J. PhyS. Chem. 1903, 85, 473-479
tension to promote formation of a fine initial emulsion. Titration with 1-pentanol rapidly saturates the aqueous phase; upon further addition alcohol forms droplets which spread over the surfaces of n-hexadecane droplets. This
473
produces highly transitory pressures in the interfacial soap f i i (also penetrated by individual alcohol molecules). The resulting very low interfacial tension allows resolution of the coarse droplets into microdroplets.
A Reexamination of the Oxygen Parameters in the CNDO/S Method. Application to UV and Photoelectron Spectra of p-Benzoquinone P. Jacques, J. Faure, Laboratoire de Photochimie Generale, Equipe de Recherche Associee au C.N.R.S. €cole Nationale Superleure de Chimle, 68093 Muihouse Cedex, France
0. Chalvet, and H. H. Jaffe’” Centre de Mecanique Ondulatoire Appliquee, Laboratoire Propre du C.N.R.S., 750 19 Paris, France (Received: March In Final Form: October 17, 1980)
IO, 1980;
The ability of various recent molecular orbital calculations to reproduce the UV spectra of p-benzoquinone (PBQ) is critically evaluated. Although the original CNDO/S method provides satisfactory results, a reparametrization of the ,@ parameters for the oxygen atom was found necessary to adequately reproduce the whole spectrum, and the set $(O) = -30 eV, NCONF = 60 was adopted. This set of parameters was shown also to improve the agreement between calculated and experimental spectra for other carbonyl compounds,while not significantly affecting the values for other compounds for which the agreement was previously satisfactory. Moreover, this new parametrization of the oxygen atom improves slightly the empirical linear correlation between the eigenvalues and the experimental ionization potentials derived from the photoelectron spectrum.
Introduction As pointed out by Morton,l the quinones are a class of compounds of considerable biological interest; moreover, they are of growing importance for the study of redox systemsa2 The parent of this class of compounds is p-benzoquinone (PBQ), the physical chemical properties of which have been investigated in numerous studies because it has proven unique in several regards: derivatives of PBQ (e.g., chloranil) are strong electron acceptors and, when combined with donor molecules, form charge-transfer complexes of great interest; PBQ is also of interest in carbonyl-olefin chemistry because of the formation of excip l e ~ e sthis ; ~ ability to form complexes has been utilized to extend photoconductivity toward longer wavelengths in certain system^,^ an application of fundamental importance. From a more theoretical point of view, this molecule is of considerable interest with regard to (i) the magnitude of the splitting of the two n P* singlet-singlet and singlet-triplet transitions, (ii) the position of the P T* triplet states relative to the two n P* triplet states, (iii) the nature and energies of the molecular orbitals, again particularly the magnitude of the splitting between the two n orbitals: n, and n-. Moreover, much experimental information is available on PBQ in the gas phase: e.g., electron diffra~tion,~ photoelectron spectra (PE),@and UV spectra: all in the vapor phase; thus PBQ provides a paramount test for the methods of quantum chemistry. In fact, many workers have investigated the above-mentioned topics in the frame of the following methods: CND0/2,1° CNDO/S,”-14
-
-
*Address correspondence t o this author a t the Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221. 0022-365418112085-0473$01.25/0
IND0,15 MINDO/S,16 ab initio,l’ and very recently MSX,l* and HAM/3.1B (In the interest of conservation of space, only recent work is cited.) From a compilation of these studies, it appears that the assignment of the highest filled orbitals is quite uncertain; the experimental UV spectrum is well reproduced by the HAM/3 method, with less success by the CNDO/S. (1)R. A. Morton, Ed., in “Biochemistry of Quinones”, New York, Academic Press, 1965. (2)C. M. Tice and A. B. Turner, J. Chem. SOC.. Perlin Trans. 1,505 (1978). (3)R. M. Wilson, R. Outcalt, and H. H. Jaffe’, J. Am. Chem. SOC.,100, 301 (1978). (4) P. J. Reucroft, 0. N. Rudyj, R. E. Salomon, and M. M. Labes, J. Phys. Chem., 69,779 (1965). (5)K.Hagen and K. Hedberg, J. Chem. Phys., 59, 158 (1973). (6)D. W. Turner, C. Baker, A. D. Baker, and C. R. Brundle in “Molecular Photoelectron Spectroscopy”, Wiley, New York, 1970. (7)C. R. Brundle, M. B. Robin, and N. A. Kuebler, J. Am. Chem. Soc., 94,1466 (1972). (8)T. Kobayashi, J. Electron. Spectrosc., 7,349 (1975). (9)H.P. Trommsdorf, J. Chem. Phys., 56,5358 (1972). (10)D. Dougherty and S. P. McGlynn, J. Am. Chem. SOC.,99,3234 (1977). (11)P. E. Stevenson, J. Phys. Chem., 76,2424 (1972). (12)G.Lauer, W. Schafer, and A. Schweig, Chem. Phys. Lett., 33,312 (197.5). ~ - -_,. .
