7233
J. Phys. Chem. 1991, 95, 7233-7239 strengthen the CI-C3 bond, while for the 4b2 orbital in the 11B2 state, the 2py orbitals mix to produce an antibonding region across the CI-C3 bond. The oscillator strength of the 2lA1 state Cf(r) in Table IV) is relatively small and further off-resonance than the other states eliminating it from consideration as one of the states leading to the products in Figure 2. An examination of the 8al orbital in Figure 3 reveals that the bridgehead bond should be strengthened; a population analysis confirms this result but also suggests weakened C-C side bonds, indicating a tendency for the 3'AI state to produce a trans-butadiene product according to the concerted pathway given in Figure 2c. It is also interesting to attempt to predict how the intermediate (2)in Figure 2, a or b, will evolve from examination of the 4b2 orbital derived from the 1 IB2 state and shown in Figure 3. The 4b2 orbital mixes in a substantial 2p, antibonding character which leads to a very weakened bridgehead bond. This result is confirmed in the population analysis given in Table VI11 showing a very negative value for the C-C bridgehead bond while the C-C side-bond populations show no significant change. Becknel14' cites the 1'B2 state as being the most likely state for forming cis-butadiene by the mechanism given in Figure 2a. It is possible that 2 would open to give a carbene (3)in Figure 2a, and subsequently produce cis-butadiene or cyclobutene (3)in Figure 2b by hydrogen migration. The population analysis of the l'BI state given in Table VI11 shows a strengthened bridgehead C-C bond and weakened C-C side bonds yielding a trend similar to the 3'AI state. Thus, the l'BI state may also participate in the formation of trans-butadiene as shown in Figure 2c. Some of the structural changes prediced by the Mulliken population analysis are partially supported by an examination of Table V. In the relaxed 1'B2 and l'BI states, the bond distance across the bridge is greatly increased over that of the ground state, reflecting the weakened nature of this bond. The flap angle y is markedly increased from ground-state value, leading to a more planar structure. The assignment of the three Rydberg states of bicyclobutane, nearly degenerate at 6.9 eV, to photochemical products is suggested by the shape of the Rydberg orbitals obtained from orbital plots and a Mulliken population analysis. However, the key word is suggested. Much more must be known about the complete
potential energy surfaces of each of the excited states before these suggestions can be taken as a definite possibility. For example, the potential energy surfaces for the excited states may cross or mix by vibrational coupling allowing each state to contribute to more than one product.
Conclusions The calculated excitation energies of three low-lying states in bicyclobutane are nearly degenerate at 6.9 eV and have essentially 3P Rydberg character. The calculated 3P Rydberg states correspond to a broad absorption band which peaks at 6.6 eV. The sum of the calculated oscillator strengths for these states agrees well with the measured oscillator strength. The predicted 4P Rydberg states correspond to a broad absorption band with a peak at 7.8 eV. The sum of these predicted oscillator strengths agrees well with the measured oscillator strength. The calculated 2'AI state, with 3 s Rydberg character, and the 'Al state with 4 s Rydberg character, correspond to weak transitions which experiment locates at 5.8 and 7.4 eV, respectively. The calculated and predicted oscillator strengths are both in good agreement with measured values for these S Rydberg states, The calculated oscillator strengths indicate that all three 3P Rydberg states are capable of participating in photochemical isomerizations that occur upon irradiating at 6.7 eV. Based upon the bonding characteristics of the excited Rydberg orbitals and population analyses, the present calculations point to mechanisms in which photochemical decomposition from the 11B2state leads cis-butadiene and/or cyclobutene while the l'BI and 3'AI excited states produce trans-butadiene via a synchronous pathway. Acknowledgment. We thank Professor Ernest Davidson for supplying us with the MELD program and for many helpful discussions. Professor Kenneth Wiberg was extremely helpful in providing us with an interpretation of the absorption spectrum of bicyclobutane. We are also grateful to Professor Jerry Berson and Dr.R. Srinivasan for their help with the experimental photochemical results. Finally, G.D.B. thanks his colleagues, Professors J. Javanainen, G. Epling, and H. Frank, for their assistance in understanding the photochemical equations, and Dr.Stephen Blechner who interfaced the output from GAMES to the POLYATOM properties package.
Nature of 2a/l a* Three-Electron-Bonded Chlorlne Adducts to Sulfoxldes Kamal Kisbore and Klaus-Dieter Asmus* Hahn- Meitner-Institut Berlin, Bereich S,Abteilung Strahlenchemie, Postfach
39 01 28,
D-1000 Berlin 39,
Germany (Received: February 12, 1991; In Final Form: April 10, 1991) Reaction of sulfoxide radical cations, R2S0.+,with chloride ions in acidic aqueous solutions (pH 5 6) leads to optically absorbing transient RsO:.Cl radicals, which are characterized by a sulfurchlorine threeelectron bond containing two bonding a-electrons and one antibonding u* electron. The same species is formed upon oxidation of sulfoxides by C12*-,although only with relatively low rate constants. The measured A, are 390, 400, and 410 nm for the R2SO:.Cl species with R = Me, Et, and n-Pr, respectively. Equilibrium constants for R2SO'+ + C1- s R2SO:.CI have been determined to be 560,600, and 575 M-I, for the same respective series of species (error limit f20%). It is considered that our three-electron-bonded species is identical with an electronically not further specified chlorine-atom adduct to sulfoxide, R2SO(CI)', observed earlier in sulfoxide-containing solutions of carbon tetrachloride and dichloromethane. The R2SO:.CI exhibit oxidizing properties and are shown to oxidize, for example, organic sulfides and disulfides (rate constants on the order of lo* M-l S-') or SCN(rate constants on the order of IO9 M-'s-l). The optical and kinetic results are discussed in light of the electronic properties of the radical species.
Introduction The direct identification and characterization of transients generated upon oxidation of organic sulfoxides has been the subject of several but not too many investigations. Detailed information exists on the neutral intermediates generated in oxidation of 0022-3654/9 1/2095-7233$02.50/0
sulfoxides by 'OH radicals as studied by pulse radiolysis' or ESR flow photoW.24 This Process Proceeds via addition of the (1) Veltwisch, D.;Janata. E.;Asmus, K.-D. J . Chcm. Soc., Perkin Trans. 2 1980, 146.
