GeneraGsed Fiirster CycleThermodynamic and Extrathermodynamic Relationships Between Proton Transfer,Electron Transfer and Electronic ExcitationBY ZBIGNIEW R. GRABOWSKI" AND WIESEAWA RUBASZEWSKAInstitute of Physical Chemistry, Polish Academy of Sciences,Kasprzaka 44, 0 1-224 Warsaw, PolandReceived 26th April, 1976The thermodynamic quantities characterizing one electron reduction, protonation and electronicexcitation, are mutually related in the ground and excited states by 6 thermodynamic (or approximatethermodynamic) cycles. The system of cycles is used to predict unknown values, and its validitymay be extended to other compounds by means of extra thermodynamic (e.g., Hammett-type)relations. Examples of known data concerning pK and pK* values of protolytic equilibria for theoxidized (Ox) and reduced (R) species are evaluated, tabulated and discussed in a search for acorrelation between the changes of pK on excitation (ApK*) and on reduction (ApK,).Both valuesare thermodynamically independent but a general common trend is empirically observed in severalgroups of systems. Some rules are derived for the excited state redox potentials and their dependenceon pH, which may be useful for photochemistry.In recent years more and more information has become available on the spectraand acid-base equilibria of free radicals,l and on protolytic equilibria in electronicallyexcited states.2 As a rule, one electron reduction causes an increase in basicity ofseveral pK units." The electronic excitation alters the electron density distributionconsiderably and often changes the pKvalues by comparable amounts ; the changeis not always an increase, numerous groups of compounds, e.g.phenols or aromaticamines, decreasing the pK dramatically on e~citation.~We have compiled the ApK values on excitation and on one-electron reductionof a few groups of organic compounds, in order to look for meaningful correlations.For the pK values, redox potentials and excitation energies, many thermodynamicor extrathermodynamic relations are known, joining any two of them. We haveattempted to combine these rules into a single system having a strong pfedictivepower. As the system is readily derived from Forster's we term it thegeneralised Forster cycle. The system of thermodynamic cycles is first defined andthen the choice of data presented.Applications of the derived systems of cycles art:shown and the system extended by extrathermodynamic relations. Finally, thesearch for correlations is discussed.1. THE THERMODYNAMIC A N D QUASI-THERMODYNAMIC CYCLESA. THREE-DIMENSIONAL GENERALISATION OF THE FdRSTER CYCLEIn fig. 1 the discussed processes are combined in a symbolic three-dimensionalform.* Throughout the paper we use the symbol pK = -log,&, where KA is the protolytic dissociationconstant of the given acid or of the acid conjugate with the given base.112 GENERALISED FORSTER CYCLEI I II I ,'II I Pnv I "nI I-, "RH I.-. I I "OrH IFIG. 1.-A cubic form symbolizing the chemical species and thermodynamic quantities in a systeminvolving one-electron transfer, one-proton transfer and electronic excitation.Explanation in thetext.Each apex of the figure represents one of the chemical entities considered, ineither its ground or excited state. The excited states and their properties are markedby an asterisk (or explicity by superscripts S , T or D for the excited singlet, tripletor doublet states, respectively), those related to the ground state have a superscriptG or are unmarked. The chemical species are symbolized by Oxz, OxHZ+l, RZ-land RH" for the oxidized base and acid forms, and for the reduced base and acidforms, respectively. Throughout the paper " reduction " and '' oxidation " meansimple one-electron transfer only; the charges often being omitted in the course ofthe paper, particularly in subscripts.A and B represent the acids (OxHZfl, RH")and bases (Ox", R*-l), respectively.Each edge of the figure represents one of the processes considered, proton transfer,electron transfer or electronic excitation ; its length should be proportional to theenergy (or free energy) change in the respective process, so that when drawn to scale,the figure becomes an irregular hexahedron, different for every system.Each face of the figure corresponds to one of the thermodynamic (or quasi-thermodynamic, i.e., approximated) cycles, are discussed below, in sections 1, B-D.FIG. 2.