11.3) M. F. Merienne-LaFore and H. P. Trommsdorf, J . Chem. Phrs., 64,‘3791(1976). (14)R. W. Bigelow, J. Chem. Phys., 68,5086 (1978). (15)N.J. Bunce, J. E. Ridley, and M. C. Zerner, Theor. Chim. Acta, 45,282 11477) \_”..,. j) J. T. Gleghorn and F. W. McConkey, J. Mol. Struct., 18, 219 I-
1197!? \_”. >
-,.
(17)M. H. Wood, Theor. Chim. Acta, 36,345 (1975). (18)J. E. Bloor, R. A. Paysen, and R. E. Sherrod, Chem. Phys. Lett., 60. 476 (1979). ’(19)L. Asbrink, G. Bieri, C. Frioh, E. Lindholm, and D. P. Chong, Chem. Phys., 43,189 (1979).
0 1981 American Chemical Soclety
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The Journal of Physical Chemistry, Vol. 85, No. 5, 1981
In the course of a general study on azo-hydrazone tautomerism?O one of us decided to calculate the UV spectra of each tautomer of a hydrazone of PBQ. As it has been demonstrated that the tautomers are generally nonplanar,21*22 the CNDO/S method was chosen. This method has proven relevant to the interpretation of the UV spectra of conjugated rn0lecules,2~even when dealing with a conformational problem.24 Some difficulties arose when dealing with the hydrazone tautomer which involves the following skeleton:
Jacques et ai.
H
o==O=N\"--ph
0
I
H
0
Figure 1. Geometry of p-benzoquinone (PBQ) wed in the calculations.
When we became convinced that we were not dealing with problems of the experimental results or their interpretation, we decided to reexamine the parametrization. Since 1967, when the CNDO/S method was first proposed,the only changesB in parametrization proposed from the originating laboratory have been the replacement of the Pariser-Parr approximation to two-center Coulomb repulsion integrals by the Nishimoto-Mataga formula, accompanied by a minor change in $ (from -17.0 to -17.5 eV), both in 1972.26 Some other modifications of parametrization have been proposed from other lab~ratories,~' but none of them seem to have found general acceptance. The real difficulty in the modification of a semiempirical procedure, such as CNDO/S, is that any change really requires a complete reevaluation of the validity of the method. We have, consequently, undertaken a reexamination of the parameters for oxygen, in the hope of finding a single parameter set to be usable with oxygen atoms in all compounds. We have, in paticular, examined in what way ionization potential, electron affinity, U,, and U monocentric electron repulsion integrals, and $ woulrkfect the agreement between calculation and experiment, not only for selected carbonyl compounds, but for a reasonable variety of other oxygen-containingcompounds as well. We have expressly attempted to avoid the introduction of different parameters depending on the nature of the compound, i.e., of the oxygen environment, in a determined effort to retain the relative simplicity of the CNDO/S method and its parameterization. In this process we have been unable to solve the difficulties with the carbonyl compounds by modification of valence state ionization potentials and/or electron affinities, or the U, and U, parameters and one-center electron repulsion integrals derived therefrom. On the other hand, we have found that the carbonyl spectra are quite sensitive to p0, an increase of $ for oxygen from -45 eV to -30 eV has brought the calculated carbonyl and quinone spectra largely into line with experimental values. At the same time, the energy of the lowest triplet has also been improved. Much to