J . Phys. Chem. 1986, 90, 5557-5560 phenol betaine 30 for each solvent, involving measurement of the absorption maximum and conversion to the parameter through the relationshipz2ET(30) = 28 590/h,,, (nm). Acknowledgment. We are grateful to the United States-Israel Binational Science Foundation, the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the European Research Office for support. Preliminary work by Dr. H. Dodiuk (Tel-Aviv) and Dr. G. Striker and Dr. T. Jovin a t the Max Planck Institut fur Biophysikalische Chemie, Gottingen, Federal Republic of Germany, showed that there were substantial solvent effects on the radiative lifetimes of several bimanes. Considerable effort was expended by Dr. J. Hermolin in the synthesis of the "zero-bridged" bimane 4 and by Marcia Ben-Shoshan and Oded Friedman in the preparation of syn-
5557
(hydr0,hydro)bimane (1). The details of these syntheses will be reported elsewhere. The active participation of Ellen Longman in part of the work is acknowledged. The gift of pyridinium phenol betaine from Prof. C. Reichardt, Universitat Marburg, Federal Republic of Germany, is appreciated. The advice of Prof. U. Even led to a successful flash-lamp design and to many other improvements in our work. Registry No. 1, 19769-56-5; 2, 98194-60-6; 3, 74235-71-5; 4, 82666-03-3; 5, 68654-19-3; 6, 68654-22-8.
Supplementary Material Available: Tables 111-VI of absorption maxima, quantum yields of fluorescence, fluorescence lifetimes, and radiative rate constants for syn-bimanes 3-6 (4 pages). Ordering information is given on any current masthead page.
Structures and Fundamental Vibrations of p -Benzoquinone and p -6enzosemiquinone Radical Anion from ab Initio Calculations' Daniel M. Chipman* and Michael F. Prebenda Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 (Received: October 21, 1985; In Final Form: April 15. 1986)
Properties of the ground electronic states of neutral p-benzoquinone and the related p-benzosemiquinone radical anion are determined by ab initio calculations. The structures, vibrational frequencies, and frequency assignments of the neutral are found to be in good agreement with the most recent experimental determinations. Good agreement is also found for the few anion frequencies known experimentally. The calculations provide new information on the structure of the anion as well as on its other vibrational modes. Significant differences between the neutral and anion can be explained on the basis of weakening of the C=O and C=C bonds and strengthening of the C-C neutral bonds upon electron attachment.
I. Introduction p-Benzoquinone together with the corresponding p-benzosemiquinone radical anion constitutes a model system for an important class of molecules involved in electron transport in biological system^.^-^ Consequently, many aspects have been H
\ c=c/ H /
o=c
I
\
c=o /
?="\
H
H
studied by a wide variety of methods. From the rich literature on these species, we list here a few representative leading references that are particularly relevant for the present study on the ground electronic states. The structure of neutral p-benzoquinone has been determined by X-ray4 and electron diffraction5techniques, and its fundamental vibrational frequencies have been studied in numerous infrared?' Ramant and optical absorption9experiments. (1) The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document NDRL2776 from the Notre Dame Radiation Laboratory. (2) Biochemistry of Quinones; Morton, R. A,, Ed.; Academic:, New York, 1965. (3) The Chemistry of the Quiniod Compounds;Patai, S . , Ed.; Wiley: New York, 1974. (4) Trotter, J. Acta Crystallogr. 1960, 13, 86. (5) Hagen, K.; Hedberg, K. J . Chem. Phys. 1973, 59, 158. (6) Becker, E. D.; Charney, E.; Anno, T. J . Chem. Phys. 1965, 42, 942. (7) Trommsdorff, H. P.; Wiersma, D. A.; Zelsmann, H. R. J. Chem. Phys. 1985. 82. ----. --.48. (8) Palmo, K.; Pietila, L.-0.; Mannfors, B.; Karonen, A,; Stenman, F. J .
Mol. Spectrosc. 1983, 100, 368. (9) Ter Horst, G.; Kommandeur, J. Chem. Phys. 1979, 44, 287.