-The protolytic Forster cycle for the system RH f R-+ Hf.B. THE PROTOLYTIC F ~ R S T E R CYCLZThe faces of the three-dimensional figure (fig.1) lying in the plane defined by thecoordinates " excitation '' and " protonation " correspond to the well knowZ . R . GRABOWSKI A N D W. RUBASZEWSKA 13(fig. 2). The cycle, in its thermodynamically well protolytic Forster cycle 3*founded form, may be expressed bywhere AH, is the standard enthalpy change in the acid dissociation reaction,A + B+H+, in the indicated electronic state, ft is the wavenumber of the pureelectronic (0,O) transition between the ground and given excited state, for the ithchemical species, and N , h and c are universal constants. The AH, values referAHZ-AH," = Nhc(v",-Vd (1)strictly to T = 0 K but eqn (1) retains its validity to a good approximation up to300 K."For practical reasons the thermodynamic cycle after further approximations isusually applied in the form which we will describe as a quasi-thermodynamic protolyticForster cycle :ApK& = P K ~ ~ - P K ~ ~ x (v"Ox-v"OxH) hc/kT(ln 10)ApKZ = pKZ - pK: x (i& - fm) hc/kT( In 10).(24(2b)The most important approximation made in the derivation of eqn (2) is that AS,* x AS:,where AS, is the standard entropy change in the acid dissociation reaction. Theapproximation usually holds well,5 as the most important contribution to ASo, thatdue to the ionic charges, cancels between the two states.At T = 298 K the cycle can be reduced toApK* x 2.07 x 10-3Av"BA (where AYBA = VB-- VA) ( 2 4v" being expressed in cm-l.discussed el~ewhere.~Limitations on the validity of the quasi-thermodynamic Forster cycle (2) areC.THE MICHAELIS CYCLEThe faces of fig. 1 lying in the plane of '' proton transfer " and " electron transfer "are (at least for the ground state) well defined since the classical work of Michaelis.'FIG. 3.-(a) Michaelis-type redox potential against pH diagram for a one-electron redox system.(b) typical " Michaelis cycle"; AGO,, AGR are the standard free enthalpies for the reactionsHence, we have given the name '' Michaelis cycle " to the description of the changesof pK due to one-electron reduction (fig. 3)OxHz+ + OxZ + H+, and RHz + Rz- + H+, respectively.ApK," E pK,G-pKEx = ( E 2 - Eg)F/RT(ln 10)ApKT = pKg-pK& = (Ez-Eg)F/RT(ln 10)(34(3b14 GENERALISED FORSTER CYCLEwhere EB and EA are the standard redox potentials of the systems Oxz/R2-l andOxH'+'/RH", respectively.At T = 298 K this simplifies towith E measured against the standard hydrogen electrode, with European signconvention. The standard redox potentials differ by an unknown constant amountfrom the standard free enthalpy change for the process Ox" +e- + RZ-l ; they arenot measurable in condensed phases, but the differences in eqn (3) are measurableand well defined. Eqn ( 3 ) does not involve any approximations; the Michaeliscycle being an exact thermodynamic cycle.ApKe = 16.92(EA-EB)/V (34D. THE ELECTRON TRANSFER FORSTER CYCLEThe remaining faces of the three-dimensional figure (fig. I), those representing'' excitation " and electron transfer, are the least known. This is due to difficultiesin measuring the redox potentials between electronically excited species.7.Numerousattempts have been made to estimate the redox potentials of the excited species,g* l obut only a few measurements of the appearance potentials, mostly at insulator orsemiconducting electrodes,' 9 can be considered successful. Nevertheless, we canbuild a cycle (fig. 4) which we will call the electron transfer Forster cycleAH,"-AH,G = Nhc(VR-VOx). (4)o x * ... ...,.. .......... I ...... oxFIG. 