Structure- and Solvent-Property Relationships for the Electronic Energies of Charge-Transfer Complexes Between Certain Benzene Derivatives

A chemical model is proposed for describing charge-transfer complexes between aromatic amines and electron-accepting benzene derivatives containing a group having a double- or triple-bond conjugated with the benzene ring. According to this model, an electron migrates from the nitrogen atom of the amine to one of the atoms of the multiple-bonded group during charge-transfer interaction. Structure-property relationships were derived for correlating: (1), the transition energies of the complexes; (2), the ionization, or oxidation, potentials of the amines, and (3), the electron affinities or reduction potentials of the electron acceptors, with the electron-donating abilities of the substituents of the various compounds. Transition energies calculated from reported spectroscopic data for these complexes were correlated using equations derived in this study. Similarly correlated were reported data for the above properties of the amine and electron acceptor. Equations were derived for correlating the effect of variation in solvent on the transition energies of the complexes. Correlation of reported spectroscopic data indicated that the greatest effect is caused by variation in the refractive index; of secondary importance was the change in dielectric constant.


. Introduction
A number of reports on investigations of electron donor-acceptor (EDA) complexes in which aromatic amines function as the electron donor and other benzene derivatives function as the electron acceptor have appe are d in the last twenty years .1 (In this investigation, the term "aromatic amine" is limited to aniline and its derivatives, while compounds like benzylamine and naphthylamine are excluded.) Figure 1 shows the structures of the components of the complex discussed.
Practical application of the complexes between aromatic amines and electron-accepting benzene derivatives have been quite diverse in materials science and applied chemistry. In one investigation, the complexes were prepared for the purpose of obtaining I Fi gures in brac kets indicat e th e literature re ferences a l the end of this paper. * This in vestigatio n was s upport ed , in p ari. by Resea rc h Grant DE02494-09 to th e Am eri .
can Denta l Assoc iation He alth Fo undatio ll from the Na tional In stitut e of De nt al Researc h a nd is part of the de nt a l researc h program co ndu c ted by th e Na tional Bureau of Sta ndard s in coo pera tion with th e Ame ri ca n De nt a l Associati on Health Found ation. This pape r is ada pt ed fro m a th esis submitt ed to th e Am eri ca n Unive rsity. Washington , D.C., in pa rti a l ful fillm e nt of th e require me nts for the M.S. Degree in C he mis try, April 1975. materials with a greater mechanical strength than that possessed by the isolated components of the complex [17,18,21]. In other cases, the complexes were used as a tool for studying certain biochemical processes and in an analytical procedure [11,13,23,24]. In some instances, complexes between aniline derivatives and other aromatic compounds have been shown to have undesirable properties, e.g., a considerable amount of color when present in otherwise acceptable composite filling materials designed for use in dentistry [25,26].
Although such donor-acceptor c~mplexes are of fundamental interest and have practical utility, an overall view of the physiochemical properties of these complexes as they vary with the natures of the substituents of the electron-donating amine and the electron acceptor and of the solvent has apparently not heretofore been undertaken. If a quantitative relationship between a measured physical property and structural and solvent parameters were effected, then a complex could be designed having the value of the physical property optimized over all possible variations in structure.
One of the most important properties of these complexes is th e appearance of an intermolecular electronic Electron-Donating Aromatic Amine X JO-z Electron-Accepting Benzene Derivative

FIGURE L Components of the Electron Donor-Acceptor Complex Studied in This Investigation_
R I and RZ are e ither H or CR'RHR'n. whe re R' , R" or R'" is any atom or group of atom s that is s ufficiently small to allow fo r coplanarit y of th e benze ne ring and th e nitroge n substitu ent.
R3 is any subs tituent in the meta-or para-pos ition ; if in the ortho-pos ition. th e sub stitu e nt mu st be small e nough to allow for copianarity of the be nze ne rin g and th e nitroge n s u bstitue nt s.
Z is a group of atom s containing a doubl e-or triple-bond conjugated with the benzene ring.
X is any substitue nt. and X may be repeated so that multiply-substituted compound s are c on sidered.
charge-transfer (c-t) transition observable by ultraviolet or visible light spectroscopy [1,4]. The term "chargetransfer complexes" has therefore been applied to these complexes as well as to others that exhibit this phenomenon [27]_ "The property of charge-transfer complexes which is normally most readily, and certainly most frequently, measured is the energy of the (usually lowest) intermolecular charge-transfer transition of the complex in solution" [28]. This energy, E et, is readily obtained by spectroscopic measurements using the relationship [29]: (1) where E et is the c-t transition energy per mole of the complex, No is Avogadro's number, h is Planck's constant, v~ax is the frequency at which the differential absorption of the complex is a maximum [5], c is the speed of light in a vacuum and .\~ax' the wavelength corresponding to v~ax-The differential absorption is obtained by measuring the absorption of the complex relative to the sum of the absorptions of the individual components rather than to the absorption of the solvent as in the usual case [26].
It must be clearly realized that in addition to the charge-transfer transition occurring in a thermodynamically stable donor-acceptor complex, charge-transfer transitions may occur during a random encounter of the donor and acceptor. Orgel and Mulliken have referred to this phenomenon as "contact chargetransfer" [30]. If only contact charge-transfer occurs in a given material, then the experimentally determined thermodynamic formation constant for the hypothetical complex assumed to be present would be found to be essentially zero_ For economy of words, both stable complexes and those interactions demonstrating charge-transfer transitions will be referred to as "charge-transfer complexes", or simply, "complexes".