Q 1991 American Chemical Society
1234 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991
hydroxyl radical to the sulfoxide function followed by sulfurcarbon bond breakage to yield sulfinic acid and a carbon-centered radical: R2SO + 'OH {R,S(O)OH)* R' RSOzH (1)
-
-C
+
Several other radicals identified by ESR, e.&, RSO', RSO;, and carbon-centered radicals resulting from H-atom abstraction in the side chain, are the result of secondary reactions. Corresponding investigations with NH3'+ and C4H90. as oxidants suggest similar reaction routes.s*6 Dimethyl sulfoxide radical cations were first indicated by optical and ESR investigations with irradiated neat MeZSO7+ or Me2SO-containing low-temperature (77 K) glassy matrices.IO Formation of a transient M e f i e + radical cation was also invoked in the S04'-induced oxidation mechanism of sulfoxides in aqueous solution,' although it completely escaped detection in these ESR studies. Very detailed information on the optical and redox properties of R2SO'+ radical cations-or more specifically its associate with one water molecule, namely, the three-electron 2u/ 1ut-bonded (R2SO;.0Hz)+-is given in a recent pulse radiolysis investigation with acidic aqueous solutions of su1foxides.I' Another interesting intermediate that has been noted is an apparent chlorine atom adduct to MezSO. It has been observed in pulse-irradiated solutions of Me2S0 in CCI4I2and CHzClZl3 and exhibits an optical absorption band at 400 nm. Furthermore it seems to exhibit moderately good oxidative properties." Considering the still existing ambiguity about the actual electronic structure and the chemical properties of this neutral sulfoxidechlorine adduct species we have now undertaken a detailed pulse radiolysis investigationon this type of radical in aqueous solution.
Experimental Section The sulfoxides and methyl iodide were purified by distillation. All other chemicals were of "analytical grade" purity and used as received. The solvent was deionized, Millipore-filtered water (>15 MQ). The pH of the solutions was adjusted by addition of HCIOl or NaOH. Buffering (between pH 5 and 8) was achieved by addition of H2PO; and HPOt- (11V2M). solution^ were deoxygenated by bubbling with N2 for ca. 1 h/dm3 sample. For *OH radical induced studies they were subsequentlysaturated with N2,0. Irradiation of aqueous solutions yields e,,-, 'OH, and H' as reactive radical species. In neutral and slightly acidic solutions the yield of hydrated electrons and hydroxyl radicals is about equal (G = 2.8 species per 100 eV of absorbed energy), whereas the yield of hydrogen atoms is significantly lower (G = 0.6). At low pH or in the presence of NzO, hydrated electrons are converted via ea,- + H+ H' or ea< + N 2 0 N2 + OH- 'OH, respectively. Selective investigations on reactions initiated by ea; were performed in the presence of high concentrationsof rerr-butyl alcohol (usually 0.5 M), which scavenges 'OH and H'.I4 Irradiations were camed out by means of pulse radiolysis. This technique provides short pulses, e.g., of I-ps duration, of highenergy electrons (e& 1.5 eV) delivered by a Van de Graaff accelerator. The concentration of radicals generated was in the
-
-
+
(2) Gilbert, B. C.; Norman, R. 0.C.; Sealy, R. C. J . Chem. Soc., Perkin Trans. 2 19775. 303, 308. (3) Gilbert, B. C.; Marriott, P. R. J . Chem. SOC.,Perkin Trans. 2 1979, 1425. (4) Daviea, M. J.; Gilbert, B. C.; Norman, R. 0.C. J . Chem. Soc., Per&in Trans. 2 1984, 503. ( 5 ) Chapman, J. S.; Cooper, J . W.; Roberts, B. P. J . Chem. Soc., Chem. Commun. 1976,407. ( 6 ) Gara, W.B.: R o w , B. P. J . Chem. Soc., Perkin Trans. 2 1977,1708. (7) Koulkes-Pujo, A. M.; Gilles, L.; Lesigne, B.; Sutton, J. Chem. Commun. 1971, 749. (8) Walker, D. C.; Klassen, N . V.; Gillis, H. A. Chem. fhys. Lett. 1971, 10, 636. (9) Bensasson, R.; Land, E. J. Chem. fhys. Lett. 1972, IS, 195. (10) Symons, M. C. R. J . Chem. Soc., Perkin Trans. 2 1976.908. ( I 1) Kishore, K.; Asmu. K.-D. J . Chem. Soc., Perkin Trans. 2 1989,2079. (12) Sumiyoshi, T.; Katayama, M. Chem. Leri (Jpn.) 1987, 1125, 1429. (13) Alfassi. 2.B.; Mosseri, S.; Neta, P. J . Phys. Chem. 1989, 93, 1380. (1 4) Asmus, K.-D. In Merhods in Enzymology;Packer, L., Ed.; Academic Press: New York, 1984; Vol. 105, p 167.
Kishore and Asmus
w
6
0
4000-
30002000-
0
0
0
0
0
0
0 0
1000-
0 ;
I
I
I
I
I
1 6000{ w x
0
0 0
0
4000
2oool
0 0
1000
0
0
1
6000A
5000w
ci
A
AA A'
A
A
4000-
A
A
A
A A
A
3000-
A A
2000-
A
1000-
0 250
300
350
450
400
500
1 5 0
h , nm Figure 1. Absorption spectra of Me$3O(Cl)' (O), Et,SO(CI)' ( O ) , and n-Pr,SO(CI)' (A) as recorded ca. 20 1 s after irradiation of pH 1.7,
N,-saturated aqueous solutions containing 5 M sulfoxide with a ca. 2 p s ( 5 Gy) pulse.
X
IO-, M C1- and 5 X IO-)
order of 6 X lo-' M/Gy of absorbed energy ( 1 Cy = 1 J kg-l) and a radiation chemical yield G E 6 (e.g., the yield of 'OH radicals in NzO-saturatedsolution; G generally denotes the number of species generated or transformed per an energy uptake of 100 eV). Further details including dosimetry (based on the oxidation of SCN- to (SCN),'-), detection of time-resolved optical and conductivity signals, and the evaluation and interpretation of data All experiments have been have been documented e1~ewhere.l~ carried out at room temperature (- 18 OC, no thermostating). Error limits of *IO% cover the uncertainties that are typical for radiation chemical and pulse radiolysis experiments. Deviating estimates are noted at the appropriate places. Results and Discussion Formation and Optid Prapertieeof R2SO(Cl)' Adduct R.diepLs.
