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4664 J. Phys. Chem. 1982, 86 , 4664-4660gests th at t he two forms are a t equilibrium also in thismolecularly dispersed system.Corresponding changes are observed in the resonanceRaman spectra of th e 1.9 X lo4 M solution accompanyingthe increase in pH. Th e Rama n intensity ratios betweenthe 1280-cm-' b and of th e hydrazone form a nd th e 1320-cm-' band of the azo form are plotted as a function of pHin Figure 9. T he contribution of the hydrazone formsharply decreases around pH 11. It can be concluded from

these results t ha t the color-change nter val of BR BS is inth e pH range from 10.5 to 12.0 a t this concentration.Acknowledgment. The authors thank Professor K.Machida of Kyoto Un iversity for his valuable discussionson the Rama n spectra of aqueous BRBS solutions. Th eauthors also thank Dr. M. Mataumoto of this laboratoryfor his guidance in surface tension and conductivitymeasurements.

Photocatalytic Oxidation of Sulfur on Titanium DioxideYasumlchl Matrumdo; Hldeakl Nagal, and EHchl Sat0Department of Ind'wMel Chemlsb y, Facutty of Englneerlng, utsunomiye Un lw i ty , Ishi-icho 2753, uh"lye,Japan(R9celveO:Ap dl2 8, 7982; In Final Form: July 27, 1982)

It was discovered tha t sulfur isdirectly oxidized to SO:-, i.e., sulfuric acid, on a Ti02photocatlyst in a suspensioninto which O2 s bubbled. Th e photocatalytic oxidation is assigned to the electron and hole produced by lightof sh orter wavelength than abo ut 400 nm, although sulfur taelf photoreacts in light of less tha n about 300 nm.The oxidation reaction is photocatalyzed on anatase b ut not on rutile, and ita rate is faster in alkaline solutionthan in water and acid. It was found that H&3is simultaneously produced as well asS in water. The reactionmechanism of this photocatalytic oxidation of sulfur s discussed on th e basis of th e various experimental data.The direct production of sulfuric acid was confirmed by a sunlight illumination test.

IntroductionMany interesting photocatalytic reactions using lightenergy have been reported. In almost all cases, it is ex-plained that the mechanisms for these photocatalyseshavebeen based on photoelectrochemical cells. T he reactionssubject to photoca talysis will be classified into two ty pesin terms of thermod ynamic energy change. One is theuphill reaction capable of th e storage of light energy (AG> 0), and t he other is the downhill reaction (AG < 0) inwhich the reaction ra te is photoassisted by a catalyst. Th eformer photocatalytic process is very impor tant from theviewpoint of chemical storag e of solax energy: for example,photolysis of water,14 photoreaction of nitrogen oxidegan dcarbo n dioxide,'O pho tosy nthe sis of ami no acids,ll photo-cleaving of hydrogen sulfide,12 and photooxidation ofcarbon with water.13J4 On the other han d, the latte r typeof photocatalysis is also very impor tant in using solar en-ergy as a sub stitute for activation energy: photodecom-position of carboxylic acid,16photooxidationsof cyanide,'*J7(1) T. Kawai and T. Sakata, J . Chem. SOC.,Chem. Common., 694(2) T. Kawai and T. Sakata, Nature (London) ,286,474 (1980).(3) T. Kawai and T. Sakata, Chem. Phys. Let t . , 72,82 (1980).(4) S. Sato and J. M. White, Chem. Phys. Let t . , 72, 85 (1980).(5) S. Sato and J. M. White, J . Phys. Chem., 86, 692 (1981).(6) F. T. Wagner and G. A. Somorjai, J . A m . Chem. SOC., 02, 5494(7) K. Kogo, H. Yoneyama, and H. Tamura, J . Phys. Chem.,84,1705(8) M. V. Rao, K. Rajeshwar, V. R. P. Verneker, and J. Dubow, J .(9) H. Yoneyama, H. Shiota, and H. Tamura, Bull. Chem.SOC. pn. ,(10) T. Inoue, A. Fujishima,S. Konishi, and K. Honda, Nature (Lon-(11) H. Reiche and A. J. Bard, J . Am . Chem. Soc., 101,3127 (1979).(12) M. Grhtzel, Chem. Eng. News, 69, 40 (July 27, 1981).(13) T. Kawai and T. Sakata, Nature (London) ,282,283 (1979).(14) S. Sat0 and J. M. White, J. Phys . Chem., 86, 336 (1981).