174
The results obtained in this investigation are thus not necessarily related to the thermodynamics of EDA complex formation and should be kept separate_ The principal purposes of this investigation were: (1), to derive e quations suitable for correlating the electronic transit jon energies of complexes (in solution) between aromatic amines and compounds from one class of electron-accepting benzene derivatives with the properties of the substituents of the two compounds and the nature of the solvent and (2), to use these relationships for correlating previously reported transition energies (or transition energies calculated from previously reported frequencies, or wavelengths, at which maximum spectroscopic absorption occurs) of the complexes_ The electron acceptors considered here are exemplified by aryl-substituted nitrobenzenes, cyanobenzenes, and benzoates, i.e_, compounds in which an electron-accepting group possesses a doubleor triple-bond that is conjugated with the benzene ring_ This class contains those benzene derivatives that most readily accept electrons, e_g_, 1,3,5-trinitrobenzene and 1,2,4,5-tetracyanobenzene_ In the course of this investigation, comparable equations were derived for correlating the ionization potentials, or oxidation potentials, of the aromatic amines and the electron affinities, or reduction potentials, of the aromatic compounds possessing a common electron-accepting group with structures in the respective series of compounds_

Transition Energies and the Natures of the Electron Donor and Acceptor-An Overview
Several equations have been derived relating the Cot transition energy to the natures of the donor and acceptor [31 and references contained therein]. The si m plest eq uation and probably the first to be derived IS: Ect=NoUP-EA +C), (2) where IP is the ionization potential of the electron donor, EA is the electron affinity of the acceptor and C is a collective term for the solvation, polarization, and nonbonding contributions to the energy [32,33]. As originally conceived, No in eq (2) is absent and thus the energy computed is for one molecule of complex. As will be seen shortly, use of No provides for the calculation of the energy on a molar basis, which is more convenient for correlation of chemical data.

. Identification of the Reaction Sites of t he Electron Donor and Acceptor
It will become apparent from the next section that, in order for the transition energies to be correlatable by the usual structure-property relationships, it is necessary to identify the reaction sites in the electron donor and acceptor and to determine if they remain the same as the structures of the reactant molecules change.
The first (and most generally accepted) hypotheses to be published regarding the locations of reaction sites in various molecules forming charge-transfer complexes were those by Mulliken in 1952 [34]. He considered electron transfer from an aliphatic amine to involve the non·bonded electrons on the nitrogen atom and therefore designated this class of compounds as ndonors. Similarly, if electron transfer to a vacant orbital of an electron acceptor occurred, then the acceptor was labeled a v-acceptor. However, on the basis of theoretical considerations, he concluded that all aromatic compounds donate or accept an electron during chargetransfer complexation primarily, if not solely, at the 7T-electron system of the benzene ring. That is to say, there is no one single reaction site although, of course, one location may be somewhat more reactive than another. He thus designated these compounds as 7Tdonors or 7T-acceptors.
This assumption with respect to the nature of aromatic electron acceptors has been used in several studies on charge-transfer complexes [26,33]. However,. Tsubomara concluded that in charge-transfer complexes of aniline derivatives with an iodine molecule that the amine can function as an n-donor [35].
In order to reach a definite conclusion as to whether t he aromatic amines and acceptors in this study involve the 7T-system or n·electrons or v·orbitals, direct experimental evidence is required. Unfortunately, this is not available. However, indirect evidence has been obtained that can be used to provide a reasonable assumption concerning the locations of the reaction sites. Recently, Janzen reviewed the literature on the electron spin resonance spectra of free radicals formed from benzene derivatives on gaining or losing an electron [36]. He indicated that an aromatic amine cation radical has the odd electron primarily located on the nitrogen atom. Likewise, an anion radical formed from a substituted nitrobenzene, cyanobenzene, or other benzene derivative possessing a group having one double-or triple-bond conj ugated with the benzene ring generally has the odd electron on the atom on the group adjacent to the benzene ring, i.e., a·atom, although in some cases, the odd electron may reside on the f3-atom.
Another approach for obtaining the location of the odd electron in aromatic radical anions has been reviewed by Hayon and Simic [37]. In water, anion radicals produced from the reaction of electrons (gen· erated in pulse radiolysis of the solvent) with various compounds are basic and can protonate. Protonarion of the anion radicals derived from benzoic and tereph· thalic acids and those from benzoyl esters occurs at the carboxyl group and not in the aromatic ring. Consistent with this is that protonation of anion radicals formed from nitrobenzene and aryl substituted nitrobenzenes takes place at the nitro group. In addition, the protonated anion radicals of benzaldehyde, aceto· phenone and benzophenone produced indirectly exist as a·hydroxyalkyl radicals. Consequently, in anion radicals of these highly electrophilic compounds, the odd electron is localized on the substituent and not the ring.
. Meisel and Nata [38] have very recently stated that "electron transfer to a nitro compound and from its radical anion is expected to involve the nitro group as the main site of the transfer." Their experimental results were consistent with this assumption.
Based on all these considerations, it will be assumed that the charge-transfer complex between an aromatic amine and a benzene derivative containing a group having a double· or triple-bond conjugated with the ring is as shown in figure 2. That is to say, electron transfer occurs between the nitrogen atom of the aniline derivative and one of the atoms of the group containing the multiple·bond, i.e., nov complexation, in Mulliken's terminology.