Pulse irradiation of an aqueous, pH 1.7, N2-saturated solution containing 5 X lo5 M dimethyl sulfoxide (Me,SO), and 5 X 1C2 M CI-, leads initially to the formation of the well-known transient C1;- absorption with a maximum at 345 nm.Is This is fully developed after admission of the 2-rs pulse. Upon decay of the CI2'- absorption another, somewhat longer lived transient remains, the spectrum of which (as recorded ca. 20 ps after the pulse) is shown in Figure 1 (e). It is characterized by its broadness and a maximum at 390 nm. Very similar transient absorptions are obtained if, under otherwise identical conditions, Me#O is replaced by other sulfoxides. ( 1 5 ) Anbar, M.; Thomas, J . K. J . Phys. Chem. 1964,68, 3829.
2a/ 1 u* Three-Electron-Bonded Chlorine Adducts
TABLE I: Rate Conatants for tbe Fornrtion of R@(CI)'
tbrougb the Raction R M + CIz'- rad for Oxidation Reactions Initiated by R,SO(CI)' (Error Limits f1096) rate const, reaction M-' s-' product radical CI,'-+ MezSO 1.2 X IO' MezSO(CI)' EtzSO(C1)' EtzSO 2.7 X IO' n-Pr$O(CI)* n-Pr2S0 3.9 x io7
+ + Me,SO(CI)*+ MeS(CHZ),SMe + MeSSMe + EtSSEt + n-PrSSn-Pr + SCN-
4.9 X Id 7.8 x IO' 5.8 X IO' 1.3 X IO' 4.9 x 109
Et,SO(CI)'+ MeS(CHJ3SMe + MeSSMe + EtSSEt + n-PrSSn-Pr SCN-
1.7 X 6.2 X 3.5 X 1.1 x 4.2 x
10'
n-Pr,SO(CI)'+ MeS(CH2),SMe + MeSSMe EtSSEt n-PrSSn-Pr SCN-
1.0 X 5.3 x 3.1 X 1.0 x 3.2 x
IO' IO' IO' IO'
+
+ + +
IO' 10' 10' 109
109
ml' (RSSR)" (scN);-
-
neutral sulfoxide-chlorine adduct radical. R2SO"
+ C1-
(RSSR)'+ (scN),-
H'
+ R2SO + H+
(scN)*-
+
We suggest that this is followed by chlorine atom transfer from C12'- to the sulfoxide: C12'- + R2SO R2SO(CI)' + CI(3) The high redox potential of CI2'-/2C1- ( E o = +2.3 V)I7 should, in principle, facilitate a one-electron transfer: (212.- + RzSO R2SO*++ 2C1(4) to yield the sulfoxide radical cation. It cannot be excluded that the CII'--induced oxidation of sulfoxide does indeed proceed via this radical cation intermediate. This would subsequently be neutralized by chloride ions according to reaction 5 to yield a +
+
(16) Dorfman, L. M.; Adams, C. E. In Reactivity of the Hydroxyl Radical in Aqueous Solution; NSRDS-NBS Reference Data; Washington D.C., 1973; Vol. 46. (17) Henglein, A. Radial. Phys. Chem. 1980, IS, 151.
(5)
-
+
R2S*+ H2O
(6)
The R2S*+could then react with chloride:
B1' (RSSR)"
R2SO(CI)'
As the redox potential of the R2SO'+/R2S0 couple has been estimated to +(1.8-2.0) V," it is not surprisin that both Br2*( E o = +1.7 V)I7 and 12'- (Eo = +1.03 V)I7Jfare not able to oxidize the sulfoxides at all. In these cases neither a sulfoxide halogen adduct nor a sulfoxide radical cation is formed. At this point it is necessary to briefly comment on a possible reaction of hydrogen atoms with sulfoxide. This is particularly relevant for the acid solutions where H atoms (from e,; + H+ reaction) are present at about the same yield as hydroxyl radicals for reaction with the solutes. It is known that the hydrogen atoms in strongly acidic solutions are able to reduce sulfoxides to the corresponding sulfide radical cation:19
B1+
With diethyl sulfoxide (EtISO) and di-n-propyl sulfoxide (nPr2SO) the maxima are marginally red-shifted to A, 400 nm (Figure I , 0 ) .and 4 I O nm (Figure 1, A), respectively. The second-order rate constants for the oxidations of MeISO, Et2S0, and n-PrISO by CI2'- are 1.2 X lo7, 2.3 X IO7, and 3.9 X 10' M-' s-l, respectively. These values have been evaluated from the pseudo-first-order decay of the CI2'- absorption (measured at 330 nm, Le., on the high-energy side of the absorption band to minimize overlap with the absorption of the sulfoxidechlorine adduct, and analyzed by an appropriate computer-fit program with correlation coefficients 20.990) in solutions of various sulfoxide concentrations, and are listed in Table I. They follow the same trend as observed for the oxidation of these sulfoxides by a variety of one-electron oxidants, easily understandable by the electron-donating function of the alkyl substituents." Transients with the same characteristicsare obtained in a second series of experiments upon pulse irradiation of aqueous, pH 4, N2-saturated solutions containing 5 X IO-' M S20B2-,0.5 M tert-butyl alcohol, 5 X IO-' M of any of the sulfoxides, and 1 X 10-2 M CI-. The optical spectra, as observed under these experimental conditions, are fully developed immediately after the pulse. The spectral characteristics resemble those in Figure 1. No such species are formed if chloride is substituted by bromide or iodide in these two sets of experiments. In these cases the only transients observable are the halide radical anions Br2'- and 12*-. Both exhibit no apparent reactivity toward the sulfoxides. Mechanisms of R2SO(CI)'- Formation. In our first series of experiments at low pH the initial step is oxidation of the chloride by hydroxyl radicals in the overall process:I6 2CI- + 'OH + H+ C12" HzO (2) +
The Journal of Physical Chemistry, Vol. 95, NO.19, 1991 7235
R2S*++ CI-
R2S;.CI
(7) to produce the also well-known three-electron-bonded R2S:.CI radical, which absorbs at about 380 nm,20i.e., at about the same wavelengths as our present transient. This process can, however, be neglected for the following reasons: (i) It has been demonstrated that the corresponding bromine and iodine species, Le., R2S;.Br and RIS:.I, are stabilized even more than R2S.a.C1,20in contradiction to our present results. (ii) Appreciable yields of M) and reaction 6 require considerably higher sulfoxide (>>IC2 proton concentrations (pH < 1.0) than in our present experim e n t ~ . ' It ~ is therefore concluded that the transients generated in our two sets of experiments and absorbing at about 400 nm are exclusively the result of a sulfoxide oxidation. In the second series of our experiments the underlying reaction mechanism involves formation of the sulfoxide radical cation R$O'+ as the key intermediate as demonstrated in an earlier study of ours:l I +
+ R2S0
-
+ 2Br-/I-
-
eaq- + Sz082SO4*-
S042-+ SO4*-
(8)
R2SO'+ + S042-
(9) The strongly oxidizing R2SO'+ subsequently reacts with the halide ion. In case of bromide and iodide this reaction leads directly to the XI'- type halide radical anion via the overall process R2SO'+
Br2'-/12*-
+ R2S0
(10)
In the presence of chloride the reaction proceeds not to the corresponding ClI'- but to the R2SO(CI)' adduct radical, Le., via neutralization of the R$O.+ radical cation by chloride according to reaction 5 . A mechanism involving direct oxidation of chloride by sulfate radical anions: SO4*-
+ 2CI-
-
C12*-+ S042-
(1 1) followed by reactions 4 and 5 may also be in effect. Considering the published rate constants of ca. 2 X IO8 M-' s-I for reaction 1 I2I and (2.7-5.0) X lo9 M-' s-I for the S04'--induced oxidation of the three sulfoxides investigated in this study," this route will contribute only to a minor extent under our experimental conditions. (In this second series of experiments the hydroxyl radicals, which are generated at about the same yield as hydrated electrons in irradiated aqueous solutions, are removed by reaction with tert-butyl alcohol. The ?err-butyl alcohol radicals, 'CHI(18) Thornton, A. T.; Laurence, C. S. J. Chem. Soc. Dalron Trans. 1973, 804. 1632. 1637.