4.-The thermodynamic electron-transfer Forster cycle in a " reduction " and " excitation "plane. AH, are the standard enthalpy changes for the processes of the type Oxz+' +e- + R" ;only their differences can be measured.The absolute values of the standard enthalpy changes for electron transferreactions, AHe = H i - (Hgx + I?:-), like the absolute potentials cannot be determined.As yet it is not possible to measure the difference on the left hand side of eqn (4).The approximation AS,* E AS: (where AS, is the standard entropy change forthe electron transfer reaction) is justified with limitations analogous to the case ofthe protolytic Forster cycle.4 The approximation leads to the quasi-thermodynamicrelations (5)E i - E z M (fox, - f ~ , ) N h c / FE;S - EZ % (fox- v"R)NhC/F( 5 4(5b)where P is the Faraday constant, Nhc/F = 1.24 x V cm.2. EXAMPLES OF EXPERIMENTAL ApKe AND ApK* VALUESTables 1-6 contain examples of data compiled or evaluated for the systems forwhich the most numerous and/or reliable values of pKcould be found for the oxidizedZ .R. GRABOWSKI AND W . RUBASZEWSKA 15reduced and excited species in several groups of organic compounds. Free radicalsappear either as the reduced (tables 1-4) or as the oxidized forms (table 5 and 6).The pKvalues for the stable free radicals are much more reliable than those for theshort lived species where the determination often requires additional assumptionsconcerning e.g., reaction kinetics or the assignment of transient spectra.pK* refers to the first excited singlet or doublet state of the molecules or freeradicals, respectively; pKT values for the first excited triplet state are also listed.The most reliable ApK* and pK* values are based on the protolytic Forster cycle (2)involving the (0,O) transition^,^ or on the kinetic analysis of the fluorescence quantumyield^.^ Data based only on the shifts of absorption bands are not exactly definedand indicate no more than the sign and order of magnitude of ApK*.Such inexactvalues are, as a rule, the only ones available for free radicals; all data involve atacit assumption that the given absorption band corresponds to the lowest energyelectronic transition.The ApKT values were determined either by flash photometry in buffered solutions,i.e., after the equilibrium had been attained during the lifetime of the triplet state,or from the shifts of the (0,O) transitions in phosphorescence. The last valuesusually differ from those obtained by means of T-T absorption in flash photometryby not more than a few tenths of a pH unit.4* l3The following abbreviations are used in the tables for the methods of generationof the free radicals : ph, photochemical reaction, flash photolysis ; el, electrodereactions; abbreviations for the methods of determination of pK are FO, Forstercycle (2) ; fk, fluorescence kinetics ; p, shift of the phosphorescence (0,O) bands ;TT, absorption within the triplet manifold in flash photometry.ApK* " evaluatedfrom . . . '' means " calculated from the absorption spectra reported in the referencequoted ".Unless otherwise stated, the tabulated data refer to room temperature, andaqueous, water +alcohol or H2S04 solutions. pKG values were determined byspectrophotometric methods and the free radicals generated by means of pulseradiolysis, their ApK* values being estimated from the shift of their absorptionmaxima.Negative values of pK are expressed in terms of the Hammett acidityfunction,3. APPLICATION OF THE GENERALISED FORSTER CYCLEThe