our surprise and pleasure, this parameter change has had only small effects on the results for other types of oxygen-containing compounds: alcohols, phenols, ethers, oxygen heterocyclics, and carboxylic acids and esters. (20)P. Jacques, Thesis, Mulhouse, 1977. (21)A. Goursot, P. Jacques, and J. Faure, Chem. Phys., 20,319(1977). (22)P. Jacques, A. Goursot, and J. Faure, Chem. Phys., 26,301 (1977). (23)R. L.Ellis and H. H. Jaffe' in "Semi-empirical Methods of Electronic Structure Calculations; Part B: Applications", G. A. Segal, Ed., Plenum Press, New York, 1977,pp 49-97. (24)P. Jacques and 0. Chalvet, J. Mol. Structure., in press. (25)J. Del Bene and H. H. Jaffe', J. Chem. Phys., 48, 1807,4050 (1968);49,1221 (1968). (26)G.W.Kuehnlenz, R. E. Ellis, and H. H. Jaffe', Theor. Chirn. Acta, 26,131 (1972). (27)Cf., e.g., ref 14.
Although the prime objective of the CNDO/S method has been the application to electronic absorption spectra, from which ita entire parameterization derived, the method has also found application in other areas, among others to PE spectra. Having found that a simple change in the value of @ for oxygen was indicated, we have further investigated whether the new value of $(O) results in better agreement between the experimental PE spectra and the calculated orbital energies, since the positions of the n, and n orbitals are expected to depend strongly on $(O).
Calculations Figure 1represents the numbering of the atoms and the geometry adopted which was derived from crystallographic data2*and an electron diffraction study.5 Calculations were made a t the Centre de Mgcanique Ondulatoire Appliquge and at the University of Cincinnati with the CNDO/S program.26 The Nishimoto-Mataga approximation was used in the calculations of singlet transitions. The configurations involved in the CI were chosen automatically, using the NCONF (number of configurations) configurations of lowest energy. Results and Discussion UV Spectra of pBenzoquinone. Our main purpose was to obtain good agreement between calculated and experimental transitions for the entire available UV absorption spectrum, that is for all experimental transition energies 16 eV. Until now this has been achieved only by the HAM/3 method as is apparent from Table I. (It must be recalled when comparing calculations made by different authors that the geometries are slightly different, as are the number of configurations (NCONF) included in the configuration interaction in CNDO/S.) The ab initio method fails to reproduce the experimental spectrum entirely; semiempirical methods perform better, but it should be recognized that either the two n T* of the two T T* transitions are separately well represented, but the four transitions together have only been reasonably reproduced by HAM/3. We report our main results concerning the influence of NCONF and p0(O)on the transition energies in Table 11. The best agreement for the entire UV spectrum was obtained with the following set of parameters: $(O) = -30 eV NCONF = 60 It may be of interest to note that the value is very close to the original $(O) (-31 eV) for CNDO/2 of Pople and co-worker~.~~ The CI composition of the excited states is given in Table I11 and their nature is in accord with previous as+
+
(28)J. Trotter, Acta Crystallogr., 13,26 (1960). (29)J. A. Pople, D. F. Santry, and G..A. Segal, J. Chem. Phys., 43, S129 (1965);J. A. Pople and G. A. Segal, zbzd.,43,S136 (1965);44,3289 (1966).
