28 92.2 216 " 41 4333 2 7 2?( ) ( ) ( ) ( ) ( ) ( )2. CH CCH 0.346 106 " 35 94.5 112 " 32 157 89 " 36 75.0 202 " 39 3513 3 2

?( ) ( ) ( ) ( ) ( ) ( )3. CH CCH C CH CH 0.362 106 " 35 91.1 121 " 40 152 191 " 32 3393 2 2 3 2? ( ) ( ) ( )4. H CCH CH 0.308 210 " 26 108 296 " 34 4012 2

?( ) ( ) ( )5. H C CH CH 0.380 141 " 28 89.72 2 2?( ) ( ) ( ) ( ) ( )6. H C CH CH 0.437 102 " 21 76.7 121 " 31 128 178 " 40 2862 2 3?( ) ( ) ( ) ( ) ( ) ( )7. H C CH CH 0.482 95 " 22 69.1 103 " 28 115 76 " 29 54.9 172 " 42 2572 2 4

?( ) ( ) ( ) ( ) ( ) ( )8. CH C 0.610 68 " 17 51.5 91 " 21 85.7 68 " 18 40.8 165 " 39 1923 3?( ) ( ) ( ) ( ) ( ) ( )9. H C C CH CH C CH 0.680 52 " 12 43.7 46 " 13 34.7 160 " 51 1632 3 2 3 2

? ( ) ( ) ( ) ( ) ( )10. C H CH 0.249 48 " 8 19.2 55 " 5 32.0 46 " 4 15.3 118 " 9 71.66 5 2? ( ) ( ) ( ) ( )11. 1-Naphthyl-CH 0.289 8.2 " 0.2 13.1 9.1 " 1.8 21.8 76 " 5 48.82? ( ) ( ) ( ) ( )12. 2-naphthyl-CH 0.250 5.7 " 1.8 10.1 8.2 " 1.9 16.8 81 " 30 37.72

? ( ) ( ) ( ) ( )13. C H CHCH 0.452 16 " 4 19.8 30 " 11 33.0 86 " 18 73.86 5 3? ( ) ( ) ( ) ( )14. C H CHCH CH CH 0.475 1.9 " 0.4 6.79 90 " 12 25.36 5 3 2

? ( ) ( ) ( )15. C H CHCHCH CH 0.521 10 1" 13.9 78 " 12 51.96 5 2 2? ( ) ( ) ( ) ( ) ( ) ( )16. C H C CH 0.651 11.8 " 0.1 8.92 17 " 3 14.8 6.2 " 0.3 7.08 133 " 8 33.26 5 3 2

?( ) ( ) ( ) ( ) ( )17. C H CH 0.497 4.6 " 0.02 11.3 7.7 " 0.9 18.8 82 " 4 42.06 5 2?( ) ( )18. C H CCH 0.702 4.5 " 0.476 5 2 3?( ) ( ) ( ) ( ) ( ) ( ) ( )19. C H CCH OC CH 0.704 4.2 " 0.7 6.76 5.6 " 0.5 11.3 3.0 " 0.4 5.37 59 " 5 25.16 5 2 2 3 3?( ) ( ) ( )20. C H C 0.741 -0.1 -0.1 12 " 3 4.856 5 3

( ) ( ) ( )Tempo: 2,2,6,6-tetramethylpiperidin-1-oxyl ; TMIO: 1,1,3,3-tetramethylisoindoline-2-oxyl ; DBNO: di-tert-butylnitroxides ; ABNO:( [ ] ) 69-azabicyclo 3.3.1 nonane-N-oxyl . The rate constants, k , determined experimentally by Ingold’s group and the values derivedT

[ ] ( )by the correlation eq. 6 in parentheses are shown. Numbers designated by bold letters in parentheses are the values of thesteric substituent parameter, V , of the corresponding nitroxides and carbon-centered radicals.s

is located at the center of a sphere with the appro-Ž .priate radius r for projection, and a light sources

Ž .is placed at this reaction center Fig. 1 . For thecarbon-centered radical, the reaction center wasseen to be a carbon atom on which an unpairedelectron was localized; in the case of the nitroxideradical, a nitroxide oxygen atom was placed at thereaction center. After placing the radical moleculesas shown in Figure 1, the shadow area projected

Ž .on the sphere arising from the remaining part Rof the radical molecules was calculated from thegeometry optimized by the molecular mechanicsmethods MM28rMM39, assuming that each com-

prising atom has a sphere of van der Waals radii.10

The V values were calculated by using theSOMEGAS905 program. To evaluate the steric effectof U? and R NO? molecules accurately, every2possible stable conformation was searched andits contribution was taken into account by sum-ming the population-weighted V value for eachsstable conformer. Stable conformations within therange of 2 kcal in steric energy relative to the moststable conformer were searched by using theCONFLEX311 program combined with theMM2rMM3 program. The values for the radii of

