dourrrnl of Mokcuh StTuct=uure, 130 (1983) Ekevier Science Pnbilshers B V., Amsterdam
VIBILATIONAL
SPECI’RA
OF TWO ISOTOPOMERS
Depatiament (Smii.3) VLuto
de Qwnaica
AZ’+ZDNORMAL
COORDINATE
OF THE TEEOSULFATE
Inorganica.
Fccultaf
de Quimica,
-4KM_YSzS
ION
UnLersrfaf
de
BarCelGM
TABACIK+
Laborntoire de Physique Moleculcre Scrences et Techmqrres du Languedoc. JAIME
235-243 - PLinted m ‘Ike Netherlands
et Crlstalline, L A. 233 Montpeil:er (Frcncel
(C _V R S ), Lrrrrversit6 des
CASABO
Departament de Quimicu Bcrcelona (Spain) (Received
Ino;aanica,
Facultct
de Ciemxes.
Unwersi~af
Aut6rzoma
de
10 M nzch 1985)
ABSTRACT The Raman spectra of ‘@G-thlosulfate ion (S,O:-) k K,‘BO soluhon and the IR spectrum of “05odium thlosuKsre in the mlid have been obtaalned Normal Coordinate caicuiations fXting 211 the fundamental wavenumbers of both I60 and I80 isotopomers have been carried out transferring the GYFF of the sulfate ion as
although the oxygen excharge of thlosulfate ion (S,O~-) k neutral aqueous solution hzs been strzdied by MiIls [l] ad by Hall and Aiexander [2], no atimpt has been made to measurz t?e vIbrational zBpectraof the ‘SC/-enriched thiosulfate However, the authors recently reported a Geneti Quadratic Force Field for the sulfa*% eon [ 31, so the aim of th‘s work was both to obtain further experimental parameters (Le., the vibrational wavenmkrs of the totaUy symmerzc ‘BO-substltuted thiosul’ate} uld to transfer some force constznts cf ‘;he s-uXa= 103 k~ order to obtain an zpproximzte force field for the thlosulfati ion. EX-PERIMENTAL
The isotopic enichment was achieved by ~IZLUI~ anhydrous sodium thlo_ ._ (dessicated at 110°C fcr 3 h) wz51 lPO~-r~ched water (81 52 atom%,
sulfate
SAukhorior
correspondence
0022-2S60/65/SO3
3C
Address
3
1565
PlaceEug~n~Eatalilon,
Elsevie
Science
Pub&hers
3+060
B V
Montpr!lier,
F-axe.
236
supplied by Mrles Martin Laborator%) at 95-100” C for 9 h. As a Bst step, 64 mg of the an&ydrous salt were dissoived in 0.323 g of enriched water, producing a mixture with 75.5 atom% of oxygen-18 and s+atisticaUy estihmated diskbunon of isotopic speczes as follows -t 3 = o.c!15;
Xl = O-136;
X2 = 0.419,
X. = 0 430;
,*- berg the molar fraction of t-hiosulfate with i-% atoms. The water was then distilled off and ths sodium thiosulfate was again dessicated at 110” C for 3 h In the second step, 13.8 mg of +be emicbed thiogJf> were again dissolved end heated m ennched water (0.345 g), giving rise to an overall ‘*O content c-f 81.4 atom% and an e&mated distribution of the isotopic species as follows x0 = 0.006;
x1 = 0.084;
x2 = 0.369;
zs = 0.540
spectra were recorded on a Coderg PIi1 spectrometer wit.3 a 90 mW (h = 6328 A). Attempts at using an argon laser’s green (h = 5145 a) or blue line (X = 4880 _&) with an output of 700 mW produced photodecomposition of the thlosulfate with sulfur deposition. The spectra (Fig. 1, upper part) were ob’kamed in solutions approxima-mly 1 Prlin sodium thiosulfate in deionized water and 1u-1 laO-e,nriched sodium tbiosulfate jr: heavy warer (81 5 IsO-atom%), usmg a mmro ccl: of 0.3 ml capacity. IR spectra of KBr pellets (Fig. 1, lower part) were recorded on a Eeckman IR20A spectrophotometer m the spectral range 4000-250 cm-’ Reman
He-Ne
reci laser source
lNTERPRETAT:ON
OF THE SPECTRA
Table 1 gives the fundamentals observed for both Cjv isotopic species along wr’tb the expected wavenumbers for the S2 “fi7j- species calculated with an approxunate General Valence Force Field previously adjusted to the spectra and experiof Lhe “l~.ght” species 143. The good agreement of the &r-_&ted mental wavenumbers supports the predominance m the enriched thiosulfate of the totally labeled species. For molecules of the C>,, group all the Lsotopomers can furnish mdependent mf on-nation on the force field 151 and the waven*Ambers are related only by the Teller-Redhch pi-duct rule [S] (~~~)10
= n(s)
(I = 1, 2, 3.