Oxygen Parameters in the CNDO/S Method
The Journal of Physical Chemlstry, Vol, 85, No. 5, 198 1 475
Lo
N
I
0
m I
m
m I
*I
0
m
*I Q, 43
3
c)
a b4
*0 rl
n nnnQ,nn
???a)?? 0 000000 v,
0
d
23
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The Journal of Physical Chemistry, Vol. 85,No, 5, 1981
Jacques et el.
TABLE 111: CI Coefficients and Configuration Energies in eV in Excited Singlet States ( p " ( 0 ) = n + n* n + n* n+n* n + 7r* B3, Bl g Bl, AU state energy 2.48 2.52 4.07 5.13 2.46 2.60 4.13 5.10 energies, symmetry and no. eV orbital configuration 1 3.42 B,, 18+ 21 0.863 2 3.81 Au 17+ 21 0.858 3 4.20 B,, 19+ 21 -0.993 B,, 20 + 21 -0.963 4 5.36 5 5.74 B,, 1 2 ' 5 A, 18+ 23 -0.421 6 6.50 9 6.80 14+ 21 -0.226 10 7.01 17+ 23 -0.412 B,, 19+ 22 -0.234 14 7.52 15 7.61 B,, '71 22 18 8.36 ' 8 1 24 0.519 27 9.21 ' 7 1 24 0.206 33 9.97 A, 14+23 0.194 36 10.17 B,, 13+ 23 41 10.58 Bii 1 3 ' 2 a Reference 13. This work.
30 eV; NCONF = 60)
n + n* B,,
5.24
-
0.83
0.87
0.32 CEO -0.41
0.28 CEO -0.35
@ = -30 eV
p0 = -45 eV
where the numbers given represent the a-electron charges on C and 0, and the a-bond order. At this stage of the discussion it would be ludicrous to search for a perfect accord between theoretical and experimental transitions energies. Instead, we want to underline yet another point of comparison which has been mentioned often: the shift of the absorption bands induced by solvents. Solvatochromy of PBQ has been studied carefully by Lam0tte,9~,~~ who found that, although PBQ possesses no dipole moment, the two a a* transition undergo considerable shift as the solvent is varied. This author was able to explain this astonishing behavior by considering the solvent interactions with two local dipole moments localized approximately on the two C=O groups. Moreover, the shifts of the two transitions are different: the first s a* band is associated with an increase of these local dipole moments upon excitation, while the interpretation of the shift exhibited by the second a a* transition is more difficult; L a r n ~ t t concluded e~~ that the variation of the dipole moments upon excitation was weak, the dispersion forces being predominant.
-
-
-
(30)J. Goodman and L. E. Brus, J. Chem. Phys., 69, 1604 (1978). (31)M. Lamotte and J. Joussot-Dubien, J.Chim. Phys., 66,161(1969). (32)M.Lamotte, G. A. Gerhold, and J. Joussot-Dubien, J. Chim. Phys., 67 2006 (1970).