Transition Energies and Extrathermodynamic Relationships
In order to correlate the thermodynamic properties (e.g., equilibrium constants and enthalpy) or the kinetic data (e.g., rate constants and activation energies) with chemical structure for reactions of a series of closely related compounds in which the reaction site is held constant and various nonreacting atoms or groups of atoms are substituted in the molecule, chemists have utilized the concept of the "extrathermodynamic relationship" [39, 40 and references therein]. (Since one major use of this concept is in correlating the free energy changes in a group of compounds during reaction, the term "linear free·energy relation: ship" has also been applied but it is probably best to use this terminology in its more restrictive sense.) According to this treatment of the data, each substituent has a numerical value, i.e., sigma value, that reflects the ability of the substituent to donate elec- trons to the reaction site and which is independent of the reaction conditions, e.g., temperature and solvent. The sigma value will, however, depend on: (a) in aromatic compounds, the position of the substituent in relationship to the reacting site, i.e., ortho, meta, or para (abbreviated as 0, m, p, respectively); (b) the nature of the intervening atoms, i.e., aliphatic versus aromatic molecule; and (c) in some rather unusual circumstances in aromatic molecules, if direct conjugation with the reacting site occurs.
In the usual case, i.e., the reaction of metaand para-substituted benzoic acid, the relationship is generally given as where K is the reaction rate, or equilibrium constant; KO is the corresponding value for the compound in the series chosen as the standard; p is a parameter that depends on the reaction and the reaction conditions, and reflects the relative sensitivity of the reaction rate or equilibrium constant to variations in the substituent constant cr ("sigma") previously described. The standard compound is benzoic acid and cr for the aromatic hydrogen atoms is defined as zero.
For ortho-substituted derivatives, two effects come into play: (1) the ability of the substituent to donate electrons, and (2) the steric interaction of the substituent on the reaction site [41]. This site generally is a group of atoms that requires a specific geometrical relationship with respect to the plane of the aromatic ring. If the substituent is small or is sufficiently flexible that no steric hindrance results, then cra -crp is approximately constant, as in one series of benzoic acid derivatives [41]. If the substituent is so large that it interferes with the reacting site then no simple relationship between these cr values is possible. This latter case is beyond the scope of this investigation.
For reaction of aromatic compounds, e.g., phenols and anilines, in which a negative charge that is in direct conjugation with the substituent in the paraposition is created or destroyed, the appropriate equation is: (4) (For most substituents, the values of cr and crare equal.) For reactions of aromatic compounds, e.g. benzylic carbonium ions, in which a positive charge that is in direct conjugation with the metaor para-substituent is generated or eliminated, the appropriate equation is: (5) For reactions in the aliphatic series, in which the substituent is bridged by methylene groups to the reacting site, the appropriate equation is : Tables of the values of the substituent constants have been compiled and are readily available [41,42].
A heuristic approach will be used to derive the corresponding relationships involving charge-transfer energies. It has previously been shown for a series of methine dyestuffs formed from an organic acid that the low level transition energies (Amax -450-600 nm), which have been assigned to an intramolecular c-t process, of the dyes vary with the logarithms of the ionization constants, K A , of the parent acids by the relationship l43, 44J: where Vrnax is the frequency at which the spectroscopic absorption of the dye is maximum, R is the gas constant and T is the absolute temperature. Solving eq (7) for log KA gives: Assuming that KA can be correlated with the electrondonating ability of a substituent by one of the previous equations, eqs (3)-(6), gives: (9) where v~ax corresponds to K~ and cr X represents cr, cretc. as the case may be.

RT
In the charge-transfer complexes considered in this investigation, it was hypothesized that electron loss occurs at the nitrogen atom of the aromatic amine and electron acceptance occurs at the multiple-bond conjugated with the benzene ring of the second compound (see previous section). For such complexes  bet wee n one se ri es of aromati c co mpound s in whi c h o nl y o ne t ype of s ub stitu e nt is varied , e.g., th e nitroge n s ubstitue nt of th e a min e or th e ary l s ub stitu e nt a nitrobe nzene, and th e second a romati c co mpo und ke pt co ns ta nt , it is reasonab le to ass um e th a t a n e quation s imil ar in form to Equat ion (9)  2.303 RT -2.303 RTper . (9') [n the only in ves ti ga tion In whi c h a co mparable e qu ati o n wa s app li e d , th e Co t tra ns iti o n e ne rgies of l -alk ylpyridini um iodid es with vario us s ub stitutents in th e 3-and 4-positio ns of th e pyridinium rin g were correlated by ass umin g th at th e 3-a nd 4-positions we re co mparabl e to th e metaa nd para-positions, res pec tiv e ly, of a be nzene de rivative [45 -47]. Although u se d in th e form: wh e re £'tX is th e tran SItIOn e n e rgy of the s ubstituted co mpound a nd E'/' , that of th e pare nt , it is written in the abstrac t of re f.