(1980).

(1980).(1980).Phys. Chem., 84, 1987 (1980).54, 1308 (1981).don) , 277,637 (1979).

sulfite,17 hydroquinone,18 a n d hydrocarbon^,'^ the photo-K olbe r e a c t i 0 n , 2 ~ ~ ~hotorea ction of dich roma te,% andphotoreaction of alcohols with water.'s2Sulfuric acid is an important material for the chemicalindustry. T he indu strial produ ction of sulfuric acid gen-erally consista of two chem ical oxidatio n processes; one isth e productio n of sulfur diox ide by th e oxidation of sulfuror iron pyrites a nd th e other is th e oxidation of sulfurdioxide into sulfuric acid. Th e overall process is as follows,if sulfur is used as the starting material:

2s + 302 + 2H20 - H2S04 (1)A high temperature (400-1000 "C) nd a s uitable catalyst(V206) re necessary for th e industrial process, althoughthis reaction process is downhill. In th e present pa per, itis demonstrated th at sulfur is directly photooxidized byillumination into sulfuric acid in aqueous sulfur suspen-sions with and without a titanium dioxide catalyst underflowing oxygen at room temp erature. Th e photocatalyticoxidation of sulfur on tita nium dioxide is especially in-teresting for t he utilization of solar energy, although th eavailable photons P 3 .0 eV, e.g., of Ti0 2(ru tile)) epresentonly about 3% of all solar photons. Ther efore, we havestudied in detail the photocatalytic oxidation of sulfur ontitanium dioxide in the pre sent paper.

AGO = -905.75 kJ

B. Kraeutler and A. J. Bard, J . Am. Chem.SOC.,00,5985 (1978).S. N. Frank and A. J. Bard, J . A m . Chem. SOC., 9, 303 (1977).S. N. Frank and A. J. Bard, J . Phys. Chem., 81, 1484 (1977).F. F. Fan and A. J. Bard, J . Am. Chem. SOC., 02,2592 (1980).W. W. Dunn, K. 0.Willbourn, F. F. Fan, and A. J. Bard, J . Phys.Chem., 84,3207 (1980).(20) B Kraeutler and A. J. Bard, J . Am . Chem.SOC., 00,2239 (1978).(21) B. Kraeutler. C. D. Jaeger. and A. J. Bard,J. Am. Chem. SOC.,100, 4903 (1978).(22) B. Kraeutler and A. J. Bard, Nouu. J. Chim., 3 , 31 (1979).(23) I. Izumi, F. F. Fan, and A. J. Bard, J . Phys. Chem., 85,218 (1981).(24) H. Yoneyama, Y. Yamaehita, and H. Tamura, Nature (London),282,817 (1979).0022-3654/82/2006-4664$01.25/0 0 1982 Amerlcan Chemical Society


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Pho tocataiytic Oxidation of Sulfur on TIO,TABLE : Photoreaction Products of Sulfur

The Journal of Physical Chemistty, Vol. 86, No. 24, 1982 4665

104(productsc o n c n ) ,mo1/50 m Lsolution catalyst bubbling gas filter 5,- s,o,2- so,2- so,,-

none 0 . 2 0 0 0UV 29 0 0 0 0UV 29 0 0 0 0none 0 . 2 0 0 0UV 2 9 0. 1 0 0 0UV 29 0.2 0 . 2 0.1 0none 0 . 3 0 0. 4 0 . 9 00 0 0V 2 9 0UV 2 9 0. 1 0 0 0 . 2 4none 0. 6 0 0 .7 3.00UV 2 9 0 0 0 0 . 2 10 . 1 M NaOH TiO, 0 2 UV 2 9 0 0 0 0.60

water none N,water none N,water TiO, N,0.1 M NaOH none N,0.1 M NaOH none N,0.1 M NaOH TiO, N2water none 0,water none 0 ,water TiO, 0 ,0.1 M NaOH none 0 20.1 M NaOH none 0 ,