system of six linear equations (2), (3) and (5) may enable evaluation of theunknown data from the 12 values characterizing the chemical system represented inOne of the most exactly investigated systems is that of N-methylphenaziniumlN-methylphenazyl radical (table 1, item 5) for which the (0,O) transitions are alsoknown :24 Gox = 20 600 em-', GOxH = 17 300 cm-l, GR = 15 900 cm-1 and fRH =13 700 cm-l ; the redox potential Eg = +0.08 V.85 These data are alreadyredundant since there are four equations [3(a), (b) and 5(a), (b)] to define threepreviously unknown values : E: = +0.62 V, Ez = + 1.07 V, Eg = +0.66 V.The values obtained in this way are presented in fig.5 in the form of a super-position of the Michaelis diagrams (E against pH) for the ground and excited states.The system is much more strongly oxidizing in the excited than in the ground state,the difference in redox potentials on excitation, E* - EG, exhibiting a distinct maximumin the range pK& < pH < pKg. Curves such as in fig. 5 can be used to predict thecourse of some photochemical electron transfer processes,fig. 116no. OxHlRH pKGl aa'b2b'c3C'd4d'ee'5f6a10.5"- 6.316 { -6.V97.615- 5.5168.815-4.321-3.524-0.33*'HC'GENERALISED FORSTER CYCLETABLE 1 .-AZA-AROMATIC COMPOUNDSApKe ApK* ApKT pK* pKYT- - 5.3;' - -11.1w+16- 15.5 - + 5*+7.71,; -w+142.2 --8.4g (+lo)"* 4.1 (5.7)%+lo(32.2") -4.724+ 6 .8 2 - + 9,2t-4.7g -10.3 --1 L Hl+H IH J+ 2r-- - -- arks*evaluated from ref.(15) and (18)*evaluated from verybroad absorptionbands ref. (1 5)*estimated with anerror of k 1.5 withsome arbitraryassumptions"evaluated from ref.(22) and (23).b' [CpH]+Z . R. GRABOWSKI AND W. RUBASZEWSKATABLE 1 .-(Contd.)17TABLE 2.-AROMATIC NITRO- AND NITROSO-COMPOUNDSOxH/RH pKG ApKe ApK* ApKT pK* pKTa - 11.329332 +5* +2;9 -6.3 -9.3 + 14.5a' 3.233,34 - - - -b -11.632 +4* - -7.6 -b' 2.935 + 5*+ 14.57.9 -- - 9.0636 +15* - 6C' 3.634.37 - - - -d 7.1638 -1329 -1.7;' -6* 5.9-9.1816 ~ + 1 3+ 2.6- - - - d' 9.837e - 4.939e' 1 1 .740 + 2"- - - -=+16- 14 -NO~H+ q?J C l DNo2:remarks*evaluated from ref.(30) and (31)*evaluated from ref.(32) (inflection point)*evaluated from ref.(3 5)*evaluated from ref.(3 6)*corrected value, thecalculatedpK* using anothervalue of pKG*evaluated from ref.(40)10 aNo2H+ HO ITNo2 e aNoH18 GENERALISED FORSTER CYCLETABLE 3.-AROMATIC CARBONYL COMPOUNDSnu. OxHiRH pKG ApKe ApK* ApKT pK* pKT remarks+7.0fk +7.6$; 12+ 1.5 *mean value from ref.+11** 5.0 (21, (411, (42) u (-6.1***evaluated from ref.(40, (431, (44)?lower limit due to themethod-+16 possible errors of 12136' 7.7j6c - 6.2*1410.0*a' 10.9;;w+10w+156.0 - *mean value from ref.(451, (46)6.9 **evaluated from ref.(47)- 4** -the equilibria may beascribed to either +4.5** +0.57 2.4 -1.5tautomer ROHi orRNH:.49*mean value of datafrom ref. (48), (49)**recalculated from ref.(49)- 1* - 6.7 - *evaluated from ref. (46)+0.2y6 + 5.4i2 - 6.0 -0.8 *mean value from ref.(411, (52)7 (54)**recalculated from ref.(52)(O# = 26 200 ~ m - l , ' ~CEO = 26 300 ~ m - l . ) ~ 'C' 9.2" - 5** - 4 - *mean value from ref.(451, ( 5 5 )(471, (55)-(58)**evaluated from ref.d -4.160 +7.7$; +10.7g1 3.6 6.69.8' 7,5 - - - - n/15 w + 1 416e - 6.85* - 2** - -4.85 - *mean value from ref.(1 6)%+16 **evaluated from ref. (62)*the reaction kineticsdata 63 are incompatiblewith pK = 6- - - -*recalculated from ref.(49) + 7.3g +2.449 y:i49 -4.9 + 8 .6 ~ ~ f { 7,34296417 %+13 - . . ~~ f ' 5.365 - 2* - 3.3 - *evaluated from ref. (65)B 4.F4 +1.8% - 6.0 -R5+8g' 126s - 1* - "evaluated from ref. (65) 11h -7.0* +11** +8.0% 4 1 *mean value from ref.18-(1 6)(43), (4.4)19 w + 1 7 **cvalua ted from ref./I' 10.5;; - 4* - 6.5 - "evaluated from ref. (47TABLE 4.-QUINONES/SEMIQUINONE RADICALS10. 0xH;RH PKG ApKe ApK* ApKT pK* pKT remarks+2* - -6 - *evaiuated from ref. (66), (67) a - 7.516 {- 8 . P20 m + 12a' 4.1' -3* - 1 - "evaluated from ref. (68)h -8.0" 45"" - - 3 - *mean value from ref. (16).