By use of isotopic substitution experiments together with the aid of empirical force constant calculations, it has been possible to assign with reasonable certainty the frequencies of all 30 fundamental vibrations in this molecule. The corresponding pbenzosemiquinone radical anion formally produced by attachment of an electron to the neutrallo has long been the subject of ESR" and optical absorptionIz studies. Recently it has also been observed by resonance Raman s p e c t r o ~ c o p y ' ~to- ~determine ~ fundamental vibrational frequencies of four of the totally symmetric modes. No experimental information is yet available on the structure or on the other vibrational modes of the anion. In this work we present the results of ab initio calculations on the structures and vibrations of the ground electronic states of these two species. Highly sophisticated calculations are not feasible on systems of this size with most present day computational facilities, so relatively crude methods, Le., molecular orbital models with small split-valence basis sets, are used here. In fact, a major goal of the study is to establish the validity of these computational methods in such systems, since we wish to use them in the future to characterize other closely related systems for which little experimental information is available. For the neutral, and insofar as is known for the anion, the agreement of the theory with the most recent experimental determinations is found to be reasonably good, with a mean absolute error of 34 cm-l and a maximum error of 102 cm-' in the vi(10) Cooper, C. D.; Naff, W. T.; Compton, R. N. J . Chem. Phys. 1975, 63, 2752.
(1 1) Venkataraman, B.; Segel, B. G.; Fraenkel, G. K. J . Chem. Phys. 1959, 30, 1006.
(12) Adams, G. E.; Michael, B. D. Trans. Faraday SOC.1967,63, 1171. (13) Tripathi, G. N. R. J . Chem. Phys. 1981, 74, 6044. (14) Beck, S. M.; Brus, L. E. J . Am. Chem. SOC.1982, 104, 4789. (15) Schuler, R. H.; Tripathi, G. N. R.; Prebenda, M. F.; Chipman, D. M. J . Phys. Chem. 1983, 87, 5357.
0022-3654/86/2090-5557$01.50/00 1986 American Chemical Society
5558 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Chipman and Prebenda
TABLE I: Geometrical Parameters in p-Benzoquinone and in p-Benzogemiquinone Radical Anion‘ geometrical parameter
R(C=O) R(C-C) R(C=C) R(C-H) Lo=C-C LC-C=C LC-c-c LC-C-H
neutral X-rayb
elec diffC
calcd
anion calcd
1.222 1.471 1.322
1.225 1.48 1 1.344 1.089 121.0 121.0 118.1
1.214 1.483 1.319 1.070 121.9 121.9 116.2 115.8
1.274 1.436 1.353 1.074 122.9 122.9 114.2 116.5
121.1 121.1 117.8
a Bond lengths are in angstroms, bond angles in degrees. 4. CReference5 .
Reference
brational frequencies. The calculations confirm the most recent assignments of the neutral and the known anion fundamentals and, in addition, provide information about the anion structure and vibrations that is not yet experimentally accessible. The major differences between the two species are found to be due to weakening of the C=O and C=C bonds and strengthening of the C-C bonds in the anion relative to the neutral form. This leads to bond length changes of up to 0.05 A as well as to very large changes in the symmetric and asymmetric C - 0 stretching frequencies and to large changes in some C=C and C-C stretching frequencies. 11. Computational Methods The results reported here were obtained with the GAUSSIAN 8zI6 program running on a VAX 11/780 computer. The standard 3-21G” split-valence basis set was utilized to obtain restricted Hartree-Fock energies for the neutral and unrestricted Hartree-Fock energies for the anion. In this program, the equilibrium geometry is located by a search procedure based on energy and analytic energy derivative calculations. The molecular force constants are then obtained at the computed equilibrium geometry by analytic evaluation of energy second derivatives. This produces a full harmonic force field which is then used in conjunction with the nuclear masses to calculate normal modes. Our earlier workI5 on this system utilized a different program, which evaluated the force field by numerical differences of analytic first derivatives at finite displacements of the nuclei. Most of the frequencies calculated by the two programs differ by less than 1 cm-I although several larger discrepancies, one as large as 16 cm-I, were found. This can be taken as an indication of the numerical precision of the calculations. It also indicates that few, if any, modes show any unusually high anharmonicity in this system. A recent comprehensive study1* of numerous representative molecules calculated at this level of theory has led to a recommendation that the calculated frequencies be multiplied by the empirical factor 0.89 to approximately correct for the combined errors due to neglect of electron correlation and anharmonicity, both of which generally tend to lower the frequencies. To facilitate comparison with experiment, this factor is applied to all the frequencies reported in this work. One might be concerned, particularly in the case of the anion, about the adequacy of the 3-21G basis set for the present study. It is certainly the case that diffuse functions are required for proper description of anions with highly localized negative charge. However, such functions are not so important for systems such as the present one with delocalized charge.19 As a practical point, inclusion of diffuse functions would make the present study im(16).Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University; Pittsburgh, 1983. (17) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. (18) Pople, J. A.; Schlegel, H. B.; Krishnan, R.;DeFrees, D. J.; Binkely, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J Quantum Chem. 1981, S15, 269. (19) It has been suggested that solvent cage effects can be mimicked by purposefully excluding diffuse functions from the basis set in anion calculations. See: Clark, T. Faraday Discuss. Chem. SOC.1984, 78, 203.