.
over the symmetry
species)
(1)
that rnusz be obeyed by the two isotoprc species of the thiosulfam ion, G and Gv bemg W&on’s inverse kmetic energy matrices [‘i] for the light and labeled (s’tazedj species respectively, w, and pi: the corresponding harmonic wavenumbers Substituting the observed anharmonk fundamental wavenumbers, Y,, _for the harmonic ones, we obtain for the left hand side cf eqn. (I) the values 0.940 (symmetry block -4,) and 0.925 (symm&y block E) and for the ngbt hand side *he values 0.921 and O-907. The dgmement
237
91g 1 Infrwed (lower, KBr pellet) and Eaman (upper. aqueous solution) spectra of isotopozers SzldOf- (dashed hnes) and S, “Oz-j !sclid lines I Intenstles and trazmissions given in vbkrvy unix Encmzicd details correspond to a sFlectrum obtained under higher resolution conditions. TABLE
1
Infrved (RBr pel1et)er.d Rzzzn (aqueoussolution) Punduncmtals ofthe thiosJ’&te mn LSOtopomers
Infrzed
c II
C,
‘60
v,!a,)
%@‘I
a.(%) V,(%) v,(e) v,(e) u,(e)
+(a’) Y.&‘)r Y&W’) ys(a’), p,(a”)
between
995 669 446 1123 541 335
InO, 949s) 330(w)
1001(s) $71(m) 451(VS) 1122(m) 54O(wj 342(m)
982 666 -
966 661 5G2
-
-
956(s) 656(S) 446(YS> 1100~s) 519(w) 329(m)
947 646 442 1094 512 330
and theoretically expected isotopic wavenumbers ratios azsgnment 01n ‘h L_e S, “Cl$- bar& to the symmetry species. The assqgment of the laG species _Cmdamentzk:; IS unambigxus because the wavenumbers are clc3se enough tcr the v2l~es for ‘he hghT&r species, as is (1)
support
observed
3
Che
238 for a small mass cilffercnce between the isotopes. The bands could not be resolved into the e~pec’v~i fine structure corresponding to the various parkially labeied thiesulfz ti, isoropomers, except for y1 I\Si) and v3 (aI ) which show a triples structure ten tativel g assigned to those species {see Table 1). to be expected
NGRMAL
COORDIKATE
ANALYSIS
The structural parameters emnloyed for the calculation of the G makix were SS = 2.013 A, SO = 1 468 A [S, 93 and retrai-edral angles. The internal coordinates vector R and the symmetry coordmates S are tbo~ defined by Kmg et al. [IO]. t'n!enceForce Constants (f matrix elements) were tmnsferred from the sulfate ion [3] assummg the force constants relative to SSO bendmgs (a) to be approxunarely equal to the analogous constants relative to OS0 bendtigs (a) and the force constants relative to the SS stretchrag (R) to be appraximately equal to those of the SO stretchings (r) except for the diagonal constant which ~2s cakulated withm the framework of the Separation of High and Low Frequencies (SHLF) method [7]. Now, in order to calculate sn lnltd set of SJ mmetry Force Consents (F matrix elements) for the leastr squares adJustment procedure from Ihe transferred GAFF, the analytrcal relationships between both types of force constants were expressed by means of the orthogonal trulsformation
F = UfU’, wdh S = UE!
