3510
J. Phys. Chem. 1081, 85, 3510-3513
Theoretical Interpretation of the Standard Redox Potential of Benzene-I ,2-diol and Its Derlvatlves Shlnlchl Yamabe,” Department of Chemistry, Nara University of Education, Takabatake-cho, Nara 630, Japan
Tsutomu Mlnato, Department of Chemistty, The University of Brltlsh Columbia, Vancouver, British Columbia, Canada V6T lY6
and Masaru Klmura Department of Chemistty, Nara Women’s University, Nara 630, Japan (Received: April 24, 198 1)
A CNDOI2 MO calculation for the electronic energy including the solvent effect is made for 11 compounds of a series of benzene-l,a-diol derivatives (catechols (H2cat’s)).It is demonstrated that both the energies of the highest occupied molecular orbital (eHOMO’s) and the differences of the total electronic energies between Hzcat and H2cat+.(aET’s)are well correlated with the standard redox potentials ( E O ’ S ) estimated experimentally through the kinetic study by applying Marcus theory to the outer-sphere electron-transfer reaction. A theoretical analysis of t?HOMO is made in terms of both the orbital interaction and the Coulomb attraction presented by the solvent charges,
Introduction Recently,’ we made a kinetic study of the oxidation reaction of ortho, meta, and para isomers of benzenediols by tris(1,lO-phenanthroline)iron(III) and estimated the standard redox potentials of each isomer by applying Marcus theory2 to the kinetic data obtained. We calculated theoretically the energies, eHOMO and A&, for each isomer, using the CND0/2 MO methoda3 We found a good correlation between the theoretical energies and the redox potential. In the present study, we extend the calculation of eHOMO and PET to 11 compounds in a series of substituted benzene-1,2-diols (hereafter called catechols and abbreviated H2cat’s). We attempt to compare them with the standard redox potentials (Eo’s)of H2cat+.+ e F! H2cat, which already have been reported by Pelizzetti and Mentasti (PM).4 This comparison may give us much significant information not only on the validity of the application of Marcus theory to estimating the standard redox potential between the organic substrate and its cation radical but also on the substituent and solvation effects for the electron transfer in the oxidation reaction of such substrate.
is found to cause some technical difficulty such as the divergence of the SCF cycle. Since eHOM0’s and PET%may be calculated after the correct molecular structures are obtained, they are determined through the geometry optimization in the CNDO/2 framework. The CNDO/2 method is known to reproduce the equilibrium structures well.3 A& is evaluated approximately in terms of the “fixed structure” scheme. This means that the common structure for H2cat and H2cat+.is used to obtain their total electronic energies, although during the oxidation some geometrical relaxation may occur. The MO calculation deals, by nature, with the free (in the gas phase) molecules. Then, it is necessary to consider because E” has been the medium effect on eHOMO and UT, measured in aqueous medium. To simulate the solvent effect on the electronic property, point charges are included in the CNDO/2 MO calculation. They are tentatively set at a position 2.0 A from the heteroatoms involved in H2cat. They are located at the extension of the lone-pair orbital of the heteroatom. For I, three point charges are included in the case of “with solvation” in Table I. The technical details of how to consider the influence of the point charges is explained in the Appendix.