Ž .reaction centers r and of the projection spheresc

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IWAO, SAKAKIBARA, AND HIROTA

Ž .r , which are optional parameters in calculatings˚ ˚V , r s 0.0 A, and r s 4.0 A, were used in thes c s

OMEGAS90 calculations.The V values were calculated for 20 transients

carbon-centered radicals for four stable nitroxidesŽTempo: 2,2,6,6-tetramethylpiperidin-1-oxyl;TMIO: 1,1,3,3-tetramethylisoindoline-2-oxyl;DBNO: di-tert-butylnitroxyl; ABNO: 9-azabicyclow x .3.3.1 nonane-N-oxyl , which were used in the NRTexperiments by Ingold’s group.6

PARAMETER FOR EVALUATING EXTENT OFRESONANCE STABILIZATION OF CARBON-CENTERED RADICALS

To evaluate properly the reactivity of reso-nance-stabilized carbon radicals, it was necessaryto evaluate the spin density on the carbon atom ofthe reaction center because the unpaired electronin these radicals is delocalized. Larger spin densityon the reaction center atom will enhance the reac-tivity of the NRT reaction. Spin density values canbe estimated experimentally from the ESR hyper-fine splitting constant with an H atom attached to

Ž H .the radical center carbon atom a or theoreticallyŽ .by the UHF unrestricted Hartree-Fock molecular

orbital calculations. Because the H hyperfine split-Ž H .ting constants a for all resonance-stabilized

carbon radicals used by Ingold’s group were notavailable in the literature, we estimated the spindensity from the semiempirical molecular orbitalcalculations using the MOPAC6 package. The ge-ometry of the most stable conformation wassearched by the MM3 calculations. By using thisoptimized structure as the input data, spin densitywas calculated by the UHF method with the PM3Hamiltonian.

CORRELATION ANALYSIS FOR EVALUATINGREACTIVITY FOR NRT REACTION BY

Ž )USING STERIC V AND RESONANCEs[ ( )]STABILIZATION r U? PARAMETERS

OF RADICALS

Ž .The rate constants k for NRT reactions, deter-Tmined experimentally by Ingold’s group werecorrelated with the V of the nitroxide radicals

Ž .V R NO? , and the carbon-centered radical,s 2Ž . Ž .V U? , in the first step, as shown in eq. 2 :s

Ž . Ž . Ž .log k s a V R NO? q b V U? q d 2T s 2 s

where coefficients a, b, and d and the correlationcoefficient r were calculated using the least-squares method.

In the next step, the term representing the ex-tent of the resonance stabilization of the carbon-

Ž . Ž .centered radical r U? was added to eq. 2 , andthe reactivity dependence of the NRT reaction uponthe steric effect and upon the extent of the reso-nance stabilization of the relevant radicals wasinvestigated by using the correlation equationw Ž .xeq. 3 :

Ž . Ž .log k s a V R NO? q b V U?T S 2 s

Ž . Ž .q c r U? q d 3

Ž .In the analysis, all r U? values for the radicalswith no resonance stabilization were assumed tobe 1.

Results and Discussion

STERIC SUBSTITUENT PARAMETER VsFOR NITROXIDE AND CARBON-CENTEREDRADICALS

The calculated V values for the 4 nitroxidessand 20 transient carbon-centered radicals are givenin Table I, together with the rate constants k forTthe NRT reaction determined by Ingold’s group. Itshould be observed that the order of ranking of thefour nitroxide radicals estimated by the V valuesswas consistent with the experimentally deter-mined kinetic results for the NRT reaction. If thek of the four nitroxide radicals against one tran-Tsient carbon-centered radical are compared, k isT

w xthe largest for 9-azabicyclo 3.3.1 nonane-N-oxylŽ .ABNO , and decreases in the order: 1,1,3,3-tetra-

Ž .methylisoindoline-2-oxyl TMIO ; 2,2,6,6-tetra-Ž .methylpiperidine Tempo ; di-tert-butylnitroxyl

Ž .DBNO . The V values for these nitroxides varysŽ . Ž .in the order: V ABNO ; 0.359 - V TMIO ;s s

Ž . Ž .0.433 - V Tempo ; 0.479 - V DBNO ; 0.501.s sIn the case where the steric hindrance of the ni-troxide is small, the experimentally determined kTtakes on a larger value. The varying trend of k byT

