J. phys. Chem. 1981, 85, 1350-1353
1950
Theoretical Characterization of the Isomers of Sulfur Dloxlde Thorn. H. Dunnlng, Jr.;
and Rlchard C. Raffenettl
Theoretical Chemishy coup, Chemlstly Division, Argonne National Laboretoty, Argonne, Ililnok 60439 (Received December 11, 1980)
Generalized valence bond (GVB)and configuration interaction (CI)calculations are reported on the isomers of SO2. From these calculations the ring isomer with Rso = 1.66 A and t9oso = 60' is predicted to lie -100 kcal/mol above the ground state (open isomer; calculated (experimental): Rm = 1.45 A (1.4308A), t9om = 120' = 120° is predicted to lie -5 kcal/mol (119.3')). The superoxide isomer with Rm = 1.67 A, Roo = 1.33 A, and higher than the ring isomer. These results strongly argue against the involvement of the isomers of SO2 in the combustion of sulfur-containingspecies and in the flash photolysis of SOP Introduction Evidence for the existence of a low-lying isomer of sulfur dioxide (SO2) was first reported by Norrish and Zeelenberg1 and by Myerson, Taylor, and In studies of flash-initiated explosions of H2S, CS2, and COS, these workers noted a strong continuous absorption band which appeared early in the explosion,the gradual disappearance of which coincided with the appearance of the SO2discrete absorption bands. These studies indicated that the species responsible for the continuous band was a direct precursor of SOz. Arguing against either electronically or vibrationally excited SO2 as the source of the continuous absorption band, Myerson et ala2concluded that it was the superoxide isomer of SO2, SO0 (l),produced in reactions
I 1I 1-3. Although they could not further characterize the so + 0 2 so0 + 0 (1) cs2 + 02 cs so0 (2) cos + 0 2 co + so0 (3) SO0 species, they did point out that the overall explosion mechanism required SO0 to be significantly less stable than SO2. These conclusions were supported by the studies of McGarvey and M ~ G r a t hwho , ~ assigned a transient spectrum in the vacuum ultraviolet to SOO,and by those of Levy and Merryman: who concluded that reaction 3 was the initial step in the oxidation of carbonyl sulfide (COS) in flames. Further spectroscopic evidence for the existence of an isomeric form of SO2 was provided by Norrish and 01der~haw.~ They found that upon photolysis the discrete bands of SOz were replaced by a strong continuum absorption band. The SO2bands reappeared as the continuum absorption faded. To account for these observations Norris and Oldershaw6 postulated the following mechanism:
--
SO2
+ hv
-
S02*
(2500 IX I3100 A)
(sod * so2
s02*
(SO21
(4) (5)
(6)
Absorption in reaction 4 is to the first allowed band in SO2, probably to the lB1 state. In reactions 5 and 6 (SO,)is an S02-reservoirspecies which is in thermal equilibrium with SOz. (Photodissociationof SO2was only a minor component of the mechanism.) Nothing could be said from their results about the exact nature of (SO,).From the effect of temperature on the ultraviolet spectrum of SO2, Brown and Burns6 concluded that the (SO2) species lies -4 kcal/mol above SOz. Support for the existence of a low-lying isomer of SO2 was also provided by theoretical studies of the isoelectronic ozone (0,) molecule. Hartree-Fock (HF) calculations of O3predicted an energy for the ring isomer (2) only slightly
+
+
(1) R. G. W. Norrish and A. P. Zeelenberg, Proc. R. SOC.London, Ser. A, 240, 293 (1957). ( 2 ) A. L. Myerson, F. R. Taylor, and P. L. Hanat, J. Chem. Phys., 26, 1309 (1957). (3) J. J. McGarvey and W. D. McGrath, Proc. R. SOC.London, Ser. A, 278, 490 (1964). (4) A. Levy and E. L. Merryman,Enuiron. Sci. Technol., 3,63 (1969). (5) R. G. W. Norrish and G. A. Oldershaw,R o c . R. SOC.London, Ser. A, 249, 498 (1959).