(66)21 w+13 **evaluated from ref. (3 I), (66)b' 5.368.69 -2* - 3 - *evaluated from ref. (68)OH OHSome authors [e.g.ref. (8) and (86)] use the concept of redcrx potentials for systemsThey can like Ox* +e- + R which we call " mixed excitation redox potentials ".be defined asE(Ox*/R) = EZ + v",,Nhc/F (6)E(Ox/R") = EF- v",Nhc/F. (720 GENERALISED FORSTER CYCLETABLE 5.-sEMIQUINONE RADTCALS/QUINOLS AND PHENOXYL RADICAL/PHENOLNo. OxH/RH2 2232 42526aa'b6'CC'dd'ee'PHPKG AP Ke ApK*4.0" ,2**= + 69.974 -- 175 + 2*1 1.374375 - 5"77 5 + 1"+6- 3"= + 1 21374.755*368,69 - 6.6"m+8-3.8** 13.7*<7751078ba' 40-OHOH--- 1 .5g8cPK*2.0-16.3810- 1 . 39.9-PKT remarks- *mean value from ref.(70)-(72)**evaluated from ref.(701473)- *evaluated from ref. (75)- 'evaluated from ref.(74)1 *evaluated from ref. (75)- *evaluated from ref. (74)- *evaluated from ref. (76)- **evaluatedfromref. (76)*caIculated from thetau tomeric equilibriaref. (77)-4.0,, 8.5OH -OHOH@HOOH I21 2. R. GRABOWSKI AND W. RUBASZEWSKATABLE AM AMINO RADICALS1 AROMATIC AMINESno. OxH/RH pKG ApKe ApK* ApKT pK* pKT remarksa 779 +2.5* - 9.5 - *evaluated from ref. (79)a' {XX~~ - - >16'lt - *in liquid NH3, 213 K27 w +21tfrom the growth of a newemission, whereas from thedecrease of anilinefluorescence, pK* < 13**extrapolated, ref. (82)- - - - b 4.283b' 22.5 a ' w+18- -28- -c l+HExcited state redox potentials have a definite thermodynamic meaning whilemixed excitation redox potentials are usually more directly related to the reactionkinetics of excited species.87* 88 Which concept to use depends on the mechanismof the particular photochemical electron transfer reaction and will be discussed inanother paper.Taking as an example the thioninelsemithionine radical system (table 1, item 6),from the redox potentials and equilibria, one o b t a i d 8 Eg = -0.19V and EF = + 0.32 V.Substituting into eqn (6) the values for the triplet state VOx = 13 640 cm-l 890 80.6 >4 .0.40.2O ' -8 -6 - 4 ' -2 0 2 , 4 / 6 8 1 0 7P G X PK& PKG, PK R"PHFIG. 5.-Superimposed Michaelis diagrams for the redox system N-methylphenazinium ion/N-methylphenazyl free radical, for the ground and excited state and E* - EG = f(pH)22 GENERALISED FORSTER CYCLEand Toxa = 10 500 cm-l we obtain E(Ox*/R) = + 1.5 V and E(OxH*/RH) = + 1.62 V (for pH > 8.1 and pH < 6.3, respectively).These values agree well withthe quantitative results obtained for the rate of quenching of triplet thionine bydifferent reducing agent^.^For the system anthraseniiquinone radical (Ox = A'Q-, OxH = AGH)/ anthra-quinol anion (R = AQ2-, RH = AQH-), the pKG values are known (table 5, item 25)as well as EF = - 1.45 V 9 2 9 9 3 and the absorption maxima.76 In view of the useof Tmax instead of 7'' the reiiiaining 5 unknown values are defined only approximatelyby the (redundant) system of 6 linear equations (2), (3) and (5). The results areshown in fig. 6. There are two marked differences with respect to the previousexample : (i) pK* < p K G for both Ox and R (which is usual for dissociation of thephenolic OH groups), and (ii) E" < E", i.e., the system is a much stronger reductantin the excited than in the ground state.As the free radicals usually have a lowerexcitation energy than the related ( & le-) closed-shell species, this behaviour (E* < EG)will be common, in view of eqn (5), to the systems in which Ox is a free radical.I II I5, 1Q690 VRH 21510li 500 I I YoxH14 750III h~ ~ AQ"---pKG, 1 13.7 -------,A6H'0 FIG. 6.