Ž .the change of V R NO? among the four nitrox-s 2ides demonstrates that the rate of NRT reactionwas retarded by the steric hindrance around thenitroxide radical center. The V parameters ofsnitroxides seem to have been evaluated fairly wellin a steric sense, although the MM2 parameters forthe nitroxides were determined by our group andwere not optimized completely. As for the V svalues of the carbon-centered radicals, the MM3parameters had already been established as reli-

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REACTIVITY FOR NRT

able parameters by Dr. N. L. Allinger.9 The V svalues for the 20 carbon radicals used in the exper-

w ximent varied in the range of 0.249 10? ; C H CH6 5 2w Ž . xto 0.741 20? ; C H C from our present study.6 5 3

As the bulkiness of the nitroxide and carbon-centered radicals seem to have been evaluatedwell by using the V parameter, the reactivity ofsthe NRT reaction could be estimated accurately bycorrelation analysis.

CORRELATION ANALYSIS BY STERICSUBSTITUENT PARAMETER VsOF NITROXIDE AND CARBON-CENTEREDRADICALS

By using the calculated V values shown insTable I, the experimentally determined k valuesTwere correlated with the steric substituent parame-

Ž .ter V of the nitroxide R NO? and carbon-s 2Ž .centered U? radicals in the form of the correla-

w Ž .xtion equation eq. 2 . The best-fit regression coef-Ž .ficients, a, b, and d in eq. 2 , and the correlation

coefficient, r for the 57 k data, were as follows:T

a s y4.30, b s y0.98, d s 3.99, r s 0.53

Ž .The correlation plot of log k vs. a V R NO? qT s 2Ž .b V U? q d is shown in Figure 2. The correlations

Ž .was very poor for the correlation eq. 2 , as easilyseen from the scattered points in Figure 2. How-ever, it is noteworthy that there exist two differentkinds of data groups in Figure 2. One is the groupfor the carbon-centered radicals without resonance

FIGURE 2. Correlation analysis plot using the stericsubstituent parameters of nitroxides and carbon-centered

[ ( ) ( ) ]radicals i.e., log k vs. a V R NO? + b V U? + d .T s 2 sBoxes = conjugated; filled diamonds = nonconjugated.

FIGURE 3. Correlation analysis plot using the steric( ) ( )parameters, V R NO? and V U? , and resonances 2 s

( )stabilization parameter, r U? , of carbon-centered[ ( ) ( )radicals i.e., log k vs. a V R NO? + b V U? +T s 2 s

( ) ]cr U? + d . Boxes = conjugated; filled diamonds =nonconjugated.

Žstabilization for which the data points filled dia-.monds in Fig. 2 seem to lie in the linear regression

lines. The other group contains the resonance-Žstabilized radicals for which the data points open

.squares in Fig. 2 are scattered. When the linearregression analysis was carried out on just thegroup containing the carbon-centered radicals

Ž .without resonance stabilization 28 k data , aTgood correlation was obtained and the correlation

w Ž .xequation was described as follows Eq. 4 :

Ž . Ž .log k s y2.46 " 0.24 V R NO?T s 2

Ž . Ž .q y0.68 " 0.01 V U?s

Ž . Ž .q 3.45 " 0.07 4correlation coefficient: r s 0.93

We can assume that the steric effect of the nitrox-ide and the carbon-centered radicals is the mainfactor controlling the reactivity of the NRT reac-tion if the carbon-centered radicals are not reso-nance stabilized. Poor correlation for the whole set

Ž .of experimental data Fig. 2 comes from neglect ofthe contribution of resonance stabilization of con-jugated radicals in the correlation analysis. Com-paring the determined regression coefficients a

Ž .and b in eq. 4 , the size of the nitroxide seems tobe a more dominant steric factor. The larger nega-

Ž .tive value y2.46 of the regression coefficient aŽ . Ž .than b y0.68 in eq. 4 indicates a larger retarda-

tion effect by steric hindrance of nitroxide radicals.

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IWAO, SAKAKIBARA, AND HIROTA

TABLE II.Parameter for Evaluating the Extent of Resonance

( )Stabilization r U? of Carbon-Centered Radicals.

( )Radical U? r U?