E x p e r i m e n t a l SectamTwo kinds of solid sulfur (99.99%, Rare Metallic Co.Ltd., and 99.690, Ka nto Che mical Co., Inc., orthorhombic(Sa)) ere used as he reactant. Th e difference is negligiblewith respect to the amounts of the products for bothsamples, but the former was used in this s tudy except forth e sunlight experiment. This sam ple of 0.4 g is groundin an agate mortar and then mixed with the reactant so-lutions (50d).n th e case where a photocatalyst is used,which is T i0 2 (99.6%, anatase, reduced a t 800 C in H2,-10 m2 /g, Merck) unless otherwise stated , the groundsulfur was mixed with the catalyst and the solutions.These suspensions were poured into a quar tz vessel andwere magnetically stirred with bubbling gas (02 r N,) andthen illuminated with an ultrahigh-pressure m ercury lamp(500W). When water or acid is used as th e reactant so -lution, the H 2S gas evolved is take n up by an alkalinesolution.S2-,SOS2-,and S2032-ons in t he solutions were indi-vidually determined by the titr ation method for iodine,in which S* and Sot- ons were ma sked with Zn2+ on andHCHO, respectively. SO:- ion was gravimetrically de-termined as BaS04.

ResultsTable I shows the quanti t ies of the photoreactionprod ucts of sulfur in aqueous suspensions with and withoutTiOP Th e reaction time is 1h for all cases. No produ ctswere detected in the dark under the various conditions inthis table. Th e filter UV 29 is a cutoff filter whichtransmits50 % of 290-nm light but completely cuts off lightshorter than 240 nm. It was found th at sulfur itself pho-toreacts primarily to S2- n N2-bubbled solutions and toSO:- in 02-bubbledsolution. In particular, alkaline so-lutions chang e from colorless to yellow owing to th e for-mation of polysulfide ion, i.e., Sx2-,under the formerconditions. More remarkable is the large quan tity ofphotoproduced Sod2-n the 02-bubb led solutions. Bothreactions proceed faster in alkaline solution tha n in water.The photoreaction for S2- production in N2-bubbled so-lution s will be as follows in water

(2 )s + 2 H 2 0-% 2H2S+ O2

2 5 + 4 0 H - -!!L 2S2-+ 2 H z 0 + O2AGO = 326.8 k J

and in alkaline solution.(3)

AGO = 407.8 kJSolid sulfur is represented as an elem ent for convenience(sulfur exists as S, in the solid). T he decrease or disap-pearance of S2- production with th e cutoff filters suggests

tha t eq 2 and 3 proceed with UV light of shorter than

I

Time (h r )Flgure 1. Amounts of photoproducedSO4- and H,S as a functlon ofirradiation time, and the variations in pH of the 0,-bubbled solutionswithout a catalyst: (a) 0.1 M NaOH, (b) water.about 300-nm wavelength. Th e large quantity of thephotoproduced SO:- in the 02-bubbledalkaline solutionis represented by the following equation:

2s + 3 0 2 + 4 0 H - -?., 2S042-+ 2 H 2 0 (4)AGO = -1334.5 kJ

These reactions are also brought about by UV light ofshorter than about 300 nm, as the w avelength depend enceof the photoproduction rate of SO:- in Figure 3 shows.Figure 1 hows the amou nts of th e photoproduced Sod2-and H2Sas a function of irradiation time a nd th e variationof pH of the solution without a catalyst. Th e quan tity ofphotoproduced 50:- in 0.1 M NaOH goes up to about15% of the initial quan tity of the reactant sulfur after 6h, and the alkaline solution changes to acid. In the absenceof catalyst, the first step for both photooxidation andphotoreduction of sulfur itself will be the destruction ofth e S-S bond of S8n the crystal25 by UV light of shortertha n ab out 300 nm. Th e resulting biradical then will reactwith oxygen and/o r HzO, OH- t o S2-,SOS2-, nd Sod2-.The photoproduction of H2S or S2- s well as S042-n02-bubbledsolutions, as th e tab le shows, will occur in th ecourse of th e reac tion of sulfurbiradicals with H 2 0or OH-.From t he influences of th e filters in Tab le I, it was foundthat TiO, photocatlyzes the above photoreactions.

(25) N. .Dhar and B. .S.Raghaven,Proc. Natl . Acad. Sci., India,(26) B.Meyer, Chem. Reu., 64, 429 (1964).