(19)-Chudhri, S.A.; Cabl, M.; Freyholdt, T.; Asmus, K.-D. J. Am. Chem. Soc. 1984, 106, 5988. (20) BonifaEiC, M.; Asmus, K.-D.J . Chem. Soc., ferkin Trans. 2 1980, 758. . - -. (21) Neta, P.; Huie, R. E.; Ross, A. In Rare Conrranrs of Inorganic Radicals in Aqueous Solution. J . Chem. Phys. Ref Data 1988, 17, 1027.
7236 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991
Kishore and Asmus
0.44
021
U.
-0.0 3
4
5
6
7
8
9
1
0
PH Figure 2. pH dependences of the R2SO(CI)' yields (normalized for pH 3) in pulse-irradiated, N,-saturated, aqueous solutions containing 5 X IO-' M S2082-,0.5 M tert-butyl alcohol, 5 X M sulfoxide, and 1 X IO-, M CI-, recorded at the respective maxima of the R2SO(CI)*absorptions. (In order to stabilize the pH in the neutral region during the
irradiation, IO-, M phosphate buffer was added.) Me2SO(CI)' (0). Et,SO(CI)* (O), and n-Pr,SO(CI)' (A).
(CH3)2COH, resulting therefrom are too weak an oxidant to participate in the sulfoxide oxidation.) pH Depenaence of R$W(CI)* Fwmath. The pH dependences of the R2SO(CI)' formation in pulse-irradiated, N2-saturated, 5 X lW3 M S2082-,0.5 M tert-butyl alcohol, 5 X IO-' M sulfoxide, and 1 X I b 2 M CI- solutions and recorded at the respective maxima are shown in Figure 2. (To stabilizethe pH in the neutral region during the irradiation, 1W2 M phosphate buffer was added.) The curves represent relative yields calculated on the basis of the respective maximum yields on the acid side. All of them exhibit a sigmoidal character with inflection points at pH 5.8, 6.5, and 7.0 for the Me2S0, Et2S0, and n-Pr2S0 systems, respectively. These values are very close to the pK's for the
+
R2SO'+ + H20 RZSO(0H)' H+ (12) equilibrium (5.6, 6.1, and 6.5, respectively)." The lower yields of R$O(Cl)' on the high-pH side can consequently be associated with the known fast and irreversible alkyl radical elimination from R2SO(OH)' (the hydroxyl radical adduct to sulfoxide):'-" R2SO(OH)' R' +'RSO,- + H+ (13)
-
which competes with the displacement reaction R2SO(OH)' C1R2SO(CI)* + OH-
+
(14) Such alkyl elimination does not seem to occur from the sulfoxide radical cation (although R2SO'+, or more precisely (R2SO:. OH2)+,'Iis just the protonated form of R2SO(OH)'); at least this process would be much too slow for competition with R2SO(Cl)' stabilization via reaction 5 . An interesting trend is noted on the high-pH side for the R2SO(CI)' yields: they increase from the M e 3 0 over the Et2S0 to the n-Pr2S0 system. As the thermodynamic stability of the R$O(CI)* does not seem to change significantlywithin this series (as will be shown and discussed below) this must have different reasons. One of them may be the kinetic stability of the respective R2SO(CI)' radicals. The observed half-lives for the first-order decay processes are generally smallest for the Me2SO- and higher for the Et2SO-and n-Pr2SO-derived species in this high pH region (at pH 7, t l = 1 ps for Me2SO(CI)', and a3 ps for Et2SO(CI)' and n-P@h(CI)*, respectively; see Figure 3). Furthermore, the lifetime of the n-Pr2SO(OH)' radicals with respect to alkyl radical elimination (reaction 13) is about twice as long as that of the methyl-substituted species.' This, in turn, also favors the competing displacement process (reaction 13) and would consequently result in relatively higher yields of the chlorine-sulfoxide adduct in case of the n-propyl species. It is noted that the pH dependence of the yields of the respective R2SO'+radical cations showed the same trend beyond the pK of equilibrium 12 (lowest yields for Me2SO'+ and comparatively higher but almost equal yields for Et2SO'+ and n-Pr2SO'+ at pH 1 7)." +
o , " ' ~ , ' ' ' ' , " " , ' ' " , ' " ' 3
4
5
PH
6
7
8
Figure 3. pH dependence of the kinetic stability of R,SO(CI)'. Experimental conditions as in Figure 2. Me,SO(CI)' (@), Et,SO(CI)' ( O ) , and n-Pr,SO(CI)' (A).