Figure 1. Singly occupied ,b radical anion.
T
molecular orbital of p-benzosemiquinone
possible with the available computational resources. Examination of this matter, as well as that of the validity of the empirical 0.89 factor, are in fact then major motivations for the present study. The discussion will be presented with these questions in mind. 111. Geometrical Structure The calculated equilibrium geometry for IA, neutral pbenzoquinone is compared in Table I to that found in X-ray4 and electron diffraction5 experiments. The calculations are in very good agreement with the X-ray structure for the carbon and oxygen atom bond lengths, all distances differing by less than 0.01 A. The agreement of these parameters with the electron diffraction results is also generally good, the only significant discrepancy being the C=C bond length where the electron diffraction result is 0.02 A longer than either the X-ray or calculated result. The electron diffraction value of the C H bond length is also nearly 0.02 A longer than the calculated one. All of the bond lengths are well within typical ranges for the respective single and double bonds to spz-hybridized carbon atoms. The bond angles agree well in all the methods with differences of less than 2 deg in all cases. It is concluded that the calculations give a very reasonable description of the geometry of p-benzoquinone. To produce the radical anion, the calculations show the unpaired electron to occupy a bzs orbital pictured in Figure 1, producing a net 2B, state. Examination of the nodal structure of the singly occupied orbital shows that it is antibonding with respect to the C=O and C=C neutral bonds and bonding with respect to the C - C neutral bonds. Thus, one would expect the C = O and C = C bonds to lengthen and the C-C bonds to shorten upon electron attachment. The calculated geometry reported for the anion in Table I bears this out. Both the C=C and C-C bonds change by about half of the amount required to reach a typical aromatic C=C distance of 1.40 A. The C = O bond changes by nearly half of the amount required to produce a typical C-0 single bond of about 1.36 A. The calculations indicate only minor changes in the C-H bond length and in the bond angles when passing from the neutral to the anion. The calculated total energies are -377.1007 au for the neutral and -377.1373 au for the anion,*O each at their respective optimum geometries. This corresponds to an electronic contribution of 1.00 eV to the adiabatic electron affinity, which is changed slightly to 1.06 eV when corrected for differences in vibrational zero-point energy. The experimental total electron affinity is 1.89 eV.l0 It has been arguedz1that reasonable structural results can be calculated for anions with Hartree-Fock-based methods even when they incorrectly show the excess electron to be unbound. The present calculation correctly shows the electron to be bound and even recovers over half of the experimental electron affinity, giving some confidence that quite realistic structural results may be obtained here for the anion.
IV. Vibrational Frequencies The calculated vibrational frequencies for both h4 and fully deuterated d4 forms are compared to the experimental values in Table 11. For experimental values of the infrared active modes of p-benzoquinone, we use the results of Becker et aL6, except for the lowest frequency one which is taken from the recent gas-phase study of Trommsdorff et al.,’ who show this mode to be somewhat sensitive (-20 cm-’) to solvation effects. The Raman active modes (20) The UHF anion wavefunction has moderate spin contamination, (S2) being 0.92 as compared to the value 0.75 for a pure doublet wavefunction. The effect of this on the present results is not known but is not expected to be large. (21) Radom, L In Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1977; Vol 4, pp 333-352.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5559
p-Benzoquinone and p-Benzosemiquinone
TABLE II: Comparison of Experimental and Calculated (X0.89) Vibrational Frequencies in p -Benzoquinone Neutral and in p-Benzosemiquinone Radical Anion’ h4
symmetry
exptl
calcd
h,-d4 shift
d4
diff
exptl
calcd
diff
exptl
calcd
3 59 -3 42 -7 1 30 -26 -24 -10 -83 23 12 19 89 49 -34 -8 5 7 19 27 -5 1 56 21 -8 90 -34 24 -7 -15 -47
5 25 325 13 12 770 175 13 76 163 23 24 215 70 788 33 20 1 93 71 194 6 785 7 213 51 32 785 1 87 89
4 21 328 33 14 773 180 17 91 157 29 19 171 124 792 44 218 78 61 225 5 791