RT
(Wh e n th e er a nd erva lu es differ e d, Koso we r used th e erva lues and re ferre d to th e m as " reso nan ce" er val ues .) A value of -] 3.4 was re port e d fo r p [45 -47].
Be ca use th e te rm for th e e quili bri um fr ee-e ne rgy c ha nge o r its ana log in kin e ti c or s pec trosco pi c data ca n be put into th e form t:.C/2.303RT, wh er e t:.C represe nts th e free -e nergy c ha nge or th e kin eti c or s pectrosc opi c co unterpart th e re of, in e xtrathe rm odynami c rela ti on s hips [39,40], it will be useful to de note thi s fun c tion of C s impl y as pC. Thi s ex press ion wi ll be called " th e extrathe rm od ynami c function" of C. Thi s co nve nti o n follows th e co nce pt di sc usse d by Sillen [48] in that in ste ad of th e elec tri c al pote nti al e of a half-ce ll, so me tim es th e dim e ns ionless quantity pE is used, whic h is de fin e d by:

RT' RT In 10
wh e re F is Farad ay's c on st a nt.
Thu s e q (9') can be writte n as: (9'C) This fun ction of th e tran sition e ner gy as well as othe rs to be di sc ussed for extrath ermod ynami c relationships is given in table 1.
It has been sh own previously that if th e extrath e rmodynami c re lati ons hip is fitt e d in th e forms ind ica ted in eqs (3)-( 6), (9)-(9'C), infinite sta ti sti cal wei ght is plac ed on th e meas ure d valu e of th e pare nt co mpound [49 ,50]. To avo id thi s, it was proposed that th e regres· sion lin e fittin g th e data not be forced to go throu gh th e ori gin , i. e., that th e re be an inte rce pt calc ulate d from the data [49 , 50]. Th e re fore, th e ex trath er mody-......   namic relationships should (and will in this investigation) be expressed in the general form where both pE¥ and p are obtained by least-squares fitting the equation.

Ionization Potential of Amines and Extrathermodynamic Relationships
The effect of the amine structure on the Cot transition energy of the complex is probably due primarily to variations in the ionization potential of the amine donor as indicated in eq. (2). Therefore, the correlation of the ionization potential of the amine with structure is an important area of inquiry.

Effect of Varying the Nitrogen Substituents
For aromatic amines, two separate structural c han ges are possible: nitrogen s ubsti tution and ring (aryl) substitution. The effect of substituents on the ionization potentials of aliphatic amines is highly correlated with that of alkyl free radicals [51]. Thus a s trai ght line is obtained if the ionization potentials of aliphatic amin es with the formula R \ R2R3N is plotted against those of the corresponding methyl free radical, i.e., RIR2R3(; . [51]. In addition the ionization potentials of these latter free radicals are approximately linearly related to the sum of the (]"* constants, !,(]"*, of the substituents on the carbon atom possessing the odd electron [51). However, Poldoja [52] proposed that for such systems hyperconjugation effects must be considered and proposed the equation: where H(n) are the intercepts, which may vary with the number of protons on the atom possessing the odd electron; n\ is the number of protons on the carbon atom of the alkyl substituent next to the atom with the odd electron, and a and a are parameters obtained by least-squares fitting the equation.
To obtain the corresponding extrathermodynamic relationship , eq (11) is substituted into eq (2) and C is assumed to be linearly related to the ionization potential, gi ving: WHere the valUe of EA is contained in the intercepts H"(n) .
The data of Foster and Hammick [1] for complexes of N-substituted anilines with 1,3,5-trinitrobenzene in cyclohexane were fitted by eq (12') (the contribution of the aromatic portion of the amine to L(]"* was ignored since it was constant throughout this series) using indicator variables [53] to obtain the intercepts H" (n) and the results are shown in table 3. (In what follows, whenever no reference is indicated after it is mentioned that data were correlated, the correlation was performed by the author. The res ults in the tables were obtained by the author). Since H" (n) are not significantly different for the various amines (95% confidence level) [53] and a" is negligible , the regression was repeated using the relationship: The results are shown in table 3. An analysis of variance [54] infers (at the 95 percent confidence level) that the goodness-of-fit eq (13) is consistent with that of eq (12') and, therefore, eq (13) describes the data adequately.
An implicit assumption made in the derivation and use of eq (13) is that the substituent produces no steric interference with the benzene rin g. ] ust as orthosubstituents that are bulky can cause serious problems in correlating ther modynami c data (sec. 4), some nitrogen substituents may also prove to be anomalous. Hickinbottom [55] found that tertiary aromatic amines such as N-methyl-N-t-butylaniline and N-methyl-N-tamylaniline are as unreactive with nitrous acid as is N,N-dimethyl-o-toluidine, which possesses a bulky methyl substituent in th e ortho-position, although other tertiary aromatic amines possessin g an un substituted para-position are generally quite reactive in forming the p-nitroso derivativ e [56). Primary alkyl substituents such as CH2R, where R may be any atom or group of atoms, attached to the nitrogen atom produce no apparent s teric problems in aniline derivatives with no ortho-substituents. If th e alkyl substituent is secondary, it is not known if steric interference with th e ring occurs. A further discus sion may be found under "Ortho Substitution" below.