pH Dependence of R2SO(CI)*Lifetimes. The entire pH dependence of the kinetic stability of R2SO(CI)' is shown in Figure 3. (Same experimental conditions as in previous section.) The measured half-lives of the generally first-order, Le., exponential, decay processes indicate a comparatively high stability in the acid pH region with t l = 35, 47, and 44 p for Me2SO(Cl)', Et$O(CI)', and n-hr2SO(C1)', respectively. At higher pH ( 1 6 ) the lifetime is reduced to just a few microseconds. The pH-dependence curves are sigmoidal and exhibit breakp i n t s at pH 4.7, 5.1, and 5.4 for the three chlorine adducts. Clearly, they do not match the thermodynamic pK curves of the R#SO'+/R2SO(OH)' equilibria" since they represent the kinetics of only one individual process. It is not unreasonable though to establish a relationship between the pH dependence of the R2SO(CI)* lifetimes and this equilibrium. Accordingly it is concluded that reaction 14 is also reversible: RZSO(0H)' + C1- s R2SO(CI)' + OH(14a) This directly connects the stability of the sulfoxide-chlorine adducts with the acid/base properties of the hydroxyl adduct/radical cation system (eq 12) and also with the irreversible decay of R$O(OH)' via reaction 13. On the acid side the rate-determining step for the disappearance of R2SO(CI)' appears to be the deprotonation of the R2SO'+radical cation in analogy to the decay of corresponding thioether radical cations, R2S*+.22At higher pH, Le., upon increasing conversion of R2SO'+ to R2SO(OH)', the fast alkyl elimination from the *OH adduct according to reaction 13 seems to take over. Since no measurable yield of transient R2SO'+ is observable, this clearly implies that all preceding processes, namely, the back reactions of equilibria 14a and 12, would have to be at least as fast as the alkyl elimination from R2SO(OH)', which occurs with first-order rate constants of (1-2) X IO7 s-l.' As will be evaluated later, this appears to be a quite reasonable assumption. R2SO(CI)*as Oxidants. The R2SO(CI)' radicals exhibit oxidizing properties conforming with similar observations made in CH2CI2 solution^.'^ In our experiments this becomes apparent by an accelerated decay of the R2SO(CI)' absorption in the presence of oxidizable substrates (electron donors, D). In this study the R2SO(CI)'-induced oxidation of SCN-, three disulfides and one dithia compound have been investigated as examples. Solutions were N2 saturated and pH 4 and contained 5 X IO-) M SzOsz-,0.5 M tert-butyl alcohol, 5 X M sulfoxide, 1 X or 1 X M CI-, and various small concentrations ( 5 X 10"-5 X M) of the electron donors. Measurements were made by following either the decay of the R2SO(C1)' absorption (at 360 nm, to minimize overlap with the absorption of the oxidized or the buildup of the Do+absorption. The observed donor Do+) kinetics were of pseudo-first-order with respect to the donor concentration but did not depend on the chloride concentration. (22) Monig, J.; Goslich, 1986, 90, 1 1 5 .
R.;Asmus, K.-D. Ber. Bunsen-Ges. Phys. Chcm.
2u/ 1 u* Three-Electron-Bonded Chlorine Adducts
The Journal of Physical Chemistry, Vol. 95, NO.19, 1991 7237
From the measured half-lives, bimolecular rate constants could be evaluated according to kls= In 2/(tlI2[D])for the underlying reaction R2SO(CI)' + D Do++ CI- + RZSO (15)
/
a
/
I
+
In the case of SCN- as donor, the oxidized form was the (SCN)*' radical anion (A,, 475 nm).23 The disulfides were oxidized to 410-440 nmh2' and the 2,6-di(RSSR)'+ radical cations (A, thiaheptane to the intramolecular (>S:.S +1.4 V. On the other hand, the R2SO(CI)*are clearly less good oxidants than the R2SO'+radical cations, which readily oxidize, for example, Br- and for which a lower limit of Eo L +I .8 V has been evaluated. This is corroborated, at least qualitatively, by the rate constants for oxidation reactions initiated by R2SO*+, which are generally higher by a factor of up to 1 order of magnitude as compared to those for the R2SO(C1)'-induced oxidations." The observed trends in rate constants parallel the trends observed in our earlier study on R2SO'+-induced oxidations" and shall therefore not be commented on in great detail. The decrease in rate constants in going from Me2SO(CI)' to Et2SO(Cl)' and n-Pr2SO(C1)' may thus be explained by the electron-inductive effect exerted by the substituents R into the reactive center which, as will be discussed below, is likely to be the sulfur-chlorine bond. A certain degree of polarization (R2SO'd+.-Clb) would also help to understand that the reactivities of R2SO(CI)' and R2SO'+ are not too different and show the same trends. A very similar situation has been described for RI(0H)' and RI" reactivities where the *OH adduct to the alkyl iodide is also highly polarized.28 The other aspect that warrants a brief comment is the trend in rate constants for the oxidation of the various disulfides. As had been found in the cases of R2SO'+ and RI'+ the fastest oxidations occur with MeSSMe, although this disulfide benefits the least from electron induction by the alkyl groups. However, dimethyl disulfide suffers the least conformational change when oxidized to the corresponding radical cation, an effect that seemingly overrules the electron inductive effect.l'.28 In addition, it has been suggested that alkyl substituents on sulfur exert only minimal electronic effects and that changes in reactivity would therefore primarily be due to steric effects.29 The oxidation reactions finally allow us to estimate extinction coefficients for the chlorine adduct radicals. On the basis of the simple assumption that these species are formed with the full yield of oxidizing SO4' radical anions (G = 2.8, which equals the yield of hydrated electrons) the respective t values would be 2.8 X lo3, 2.9 X 103, and 2.1 X lo3 M-' cm-I for Me2SO(Cl)', Et$O(CI)', and n-Pr2SO(C1)'. Since the measurable yields of oxidized donor from reactions 15 amount, however, to only ca. 50% of the maximum possible yield, these values are probably too low. Presently it is not possible to decide unambiguously which of the (23) Baxendale, J. H.; Bevan, P. L. T.; Stott, D. A. Tram. Faroday Sm. 1968.64, 2389. (24) BonifasEiE, M.; SchBfer, K.; Miickel. H.; Asmus, K.-D. J. fhys. Chem. 1975. 79. 1496. .. h m d , K.-D.; Bahncmann, D.; Fischer, Ch.-H.; Veltwisch, D. J . Am. Chem. SOC.1979, IOI, 5322. (26) Nord, G.; Pedcrsen, B.; Floryan-Lovberg. E.; Pagsberg, P. fnorg. Chem. 1982, 21, 2327. (27) BonifaEiE, M.; Asmus, K.-D. J . Chem. Sa.,Perkin Trans. 2 1986. 1805. (28) Mohan, H.; Asmus, K.-D. J. fhys. Chem. 1988, 92, 118. (29) Charton, M.;Charton, B. 1. J . Org. Chem. 1978, 43, 68.