(2)
‘The correspondmg analytical expresslons aid of the program SLMBORT [43 _
F,,‘Ad
= fr + 2f-r
F,,:Al) = 31Rfe, F,,(-4
I) = fe
F13{A 1)= 2"2[(2f,, Fu@I)
= 3Uk,-%,)/6’
F,a(A 1) = F2<(Al)= F,,(A1)= F,,(A,)=
f &)
2
(2&
+ f@)] /2
(3) anii (4) ere obtained
with the
239
Regarding the expresslons m (3) It can be seen that the symmetry force constants FII, F-2, and Fz2 of the Al symmetry block may be calculated from the GVFF of the slulfate ion with the only al:)roximation of the transferability of tie force constants f,, fR, f, and fRr_ _4.?sothe F:,(E) force constant may be obtained directly from the Flz(Z’s) constant of the sulfate Ion assting tianzfembility. &s the mbratlonal wavenumbers of both full-symmetry lsotoplc species of the thiosulfate ion are related 5y an isotopic product rule for each sgm; retry block,
only
fwe
independent
force
czmstants
cat
be calculated
for each
block, and one force constant must be constrainc~dto a selected valu :. We then adopted for the force constants Fll(Al) and F12(E) the value obt lined by t,ransfer from the sulfate ion but adjusted all remaining force consta! ifs to the experimental wavenumbers of both isotopic species by the usuai ‘easisquares procedure [ 111, with the aid of Shimanouchl’s programs [12] _ The q-GQFF (QuasiGeneral Quadratic Force Field) obtained (Table 2) reproduces the experimental xwvenumbers (Table 3) with average relative errors of 0.26% and 0.36% for the A 1 and E vibrations respectively m the case of the IsO species, and 0 33% and C-45% for the ‘“0 species. The standard deviation of the calculated wavenumbers from the exnerunental ones over the isotopomer is k2.3 cm-’ for 1503 ancl k2.6 cm-’ for “0,. The o_GVFF of the tbosulface ion (Teble 4) w xs caicuIa%edfro111the Just obtained q-GQFF using the relatlonshrps in (eqn. 5) which are the mverse of (eqn. 2) f, = [F~l(Alj L =1:(E)] f,
= [F,,(A,)
--F,,(E)1/3
/3
ill = r_,z(A 1) ’ Kot affected by far = ~~~(-4, )/31<*,t convention (6)
240 TABLE
2
Independent force ccmstants of the q-GQFF Ion (all values in mdyn P_--)
4,
cocrdinares) for the thiosrllfate
E-block
A ~-block
6 0 0 0 0 0
a-3442= 1.2301 3 2900 0 0682 -0 2670 0 6541
F11 I; 1: F ::2 F,, F33 J’,,
(symme~
613ab 0762 6253 0710 2408 7494
=I?,, = it, = F,, = F,, = C (by convention, see text). aV2l~e adopted (see text:- with f, = 6 8868 [3), fr, = 0.7285 [3] bValce adopted (see text) with f, = -f;, = F,, (T,)/B”= = 0 0381
[3j_
TABLE 3 Observed and cclctiatid chlosclfate ion (cm-’ ) Normal mode
waver.umbers for the two full-symmetry
(=s,1=03)+ “ohs
1001 671 4:1 1122 540 342
v,(a,) v,(a,) y, (e) “5 (e) ye (e)
“@AC
“cbs
1002 1 672.4 453.1 1126 4 540.6 344.1
Standard deviation (cm-’ ) TABLE
of the
(3?S1 *no3)z-
(c-GQ W) *
v,(a,)
isoto~zzers
(q-GQFF) 956 656 445 1100 519 329
-12 3
UCalc
955.0 658 6 442 8 1096 4 517.8 326 7 ~2.6
4
GeneA Valence Force Field fo: the tblosulfate 1011obramed from the q-GQF’? hy means of the =ormz.ltlvatlon co~~ent:on (see text) A11 values III mdyn A-’ Force cnnstacti not affected by normaluation
(6)
fr =
7 190 x-r= 0 577
Force cc n&ants a’fected by ncxrnakation
f jc&=o109 fR’Ra = 0 109 fop= 0 029
(6)
fS
=
f$ f’i-2 fee fE$ f&
= 0 031 =-o 040 =-a099 =-o 141 =-C 270
0 609
2rl