Effect of Varying the Ring (Aryl) Substituents
Although few investigations on the effect of varying the nitrogen substituent have been made, a number of them have indicated the effect of ring substitution. Since the ionization potentials of alkyl free radicals are linearly related to the ionization potential of the corresponding substituted aliphatic amines [51], it would not be surprising to find that the ionization potentials of aryl-substituted benzylic free radicals are linearly related to those of the correspondingly ring-substituted anilines possessing nitrogen substituents held constant throughout the series under comparison. However, the correspondence does not appear to have been made previously.
In the case of metaand para-substituted be nzylic free radicals, the ionization potential is linearly related to (]" + of the ring substituent [57]. Crable and Kearns [58] found that for para-substituted anilines, the ionization potential is linearly related to cr +. A plot of their data (not shown) for metaand para-substituted anilines shows that by excluding the metaand para-amino substituted compounds, the correlation between ionization potential and cr + is quite good. This plot indicates that the maximum de viation (if the amino substituents are ignored) is approximately 0.02 electron volts which is in agreement with the finding that the average deviation between determinations for the same compound was approximately 0.03 electron volts. The corresponding extrathermodynamic relationship is given by (see table 1): (14) The re sults of correlating the data by eq (14) are given in table 3. In this case, two results are s hown , one including all the data and one in which the a mino substituent values are excluded. A test for outliers [59] (95% confidence interval) indicates that the amino substituted compounds come from a population different from the others. This lack of agreeme nt for the amino sub stituents has been found in correlating the effect that aryl substituents have on the electron spin resonance spectra of N,N-dimethylanilinium radical cation [36], a topic that will be discussed below.

Polarography of Aromatic Amines
An indirect method for assessing the relative ionization potentials of aromatic amines involves polarography. According to Foster [60] "polarographic oxidations may provide, by their experimentally determined half-wave oxidation potentials Eff'/J., a measure of the ionization potential of a compound. " If certain requirements are met, then the following equation holds: (15) where "/l.FSOlv is the difference in solvation-energy between the compound and its positive ion. If it is assumed that, for a series of compounds, variations in IP are much greater than /l.Pso1v , then Ef/~ may be used as a measure of the electron-donating ability of a donor. Because of this restriction it is obviously advisable to compare compounds which are chemically related" [60]. Correlation of the polarographic halfwave potentials of a series of aryl singly and multiply substituted N ,N-dimethylanilines in acetonitrile [61] with ~cr + of the substituents gives results shown in table 3. In this case, the p-dimethylamino group gives a res ult consistent with other s ubstituents. In contrast to thi s, Lagutskaya and Dadali [62] discuss their own and previous efforts to correlate the half-wave potentials of aromatic amines dissolved in aqueous solutions of various pH with cr and cr -values of the substituents and remark that a poor correlation is obtained. No mention of cr + values was made. According to Zuman [63], who has probably succeeded more than anyone else in correlating polarographic data, in describing the reactivity of benzene derivatives, the use of cr + is needed " in those so far rare examples in which the reaction constant p is negative," which in Zuman's terminology indicates polarographic oxidation. (Zuman e mploys a sign convention opposite the one in this paper.)

Electron Spin Resonance Spectroscopy
A practical way to evaluate the effects of substituents on the properties of free radicals is through the use of electron spin resonance (ESR) spectroscopy [36]. From observed coupling constants, a measure of the electronic spin density of the atom possessing an odd electron is ascertainable . .Janze n correlated the nitrogen ESR hyperfine coupling constants of metaand para-substituted N, N-dimethylanilinium cation radical against a + and obtained a good correlation if the amino groups were excluded [36]. Th e only s ubstituents to be at a considerable di s tance from the regr ession line were m-OH, m-C0 2 H a nd m-C0 2 C zH5• He "also obtained ESR data for s ubstituted nitrobe nze ne anion radicals to be disc ussed in section 6_

Ortho Substitution
In the case of ortho s ub stitution both elec trondonating ability and a steric effect of the substitu e nt may playa role, as di sc ussed in sec tion 4. This steri c effect causes th e reacting site, in thi s case, the amino group, to be out of the plane of the be nze ne ring [64]. A s imilar effect occurs when a dialkylamino group acts as a s ubstitue nt [65]. Since th e steri c effe ct dep ends on the sizes of the aryl and th e nitrogen s ubstitu e nts, it would be diffic ult , if not impossible, to correlate s uc h data with res pec t to sub stitue nt con stants and it will not be atte mpted in thi s inves tigation.
A simple rule to predi ct if s teric interference pre ve nting the coplanarity of the aromatic rin g and the nitrogen s ubstituents is absent is an adaptation of "the rule of six" [66]. In a secondary or tertiary aromatic amine, co nside r each of the atoms attached to the be nzene rin g at th e ortho-position as number l. A co unt of th e attac hed atoms in succession s hows that the atoms attached to th e a-carbon of eac h of the nitroge n s ub stitue nts are numbe r 6. If the number 1 atoms and two of the number 6 atoms in each s ubs titue nt are hydroge n (or are absent as in the case of the secondary amine), molec ular scale models indicate th a t steric interferen ce is absent, no matter the res t of the molec ule. Otherwi se, steric inte rfere nce may be prese nt.

Spectroscopic Evaluation
The only pre vious inves ti gation In whic h" spectrosc opic data of EDA co mplexes of aryl-substituted anilines with another benze ne derivative we re correlated agains t a + of the sub stitue nt is that of Kravtsov and Faingor [14], who correlated the frequencies of the absorption maxima of co mplexes of para-substj: tuted N, N-dimethylanilines with trinitrobenzene in chloroform versus a + of the para-substituents. The extrathermodynamic relations hip for their data is given in table 3.
Finally, it s hould be noted that Farrell and Newton proposed that the c harge-transfer transition energies of the anilin e complexes of te tracyanoethylene in chloroform be us ed to assess the ionization potentials of the amines [67]. Howeve r, the slope obtained from their data for para-s ubs tituted N, N-dimethylanilines (s ummarized in table 3) is inconsistent wi" th that from the data of another inves tigation [141 and with th e slopes from the extrathe rmodynamic relationships correlating ionization pote ntial data [58]. The reason may be as follow s. In the case of complexes of aromatic amines with other aromatic compounds, the amine is assumed to act as an n-donor with the electrons primarily of th e nitrogen atom involved in the complexation. On th e oth er h a nd , it has been shown that te tracyanoe th yle ne reac ts with aromatic a mines at the para-position by, accordin g to one hypoth esis, firs t forming a 7T-com plex , then a a-complex and finally a new co mpound [68]. Thus th e ionization potentials calc ulated from the transition energies of these latter complexes are not readily related to those obtained by other means_