Bl, a 5.75b
-0.466
-0.943 -0.640 -0.486 -0.121
2:
signments. The splitting energy of the two n a* transitions is considerably decreased when NCONF is increased from 20 to 60, but then slightly increases. For NCONF = 60, the splitting energy is 0.14 eV, more than four times the experimental value (-0.03 eV) derived by T r o m m ~ d o r f , ~and J ~ Goodman and Brus proposed recently30an even smaller splitting: 50.01 eV. The calculated splitting energy was 20.09 eV in all the methods employed. The role played by p0(O) appears clear: all transitions calculated with p"(0) = -45 eV are of too high energy. The increase of p " ( 0 ) shifts all the energies toward the experimental ones. From a more theoretical point of view, the modification of po(0)results in an enhanced conjugation and a more polar a character of the C=O bond:
u + n*
0.348 -0.268 0.121
A crude estimation of these dipole moments was made by starting from the atomic charges obtained in the ground and the lB1,,, a* excited states: the values obtained are, respectively, 2.9,4.9, and 2.3 D and account well for the conclusions of L a m ~ t t e .Further ~~ computations are in course which include the solvent according to the model proposed by Constanciel.28 Finally, we find instructive the examination of the 5.6-eV region on the spectra of PBQ: Bigelow14 has called attention to a weak absorption at 5.6 eV, for which he proposed a lB2, lA, transition, which had not previously been observed. Our calculations indicate that this transition occurs at 5.25 eV and so it may borrow intensity from the strong lBlu lA, transition. Alternately, the absorption may be another transition, lB1, lAg, calculated at 5.75 eV. From inspection of the UV spectra reported by Kuboyama,s4it is reasonable to relate the asymmetry (precisely toward the shorter wavelengths) of the 240-nm absorption band to the above-mentioned transitions (note the nonzero absorption in the 5.8-eV region). We have also reexamined the lowest triplet states of PBQ. The lowest state, 3B1 in either case, has been improved from 3.02 to 2.79 e t by the parameter change, compared with an experimental value of 2.6 eV. PE Spectrum. Numerous workers have been interested in correlating P E spectra with orbital energies to the relation
-
-
IP = -€i
-
(1)
based on Koopmans' theorem. Equation 1is approximate since it assumes that the energetic effect of charge reorganization due to ionization is nearly balanced by a change in correlation energy. It has been suggested and empirically ~ e r i f i e d that ~ ~ - these ~ ~ neglected effects could be (33)R.Constanciel and 0. Tapia, Theor. Chim. Acta, 48, 75 (1978). (34)A. Kuboyama, S. Matauzaki, H. Takagi, and H. Arano, Bull. Chem. SOC.Jpn., 47, 1604 (1974). (35)E. Heilbronner, R. Gleiter, H. Hopf, V. Hornung, and A. deMeisere, Helu. Chim. Acta, 64,783 (1971). (36)P. A. Clark, F. Brogli, and E. Heilbronner, Helu. Chim. Acta, 65, 1415 - - - - (19721. \--.-,(37)J. P.Maier and D. W. Turner, J. Chem. S O ~Faraday ., Trans. 2, 69,196 (1973). (38)R. Boschi, E.Clar, and W. Schmidt, J. Chem. Phys., 60, 4406 (1974).
Oxygen Parameters in the CNDO/S Method
accounted for by the relation IP = A - Bci
(2) The nature of the highest occupied orbitals of PBQ has attracted much attention and the following orbital sequences have been proposed:
(1) n-('B3J, n+('Bz,), al('B3uh adBlg) (6) (10) (16)
(11) n('B3J, ?T1('B3u)t n+('B2U),aABlg) (8) (15) (18)
(111) n-('B3J, al('B3uh az('Blg), n+('Bz,) (7) (14) (IV)
a l ( l B d , n-('B3g),
n+('BzJ (17)