Of course, the FIe (A,) (1 = 1 to d) force constants are undetzmined, cc we adopt the conventronal hypotheses 131, proposed by Hubbard 1131 h order to calculate the q-GVFF&
(Aij
= F24 (A,)
=
f-34
(XI)
=
Fa4
(A I) = 0 (‘cnormalization”)
(6)
The four q-GAFF force constants are related only mth stietchmg coor&nates and are independent of the normalization adopted (see eqn. 5), whenas the other tzvelve force consents are dependent_ The analytical expressions III-Ieqn. 4) am then relationships binding those tweive valence force constants DISCUSSION
OF THE
RESUL’iS
It is noteworthy that the transferabihty of the force field of the sulf2te ion in the GVr’F scheme gwes satrsfactory results The hypothesis adopkd 111 the A, block, (f, + 2fm)(SOf-j = FIi (S#z-j, seems reasonable m the light of the results, because although vI depends marnly upon FII(A ,) according to the Jacobian matrix, it is well reproduced (Table i) by the initial s-d of force constants (SD. = r8 cm-‘) and almost perfectly reproduced by the q-GQFF (see Table 3) The symmetry force constants (Table 2) show an tiLeresting feature. the correspondmg A i and E values z-e very similar with the exception of those related to the S-S stretch (i-e , F12, Fz2 and F1 in the A 1 blockj. Moreover F,(E) = Fu(A 1)._ both bemg related to the OS0 c’eformations. F=(E), related to the SSO defo_rmatron E equally near to the OS0 values. in the same vem, interaction. Fn(E) zz FJA I ), both being related to S-O stretch!bending Tine analogue valence force con&an-s correspondmg to OS0 and SSO ‘bendings am roughly equal and of the same sign, as nnght be expected for two snnilar valence bending coordllarez (Table 4 I. The assignments and ‘he PED matrix resulting from the q-GQFF are shown in Table 5 An rmportant rqizng is appai-ent between the SS stretching and the hnding cooxlinates m the Al block, while the mixmg IP still larger between the ?CWObending coordinates in the E block. Some comments must be made on the values of the q-GVFF (Table 4) stretching force constants, which are not affected by Lhe conventional hypothesis (eqn. 6). (aj The fr cc~tmt 1s a httle greater than th& found for the sulfate ion [3], in accordance worth the smaller SO bond du;tance m +he throsulfate and followmg a rule of the type postulated by Lin?er;r; [14] : /‘;, = C’r7;r being n = 6. This rule is obeyed by the f, constants of both the sulfate and tiosulfate ion taking C = 61.53 and R = 5.59 (bj Mso fx B notably smaller than f,, as expected from the greater SS bond distance (c) The relationship between stretching force constants and frequencre: postulated by Gillespie and Robinson 1151 and Gabelica [16], considerng a diatolmic xy virijrator, yields values of the stietching force constants (takmg LJ- as the arithmetic mean of Y~ and JJ,) in good zgreament v&h the q-GVFF
2?2
PZD
Matrix
for
the
‘6G-thlasulfate
ion
PED
for
the YK&)
sotopomer
15 c_tite the
same Symmetn block
Symmetry coordinate
Description
Calculated
1002.0
A
,
s,
4SOJ
s, s,
v(SS) 6 (CSO,
672.4
10176 2 13 5 70
SSO)
1126.4 E
TABLE Reported Compd s20:-
S,Ojs,o
s,, s, s,, s, s,> s,,
mavenumber
540.6
89 68 4 5p 4 66
n(SO) s(OS0) s (SSO)
0 52 42 73 74 53
IS 44 34 05 27.79
453
1
4 15 65 i4 23 59 314-l 0 04 8195 8s 02
6 S-Sstrekh~~gfcrce fR 3 25 4 15
constant
(mdyn
A )_ Compare
to 3 29 for SIOi-
(this work)
Ref.
Compd.