Previo usly R eported Correlations
In compari son with studies on electron-donatin g aromati c amines, no exact relations hip has a ppare ntly been publis hed that correla tes the Cot transition e ne rgies of co mplexes with th e sub stituents of the electron acceptor if th e acceptor is a benzene derivative.
However , approximate tec hniques have been derived. Le pley and Thelman [33] noted that the electron affinity of an electron acceptor ge nerally in creases with the number of strong elec tron withdrawing substitu ents and the location of these substituen ts in the acceptor structure. Based on the previous investi gation of Hammond [69], who correlated the frequencies of the c harge-transfer absorption peaks of co mplexes of mono-substituted p-be nzophenones with hexam e thylbe nze ne with ap of the benzophenone s ubstitue nt , Lepley and Thelman postulated that the electron affinit y of a benzene derivative could be related to a p of the substituent but they did not report any mathematical relationship. Arge ntar and Bowen used the s um of the ap values of the substituents of aromatic co mpounds functioning as electron acceptors, the geo metry being ignored, in correlating the Cot transition e ne rgies of complexes of N, N-dime thyl-p-toluidin e by a linear regression [26]. In these cases, the electron acceptors were assumed to fun ction as 7T-acceptors.
According to Kosower (me ntioned above in section 4) the Cot transition energies of I-alkyl, 3-and 4-substituted pyridinium iodides, which form a charge-transfer complex by themselves, can be correlated with the avalues of the ring-sub stituents by assuming that the 3-and 4-positions of the pyridinium ring are analogous to the metaand para-positions of an aromatic compound, respectively [45-47].

Determination of the Exact Extrathermodynamic Relationship
Before attempting to derive the extrathermodynamic relationship for the substituent effect on the elec tron ...... 180-2700 c [74] aThe parent com pound is that co mpound in the family taken as the standard ; the interce pt in the regression results shown in table 5 is an estimate of th e value of the ET function of the energy under consideration involving this compo und. bIn all cases, when th e temperature was not reported, 25° was used in the calculation of the ET function. cThe average temperature of 193°C was used.
acceptor, th e correc t se t of "sigma" values for the substituent must be establis hed . Since th ere is no precedent for this, the correlation of ESR data as previously stated in the case of aromati c amines (sec. 4) furnishe s this information indirec tly. lanzen [36] showed that for metaand para-s ubstituted nitrobenzene anion radicals the nitrogen hype rfin e couplin g con stants form two lines whe n correlated with (Jof the subs titue nt. Mo st of the values fall on one line. Howe ver , the un s ub stituted compound and the two dinitro compounds form a second lin e, whic h intersects the first at the value of the un s ubstituted nitrobenze ne. This was explained by assumin g that th e second nitro group has more than jus t a minor perturbing influe nce on the nitro group th a t has gained an electron. The use of uhas also bee n reported by others in correlating the co uplin g constants of nitrobe nze ne anion radic als [70 and references therein]' The ass umption that th e logarithm s of the coupling co nstants are correlated with the s ub stitue nt consta nts [71] requires th at new ad hoc s ubs tituent co nstants be de fin ed and is th e n~fore to be avoided .

Polarography of E lectron Acceptors
Analogo us to th e situation regarding aromati c a min es di sc ussed in (sec. 4), polarogra phi c meas ureme nts provid e a relative me as ure of th e electron affinit y. " By a nalogy with one-electron oxida tion pote nti als .. . de terminati ons of polarographi c oneelectron redu ction pote nti als, E~ed, whilst not directly meas uri ng E , ne verth eless provi de one of th e few inde pe nde nt experime ntal estim ates of E whi ch are available fo r a range of acce ptor s pecies [72]," In this quota ti on, E is the electron affinit y. " Within experime ntal error, the reduction pote nti al (E~ed) is equal to the h alf-wave pote nti al (E~'fg) . For measureme nts against a stand ard calomel electrode: where 6.Fso1v is th e differe nce in solvation energy between the compound and its negative ion, and re presents mainly the solva tion of th e anion. r,oH g is the work function [for the half-reaction :F e-(in Hg) ~ Hgliq + e-(equal to 4.54 e V) and EH g: H g~+ i s the a bsolute value of th e c alomel electrode (equal to 0.53 V). For two differe nt acceptors Al and A2, is 6.Fso1v is ass umed to be constant, the n [72]" In di sc ussing subs titue nt effects on th e p olargraphic redu ctio n pote nti als of aromati c compound containing a reducible group h aving a double bond conjugated with the benze ne rin g, Zuma n indicated tha t (J -should be the preferable substitue nt constant for correlatin g the data [73]. However, in some ins tances, experi-2 Author's editorial c ha nge. 183 me ntal evide nce was available for preferring (J over (J - [73]. In no instance was there mentioned an equation of the form shown as Equation (9'D) although lin ear structure-property equations were used for treatin g thi s type of data.
The electron affiniti es and polarographic half-wave potentials of se veral aryl substituted methyl benzoates have been me as ured [74]. Howe ver, there was no me ntion of correlating the data with the s ub stituent parame ters . Th ese are correlated here and the results giv en in ta ble 5. In this se t of da ta and the followin g, the uvalue of the ortho-sub stitu ent is set equal to (J p . In on e pre vious inves tigati on where steri c factors were not important, (Jo -(Jp was approximately con stant (as disc ussed in sec. 3).
P e over has determin ed the half-wave reduction pote ntials of a numbe r of s ub stituted nitrobe nze nes [75]. Th e res ult of correlatin g the data by an extratherm odyn ami c rela tion s hip is give n in tabl e 5. Although ortho-substituents are appare ntly well-behaved in th ese in sta nces , furth er inves ti gation is need ed to de termine the limita tion s in ass umin g that (Jo-equals U p.