0022-3654/81/2085-1350$01.25/0
c23
133 above that of the open isomer (3).' On the basis of these results and semiempirical calculations on SO2,Hayes and Pfeiffer8 identified the (SO,) species of Norrish and 01dershaw6 with the ring isomer of SO2. However, Hay, Dunning, and Goddard@showed that the low isomerization energy obtained for the ring isomer was an artifact of the HF model. Their generalized valence bond (GVB) and derived configuration interaction (CI) calculations placed the ring isomer some 30 kcal/mol above the open isomer. While there is some controversy about the magnitude of the isomerization energy,1° it is likely that it is in the range 20-25 kcal/mol. 11-14 (6) J. Brown and G. Burns, Can. J. Chem., 47, 4291 (1969). (7) S. D. Peyerimhoff and R. J. Buenker, J. Chern. Phys., 47, 1953 (1967); see, however, S. Shih, R. J. Buenker, and S. D. Peyerimhoff, Chem. Phys. Lett., 28,463 (1974). (8) E. F. Hayes and G. V. Pfeiffer, J.Am. Chern. SOC.,90,4773 (1968). (9) P. J. Hay, T. H. Dunning, Jr., and W. A. Goddard 111, J. Chem. Phys., 62, 3912 (1975). (10) P. G. Burton and M. D. Harvey, Nature (London), 266, 826 (1977); P. G. Burton, J. Chern. Phys., 71,961 (1979). (11) R. R. Lucchese and H. F. Schaefer 111, J. Chem. Phys., 67,848 (1977). (12) P. J. Hay and T. H. Dunning, Jr., J.Chem. Phys., 67,2290 (1977). (13) L. B. Harding and W. A. Goddard 111, J. Chem. Phys., 67,2377 (1977).
0 1081 American Chemical Society
Characterization of the Isomers of Sulfur Dioxide
While the evidence for the existence of a low-lying isomer of SO2 is substantial, other interpretations of the experimental data have been advanced. Noting that the continuous absorption band was in the same region as the discrete bands of SO2 and had approximately the same overall absorption coefficient, Herman, Akrsche, and Grenatls and Gaydon, Kimbel, and PalmeP concluded that the apparent continuum was just due to an increase in the complexity of the rotational structure of the discrete SO2 bands upon heating. Giguere and Savoie,17 who measured the temperature dependence of the infrared spectrum of SO2, also concluded that the observed shifts in the IR bands were not consistent with those expected for the hypothetical SO0 isomer. We report here GVB and derived CI calculationson all three isomeric forms of SO2, 1-3, determining the equilibrium geometries and isomerization energies. From the calculated isomerization energy for the superoxide isomer and the known dissociation energy of SO2,it is also possible to estimate the energetics of reactions 1-3. Computational Details The details of the generalized valence bond (GVB) and derived configuration interaction (CI) calculationson the isomers of SO2 are given in the following sections. Basis Sets. For the sulfur and oxygen atoms we used the primitive (lls7p) and (9s5p) atomic sets of Huzinaga18 contracted to [4s3p] and [3s2p], respectively, using the general contraction method of RaffenettiIg (for further details see ref 20). These atomic sets were augmented with polarization functions, a (2d) primitive set contracted to [1dI2Ion sulfurn and a single set of primitive 3d functions on oxygen. The scale factor (sulfur) or exponent (oxygen) for the polarization functions, rs = 2.14 and a0 = 0.72, were optimized in Hartree-Fock (HF) calculations on the ground state (open isomer) of SO2. Only the five 3d functions on each atom were included in the calculations. GVB(pp) Wuuefunctions. The GVB(pp) wavefunction for the ground state (open isomer) of SO2 is of the formg (omitting the core orbitals) 3s8 2 s ~ 1 2 s ~ r 2 p ~ f p O 1 2 p ~ f p O r 3 p ~ f p S ( 3 p ~ b l+S ~ P ~ b O l 2p~bO13p~ba)(3pubrS2p~bo, +
2pubOr3pubrS)(2Prb012PrbOr + 2PrbOr2PrbOl) (7) In (7) 01and Or refer to the left and right terminal oxygen atoms and l p and b to lone-pair and bond orbitals; u and r are defined as usual by reference to the molecular plane. The notation used in (7) is a shorthand notation; in the GVB(pp) wavefunction the orbitals are, of course, optimized. In natural orbital form (7) becomes (unnormalized) laf2af3aflb$2b% l b f ( & ~ + X,u&)(&, + XUu&J X (la%+ X,2bf) (8) where (6901, uiOr)and (usor, ukOr)are the left and right bonding and antibonding sulfur-oxygen u orbitals and la2 (14) G. Karlstrom, 5.Engstrom, and B. Johnson, Chem. Phys. Lett., 57, 390 (1978). (15) L. Herman, J. Akrische, and H. Grenat, J . Quant. Spectrosc. Radiat. Transfer, 2, 225 (1962). (16) A. G. Gaydon, G. H. Kimbel, and H. B. Palmer, Proc. R. SOC. London, Ser. A, 276,461 (1963). (17) P. A. Giguere and R. Savoie, Can. J. Chem., 43, 2357 (1965). (18) S. Huzinaga, “Approximate Atomic Functions. I”, and “Approximate Atomic Functions. 11”, reports from the Department of Chemistry, The University of Alberta, Edmonton, Alberta, Canada, 1971. (19) R. C. Raffenetti, J. Chem. Phys., 58, 4452 (1973). (20) T. H. Dunning, Jr., and P. J. Hay in “Modern Theoretical Chemistry”, Vol. 1, H. F. Schaefer 111, Ed., Plenum Press, New York, 1977. (21) T. H. Dunning, Jr., J. Chem. Phys., 55, 3958 (1971). (22) The Hartree-Fock energy for SO2with the (2d)/[ld] set is 0.0821 hartree lower than that obtained with a (Id) set.