-Anthrasemiquinone radical anion (AQ- = Ox)/anthraquinol dianion (AQ2- = R) system :schematic display and its characteristics. Approximate values, evaluated from the remaining knowndata, are underlined.4. EXTENSION BY EXTRATHERMODYNAMIC RELATIONSHIPSFor numerous series of structurally related compounds some of the discussedthermodynamic data, pK, Eredox or v", are found to be approximately linear functionsof structural parameters ('' linear free energy relationships " 94* 9 5 ) .We will derivesome rules based on the Hammett " substituent constant " 97 though the scopeof these rules is much broader than the range of applicability of this kind of structuralparameter .As in most series of aromatic compounds containing a common reducible oroxidizable group, the redox potentials of aromatic ketone (or aldehyde)/ketyl radicalanion systems obey eqn (8) 9 5 * 98* 99where X = substituent, (X) and (0) denote the substituted and unsubstituted system,respectively and p is the " reaction constant ", independent of X.As a rule, theHammett equation applies to the protolytic equilibriaEB(x) -'%(o) p(EB)aX, (8)PK(X)-PKi(O) P(PK~)~,* (9Z . R . GRABOWSKI AND W . RUBASZEWSKA 23This is the case for the protonation of ketones loo (i = Ox). Assuming eqn (9) tobe valid for the ketyl radicals (i = R) we obtain a mutual correlation avoiding theexplicit use of the structural parameter(104or simplypK, z5 C,E,+C, (lob)where C , and C2 are constants for the structually related series. Eqn (lob) is thecorrelation found empirically by Hayon for a large group of carbonyl compounds ;it is shown in a corrected form in fig. 7.PKR(x) -pKR(o) a b(pKR)/P(EB)l[EB(x) -'%(0)11210< 864I , I / l , l / I I I I I I I .-2.0 -1.0 0FIG.7.-Correlation between pK$ values of the free radicals and the redox potentials Eg of thecorresponding ketone/ketyl systems, for a large variety of ketones, [see Hayon and Simic, ref. (l)].In the original paper the redox potentials referred to pH = 7. To obtain the data related to definitechemical species, we corrected the values for all ketyls with PKR > 7 : EB = E p ~ , - 0.059(pK~ - 7).The amendment improves the correlation. The points are for 1, acetone ; 2, cyclohexanone ; 3,acetaldehyde ; 4, propionaldehyde ; 5, acetophenone ; 6, formaldehyde ; 7, crotonaldehyde ; 8,p-chloroacetophenone ; 9, benzaldehyde ; 10, p-bromoacetophenone ; 11, acrolein ; 12, benzo-phenone ; 13, p-cyanoacetophenone ; 14, fluorenone ; 15, benzalacetophenone ; 16, benzil ; 17,9,lO-anthraquinone ; 18, 9,lO-anthraqujnone-1 -sulphonate ; 19, 9,l O-anthraquinone-2,6-disulpho-nate ; 20, 2-hydroxy-1,4-naphthoquinone ; 21, biacetyl ; 22, vitamin K ; 23, menaquinone ; 24,1,4-naphthoquinone ; 25, duroquinone ; 26,l ,2-naphthoquinone ; 27,2,5-dimethyl-p-benzoquinone ;28, 2-methyl-p-benzoquinone ; 29, p-benzoquinone ; 30, epinephrine ; 3 1, adrenalone ; 32, dipheno-quinone.The extrathermodynamic relations can be used to extrapolate the thermodynamic(and quasi-thermodynamic) cycles from one system to another, by a procedure whichmay be described as a projection along the chosen structural parameter. Each of thecycles, (2), (3) and (5), inter-relates four thermodynamic values. If any three of themobey an extrathermodynamic linear relationship, like (8) and (9) (i = Ox or R) inthe above example, the fourth value must obey the same kind of relationship.Inthe present example we can predict that the redox potentials for the systems protonatedketones/ketyl radicals obey eqn (1 1)where, by virtue of eqn (3a), (8) and (9), the " reaction constant "EA(x) - EA(o) p (EA) bX (1 la>(1 1b) P@A) = P ( 4 J + IP(PKR) - P(PKo,)lRT(ln lO)/F24 GENERALISED FORSTER CYCLEIf two of the thermodynamic quantities from a given cycle obey an extrathermo-dynamic linear relationship, the difference (or sum) of the other two must obey thesame type of relationship. We will demonstrate the usefulness of the rule onextrapolations of the Forster cycle (2) from one system to another.The excitation energies, 5, do not usually correlate with the Hammett-typesubstituent constants, or else the correlations are observed in a very limited range ofvariation of a.1o1 In some cases special substituent constants were suggested whichfit for the spectra-structure correlations only.'02 It is known, however, that the pK*values often obey the Hammett equation ;lo3 those for para-substituted phenolscorrelate well with the substituent constant a: .'' Taking these pK* values as internal8:2 3 4 53000rl2800 &2.m2600 742400a>.7122002 3 4 5(6)FIG. 8.