?4? H CCH CH 0.532 2?10? C H CH 0.366 5 2

?11? 1-Naphthyl-CH 0.282?12? 2-Naphthyl-CH 0.132

?13? C H CHCH 0.536 5 3? ( )14? C H CHCH C CH 0.176 5 3 2?15? C H CHCHCH CH 0.206 5 2 2? ( )16? C H C CH 0.426 5 3 2

?( )17? C H CH 0.376 5 2?( )18? C H CCH 0.436 5 2 3?( ) ( )19? C H CCH OC HC 0.366 5 2 2 3 3?( )20? C H C 0.286 5 3

MULTIPLE CORRELATION ANALYSIS BY( ) ( )USING STERIC V R NO? , V U?s 2 s

PARAMETERS AND RESONANCE( )STABILIZATION PARAMETER r U? OF

CARBON-CENTERED RADICALS

The extent of resonance stabilization of the con-Žjugated carbon-centered radicals 4? , 10? , 11? , 12? ,

13? , 14? , 15? , 16? , 17? , 18? , 19? , 20? radicals listed.in Table I should be considered to be closely

correlated with the spin densities of their radicalŽ .center atoms. Thus, the r U? value qualitatively

estimated by the PM3 UHF molecular orbital cal-culations was used as a parameter, which standsfor resonance stabilization. It was derived from

Ž .eq. 5 :

Ž . < Ž . < < Ž . < Ž .r U? s SD c rÝ SD i 5

Ž . Ž .where SD c and SD i refer to the calculated spindensity on the radical center and on individualcarbon atom in the radicals, respectively. As thecalculated spin density can take positive and nega-tive values in the UHF calculations, absolute val-ues were used to estimate the resonance-stabiliza-

Ž . Ž .tion parameter r U? . The determined r U? areshown in Table II, where the values range from

Ž .0.13 to 0.53. Although the r U? parameters usedto estimate the extent of resonance stabilization arequalitative, the correlation for the regression of

Ž .correlation eq. 3 was improved. The correlationŽ .coefficient r for the 57 kinetic data for the NRT

reaction was 0.912, and the correlation equationexpressed as:

Ž . Ž .log k s y4.74 V R NO? y 1.00 V U?T s 2 s

Ž . Ž .q 1.24 r U? q 3.36 6

where the standard deviations of the regressionŽ .coefficients a, b, c, and d of eq. 3 are 0.56, 0.20,

0.09, and 0.23, respectively.The values of the regression coefficients a, b,

and c seem to reflect the relative importance ofsteric and resonance stabilization effects on reac-tivity in the NRT reaction. Thus, the larger nega-

Ž .tive coefficient value a s y4.74 indicates thatthe size of the nitroxide has more of a retarding

Ž .effect than the carbon-centered radical b s y1.00Ž .in the NRT reaction. The positive value 1.24 of

Ž .coefficient c for the r U? parameter suggests thatthe larger spin density value on the reaction centeratom should lead to a higher reactivity for thecoupling with the nitroxide. Judging from the re-sults of the correlation analysis using the steric

Ž .parameter V of the nitroxide R NO? , thes 2Ž .carbon-centered radical U? , and the resonanceŽ .stabilization parameter r U? , these parameters

seem to be evaluated well as a whole because therate constant, k , of the NRT reaction may beT

Ž .correlated well by eq. 3 with a correlation coeffi-cient of r s 0.912. As it is otherwise very difficultto determine the rate constant of the radical reac-tions, the V steric parameter for the nitroxide andsthe carbon-centered radical are useful in evaluat-ing the steric effect of these radicals. V can besdetermined easily within the practical cpu time forany radical molecules used routinely in chemicallaboratories by taking advantage of the speed andaccuracy of molecular mechanics. As for the reso-

Ž .nance stabilization parameter, r U? , further studyseems necessary because this parameter is imper-fectly quantitatively and used only tentatively inthis study.

Conclusion

The steric substituent parameter, V , which cansbe determined on the basis of optimized geome-tries and conformational energies calculated bymolecular mechanics, is shown to be a useful pa-rameter for estimating the steric effect of radicalspecies, as well as for the diamagnetic organiccompounds. The reactivity in the NRT reactioncould be evaluated easily by correlation analysis in

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REACTIVITY FOR NRT

Ž .terms of the V of nitroxide radicals, V R NO? ,s s 2Ž .and carbon-centered radicals, V U? , with the res-s

onance stabilization parameter of carbon-centeredŽ .radicals, r U? .

Calculations

The optimized geometries of the carbon-centeredŽ .radicals were calculated by the MM3 92 program

with the full matrix minimization method. Thestructure of the nitroxides were optimized by the

Ž .MM2 91 program. By using the optimized geome-tries and the conformational energy of the stableconformers of these radicals, the steric substituentparameters, V , of these radicals were calculatedsusing the OMEGAS90 program. UHF semiempiri-cal molecular orbital calculations were carried outwith the MOPAC 6 program. All calculations wereperformed on the Sun SPARCstation IPC.

Acknowledgment

The authors express their thanks to ProfessorNorman L. Allinger, University of Georgia, for hishelpful discussion and advice.

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