c5)
f' I
I
I
,
500
1000
1500
2000
1 1
0
2500
l/[chloride], M-'
Figure 4. Analysis of R,SO(CI)' yields as a function of chloride concentration according to eq 1. Me,SO(CI)' (@), Et2SO(CI)' ( O ) , and n-Pr,SO(CI)' (A).
individual reactions leading to the sulfoxide-chlorine adduct radicals do not occur quantitatively. A prime candidate would probably be H-atom abstraction by SO4*-from, e.g., the alcohol present at 100-fold excess over sulfoxide in our systems. It is known that such reactions occur with rate constants in the order of 106-10' M-' s-1.21,30 In good accord with this, the S04'--induced oxidation of sulfoxides to R2SO'+ (eq 9) has been found to occur with an efficiency of at most 75%." An exact determination of the extinction coefficients of the R,SO(CI)' species is, therefore, not yet possible. The real 6 values are, however, very likely to be higher than the above-mentioned figures and may well attain values close to (5-7) X lo3 M-I cm-I, which are typical extinction coefficients for the structurally similar >S:.X type and other three-electron-bonded radical specie^.^^-"*^^ Dependence of R2SO(CI)' Formation on Chloride Ion Concentration. The measurable yield of the respective RfiO(C1)' radicals depends strongly on the chloride ion concentration. A quantitative evaluation could be done with acidic solutions, Le., under conditions where the R2SO'+ radical cation is the prevalent form in equilibrium 12. For example, in N2-saturated, pH 4 solutions conM S20g2-,0.5 M tert-butyl alcohol, 5 X IO-' M taining 5 X sulfoxide, and chloride concentrations ranging from 5 X lo4 to 1X M, the R,SO(Cl)' absorption is fully developed immediately after the I-pspulse and the rate of its formation does not depend on the chloride concentration. This shows that the rate-determining step of the R$O(CI)* formation in such systems is the oxidation of the sulfoxide by SO4'- (eq 9) rather than the subsequent and, in fact, much faster neutralization of R2S0.+by CI- (eq 5 ) . Yet the R2SO(CI)' yields increase by about a factor of 3 over this CI- concentration range. This suggests reversibility of reaction 5 as noted in R2SO" + CI- .S R,SO(CI)' (sa) The equilibrium constant is defined as
K = [R2SO(Cl)*]/[R2SO'+][Cl-] With c = [R2SO*+]+ [R2SO(CI)'], representing the total concentration of oxidized sulfoxide, and u = [R2SO(Cl)*],this equation converts to a C or - =1- K= 1 (c - a)[Cl-] K[CI-] a Further rearrangement gives
-C --I + a
1
or -1 = -1
1 +c cK[Cl-]
K[CI-]
a
(30) Schuchmann, H.-P.; von Sonntag, C. Radial. fhys. Chem. 1988,32, 149. (31) Anklam, E.; Asmus, K.-D.; Mohan, H . J . Phys. Org. Chem. 1990,3, 17. (32) Anklam, E.; Mohan, H.; Asmus, K.-D. J . Chem. Soc., fer&inTram. 2 1988, 1297.
7238 The Journal of Physical Chemistry, Vol. 95, No. 19, 1 5191 TABLE 11: Equilibrium Constants for R&O" + C r F? R&O(CI)' and Relevant drta Derived from Figure (Error Limit for-K *ZO%) R,SO(CI)' 1 /(Gc),' (Ge), 1IIK(Ge),lb K. M-' 2910 2.282 X 560 Me,SO(CI)' 1.274 X IO4 3015 2.053 X IO-' 600 Et,SO(CI)' 1.228 X IO4 2205 2.934 X 575 n-Pr2SO(CI)' 1.680 X IO4 Intercept. bSlope.
With the measured optical absorption, expressed in terms of Gc, being proportional to the R2SO(CI)' radical concentration ( a ) , and (Gc), representing the yield of R2SO(CI)' (=c) at infinitely high chloride concentration, the last equation reads I + 1 - 1= (1) Gc (Gc), (Gc),K[CI-] Correspondingly, a plot of I /(Gc) vs l/[Cl-] should give a straight line with I/(Gc), as intercept and I/((Gt),KJ as slope. Such functional relationships are indeed obtained from the experimental data as is demonstrated in Figure 4 for the Me2S0, Et2S0, and n-Pr2S0systems. The respective (Ge), and K values derived from these plots together with the relevant I/(Gc), and I/((Gt),K) data are summarized in Table 11. The equilibrium constants are found to be very similar for all three R2SO(CI)' species with no noticeable trend upon variation of the alkyl substituent. They are higher by almost 1 order of magnitude than the equilibrium constants for the ionic dissociation of the corresponding chlorine adduct to dimethyl sulfide (MqS:.CI s Me2S*++ CI-)," indicating a comparatively greater stability of the sulfoxide-derived species. The forward reaction of equilibrium 5a is very fast and can be assumed to be diffusion controlled, Le., k5, = loio M-I s-l. On this basis the rate for dissociation of R,SO(CI)' into its ionic components is calculated to k+, = k5,/K = 2 X IO7s-l. This fully corroborates the requirement postulated above in the "lifetime" section that the R2SO(Cl)*dissociation should occur with 3 1 - 2 ) X lo7 s-l. In any case, under all experimental conditions of the present study equilibration is achieved practically instantaneously in both directions. This is also of significance for the interpretation of the redox reactions initiated by R,SO(Cl)'. On the basis of equilibrium Sa it could have been argued that the oxidizing species was, in fact, the free R2SO'+ radical cation and that the slower rate constants were due to slow equilibration (although the lack of chloride concentration dependence would probably speak against it). With equilibration in both directions occurring much faster than the oxidation reactions it seems therefore safe to attribute the actual decay kinetics of the R2SO(Cl)' absorption to redox processes initiated directly by this species via reaction 15. Structure of R2S(Cl)'. Considering all the properties reported in the present and previous publications on the chlorine adduct to sulfoxide and particularly the similarities with radical intermediates obtained, for example, in the oxidation of organic sulfide~,''"~organic halide^,'^ and radicals with sulfur-halogen interaction,20q32it is most reasonable to propose a 2u/1 u* threeelectron-bonded structure for the R2SO(CI)' radical, i.e. U
R,ll
R,S
:.