At present this situation is quite confused. In order to make progress in this discussion, one finds it convenient to distinguish two facets of the problem: the nature and sequence of the orbitals, and the magnitude of the splitting between n, and n- energies. However, Trommsdorf,Bfrom an investigation of the n, a* and na* transitions has concluded that the lone pair splitting cannot exceed about 0.25 eV, which appears consistent only with sequence I. Lauer12showed that this problem was misleading and that use of configuration interaction is able to give account of the small splitting. The semiempirical CNDO/S method was derived in order to adjust UV theoretical spectra to experimental ones. Nevertheless, it seems reasonable to test the orbital energies by comparing them with the experimental PE spectrum according to eq 2. This was done recently for PBA by Bigelow,'" by Bloor,leand by Asbrink19and their respective coauthors with moderate success. It should be underlined that no unique interpretation of the experimental PE spectrum of PBQ is available, so that the above-mentioned procedure is subject to caution. Bearing in mind this remark, we were interested in investigating the influence of the reparametrization of the oxygen atom on the validity of eq 2. Turner et al.6 and Kobayashi*have reported the same PE spectrum of PBQ which is slightly different from the one published by Asbrink et al.19 The following discussion considers the former as reference. Examination of Table IV shows several interesting features: the orbital energies are strongly dependent on $(O); e.g., orbital 20 (a)is destabilized, in contrast orbitals 19 (a), 18 (n-), and 17 (n+) are stabilized by the change in parameters. With the parameter adopted in the UV spectral study, $(O) = -30 eV, the two n orbitals are now found more stable than the two a orbitals, suggesting the orbital sequence
-
(V)
-
al('B3u), adlBlg), n-('B3J, n+(lBZu)
The lone pair splitting is now too great, 0.7 eV (although not excessively so), and we can reasonably suppose that the configuration interaction suggested by Lauer12would reduce this value. The ordering of the other orbitals is independent of $(O) except for orbitals 15 and 16 which invert between p0(O) = -35 eV and @(O) = -30 eV. Figure 2 shows a good linear correlation between ti and (IP)iin accord with e.g. (2). The slope ( B ) is near unity (0.958),indicating that all IP are affected by about the same error, as previously postulated.23 Our interpretation of the P E spectrum differs more or less from those proposed by previous authors: (1) We are in general agreement with the assignments of Bigelow,14 except that we find no evidence for his transitions 5 and 12. Our assignment is substantiated by the relative areas under the experimental peaks in the 10-16-eV range.
The Journal of Physical Chemistry, Vol. 85, No. 5, 1981
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The Journal of Physical Chemistty, Vol. 85, No. 5, 1981
Jacques et al.
TABLE V: Calculated and Observed Spectroscopic Data for a Series of Oxygen Compoundsa calcd state l'A, 1'A, l'B, l'A, llA, l'A, l'B, 1'A" 1'A l'Au l'B, 2'Au l'Bu l'A, l'B, 1'A, l'B, l'A, 1'A, l'B, 1'A' 2' A l'B, 1'A, l'A,
pa = 30 eV
calcd
p" = -45 eV