Method of Calculation PM4reported Eo’s of 15 benzenediol derivatives (I-XV). Among them, we have chosen the following 11compounds for the CNDOI2 MO calculation. The numbering and the nomenclature are the same as in PMs paper: (I) 3methoxybenzene-1,2-diol;(11) 4-methylbenzene-1,2-diol; (111) 3-methylbenzene-1,2-diol;(IV) 4-(l,l-dimethylethyl)benzene-1,2-diol; (V) benzene-1,2-diol; (VI) 4chlorobenzene-1,2-diol;(IX) 3,5-dichlorobenzene-1,2-diol; (X) 2,3-dihydroxybenzoicacid; (XI) 3,4-dihydroxybenzoic acid; (XIII) 3,4-dihydroxybenzonitrile;(XIV) 4-nitrobenzene-1,Pdiol. The calculation of four other compounds
Results of Calculation In Figure 1, the structures determined theoretically are displayed. For 11species, values of f?HOMO and mTare obtained and are shown in Table I together with values of E”. The downward arrow in the table indicates that the oxidation of the lower compounds is more difficult. eHOMO and A E T without solvation effect are found to be poorly correlated with E”. With solvation effect, the correlation turns out to be good, and the results are shown in Figure 2. We may say that favorable linear relations are established in the figure. Point I’ (4-methoxybenzene-l,2-diol) is tentatively indicated instead of I (3-methoxybenzene1,2-diol),because point I deviates remarkably from the line. In view of the data in Table I and the discussion given in the next section, compound I in PM’s paper seems to be 4-methoxybenzene-1,2-diol. These good correlations indicate that Eo’s of the catechols are determined by both the substituent electronic effect and the Coulombic field
(1) M. Kimura, S. Yamabe, and T. Minato, Bull. Chem. SOC.Jpn. 64, 1699 (1981). (2) R. A. Marcus, J. Phys. Chem., 72,891 (1968). (3) J. A. Pople and D. L. Beveridge, “Approximate Molecular Orbital Theory”, McGraw-Hill,New York, 1970. (4) E. Pelizzetti and E. Mentasti, 2. Phys. Chem., 105, 21 (1977). 0022-3654/81/2085-3510$01.25/0
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No.
Standard Redox Potential of Benzene-I ,2diol
23, 198 1 35 11
TABLE I: Correlation between the Standard Redox Potential ( E ” ) of Catechols Estimated with Marcus Theory and the Theoretical Data (eHnMoand & E T ) Calculated with the CNDO/2 MO theoretical energies,O au without solvation with solvation compda
Eo,b V
HOMO
AET
I I‘ I1 I11 IV V VI IX X XI XI11 XIV
1.18
-0.430 - 0.409 -0.419 -0.431 - 0.411 -0.433 -0.431 - 0.441 -0.435 -0.436 -0.432 -0.472
0.395 0.379 0.375 0.395 0.379 0.403 0.407 0.417 0.400 0.402 0.404 0.408
1.19 1.19 1.20 1.25 1.25 1.29 1.36 1.38 1.43 1.46
Nd
AET
HOMO
-0.462 - 0.449 - 0.443 - 0.461 -0.439 -0.463 -0.461 -0.472 -0.487 - 0.487 -0.499 -0.512
3
0.428 0.420 0.414 0.428 0.407 0.434 0.438 0.441 0.453 0.456 0.466 0.462
a I’ is 4-methoxybenzene-1,2-diol. Other compounds are shown in Figure 1. Taken from ref 4. Experimental conditions: 1.00 mol dm-3 perchloric acid; H,cat+. + e 2 H,cat ( E ” ) . The designations “without solvation” or “with solvation” denote the absence or the presence of the counter charges located near the heteroatoms, respectively. 1 au = 627.565957 kcal/mol. Number of point charges.
0
“
/ IX
XI11
@a
XIV
@a
I B
’//
d
Figure 1. Computer-plotted swuctures of catechol derivatives optimized by the CNDOIP MO. In the optimization,the benzene ring (C-C = 1.40 A), the C-H bond (=1.08 A), and LHCC (=120’) are kept frozen. The small empty circles denote hydrogen atoms. The optimization Is carried out for angles and bond lengths of two OH groups (where the intramolecular hydrogen bond is present) and the functional group, X.
presented by counterions of solvent. However, points IIIV deviate noticeably from the lines in the figure. While experimental E O ’ S for I1 and I11 have the same values (1,19), their eHOMO and AE, values are different. It seems that there is room for doubt in taking the same redox potential for I1 and I11 and that the determination of E’ with kinetics data from Marcus theory is not sensitive to such small differences.