20
1
15 43 22
317 9 23
4 26 319 6 33 771
diff
p-Benzoquinone
agb
b b b:) b3gb
aue blud
bud
b3,d
447 774 1160 1657 1663 3058 766 249 800 1018 459 60 1 1230 1388 3057 330 989 728 944 1354 1666 3062 409 1066 1299 1592 3062 89 505 882
443 711 1166 1635 1736 3032 797 278 826 1095 443 584 1167 1353 3012 375 1091 706 914 1359 1716 3012 386 1036 1262 1629 3029 98 523 94 1
4 63 -6 22 -73 26 -3 1 -29 -26 -7 7 16 17 63 35 45 -45 -102 22 30 -5 -50 50 23 30 37 -37 33 -9 -18 -59
442 749 835 1644 1651 2288 591 236 724 855 436 577 1015 1318 2269 297 788 635 873 1160 1660 2277 402 793 1248 1560 2277 88 418 793
48 1
464 78 1 1148 1390 1607 2983
17
480
13 45 13
844 1426 1597
439 690 838 1602 1722 2258 617 260 734 938 413 565 996 1229 2220 331 873 628 854 1133 1711 2221 38 1 80 1 1158 1594 2253 95 43 3 840
5 235 104 35 776 3 89 101
1
4 -3 -20 -2 -3 -5 -4 -15 6 -6 5 44 -54 -4 -1 1 -17 15 10 -3 1 1 -6 2 38 -53 -3 9 -2 -2 -12
p-Benzosemiquinone agc
1161 1435 1620
460 755 829 1383 1575 221 1
-3 -2 3 -10
“All frequencies in cm-I. bExperimentalvalues for Raman active a8, blg, b2g, and b3, neutral modes taken from ref 8. CExperimentalvalues for a, neutral modes taken from ref 7. “Experimentalvalues for IR active b,,, bIu, and b3, neutral modes taken from ref 6, except that lowest frequency b3,, mode taken from ref 7. CExperimentalvalues for resonance Raman active ag anion modes taken from ref 15. are taken from the recent work of Palmo et a1.,8 who propose some different assignments than proposed by earlier workers. The two a, modes are taken from Trommsdorff et al.,’ who obtained them from a reanalysis of the electronic absorption spectrum. The above studies together with other references given in them show that solvation effects on vibrational frequencies are generally small, rarely more than a few inverse centimeters. For experimental values of p-benzosemiquinone, which are only available for four of the resonance Raman active a, modes, we use the results of Schuler et. al.ls The generally good agreement of the calculations with the latter indicate that solvation effects are not large for the anion either. Examination of Table I1 shows that agreement of theory with experiment is quite good, with the same mean absolute error of 34 cm-l for each of the h4 and d4 sets. Moreover, the errors are almost evenly divided between positive and negative discrepancies, indicating that the empirical scaling factor of 0.89 applied to the calculated frequencies is near optimum for this system. The largest error is 102 cm-I, occurring for the higher frequency a, neutral mode. However, this should not necessarily be regarded as shedding doubt on the experimental value since the calculated h4-d4isotope shift for this mode agrees well (within 17 cm-I) with experiment. In fact, most of the calculated h4-d4 isotope shifts agree somewhat better with experiment than do the frequencies themselves. The good agreement between theory and experiment provides strong support that the fundamental frequencies have been correctly assigned in the experimental works quoted, which differ
from earlier assignments in many cases. It is therefore evident that the full vibrational structure of the neutral species is now well understood. These comparisons also give confidence that the theorectical calculations on the anion are generally about the same quality as the neutral, at least as far as the force field is concerned. While agreement between theory and experiment is quite good, there are some systematic differences worthy of mention. Most notable is that the in-plane modes (ag, b3g,b,,, and b2,) generally have calculated frequencies a little lower than experiment, while the out-of-plane modes (big, bZg,a,, and b3,,) have calculated frequencies higher than experiment. This indicates that the inplane force constants are generally underestimated, while the out-of-plane force constants are overestimated somewhat in the (scaled) computational results. V. Neutral-Anion Vibrational Shifts It is of interest to examine the changes in frequency of the various vibrational modes upon electron attachment to the neutral. This comparison is given in Table 111. Only the calculated results are reported there since full experimental information is not available for the anion. In most cases, it is found that the h4 and d4 forms behave similarly, so only instances of significant differences will be explicitly noted. The in-plane modes will be discussed first and then the out-of-plane ones. In the a, set a very large change occurs for the symmetric C=O stretch, which shows a calculated decrease of 346 cm-l (228 cm-I experimental). This causes it to be below the frequency of the symmetric C=C stretch in the anion, whereas it was above in the