Formaldehyde 3.29 (0) 3.53 (0) 6.90 (0.01) 8.59 (0.01) 7.39 (0.25) 9.81 (0.40) Ketene 3.03 (0) 3.33 (0) 5.51 (0.23) 5.61 (0.31) 6.45 (0.008) 6.43 (0.03) Acroleine 3.16 (0) 3.32 (0) 5.99 (0.70) 6.32 (0.68) Glyoxal 2.47 (0) 2.68 (0) 3.35 (0) 3.78 (0) 6.16 (0.005) 7.80 (0.012) 6.65 (0.51) 8.26 (0.48) Acetone 3.45 (0) 3.59 (0) 6.38 (0.001) 7.92 ( 0 ) 7.26 (0.28) 9.79 (0.57) Furan 5.12 (0.21) 5.40 (0.28) 6.00 (0.01) 5.97 (0.06) 6.49 (0) ' 7.07 (0.63j 6.68 (0.004) Phenol 4.77 (0.005) 4.70 (0.02) 5.94 (0.07) 5.86 (0.08) Phenolate Anion 4.15 (0.10) 3.92 (0.13) 4.47 (0) 4.12 (0) 4.97 (0.38) 4.94 (0.43)
obsd 3.47-5.39b 7.07c 8.06c 3. 22-4.67d 5.82-6.42 6.70-7.29 3.76d 6.05-6.89 2.73d 6.05-6.70
3.76-5.64d 6.38 7.46-8.09 5.88
- -
state 1'A 2'A' 1'A" 1'A' 2'A 1'A" 1'A 2'A l'B, l'A, l'B, 2'B, llA, 2'A, 2'A1 2'B, 1'A" 1'A' 2'A
6.47 4.6 5.8
lBl l'A, l'B, llA,
p" = 30 eV
pa = -45 eV
obsd . . Anisole 4.77 (0.004) 4.72 (0.02) 4.46, 4.59,4.73 6.94 (0.06) 5.06 (0.11) > 5.5 Benzaldehyde 3.13 ( 0 ) 3.35 (0) 3.66(h), 3.83(e) 4.66 (0.02) 4.74 (0.01) 4.46(h), 7.41(e) 5.38 (0.50) 5.66 (0.36) 5.14(h), 5.04(e) Benzoic Acid 3.64 (0.005) 4.08 (0.001) 4.60 (0.025) 4.68 (0.014) 4.42 (0.013)" 5.34 (0.48) 5.66 (0.30) 5.38 (0.19) Benzoate Anion 3.61 (0) 3.78 (0) 3.76 (0) 4.19 (0) 4.68 (0) 4.71 (0) 4.99 (0.044) 5.06 (0.023) 5.34 (0.006) 6.27 (0) 5.36 (0) 5.06 ( o j 6.62 (0.30) 5.78 (0.17) 5.74 (0.006) 5.67 (0) Methyl Benzoate 3.61 (0.0001) 3.98 (0.001) 4.60 (0.023) 4.68 (0.012) 5.36 (0.47) 5.66 (0.30) Nitrobenzene 2.59 (0) 2.75 (0) 3.31 (0) 3.03 ( 0 ) 3.665 4.44 (0.03) 4.06 (0.04) 4.30 4.89 (0.44) 4.35 (0.54) 5.17
4.3 5.3
a Calculated and observed transitions, in eV for calculated values, oscillator strengths in parentheses. Values at -45 eV may differ slightly from previously published values since the exact geometries for which calculations were made are no longer available. All geometries were best guesses of experimental geometries. J. C. D. Brand, J. Chern. SOC.,858 (1956). D. C. Moule and A. D. Walsh, Chem. Rev., 75, 67 (1975). G. Gerzberg, "Molecular Spectra and Molecular Structure", Vol. 111, Van Nostrand-Reinhold, New York, 1966. e C. Seliskar, private communication. f C. Seliskar, 0. Khalil, and S. McGlynn in "Excited States I", E. C. Lim, Ed., Academic Press, New York, 1974, p 259.
(2) Our interpretation is considerably different from that of Bloor.ls (3) Our interpretation also does not agree with that of Asbrink et al.,19 who conclude that the orbital sequence is I. More elaborate methods of computation, such as ab initio1' and do not seem to give better results. U1timately, of course, interpretation of PE spectra on the basis of orbital energies always remains questionable because of the assumptions inherent in Koopmans' theorem. Calculations of the energy levels of the molecular ion seem to be a more reasonable approach.39 Unfortunately, the fact that the first two excited states of the molecular ion lie within 0.25 eV of the ground states has led to serious problems in convergence. General Applicability of the New Parameter. Table V compares the results of an extensive series of oxygen compounds for both parameter sets, and with experiment. I t is apparent from this table that the overall agreement is vastly improved. In the molecules which are not carbonyls the changes are minor, while the carbonyl compounds now seem to fall in line. It is particularly encouraging that the results for some of the very small carbonyls (formaldehyde,ketene), which were completely out of line with 9 = -45 eV, have become reasonable with P (39)R. L.Ellis and H. H. Jaffe', J.Am. Chern. SOC.,96,2623 (1974).
1
12
14
16
18
20
Experimental ionization potential (*VI
Flgure 2. Tentative correlation of the CNDO/S p(0)= -30 eV orbital eigenvalues with the experimental ionization potentials.