Spectroscopic Evaluation
In a ppa re ntly the only investigation of its type, P eover obtain ed the c-t tran sition energies of complexes of s ubstituted nitrob enze nes with N ,N ,N ,Nte tra me th ylph e nylenediamine and correlated the en ergies with the polarographic half-wave reduction pote ntials of the electron acceptor [75]. No correlati on of the e nergies directl y with s ub stitue nt para meters was reported . The results of correlatin g the calc ulated pET values vers us (J -of the metaor para-substituent is give n in table 5.

Effect of Solvent on the CoT Transition Energy-Solvatochromic Relationships
The mos t popular equ ati on for correlating the effect of solve nt on the transition e nergy of c harge-transfe r complexes is that due to McRae [76] as re vi e wed by Mataga and Kubota [77]. This is give n a s : [ D-l n 2 -1] 2 + F a bs D + 2n 2 + 2 (18) whe re 6.Va bS is the difference in the frequ e nc y at whi c h maximum absorption occurs in solution relative to that of the complex in vacuum (gas phase); A, B, C, E abs , and F a bs are cons tants de pend e nt only on the . solute; nand D are the refractive index a nd di electri c con s tant of the solve nt, respecti vely.
Emslie and Foster [8] correlated the frequencies of the ultraviolet absorption peaks of four complexes, of which two were of the aniline-substituted benzene type, against Kosower's Z value [79] of the solvent. This value is the transition energy (in kcal/mol) of the charge-transfer complex, l-ethyl-4-carbomethoxypyridinium iodide, dissolved in the solvent. They obtained two sets of straight lines depending on whether the solvents contained hydroxyl groups. Some nucleophilic solvents, e .g., acetone, did not fit the correlation.
Koppel and Palm [81] have suggested the use of a multiparameter solvent effect relationship : (20) where A is the measured property or a simple mathematical function thereof; Y is the polarity of the solvent, (D -1)/(D + 2) or (D -1)/(2D + 1); Pis the polarizability, (n 2 -1) / (n 2 + 2); E is the electrophilic solvation power, which is based on Dimroth's solvent polarity parameter, ET [82] and which is used in this case primarily to measure the ability of the solvent to hydrogen-bond to the solute; B is the nucleophilic (n 2 -1)/(n 2 +2) were preferred.
In correlating the transition energies of N-phenyl pyridinium betaine (E T parameters) and the chargetransfer bands of l-ethyl-4-carbomethoxypyridinium iodide complexes (Z parameter), the values of y, p, and e are not substantially different for the two sets of data [81]. Interestingly, statistical analysis [54] infers that in both cases p is not significantly different from zero at the 95 percent confidence level, indicating that for these systems, the refractive index is unimportant.
In order to obtain the relevant solvatochromic relationship, the pET values calculated from the spectroscopic data for the complexes of N,N-dimethylaniline with 1,3,5-trinitrobenzene or 1,2,4,5-tetracyanobenzene studied by Emslie and Foster [8] were correlated using a simplified form of Koppel's equation in which the B term was eliminated. This deletion was made because there are few solvents for which this value is known. Furthermore, this term was found necessary in very few previous cases [81]. Values of n, D, and E with the following exceptions were taken from the compilation of Koppel [81]; the refractive index of chloroform was taken as 1.4459 [83] and the values of E for chloroform, 1,1-dichloroethane and 1,1,2,2tetrachloroethane were taken as 3.04, 3 and 3, respectively. The results are shown in table 4.
Statistical analysis [54] implies (at the 95 percent confidence level) that only the coefficient for the refractive index term is significant different from zero in the case in which 1,3,5·trinitrobenzene is the electron acceptor and that the coefficients for both refractive index and dielectric constant terms are significantly different from zero in the second case. Further analysis [84] indicates (at the 95 percent confidence level) that the intercepts and the corresponding slopes in the two cases are not significantly different from each other.
Since the standard errors of regression in the two cases are not significantly different from each other (at the 95 percent confidence level) [85] the data for ' T he polarity of th e so lv ent , estim a te d by (D -1) /( D + 2). wh ere D is th e di e lec tri c co nsta nt a t 20°C.
" Th e polarizab ilit y of t he so l ve nt , esti mated by (n 2 -1 )/ ( n 2 + 2). whe re n is t he refractive index a t 20°C.
' Th e elec trop hili c so lvati on pow e r, whi c h me as ures th e ab ilit y of th e so lve nt to h yd roge n. bond to th e so lut e. 'A n indica tor variab le sc t e qu al to ze ro for th e co mpl ex of I ,3,5· trinitro be nze ne and to one, oth e rwi se. Th e use of th e ,,~ !e :':"s is ex pl ain ed in th e t ex t.
No te mper ature fo r th e de tertTIl nat ion of th e raw da ta was re port e d by th e inv es tigators. S in ce th e so lv e nt pa rame te rs, Y a nd P , were de te r· min e d at 20°C, pE,/,was calculat ed us in g thi s te mpe rature.
the two complexes may be pool ed a nd fitted by th e equ ation