Chipman and Prebenda
5560 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
TABLE III: Comparison of Calculated (X0.89) Fundamental Vibrational Frequencies in p -Benzoquinone (Neutral) and p -Benzosemiquinone (Anion) and the Neutral-Anion SbifP oversimplified description
symmetry a,
bl, b2, b3g
C-C-C bend C-C str C-H bend C=C str C=O str C-H str C-H bend C=O chair bend ring chair bend C-H bend C=O bend C-C=C bend C-C str C-H C-C str - C-H C-H str C-C=C bend C-H bend C-C-C bend C-C str C-H bend C=O str C-H str C=O bend C-C str C-H C-C str - C-H C=C str C-H str C=O boat bend ring boat bend C-H bend
+
a" bl"
b2"
b3"
+
bend bend
bend bend
neutral
h4 anion
443 71 1 1166 1635 1736 3032 797 278 826 1095 443 584 1167 1353 3012 375 1091 706 914 1359 1716 3012 386 1036 1262 1629 3029 98 523 94 I
464 781 I148 1607 1390 2983 826 362 781 1041 443 621 1238 1410 2955 434 1040 736 92 1 1394 1195 2954 363 1016 1150 1452 2977 146 523 892
shift -2 1 -70 19 27 346 49 -29 -84 44 53 0 -43 -7 1 -56 56 -60 51 -3 1 -6 -35 52 1 58 23 20 112 177 52 -48 0 50
neutral
d4 anion
439 690 838 1602 1722 2258 617 260 734 938 413 565 996 1229 2220 33 1 873 628 854 1133 1711 2221 381 80 1 1158 1594 2253 95 433 840
460 755 829 1575 1383 221 1 642 344 67 1 91 1 412 608 1002 1351 2178 381 840 660 833 1144 1241 2176 358 796 1062 1398 2205 143 430 798
shift -2 1 -65 10 27 339 47 -25 -84 63 27 1
-4 3 -6 -122 42 -50 34 -32 20 -1 1 470 45 23 4 96 196 48 -48 3 42
'All frequencies are in cm-'
neutral. A significant decrease in the symmetric C=O stretching frequency is consistent with the weakening of the C=O bond seen in the geometrical structure of the anion. It is then surprising that a similar effect is not also seen for the weakened C=C bond-the symmetric C=C stretching frequency shows a calculated decrease of only 27 cm-l (37 cm-' experimental). The strengthened C-C bonds participate primarily in the two lowest frequency modes, which each then show an increase in frequency upon electron attachment. The C-H bend and the C-H stretch are not expected to, and do not in fact, change much between the neutral and anion. In the b3gset there are no large changes or reversals of order upon electron attachment. The four lowest frequency modes increase and the highest frequency C-H stretch decreases in frequency in the anion. The C-C stretch and C-H bend are close in frequency and are strongly coupled. The coupling is apparently largely kinetic since the neutral-anion shift for these two modes differs considerably in the d4 form compared to the h4 form. Evidence for this interpretation is given by the fact that the total neutral-anion shift for both modes added together is almost exactly the same in the two isotopic forms. In the b,, set, there is a very large change in the asymmetric C=O stretch, which shows a calculated decrease of 521 cm-I. This causes a reversal in order of this mode with a C H bending
mode in the h4 form, although not in the corresponding d, form. Again, this large shift is attributed to the weakening of the C = O bond in the anion. The three lowest frequency neutral modes show a small increase in the anion, and the highest frequency mode shows a moderate decrease. In the b2, set all the modes show a decrease in frequency in the anion. A notable large change occurs in the asymmetric C = C stretch, which shows a calculated decrease of 177 cm-l. This is consistent with the weakening of the C=C bond in the anion. No large absolute changes are seen in any of the out-of-plane a,, b,,, or b3, modes. There is, however, a large relative change in the lowest frequency mode of this system, namely the b3, vibration in which the two C=O bonds bend to produce boat forms of the molecules. This mode shows a calculated increase of 48 cm-' from the very low neutral value of 98 cm-' to the still low anion value of 146 cm-I. It is concluded that the vibrational modes of the anion are generally similar to the neutral. The few large changes that do exist can be easily understood on the basis of the weakening of the C=O and C=C bonds and the strengthening of the C-C bonds in the anion relative to the neutral. Registry No. p-Benzoquinone, 106-51-4; p-benzosemiquinone radical anion, 3225-29-4.