CI
The particular stability of this species can be rationalized on the '~ for basis of the three-electron-bond ~ o n c e p t . ' ~ *Considering, example, the dimer radical cation obtained upon oxidation of an organic sulfide, (R2S:.SR2)+, the electrons are accommodated on the bonding u and antibonding u* energy levels as schematically shown in the completely symmetrical MO diagram I (half-electron (33) Asmus, K.-D. In Sulfur-Centered Reactive Intermediates in Chemistry and Bfology;Chatgilialoglu, C., Asmus, K.-D., Eds.: NATO-AS1 Series A, Life Sciences; Plenum Press: New York, London, 1990 Vol. 197, p 115. ( 3 4 ) Asmus, K.-D. Ace. Chem. Res. 1979, 12, 436. (35) Mohan, H.; Asmus, K.-D. J . Chem. Soc., Perkin Tram. 2 1987. 1795. (36) Clark, T. In Sulfur-Centered Reactive Intermediates in Chemistry and Biology; Chatgilialoglu, C.,Asmus. K.-D., Us.: NATO-AS1 Series A, Life Sciences; Plenum Press: New York, London, 1990; Vol. 197, p 13.
Kishore and Asmus model). Whenever the interacting moieties differ in energy (e.g., l
o
*
s=o-
::;+
r a U
I II because of different electronegativities), an asymmetric situation is established as depicted in diagram I1 for the R2S:.CI radical. The result is a comparatively smaller stabilization energy of the . ~ ~ was substituted by three-electron-bonded s p e ~ i e s . ~If~chlorine bromine or iodine in this species, the respective energy levels are raised toward that of suifur and the resulting M O diagrams for R2S:.Br and R2S:.I attain more and more that of (R2S:.SR2)+, i.e., model I. Accordingly, the stability of the three-electronbonded species increases. Substituting the sulfide moiety by sulfoxide (essentially this means addition of an oxygen to a free electron pair at sulfur) leads to a lowering of the corresponding energy level so that the resulting M O diagram again approaches a more symmetrical and energetically thus more favorable situation for the establishment of a 2u/lu* bond. At the same time interaction between the sulfoxide moiety and bromine or iodine becomes less advantageous, providing a simple rationale for the lack of R,SO:.Br and R2SO:.I stabilization. An exact location of the sulfoxide energy level can, of course, not be given and constitutes a perhaps interesting problem for a theoretical calculation. The particular stabilization of R2SO(CI)' may also be viewed in terms of the HSAB (hard-soft acid-base) concept37extrapolated to radicals. It is generally accepted that "hard" acids bind tightly to "hard" bases and usoft" acids to "soft" bases, whereas "hard-soft" interactions result in only weak if any bonding. In the series of halide ions CI- is classified as a hard base, Br- as an intermediate case, and I- as a soft base. Considering sulfurcentered cationic Lewis acids, those without oxygen (e.g., RS+) are listed as soft and their oxygenated analogues (e.g., RS02+) as hard. The cationic radical counterparts of the halides in R#:.X and R$O:.X, namely, R g + and R2S0.+, should therefore follow the same trend. Accordingly, the particular stabilization of R2SO:.C1 and R2S:.I could be rationalized as a result of "hard acid-hard base" and "soft acidsoft base" interaction, respectively, while any of the "hard-soft" cases such as R2S0.-.Br and R2SO:.I in the sulfoxide series as well as R2S:.CI in the sulfide series would be disfavored. Although our present data refer to aqueous solutions, there is no reason to assume that the electronic structure of Me2SO(Cl)' would be principly different in other solutions, except perhaps for solvent-assisted polarization which, in a less polar environment, may disfavor ionic dissociation of R2SO:.CI according to the back reaction of equilibrium 6a. This, in turn, could result in much higher stability constants for the three-electron-bonded species. Possibly, equilibration involving dissociation of chlorine atoms (rather than chloride ions) could take over in the low-polarity solvents:
RpSO(CI)' CI' + R2SO (16) This process is probably of no significance in high-polarity systems such as water as can be concluded by extrapolation from the sulfide analogue, R2S:.CI, for which C1' elimination has no chance to compete with ionic dissociation (more than 10 orders of magnitude difference between respective stability constants).20 A similar equilibrium being of significance, however, even in aqueous solution seems to be the I' elimination from RzS:.I.20 One may thus speculate on the possibility of generating R2SO(Br)' and R*O(l)' (37) Fleming, I. Grenzorbiraleund Reaktionen Organischer Verbindungen; VCH Verlagsgesellschaft, Weinheim, 1988.
J . Phys. Chem. 1991, 95, 7239-7244
as transients through direct Br' and I' reaction with sulfoxides in low-polarity solvents. [Me2SO(Br)' has, in fact, recently been suggested to be formed upon radiolysis of Me2S0 in dibromomethane.'*] Considering all R2SO:.X, it may also be of interest to investigate the possible influence of equilibria such as in eq 16 on the kinetics and yields of halogen atom reactions.
under the terms of an agreement on scientific cooperation between the Federal Republic of Germany and the Republic of India is gratefully acknowledged. Dr. Kamal Kishore has been on deputation from Bhabha Atomic Research Centre, Bombay. Registry No. Dimethyl sulfoxide radical cation, 66514-98-5; diethyl sulfoxide radical cation, 127182-42-7; dipropyl sulfoxide radical cation, 127140-66-3; chloride, 16887-00-6; dimethyl sulfoxide, 67-68-5; diethyl sulfoxide, 70-29-1;dipropyl sulfoxide, 4253-91-2; dichlorineradical anion, 12595-89-0; dimethylchlorothionyl,135073-68-6; diethylchlorothionyl, 135041-75-7; dipropylchlorothionyl,135041-76-8; 1,3-bis(methylthio)propane, 24949-35-7; dimethyl disulfide, 624-92-0; diethyl disulfide, 110-81-6; dipropyl disulfide, 629-19-6; thiocyanate, 302-04-5.
Acknowledgment. The financial support provided for this work through the "Intemationales Biiro des Forschungszentrums Jiilich" (38)
Shoute, L. C. T.; Neta, P. J. Phys. Chem. 1990, 94.
7239
2447.