Sect. A , 17, 7 (1948).


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4666 The Journal of Physical Chemistry, Vol. 86 , No. 24, 1982 Matsumoto et al.

' 2 3 4 5 6Time (hr)

Flgure 2. Amounts of photocatalyticaily produced SO4'- and H,S asa function of irradiation time, and the variations in pH of the Orbubbledsolutions with TiO,: (a) 0.1 M NaOH, using UV 33 filter; (b) water, usingUV 29 filter.

t l. 0.6:c-. ,

5 :;! %-2 0LA_ %' 250 300 350 453 L50

Cut-off wavelength (nm)Flgure 3. Wavelength dependence of the photoproduc tion rate ofSO,2-. a: (0) .1 M NaOH with TiO,, (A) .1 M NaOH without catalyst,(0 )wate r with TiO, c atalys t, (A) ater without catalyst. b: Photo-catalytic production rate on TiO,; (0 )0.1 M NaOH and (0 )waterMoreover, no S2-, S2032-, nd S032- roducts by photo-catalysis were observed in the 0,-bubbled 0.1 M NaOH,but H2Swas observed in the 02 -bu bbl edwater as TableI shows. Figure 2 shows the amounts of the photoproducedSO4*-and H2Sas a function of irradiation time and thevariation of pH of the solution with TiO,. Cutoff filtersU V 29 and UV 33, which transmits 50% of 330-nm lightan d completely cuts off light shorter tha n 270 nm, are usedin water and 0.1 M NaO H, respectively. The refo re, nophotoreaction of sulfur itself occurs but only the photo-catalytic oxidation by Ti02 occurs, as Figure 3 shows.Linear increases in th e photoprod ucts with irradiation timeare observed in the initial range for both Figures 1 and 2.Th e photoproduction rate of H,S was about 0.3 times th atof S042-s shown in Figure 2b. Th e photocatalysis of TiOzis more intere sting than t he photoreactions of sulfur itselffrom the viewpoint of the utilization of solar energy, be-cause UV light available for the photoreactions of sulfuritself are contained in negligible amounts in the solarspectra. Although the photoprodu ction of S2-or H?S in

Pl-lFigure 4. pH dependence of the photoproduction ates of SO:-: (0 )the solutions without catalyst, (0 ) he solutio ns with TiO,; UV 29 andUV 33 f i lters are used in the solutions with pH 12,respectively.eq 2 or 3 is interestin g from th e viewpoint of th e storageof light energy, the photoproduction of SO:- ion, i.e., thedire ct production of sulfuric acid in the case of water, willbe more impor tant in the chemical industry. Therefore,we have studied in de tail the photocatalytic o xidation ofsulfur in the s ubseque nt experiments.T he wavelength dependence of th e photoproduction rateof SO:- in Figure 3 was measure d by using cutoff filters.Each of th e filters has some tailing off in ligh t passed, assta ted above. Figure 3a gives the photoproduction ratesin the solutions with a nd w ithout TiOz,while Figure 3bshows those by photocatalytic oxidation which were ob-tained by simply subtracting the results in the solutionswithout TiO, from those with Ti 02 n Figure 3a. Th e ratesof th e photor eaction s of sulfur itself in the solutions withT i 0 2are slower tha n in the solutions without T i0 2,becausethe T i0 2catalyst disturbs illumination on sulfur. The re-fore, the pho toproduction rates of SO:- in Figure 3b de-termined by the above method will be underestimated inth e case of UV illumination w ith light shorter tha n abo ut300 nm. Th e drops in the qua ntities of SO4*-a t 250 nmin Figure 3b are based on this reason. Figure 3b, however,clearly shows th at th e photocatalytic oxidation of sulfuron Ti 02 proceeds by the electron and hole produced bythe light having TiO, band-ga p energy.Figure 4 hows the dependence of the pho toproductionrates of Sod2-n the pH of the solution. Th e UV 29 cutofffilter was used in the solutions with TiOz whose pH w asless than 11,and the UV 33 was used for o ther alkalinesolutions, because of screening the photoreaction of sulfuritself. Th e photocatalytic oxidation rate has a negligibledependence on pH for the former solution but no t for thelatte r alkaline solution, and the slope of a log u/a (pH ) was1.0. T ha t is, the reaction order of OH- for th e photopro-duction of SO4* is concluded to be 1. In this figure, thephotoreaction of sulfur itself is also given for comparison.Th e dependen ce on pH is different from th at for thephotocatalytic oxidation stated above, suggesting a dif-ference in the mechanism for the two reactions.Figure 5 shows the photoprodu ction rate s of SO4' andHzSby the photocatalysis of TiOzasa function of the lightintensity. Th e linear relationships of a log u / d log I forSO,?- an d H2Swere observed in water, and the slopes wereabout 1 O. where f denotes the light intensity. However,the photoproduction ra te of SO depends only s l ightlyon the light intens ity in 0.1 M NaO H as shown in Figuresa. This result shows that th e rate-controlling ste p in-volving OH- exists before the reactions contributed th e