The Journal of Physlcal Chemistry, Vol. 85, No. 10, 1981 1851
TABLE I: Comparison of Calculations on the Open Isomers of Ozone and Sulfur Dioxidea
HF, hartree GVB (3,PP)
A E ( ~ o o , Q S O )eV ,~ A E ( ~ o o ) , eV ~ AE,C eV
-224.306 40
-547.233 86
0.85 2.83 4.30
0.40 0.85 1.52
GVB-CI( 2) A E , eV‘ ~ 1.84 1.51 POL-CI(2) AE: eV 3.61 4.10 a At the Experimental Geometries of ozone and sulfur dioxide. Pair energy lowerings. Relative to the preceding calculation.
and 2b1 are the antibonding and bonding oxygen-oxygen r orbitals. The wavefunction (8) can be written entirely in terms of symmetry-adapted orbitals by the transformation 4a193b2= ( 1 / d % s O l *
(Qa)
(9b) 581, 4b2 ( l / d % ( & i f ubr) of which the dominant term is just the HF configuration laf2af3af4aflb$2b$3bilbflai (10) In terms of the symmetry orbitals (91, however, (8) does not have such a simple form. In Table I we compare the GVB(pp) calculations on the open isomer of SO2 with those reported earlier on OPg While the r-pair energy lowering is the largest of the pair lowerings, 0.85 vs. 0.40 eV, it is decidedly less important in SO2 than in 03, 0.85 vs. 2.83 eV. Nevertheless, the two-configurationGVB(pp) description of this pair is to be recommended. The GVB(pp) wavefunction for the ring isomer of SO2 in natural orbital form is laf2aflb%lbf2bfla$ (u80.01+Xga&)(&r + X#u&) X (3af + hb3ba) (11) where the last pair in (11) describes the u bond between the two oxygen atoms. Again (11)can be rewritten in terms of symmetry-adapted orbitals using relations such as (9). The HF configuration of the ring isomer is laf2af3af4aflba2b$lbf2bfla$ (12) The GVB(pp) wavefunction for the superoxide isomer of SO2can be obtained from (8) simply by interchanging the S and 01orbitals. For this isomer the energy lowering for the r pair, 3.68 eV, is even larger than that obtained for 03:indicating again the importance of a two-configuration description of this pair. CI Calculations. For the CI calculations we used as reference configurations the configurations resulting from the two-configurationdescription of the rOlor pair in the open isomer, the rsorpair in the superoxide isomer, and the uolorpair in the ring isomer: open: laf2af3af4aflb$2b%3b$lbfla$ ring:
laf2af3af4aflb$2b$3bfl bf2bf laf2af3af4aflb$2b$lbf2bfla$
laf2a~3aflb~2b~3b$lbf2bfla$ superoxide: 1a’22a’23“4a’”a’26a’27a’21a’’22a’‘2
(13a) (13b)
1a’22a’23“24a’25a‘26a‘27a’21a‘’23a”2 (13c) As noted above, a two-configuration description is required for a consistent treatment of the isomers of SOa. All of
1952
Dunning and Raffenetti
The Journal of phvsicel Chemistry, Vol. 85, No. 10, 1981
TABLE 11: Summary of Results on the Calculations on the Open Isomer of SOZa GVB-CI POL-CI GVB t 1+ 2, exptl16
-547.346 71 -547.498 43 -547.644 68 Ee hartree 1.4308 1.46 1.45 R s o , A 1.45 120 119.3 120 120 eoso, deg a Experimental data have been included where available.