Discussion According to the analysis of the theoretical energies given in the previous section, the standard redox potential of substituted benzenediols is controlled by two factors,
1.2
11
14
15
En ( v )
Figure 2. Correlations of e n W vs. E’ (empty squares) and AET vs. E’ (empty circles). The values of eHOMO and AhET are those with solvation in Table I. The line for emO vs. Eo is drawn arbitrarily so as to pass midway between points V and V I and between points X and XI. Similarly, the line for AET vs. Eo is taken to pass through points V and X.
the substituent effect and the solvent effect. We investigate how they influence eHOMO. Substituent Effect. HOMO of the substituted catechols is mainly composed of the highest occupied MO of the parent molecule (homoP) and the highest occupied MO (homoX) or the lowest unoccupied MO (lumoX) of the substituent X.6 Which combination (homoP-homoX or homoP-lumoX) is more significant for HOMO is determined by the character of X (see Scheme I). For homoP-homoX (X = -OMe, -Me, -OH, and-Cl), the lobe of homoX can overlap substantially with that of homoP, resulting in much orbital interaction. This brings about the large energy splitting between HOMO and (6) S. Inagaki, H. Fujimoto,and K. Fukui, J.Am. Chem. Soc., 98,4064 (1976).
The Journal of Physical Chemistry, Vol. 85, No. 23, 1981
3512
Yamabe et al.
Scheme I
homop - homox
homop
0. II
-
,
lumox
,
I
I
-:homop , "--' HOMO
,
,,%-e-
lumox
'\,
, I
I I
homox
-\"'
HOMO-1
level deepened and the oxidation more difficult), This is demonstrated in the comparison of eHOMO of compound X with that of compound XI (without solvation in Table
Scheme I1
horn
horn
I).
H 1 I + ~
V
I
o v e r l a p zero (no eneruv
W
I
r\ U
+
o r b i t a l overlap (energy s p l i t t i n g
LJ
HOMO-1. That is, this interaction raises the HOMO level. According to perturbation theory, the extent of the splitting depends on the energy gap between homop and homoX and the extent of the overlap between them. The smaller energy gap and the larger overlap give a greater raising of the HOMO level. Thus, eHOMO for homoP-homoX is determined by the position of X on the benzene ring of catechol. Since the atomic-orbital (AO) coefficient of the 4 or 5 position is much larger than that of the 3 or 6 position (see the numbers at the left edge of Scheme I), the attachment of X to the former position may cause a more notable orbital interaction (Le., the HOMO level raised more) than the latter. In fact, IeHoMol of I1 (=1-0.4191) is smaller than that of I11 (=(-0.4311) without solvation (see Table I). For homoP-lumoX (X = -CN, -COOH, and -NO2), the lobe of homoX has either a node or only a small A 0 coefficient at the atom connected to the benzene ring. Consequently, the homoP-homoX interaction becomes unimportant because of the zero or small orbital overlap (see Scheme 11). Instead of the homoP-homoX combination, the homoP-lumoX interaction is a major factor to determine the level of HOMO, eHOMO. This difference comes from the nodal property of these orbitals. The homoP-lumoX interaction lowers the HOMO level. In this interaction the smaller energy gap and the larger overlap give a greater lowering of the HOMO level. Thus, the attachment of X to the position with larger A 0 coefficient (4 or 5) of homoP gives the larger IeHoMol (Le., the HOMO
This discussion is summarized as follows. For homoPhomoX, the inclusion of X gives the smaller IeHoMol than that of the parent molecule (X = -OH, -OCH3, -CH3, and -Cl), and the oxidation of the substituted catechol is easier. For homoP-lumoX, the inclusion of X gives the larger leHOMOl than that of the parent molecule (X = -CN, -COOH, and -NO2), and the oxidation of the substituted catechol is more difficult. In both cases, the attachment of X to site 4 (or 5) causes such changes more significantly. In view of this theoretical interpretation for the substituent effect on eHOMO, we may cast doubt on the almost equal values of E" of I-IV. For the Eo values in Table I, the compounds involving electron-attracting substituents reveal an increase of E" in the order expected from the attractive abilities of the groups (X = -NO2, -C1, and -COOH; see E" of VI-XIV). On the other hand, electron-releasing