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Photocata lytlc Oxidation of Sulfur on TiO, The Journal of Physical Chemistty, Vol. 86,No. 24 , 1982 4667TABLE XI: Effect of the Crystal Structure of TiO, on the Photocatalysi8

104(productsconcn), mo1/50 mLTiO, catalyst heat treatme nt crystal structure Sa - SaOs2- SO,a- Soha-

99.9% (Rare Metallic Co. Ltd .) none800 "C (in air)99.6% (Merck) none800 "C (in air)800 "C (in H,!120 0 "C (in air)

800 "C (in air)1200 "C (in air)

800 "C (in air)1200 "C (in air)

99% (Wako Pure Chemical noneIndustries Ltd. )

99% (Wako Pure Chemical noneIndustries Ltd.)

a UV 29 cutoff filter, in 0,-bubbled water, for 1 h .

1 10.5 1 5Light intensity (a.u.1

Figwe 5. photocatalytic productkn rates on TIO, catalystas a functionof ll@t Intensity: (a) 0. 1 M NaOH , using UV 33 fllter; (b) wate r, uslngUV 29 fllter.photoproduced electron and hole.Ta ble I1 shows the effect of th e crystal stru ctur e of TiO zon photocatalysis. Four comm ercial samples were used asthe catalyst. T he test was conducted in Ogbu bbled waterfor 1 h, using the UV 29 cutoff filter. From th e photo-products inthis able, it is concluded that Sot- productionis assisted by the catalyst with an anatase structure. Thisis clearly proved by no production of 50:- ion on thecatalysts heated a t 1200 OC a t which anatase completelyrearranges to rutile in structure. Th e reduction procedureby H z brings about a slight increase in th e catalysis, as th eanatase catalys t (Merck) shows. Other semiconductiveoxides (FezOS,WOs, VzOa,CuO, Nbz 06,ZnO, S ic , SnOz,BaTiOs, ZnzTiO4, and N iO) were also tested as he catalystunder t he same conditions. Only a slight amou nt ofphotoproduced HzS was observed for ZnO, W 0 3 , NiO,ZnzTiO4, but 7 X 10" mol of 5042-was observed for Fez0 3.Similar resulta were also observed in allraline solutio n usingthe UV 33 cutoff filter.DiscussionIt is clear in th e present study th at th e photocatalyticoxidation of sulfur on Ti 0 2 s based on the electron andhole produced by the band-gap light. If the mechanismof t he photocatalysis is simply assumed t o be an electro-chemical local cell, O2 ill be reduced to OH- or HzO byelectrons and s ulfur will be oxidized with O H- or HzO toby holes on the ca talyst surface. Sulfur should bephotocatalytically oxidize d to S042-when other oxidantaare used instead of 02,f th e above local cell mech anism

anatase, rutile 0 0 0 0.11anatase, rutile 0.1 0 0 0.31anatase 0.1 0 0 0.10anatase 0.1 0 0 0.20anatase 0.1 0 0 0.24rutile 0 0 0 0rutile 0.1 0 0 0rutile 0 0 0 0rutile 0.1 0 0 0anatase 0. 1 0 0 0.07anatase 0 0 0 0.10rutile 0.1 0 0 0

proceeds on th e catalyst. However, no SO:- was detectedin th e solution when Cu2+or Fe (C N) l- was used as theoxidant. Thu s, the photocatalytic oxidation of sulfur onT i0 2 s not explained by the simple local cell mechanism.I t is well-known that O2 s photoadsorbed on T i0 2as0;by tp electron trap. The produced 0;may react with HzOor H to form th e radical OzH whose existence is suggestedby Cundall et alSn nd Bard et al.28i29On the other hand,the pho toproduction of th e hydroxyl radical OH by a holeis suggested by man y investigators. Th us , sulfur will reactwith OzH and /or OH on t he T iOz catalyst surface in wateras follows:

(5 )4SOH(ad) + 40zH(ad )- zS + 6H+ + 3 s 0 4 2 - (6)S + OH(ad)- OH(ad)

and/or(7)

If OH(a d) in eq 7 is produced from H 2 0 and a hole, themechanism is the sim ple local cell. Th is is not in harmonywith the experimen tal results as stated above. Therefore,in this case, bH (ad ) wi l l be produced from OH- producedby O2 reduction. T he above reaction mechanisms wellexplain the experimental result tha t H2S as well as HzSO4are sim ultaneously photoproduced in 02 -bub bled water.In practice, S8 olecule in th e solid sulfu r will react with6H (a d) and/or 6,H(ad) on the catalyst surface.In alkaline solution, th e mechanism will be differentfrom that stated above, for no HzS or S2-s produced.Since ther e will be many OH -(ad) on the catalyst surfacein alkaline solution, man y O;(ad) may exist on the surfacewhile the production of 6,H (ad) may be suppressed, ac-cording to the prod uction mechanism of O zH( ad) proposedby Cund all e t a1.27 an d B ard e t al.28~29Consequently,S0,2-(ad) will be produced as an intermediate by thefollowing reaction:

02-(ad)+ SOH(ad) + OH- - 032-(ad)+ HzO (8)SOs2-will be im media tely oxidized to 50:- as Table I1shows. This o xidation may be based on t he local cellmechanism as Bard e t al." propose.Th e rate-controlling step in alkaline solution may be th eabsorption process of OH- in the bulk onto th e catalystsurface, since the production rate of SO:- does not depend

2s + 4OH(ad)- 2S + 2H + + Sod2-

(27) .B. Cundall, R. Rudham, and M. S. Salim, J . Chem. SOC. ,(28)C. D. aeger and A. J. Bard, J. Phys. Chem., 83 , 3146 (1979).(29) . Izumi, W.W. unn, K. 0.Wilbourn, F. F. Fan, and A. J. Bard,

Faraday Trans. 1,72,1642 1976).

J.Phys. Chem., 84, 3207 (1980).


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4868 J. Phys. Chem. 1982, 86, 4668-4674TABLE 111:S,03'-, and SO,.Photocatalytic O xidations of Sz-,

104(product oncn),mol/50 mLs ta r t ing TiO,solutionb catalystC sZ - S-0,'- SO,2- SO,'-Na,S none

rutilen o n eNa2S203 anatase

(pH 6.0) ru t i lenoneN a , S 0 3 anatase( p H 9.8) rutile

( p H 1 2 . 4 ) anatase 1.1 0.5 0.32 . 1 0.8 5.32 .1 0.4 0.60 0 0.50 0 1.00 0 00 0 0.60 0 7 .90 0 5. 5

a U V 2 9 cutoff filter, in the presence of 0, for 1 h .10 x mo1/50 mL . 0.02 g.on the light intensity (Figure 5a, and t he reaction orderof OH- is 1 Figure 4)). However, we do no t conclude otherreactions paralleling those state d above. In these reactions,the intermed iates, for example, S2-,S2O?-,032-,tc., willbe produced. Table 111shows the photocatalytic oxidations