the CI calculations were carried out in terms of the symmetrized GVB(pp) natural orbitals. For the CI calculations the orbitals are grouped into three sets: the core orbitals, the valence orbitals (lal-5al, lb2-4b2, lbl-2bl, and la, or laC9a’ and la”-3a”) and the virtual (remaining unoccupied) orbitals. Three levels of GVB-based CI calculations were then considered: 23 (i) GVB-CI, all single and double excitations from (13) within the valence orbitals; (ii) POL-CI, all single and double excitations from (13) with the restriction that no more than one electron occupy a virtual orbital; (iii) GVB+1+2,, all single and double excitations from (13) with the restriction that no more than one electron be excited from the ns-like orbitals (lal, 2a1, 1b2). GVB+1+2, calculations on the superoxide isomer were not practical. In all calculations the core orbitals were taken to be doubly occupied. For the open isomer, the number of space and space/spin configurationsincluded in the calculations were as follows: GVB-CI (152,1981, POL-CI (2102,35731, and GVB+1+2, (9426, 16641). All configurations were included in the calculations. The energy lowerings obtained from the GVB-CI and POL-CI calculations on SOzare compared with those from Osin Table I. As can be seen, the energy lowerings are remarkably similar, a difference of -0.33 eV (18%)at the GVB-CI level and +0.43 (12%) at the POL-CI level. The profound differences in the electronic structure of SO2and Osare thus a result of the differences in the GVBtpp) descriptions of these molecules. Molecular Codes. The integrals over the Gaussian basis functions were evaluated by using the BIGGMOLI and ordering programs of Raffenetti.1g,24The GVB(pp) calculations were carried out by using a version of GVBTWO written by Bobrowicz and Wadt,%as modified by Walch to make use of BIGGMOLI integral files. The molecular orbital integral transformations used a program written by Raffenetti. The CI configuration lists were generated by the program GNCFG written by Ladner and Olafson and extensively modified by Dunning and Walch, while the CI calculations were carried out by using the program CITWO written by Bobrowicz26as modified by Walch.
Results The results of the GVB and CI calculations on the isomers of SO, are summarized in Tables I1 (open),I11 (ring), and IV (superoxide). The quoted equilibrium geometries and energies were obtained from quadratic expansions of the energies; the precision of the interpolated geometries and energies is expected to be (f0.02%, f2’) and fO.OO1 hartree, respectively. Also listed in Table I1 is the experimentally determined geometry2*of the ground state of SOz. The error in the (23) T. H.Dunning, Jr., J. Chem. Phys., 65, 3854 (1976). (24) BIGGMOLI is available from the Quantum Chemistry Program
Exchange. (25) F. W. Bobrowicz, Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1974. (26) Y. Morino, Y. Kikuchi, S. Saito, and E. Hirota, J. Mol. Spectrosc., 13, 95 (1964).
TABLE 111: Summary of Results of Calculations on the
Ring Isomer of SO, GVB-CI
POLCI
G V B t 1 t 2,
Ee, hartree
-547.202 30 -547.346 85 -647.483 91
Rso,A Roo,A 6 0 ~ 0 deg , AEisomer, kcal/mol
1.68 1.69 60.3 91
1.67 1.67 60.0 96
1.66 1.68 60.7 101
TABLE IV: Summary of Results of Calculations on the
Superoxide Isomer of SO, GVB-CI
E,, hartree
Rso, A ROO, A
esoo, deg AEisomer,kcal/mol
-647.200 66 1.67 1.33 120 92
POLCI -647.33943 1.67 1.33 120 100
calculated SO distance ranges from 0.04a,,(GVB+1+2,) to 0.05%(POL-C1), while the error in the OS0 bond angle is small (f0.7’). Comparable errors would be expected in the calculated geometries of the other isomers. Comparing the P O W 1 and GVB+1+2, calculations on the open and ring isomers, we see that the inclusion of configurations involving two electrons in virtual orbitals in the calculations has little effect on the predicted geometries and isomerization energies. They do, of course, lead to a substantial lowering, -0.145 hartree, in the total energies.