Reiativistlc Electronic Structure of Staggered and Eclipsed Conformations of Octachiorodiosmate( I I I ) Ramiro Arratia-Perez Facultad de Qubica, Pontificia Uniuersidad Catdlica de Chile, Casilla 6177, Santiago Chile (Received: March 19, 1991) Symmetry-adapted angular momentum basis functions have been generated for the Du* and D4** molecular double point groups. These basis functions are used to obtain the relativistic molecular orbitals for the staggered (D.,,,) and eclipsed (DG) rotameric geometries of octachlorodiosmate(II1) via the self-consistent field Dirac Scattered-Wave (SCF-DSW) method. Double-point-group symmetry arguments and relativistic molecular orbital calculations for the os$182- ions indicate that the molecular orbitals involving the u, T , 6, and 6* metal-metal bond components remain nondegenerate in both conformations. Spin-rbit interaction splits the 'A bond component of both conformers by about 0.35 eV and removes the orbital degeneracy involving the 6 and 6* bond components of the staggered conformer. Double-point-grouparguments and the results of DSW calculations on the staggered conformer allow us to reassign the two lowest absorption bands seen in the visible spectrum as being primarily metal-metal based.
I. Introduction The existence of multiple bonds between osmium atoms has been recognized for about a It has been observed that organometallic compounds containing the unit show temperature-dependent paramagnetism.'S2 However, five years ago Walton et al? reported the first example of a diamagnetic diosmate octahalo complex, 0s2CleE,having a staggered rotational structure (DM), thus extending the field of multiple-bonded dimetal ions to the platinum metals.'~~ Since then, both geometrical structures for the octachlorodiosmate(II1) anion! and the staggered compounds for the octabrome and octaiodo-diosmate anions have been ~ynthesized.~,' It is known that the multiple-bonded octachloroditungstate and -dirhenate anion^^.^ are characterized by having singlet ground states and eclipsed rotational structures with a formal quadruple bond (u2r46*)between the metal atoms. On the other hand, the octachlorodiosmate(II1) anion exhibits both eclipsed and staggered geometrical structures with a formal triple bond between the osmium atoms5v6in accord with the u * ~ ~ 6 * 6 * ~ configuration. ( I ) (a) Cotton, F. A.; Walton, R. A. Multiple Bonds Between Metal Aroms; Wiley: New York, 1982. (b) Cotton, F. A.; Walton. R. A. Strucr. Bonding (BerNn) 1985, 62, I . (2) (a) Cotton, F. A.; Thompson, J. L. J . Am. Chem. Soc. 1980,102,6437.
(b) khling, T.: Wilkinson, G.;Stephenson,T. A,; Tocher, D. A.; Walkinshaw, M. D. J. Chem. Soc., Dalton Trans. 1983, 2109. (3) Fanwick, P. E.;King, M. K.; Tetrick, S.M.; Walton, R. A. J . Am.
Chem. Soc. 1985,107,5009. (4) Fanwick, P. E.; Fraser, I. F.; Tetrick, S. M.; Walton, R. A. Inorg. Chem. 1987, 26, 3786. (5) Agaskar, P.A.; Cotton, F. A,; Dunbar, K. R.; Falvello, L. R.; Tetrick, S.M.; Walton, R. A. J. Am. Chem. SOC.1986, 108,4850. ( 6 ) Fanwick, P. E.; Tetrick, S.M.; Walton, R. A. Inorg. Chem. 1986, 25, 4546. (7) Cotton, F. A.; Vidyasagar, K. Inorg. Chem. 1990, 29, 3197. (8) Cotton, F. A.; Mott, G. N.; Schrock, R. R.; Sturgeoff, L. G. J . Am. Chem. Soc. 1982, 104, 6781. (9) Cotton, F. A.; Frenz, B. A.; Stults, B. R.; Webb, T. R. J . Am. Chem. SOC.1916, 98, 2768.
0022-3654/9 1 /2095-7239%02.50/0
Even with the recent advances in the development of reliable methods to calculate the electronic structures of molecules containing heavy atoms,I0 theoretical studies of third-row transition-metal compounds represent a major challenge to conventional methods of quantum chemistry.'*'2 Several scalar relativistic methods use a Pauli Hamiltonian to calculate only the large two-component structure of the molecular wave function, which transforms according to the irreducible representations (irreps) of the single-valued point groups. Commonly, the Darwin and mass-velocity corrections are included in the self-consistent procedure, and the spin-orbit operator may be added in a second step, either via perturbation theory" or by configuration interaction (CI), thus taking into account electron-correlation effects." These quasirelativistic approaches, in which spin is still a good quantum number, yield useful insights into the bonding, energetics, and J~ optical properties of heavy dimetal c o m p o ~ n d s . ~ J ' However, it is now well established that relativity is significantly important to understand the behavior of both the cores and the valence electrons in heavy-atom-containing molecules. It is also recognized that relativistic effects may be too large to be accurately modeled by non-fully Dirac molecular oribtal m e t h o d ~ . ' ~ J ~ - ' To ' - ~our ~ (IO) (a) See The Challenge ofd andfElecrrons; Salahub, D. R.; Zerner, M. C., Eds.; ACS Symposium Series 394; American Chemical Society: Washington, DC, 1989. (b) Salahub, D. R. In Ab Initio Methods in Quantum Chemistry; Lawley, K. P., Ed.; Wiley: New York, 1987; Vol. 11, p 447. ( I 1) Pyykkb, P. Chem. Rev. 1988, 88, 563. (12) Malli, G. L. In Molecules in Physics, Chemistry, and Biology; Ma-
ruani, J., Ed.; Reidel: Dordrecht, The Netherlands, 1988; Vol. 11. p 85. (13) Spin-orbit symmetry bases are obtained at the CI step: Hay, P. J. J . Am. Chem. SOC.1982, 104, 7007. (14) Ziegler, T. J. Am. Chem. Soc. 1985,107,4453; Ibid. 1984,106,5901. (15) Malli, G.L.; Pypcr, N. C. Proc. R . Soc. London, A 1986,107,377. (16) Ramos, A. F.; Pypcr, N. C.; Malli, G. L.Phys. Reo. A 1988,38,2729. (17) Arratia-Perez, R.; Ramos, A. F.; Malli, G.L. Phys. Reu. B 1989, 39, 3005. (18) Yang, C. Y.; Case, D. A. In Local Density Approximations In Quantum Chemistry and Solid State Physics; Dahl, J.; Avery, J. P., Eds.; Plenum: New York, 1983. (19) Case, D. A. Annu. Rev. Phys. Chem. 1982, 33, 151.
0 1991 American Chemical Society