479
J. Phys. Chem. 1981, 85, 479-481
= -30 eV. We have also rerun a series of hydroxybenzofurans and their ions, and found the dependence of calculated spectra of $(O) even less sensitive than for the smaller molecules of Table V. The new parameter has also been tested by Bigelow, who agrees with our conclusions.m
Conclusion The aim of this work is attained CNDO/S can provide a good interpretation of the entire W absorption spectrum of PRQ if reparametrized. The accepted value of @ for oxygen is -30 eV instead of the -45 eV originally used. It is further shown that this reparametrization is valid for other carbonyl compounds and does not significantlyalter (40)R.W.Bigelow, private communication.
the agreement observed for other molecules. Furthermore, the energy of the lowest triplet is improved. The new value of $ improves slightly the correlation between ci and the experimental ionization potentials of the PE spectrum of PBQ. On the other hand, the nature of the highest orbitals seems to be in contradiction to the experimental results, albeit the PE spectrum of PBQ is open to multiple interpretations. As a consequence, we have replaced @(O) by the new value of -30.0 eV in all the CNDO/S programs to which we have access. Acknowledgment. We extend our thanks to Mr. Fouquet (Centre de MGcanique Ondulatoire Appliquge) for the effective technical assistance.
Conversion between Framework Group Notation and Permutation Group Notation for Molecules Darl H. McDaniei Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 4522 1 (Received: Ju& 29, 1980)
The cycle structure of the permutation group for a molecule is used to construct the Pople framework group notation for the molecule, and vice versa. A simple extension of the framework group notation to nonrigid molecules is proposed. Examples are given showing the relationship of spectral patterns such as those due to molecular vibrations and nuclear magnetic resonance to framework groups, and it is shown how permutation functions for isomer enumeration are contained in the framework group notation. A plea is made to include framework group notation in abstracts.
Recently, Pople has pointed out that the point group of a molecule frequently provides incomplete symmetry information about the molecule. To remedy the situation he has generated a framework group notation1 which carries information about nuclei invariant under (classes of) point group operations taken in a hierarchical order such that each nucleus is counted only once. Complete permutational information available from a static molecular structure is thus contained very compactly. The identical information in slightly less compact form is available in the cycle structure of the permutation group of a molecule of known structure. It is the purpose of this letter to show how one may readily go from group framework notation to the cycle structure associated with each point group operation on the molecule. Since chemists are usually more familiar with point groups than with molecular permutation groups,2 the utility of the latter will be shown in some typical applications. Graphs of the cycle structure of the permutation group of a molecule, or more simply, partition diagrams, may be constructed for each operation of a point group by carrying out the particular operation a sufficient number of times to return the species to its original configuration and noting the number of positions a particular atom occupies. This number is the same as the number of boxes on a horizontal line of the partition diagram. The atoms will be divided (1) Pople, J. A. J. Am. Chem. SOC.1980,102,4615-4622. (2)See the following for discussion of permutation groups and related topics. Flurry, Jr., R. L. “Symmetry Groups, Theory and Chemical Applications”; Prentice Hall: Englewood Cliffs, NJ.; 1980. Bunker, P. R. “Molecular Symmetry and Spectroscopy”; Academic Press: New York, 1979. 0022-365418 112085-0479$01.25/0
into sets, equal to the number of horizontal lines in the partition diagram. Each line of the partition diagram is termed a cycle, and the number of boxes on a given line is the length of that cycle. For a molecule such as PF5 having trigonal bypyramidal geometry (DSh)the appropriate partition diagram is shown in Diagram I. The cycle Diagram 1
€P 123
1 3
3
l2 2*
142
1 4
2
16
structure is listed beneath each partition diagram; the identity operation has six cycles of length one, each C3 operation has three cycles of length one and one cycle of length three, etc. The total number of boxes in each diagram is, of course, the same as the number of atoms in the molecule. Planar (1) and perpendicular (2) structures for difluoromethane, examples taken from Pople,l would have the partition diagrams shown in Diagrams I1 and 111. Pople’s rules for framework group notation may be rephrased in terms of partition diagrams as follows: Only cycles of length one (atoms appearing in a single box on a given line) are considered. Each atom is assigned to the first listed category below in which it appears. (a) An atom appearing in all diagrams is listed under 0 (a central point) if a center of inversion is present or if two 0 1981 American Chemical Society