Discussion For the ring isomer, with an OS0 bond angle of 60°, the SO distance is considerably longer, 0.21 A, than that of the open isomer. This same trend was observed in O3(hRm = 0.16 A) and attributed to the repulsive interactions between the doubly occupied ?r orbitals (compare (8) and (ll)).g In contrast to ozone, however, the ring isomer in SO2is found to lie 95 kcal/mol above the open isomer. In O3the isomerization energy is only 20-25 kcal/mol.ll-“ This difference is in large part due to the increased stability of the open isomer of SO,; note, e.g., that the &SO bond energy in SO2 is 132 kcal/mol,2Bwhile the 0 - 0 2 bond energy in Osis just 25 kcal/mol.2s This explanation is strengthened by a detailed analysis of the wavefunction for the open isomer of SO2 which indicates substantial double-bond character in the SO bonds?’ Clearly, from the calculations presented here the ring isomer cannot be the “high-temperature” isomer of SO2, as suggested by Hayes and Pfeiffer.6 In fact, as we shall see below, both of the isomers of SO2 lie far above the ground state (open isomer). It is likely, therefore, that the high-temperature isomer of SO2is vibrationally-rotationally excited SO2, as suggested by Herman et al.lS and Gaydon et al.16 The superoxide isomer, an asymmetric structure with an SO0 bond angle of 120°, is found to lie 100 kcal/mol above the ground state of SOz. The SO bond length in the superoxide isomer, 1.66 A, is comparable to that of the ring isomer, 1.67 A (POL-CI). The 0-0bond length, 1.33 A, is somewhat longer than the calculated 0-0 bond distance in Os,1.30 A.12 An estimate of the bond energies of the superoxide isomer can be obtained from eq 14, where (SO-O,S-o,)
0,”“p”’
= DeOp”n (O-SO,S-02)
- Alq:!.:, (14)
(27) T. H. Dunning, Jr., unpublished resulta.
J. Phys. Chem. l Q 8 1 , 85, 1353-1358
D,""W is the SO-0 or S a 2bond energy of the superoxide isomer, D2pn is the experimentally known bond energies of the open isomer (132.1 and 137.2 kcal/mol, respectively26),and b E B A z r is the calculated isomerization energy. From eq 14 we obtain D,8upr(SO-O) = 33 kcal/mol and D:'pr(S-02) = 38 kcal/mol. Thus, the bonds in the superoxide isomer are substantiallyweaker than the bonds in the open isomer but are comparable to the 0-O2 bond strength in ozone (25 kcal/moP). When the bond energies determined above are used, reactions 1-3 are estimated to be endoergic by ca. 90,65, and 35 kcal/mol, respectively.26 It should also be noted that since (CS2,CS) and (OCS, CO) have singlet states only reaction 1 is spin allowed; the SO0 species produced in reactions 2 and 3 correlated with an excited triplet state of the superoxide isomer. The large endoergicities of reactions 1-3, coupled with the spin-forbidden nature of reactions 2 and 3, strongly argue against the assignment of the continuous absorption bands observed in the combustion of H2S, CS2, and OCS to the superoxide isomer of sop While the superoxide isomer of SOz is not expected to be involved in reactions 1-3, it can participate in the reaction of sulfur atoms with molecular oxygen (eq 15).
s+0 2
- -
[SOO]+ so + 0 (15) Studies of this reaction28*29 indicate essentially no activa-
1353
tion energy and a low collisional efficiency, both of which are consistent with the formation of a bound superoxide intermediate. These studies%also suggest a short lifetime, and hence a low bond energy, for the SO0 species. The calculations reported here considered only the structures and energies of the isomers of SO2. Characterization of the interconversion of these species requires information on the barriers to isomerization. While the calculations reported here have no direct bearing on these questions, it may be noted that both the open and superoxide isomers have four ?r electrons while the ring isomer has six ?r electrons. Substantial barriers to the interconversion of these species would therefore be expected. Similarly, interconversion of the superoxide and open isomers involves substantial rearrangements in the a system and would thus also be expeded to involve a large barrier.
Acknowledgment. We thank one of the referees for a number of valuable comments on the manuscript. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy. (28) D. D. Davis, R. B. Klemm, and M. Pilling, Znt. J. Chem. Kinet., 4, 367 (1972). (29) M.A. A. Clyne and P. D. Whitefield, J. Chem. SOC., Faraday Trans. 2,711,1327 (1979).
Reactions of the Excited Singlet State of Pyrene with Metal Ions. Intermolecular Electron Transfer in Caffeine-Solubilized Aqueous Solution Yoshlo Nosaka," Aklra Klra, and Masashl Imamura +
The Instltute of Physbl and Chemksi Research, W a k W , &/&me, 35 1 Japan ( R e c e M : July 31, 1080; In Final Form: December I I, 1080)
Intermolecular electron transfer occurs upon reaction between metal ions and the singlet excited state of pyrene which is solubilized in water by caffeine. The pyrene cation yields for the infinite quencher concentrationwere 0.68,0.39,0.2, and 0.15 for Cu2+,Eu3+,Fe3+,and Hg2+,respectively. The intersystem crossing efficiency was enhanced by reaction with Ag+, TP, Co2+,Ni2+,Sm3+,and Tb3+,where the cation yields were small (