of these ions on Ti 0 2 n 02 -bub bled solution. A largeamo unt of SO is produced from S2 -and SO solutionson anatase. Thus, S2-and SO?- have been easily oxidizedto SO on anata se, even if the se ions were produced asintermediates as in the case of eq 8.According to the above photocatalytic mechanism, 4 / 3photons (eq 5 and 6) or 4 photons (eq 7) are required forth e produc tion of one molecule of SO in water, and 3photons are required in alkaline solution (2 photons arerequired in the oxidation of S032- ccording to t he localcell mechanism). Th e qu antum efficiencies, therefore, werecalculated to be about 0.3% (for 4 / 3 photons) or 0.9% (for4 photons) in water, and 0.7% in 0.1 M NaOH for photonshaving the Ti 02 band-gap energy in the present experi-me ntal system. In this calculation, a rutile single-crystalelectrode whose quant um efficiency has been already de-termined was used in order to determine t he q uantity ofT i0 2 band-gap photons from the l ight source. Undersunlight illumination for 12 h (Utsunomiya University,which stands at la t. 36'33' N , long. 139'55' E , a t9:00-15:00, Dec 3 and 4 ,1981) , the am oun t of sulfuric acidphotocatalytically produced by Ti 02 n water was about8 X M.

Topological and Group Theoretical Analysls in Dynamic Nuclear Magnetic ResonanceSpectroscopy

K. BalasubramanlanDepartment of Chemistry and Lawrence Berkeley Laboratory, Universtty of California, Berkeley, California 9472 0(Received: May 12, 1982; In Final Form: July 27, 1982)

A method is developed for constructing NMR reaction graphs which give the N MR signal and intensity ratiopattern s. Th is is done by generating the irred ucible representations spanned by nuclei (whose NMR are ofinterest) with generating functions obtained from group cha racte r cycle indices (GCCI's). The method generatesthe symm etry species spanned by the nuclei in both the rigid and nonrigid groups without having to know thecharacter of the representation spanned by nuclei. For nonrigid molecules which e xhibit inter nal rotationsthe GCCI's can be obtained without having to know their character tables. We outline a double-coset techniqueto obtain the equivalence classes of nu clei and thus t o cons truct NMR reaction graphs. Using this techniqueone can obtain the NM R signal and intensity ratio patterns. We introduce the concept of re stricted charactercycle indices (RCCI's) which generate the ir reducible represen tations spanned by a given equivalence class ofnuclei. This in turn enables the prediction of coalescence, splitting patterns, and intens ity ratios of NMR signalsin dynam ic processes. Applications to spontaneous generation of chira l signals are outlined , where a nonrigidmolecule which possesses no chira l signals suddenly possesses chiral signals (which can be resolved with chira lshift reagents) at lower temperatures.

1. IntroductionTopological an d group the oretica l analysis of dynamicalsystems such as molecules exhibiting large-amplitudenonrigid motions has been of considerable interest in re-cen t years.'-13 Seve ral of the se topoligical schem es de -(1)K. Balasubramanian, Theor. Chim. cta , 51,37 1979).(2)K. Balasubramanian, Theor. Chim. cta , 53, 129 (1979).(3)K. Balasubramanian, J.Chem. Phys . , 72, 665 (1980).(4)M. RandiE, and D. J . Klein, In t . J.Quantum Chem., in press.(5)M. RandiE and B. C. Gerstein, J.Magn. Reson., 43, 207 (1981).(6)M. RandiE, J . Chem. Phys . , 60, 3920 (1974).(7)M. RandiC, Int. J.Quantum Chem. Symp ., 14,557 1981); hem.(8) M. RandiC, Int . J . Quantum Chem.,21, 47 (1982).Phys . L e t t . , 42, 283 (1976).

0022-3654/82/2086-4668$0l.25/0

scribe interrelationships among a set of isomers which getinterconverted into one another by nonrigid motions. They(9) . T. Balaban, Ed., "Chemical Application of Graph Theory",(10) . T. Balaban, Rev. Roum. him., 18,841 (1973).(11) . T . Balaban, Reu. Roum. C him., 2 , 733 (1978).(12) .W. obinson, F. Harary, and A. T . Balaban, Tetrahedron, 2,(13)K. Balasubramanian, Int. J.Quantum Chem., 22, 385 (1982).(14)K. Balasubramanian J . Magn. Reson., 48, 165 (1982).(15) .G.Williamson, J.Combinational Theory, 11A, 22 (1971).(16) . Merris,Linear Algebra and I t s Applications, 29, 55 (1980).(17) . alasubramanian, presented at the SIAM C onferenceon Ap-(18)K. alasbramanian, I n t . J.Quantum Chem., in press.

Academic Press, New York, 1976.

355 (1976).

plication of Discrete Mathematics, Troy, NY, 1981.

0 1982 American Chemical Society

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