K4
Ref
17
szo:-
3 05
22
2 75 2 40 2.68
23 24 25
2.64
26
2 68 2 59
18 19 18
2 213
20
1 d-5
2I
S,Br,
calculated in th:s WGZ'~L, except for fR(fR(d12t ) = 1.90). The justd&cussed raring m the IJ,(c!) rzcde probably explams this d’rscrepancy. (d) The stretchmg constant fH, nevcbrtheless, falls well within the range of sulfursulfur stretching: constants repcrted by other a~tizs for several compounds (Table 6). zqd -k fairly near we value fomd for the related sulfurcxygerz force constant. (e) It cm be seen that the values of f, and fR presented here ars sensibly thougn not dramatically hfferenr; from those obtamed by Siebert [22] by usingthe frequencies of the normd isotopic species only (6.69 and 3.70 rndyn Other zuthors 117-19, 27, 2Sj have adjusted mon force A-‘, respectively). constants than the number of avdable expermental wa-renumbers, and the reported force fields are therefore meaningless because the inverse secukr eqllation problem is then mathematically undetermined [29]_ As compared with those of the suTate ion [33, the rengkmg GVFF force constants are very sirnil-, except fbr those related wth the SS stretching, as ~2s to be expected
vakes
243 REFERENCES
1 G A h!ills. J. Am Chem Sot , 62 (1940) 2534 2 N. I?_ Hall and O_ R Alexander, J. An-- Chem. Sot_, 3 S. Aharez, V. Tahacik and J Casabo, J MoI Sh-uct
62 (1940) 3155. , 106 (1984) 293. 4 S. Alvarez, The& Doct;ldl, Universidad de Barcelona ( 1960). 5 S. Brodersen and A. Langseth, Mat Fys Skr Dan Vid SeIsk.. 1 (195Sj 5 6 G. Herzberg, Infrared and Raman Spectra of Polyatcmic Molecules, Van Nostrand, New York, 1945, p 231 7 E B W:lson, J. C. Decius and P C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1955. p_ 74 and 311 8 S Baggio, Acta Crystallogr , Sect. A, 25 (1969) 5119. 9A A Uraz and N Armagan, Act2 Crystdlogr , Sect B, 33 (197’i) 1396 1OW. T King, L M. Mdls and B. Craa?ord_ J. Chem Phys_, 27 (1957) 455 11 D. E. Mann, T Shunenouchi, J. H Xieal and L. Fano, J Chem Phys , 27 (i95i) 42. 12 T. Shirnanouchi, Compu’ler Progra.ms for Normal Coordinate Treatment of Polyatimic Mo!ecules, University cf Tokyo, Tokyo (1958) 13 R L. Hubbard, 3. Mel_ Spectrosc., 6 (1961) 272 14 J W Linnett, Q Rev Chem Sot., l(l947) 73. 15 R J Gillespie and E A. Robmson, Can J Chem ,41 ( 1953) 2074 16 Z Gabelica, Bull Sot. Chirn. Belg , 86 (1977) 651 17 G Negarajan, J. Sci Ind. Res Sect. B, 21 (1962) 42. 13 C Revitab and S. Baggio, Rev. Latmoamer. Quun , 7 (1.976) 54 19 Yu Kharitonov. N. -4. Knyazeva and L V. Goeva, Opt Spcktrosk., 24 (1966) 639. 20 V Devaraian and H F. Shurvell, Spectrochim _4cta, Part A. 33 (1977) 1041. 21 R. Strudel, Angew Chem , 67 (1975) 663 22 H. Sie‘bert, Z Anorg Allgem Chem., 275 (1954) 225 23 I. R Beattie, M. J GaB and G. A. Oziu, J. Chem. Sot. ji, (1969) 1001. 24H Gerdmg and K EELS, Ret Trac Chun Pays Bas, 61 (lS50) 5% 25 M. Eucken and J. Wagner. Acta Phi-s Austr?aca, 1 (19. 8) 345. 26 K Ramaswamy and S Jayamman, Acta Phgs Pcl , Se1 A, 40 (7 971) 683 27 E. Stieger, I C Cmrea and A Fad:m, Z. Anorg AIlgec _ Chem.. 350 (1967) 225. 26 H Takahashi, N Kaneko and K Miwa, Spectochrm .! C’J, Part A, 38 (1982) 1147. 29B S Averbukh, L S Mayants arzd G B Shaltuper, J. Mel Spectrosc , 30 (1969) 310.