groups change only slightly the E" of the catechol (see E" of I-IV). For I-IV, all of the substituents including the hydroxy group have an electron-releasing character to displace the 7~ electron into the benzene ?r orbitals and to increase the ?r electron density in the ring. The inclusion of an electron-releasing group (X = -CHs, -OCH3, and -C(CH3),) has only a minor effect on the electron density at the OH group and accordingly on E" because the electron transfer in the redox reactions may occur at the OH group. Solvent Effect. In protic aqueous solution, polarized heteroatoms in X may call for counter (positive) charges and lead to the formation of hydrogen bonds. The approach of protons toward lone-pair electrons lowers eHOMO through the stabilization of the Coulombic field. Therefore, leHoMolbecomes larger than that without solvation, particularly for compounds X, XI, XIII, and XIV. For these species, eHOMO is found to be controlled by the number of counter charges put around them rather than by the genuine electronic properties of the free molecules, as is shown in Table I. Point XIV, which deviates somewhat from the line in Figure 2, would be corrected through
Standard Redox Potential of Benzene-l,2-diol
some other way of evaluating the extent of hydrogen bonding. We ascribe the deviating points to two reasons. For 11-IV, the experimental assumption involved in Marcus theory may not give the difference of the oxidation potential, where the MO calculation shows a definite difference. For XIV, which calls for a strong hydrogen bond around the NO group, the uniform use of counterions (S;. = 0.1 and 2.0 assumed here does not sufficiently reproduce the real 0.4+ interaction.
1)
Concluding Remarks In this work, we have compared the two energies, eHOMO and AET,calculated by the CNDO/2 MO to the standard redox potential, E O , for catechol derivatives. A good linear correlation has been found except for a few compounds. The few exceptions may come from two sources. One is that, when X is an electron-releasing group , Eo is insensitive to the positional difference of X on the benzene ring and is affected solely by the electron density on the OH group. The other is the way of estimating the solvent effect. The theoretical analysis has revealed that the standard redox potential of catechols is governed by two factors. One is the extent of the orbital interaction between homo of the parent molecule and homo or lumo of the substituent. The other is the solvation toward the heteroatoms involved in the substituent. Acknowledgment. This work is partly supported by a Grant-in-Aid for the Scientific Research B (No. 447039) from the Japanese Ministry of Education. We thank the Computer Center, Institute for Molecular Science, for the use of the HITAC M-200H computer. The geometries in Figure 1 were drawn by the use of the plotter program, NAMOD.~
Appendix The solvent effect on the electronic property of a molecule is represented as the origin of the electrostatic field. Then, how to include the Coulomb effect of point charges on eHOMO and AET is presented. First, a modified Fock matrix, F,,’, is defined: (6)Y.Beppu, QCPE, 370, 11 (1979).
The Journal of Physical Chemistry, Vol. 85, No. 23, 1981
F,,’ = F,, +
v,,
3513
(AI)
(x,, x,) matrix element in the CND0/2 frameq3 Ywvis the matrix element of any oneelectron operator, V(1).
F,, is the regular A 0 V,, =
S X , ( ~ )x,(U dT1
(A2)
v(1) represents the effect of thtexternal field. In the case of the N Coulombic charges, V(1) is given by (-43) {j denotes the effective charge of the jth center. Here, the Mulliken and point-charge approximations for V,, are introduced.
v,, = f/2SPY(V,,+ VvJ = N
N
1/2SpukC rje2/Rja - C Cje2/Rj,d (A41 j-1
J=1
AO’s x, and xv belong to atoms a and p, respectively. S, is the overlap integral (=Sx,(l) x,(l) dT1) and Rja is the distance between the nucleus a and the jth point charge. In this work, eq A4 is incorporated into the CNDO/2 program to evaluate F,;. lj is taken to be 0.1 as the effective charge for any counterion, and Rja is taken to be three 2.0 A uniformly. For I’ (4-methoxybenzene-l,2-diol), point charges, ( N = 3), are included in the MO calculation. 0,5=0.1 ”\
0
2.0 A