[ D-1] [n2-1]
+~yX D +2 + p n 2+ 2 (20) where pE~. is th e inte rce pt, whi c h es timates the extrathermodynamic function of th e c-t tran SItIOn energy of the trinitrobe nze ne co mplex in a vacuum; X is an indi cator variable set equal to zero in the case of the trinitrobe nze ne co mple x and to one otherwise, and~pE~. and ~y, whi c h are obtained by least·squares fitting of th e equation , are th e diffe re nces in the pE~ and y values for the trinitrobe nzene and te trac yanobenze ne co mplexes res pec tively. Th ese res ults are given in table 6. S tati sti cal analys is [53] implies that (at th e 95 percent co nfid e nce level) y and ~y are not significantly diffe re nt fr om zero. Re peating th e regres· sion after eliminatin g th e ~y term gives th e final res ult sho wn in tabl e 4. This co rre la tion indi cates that the effect of solve nt on th e c-t transition e nergi es of the two co mplexes is parallel.
A correla ti on in whi c h th e y te rm was eli min ated (not s hown) indi cates that th e s lopes of the dielec tri c co nstant te rm s are signifi ca ntly diffe re nt for th e tw o co mpl exes, a nd that th e s lo pe of th e di electric co nstant te rm [or th e trinitrob e nze ne co mplex is zero. Although thi s latter co rrelati on is co ns iste nt with th e data, th e close ness of the slopes of th e refrac tive index te rm in th e two cases te nd s to persuade one that th e slopes of the dielectri c cons tant term s hould also be similar. More data on the tran sition e ne rgies of oth er co mplexes in this series in variou s solv e nts is required before it can be decided definitely that the solvent effec ts on this type of complex are indeed the same in all c ases, i.e., that y and p always have the same values (within experimental error) as those found in this inve stigation.
These results along with those of Koppel [81] indicate that in correlating th e charge-transfer tran si· tion energies of complexes between species that are uncharged in the ground state, the refractive index term is of primary importance; with species that are charged, the dielectric constant term is of s upre me importance.

Summary and Conclusions
The mathe matical re lationship s for th e variations in the c harge-trans fe r tran s ition e nergy of a co mplex · between an aromati c amine and a be nze ne d erivativ e possessing an electron-accepting group may be summarized as follows: For c hanges only in 1. Nitrogen substituent of the amine pET=pE~+PL(J"* (22) 2. Aryl substituent of the amine (23) 3. Substituent of the electron-accepting benzene derivative (with the electron-accepting group kept constant)

Solvent
[ n2 -1] [D-l] pET=pE~+a n 2 +2 +b D+2 . (25) In these four equations, pEr is the extrathermody· namic function of the charge-transfer transition energy defined as Eet/2.303RT, where Eel is the transition energy (equal to Nohv~ax' where No is Avogadro's number, h is Planck's constant, and v~ax is the frequency in the ultraviolet or visible spectrum at which the differential absorption of the complex is maximum), R is the ideal gas constant and T is the temperature (K); (J"*, (J"+, and (J"are the appropriate substituent parameters available in the literature; nand D are the refractive index and dielectric constant of the solvent, respectively, and pE~, p, a and bare parameters obtained by least-squares fitting the line. For this system, a is much greater than b.
For changes, either in the nitrogen substituent of the amine or in the aryl substituent of either compound, the implicit assumption is that the substituent does not prevent coplanarity of the reacting group and the benzene ring. In addition, anomalous results may possibly occur if: for the amine, the (J"; value of the aryl substituent is approximately equal to, or less than , the (J"; value of the substituted amino group, which acts as the electron source; and for the electron acceptor, the (J";; value of the substituent is approximately equal to, or greater than, the (J"; value of the electron-accepting group of the parent compound. The extrathermodynamic relationships for the electron-donating ability of the amine in the chargetransfer process with respect to variation in the aryl substituent is (26 ) where pED is the extrathermodynamic function of the ionization potential, IP, or of the polarographic oxidation half-wave potential, E ~~, of the electron donor equal to No(IP)/2.303RT or FE~M2.303RT, respectively.
The corresponding relationship for the electronaccepting ability of the electron acceptor with respect to variations in the nonreacting substituent is (27) where pEA is the extrathermodynamic function of the electron affinity, EA, or of the polarographic reduction half-wave potential, E~/f, of the electron acceptor equal to No(EA)/2.303RT or FE;ig /2.303RT, respectively.
The same requirements of coplanarity and of the restrictions on the magnitudes of the sigma values of the substituent mentioned for the c-t transition energy of a complex hold in the above cases also.
Note added in proof: After the present investigation was completed, Davidson [86] proposed that the mechanism illustrated in figure 2 was the first step in the photoreaction of aromatic nitrocompounds with N-alkylanilines to yield primary aromatic amines.
The author wishes to thank M. H. Aldrich and P. F. Waters of the American University for their helpful discussions.