-Extrathermodynamic correlations for protolytic equilibria in para-substituted phenols.(a) pKG plotted against pK* taken as an internal standard for the substituent effect, and the bestcorrelation line ; (b) (Crg - 5 ~ ) against pK*, Oi being the average of the absorption and fluorescencemaxima of the ith species.Experimental data taken from ref. (78) for the following substituentsin the para-position : (1) H ; (2) F ; (3) C1; (4) Br ; (5) CH3 ; (6) C2H5 ; (7) OCH3 ; (8) OC2H5 ;(9) SO; ; (10) N(CH3);.standard (to avoid the direct use of the 0: values) we have plotted pKG against pK*[fig. 8(a)]. A marked correlation is found (correlation coefficient Y = 0.922), wherebyAs two of the quantities (pKG and pK*) obey the same extrathermodynamic structuralcorrelation, their difference must obeyBy virtue of cycle (2) this is equivalent to the correlation of A7BA with pK* [fig. 8(b)],wherebyThe Hammett-type eqn (14) may be valid for the differences of excitation wavenumbers?B-FA,104 even if the FA and VB values taken separately do not correlate with pK* orCT+.In the present case, for para-substituted phenols, we find the following correlationcoefficients for the correlation with pK* : for CB (average from the absorption andfluorescence maxima) r = 0.563 ; for VA [(0, 0) transition approximated in the sameway] r = 0.743 ; for F,-VA [fig. 8(b)] Y = 0.904.dPKGldPK* = P(PKG)/P(PK*). (12)dApK*/dpK* w 1 -p(pKG)/p(pK*). (1 3)dA?BA/dpK* % [I -p(pKG)/p(pK*)]kT(ln lO)/hc. (142. R . GRABOWSKI AND W. RUBASZEWSKA 255 . SEARCH FOR A CORRELATION BETWEEN hpK* AND APK,Walsh pointed long ago lo5 to the analogies in effects on molecular structure ofone-electron reduction and one-electron excitation.Since his structural rules provedtheir usefulness,' O6 9 we have examined whether analogies exist between ApK*and ApK: values [for definitions see eqn (2) and (3)J The data from the tables2 to 5, related to a variety of systems, are plotted in fig. 9. For pK* only thepKs and pKD values were plotted. The ApKT values in general follow similar trendsto the ApKS values.1050 %4-5-1 00 21* El713 O8A ' 6 00140 7 8 20 2324I I I5 10 15APK,FIG. 9.-Plot of ApKgX against ApKz values for several series of compounds : 0 aromatic nitro-compounds ; 0 carbonyl compounds ; A quinones ; @ semiquinone radicals. Numbering ofthe compounds as in the tables.A very rough correlation, more a general trend, is evident.An analysis of theequations given in section 1 reveals no direct relation between ApK* and ApK, values.Extrathermodynamic relations may provide the reason since they often allow us totreat the acidic and basic species as differing in the substituent (e.g., X- for the base,XH for the acid), provided neither the electronic excitation nor the additional electronare localized on this swbstituent. The redox potentials, EZ and Eg, then follow arelation like (8). This is seldom the case for TOx and iioxH which define ApK,*, ; evenif it holds for ApK& the slope of the regression line [the " reaction constant " p ( f ) ]may be of opposite sign to p(E)lo8 (cJ: the spectra of nitrosobenzenes log).The trend observed in fig. 9 cannot be derived from this type of relationship, asthe site of proton attachment cannot be treated as a substituent, e.g., in ketones orquinones.In the series of aza-aromatic compounds this condition is not fulfilled,nor is any correlation observed for ApK* or for ApKT. 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