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Characteristic vibrational frequencies of the SOS group
Spectmchin~ica
PergamonPressLtd. Printedin NorthernIreland
Acta, 1063, Vol. 19, pp. 741 to 740.
Characteristic vibrational frequencies of the SOSgroup R. J. GILLESPIE Department,of Chemistry, MeMaster University, Hamilton, Ontario and E. 8. ROBINSON Department of Chemistry, University of Toronto, Toronto, Ontario (Received 29 August 1962)
Abst~t-The ~si~ment of frequenciesfor the three vibrations of the SOS groups in molecules of the type X,SOSX, is discussed. It is shown that 8 consistent assignment can be given for all ten molecules of this type for which data are available. This assignment gives reasonable values of force constants in a simple valence force-fieldcalculation. It is shown that there are linear relationshipsbetween the frequenciesof the symmetrical stretching and bending modes of the SOS group and the square-root of the mass of the groups SX, attached to the oxygen atom. WE HAVE recently proposed assignments for the Raman spectra of the disulphuryl 150, 300 halides S205X2, (I), in which we attributed frequencies of approximately and 800 cm-l to the bend, Q, symmetric stretch, vs, and asymmetric stretch, v,, respectively, of the SOS group [l]. We have subsequently shown that these vibrations in disulphuric acid, H&&O,, chlorodisulphuri~ acid, HS,O,Cl, and ~uorodisulphuric acid, HS,O,F, may be assigned essentiahy the same frequencies [2, 31.
Other workers have assigned somewhat in Table 1. Table
S,O,Cls SsO$s S,O,(CH& H&%0,
K&%0, N@sO 7 [1] [2] [3] [4] [5] [6] [7]
different frequencies
to v8and vb as is shown
1. Previous assignmentsfor vibrations of the SOS group V,
VE
vb
Method
773 818
716 731
486 488
R R
661 806
617 732
-
800 793
743 346
321 741
R I.R.
R + I.R. R + I.R.
R. R. R. H. A. P. A.
Reference GERDINC and LINDEN[4] SIPAON and LEHMANN [S] SIMON and KRIECBMANN [S] GI@UI%REand SAVOIE[6]
SIMONand WAGNEX.[7] SIMONand WAGNER[7]
J. GILLESPIE and E, A. ROBINSON,Co?%.J. Chem. 39, 2179 (1961). 3. GILLESPIE and E. A. ROBINSON,Can. J, Chem. 40, 658 (1962). J. GILLESPIE and E. A. ROBINSON, Can. J. Chem. 40,676 (1962). GERDINC and A. C. LINDEN, Rec. Truv. Chim. 61, 735 (1942). SIMON and H. A. LEHMANN, 2. Anoyq. Chem. 311, 224 (1961). A. GIG&RE and R. &VOTE, Can. J. Ghem. 38, 2467 (1960). SIMON and H. WAGNER, 2. Anorg. Chem. 311, 102 (1961). [S] A. SIMON and H. KRIEGSMANN, Chem. Ber. 89, 2378 (1956). 741
742
R. J. GILLESPIE and E. A. ROBINSON
The purpose of this paper is to show: (i) that the three characteristic vibrations of the SOS group in all of the molecules of the type X,SOSX, that have been studied can be assigned in a way which is consistent with our new assignments for these vibrations in the disulphuryl halides; (ii) that these assignments lead to reasonable values of the force constants and SOS bond angles; (iii) that there are linear relationships between the frequencies of the SOS symmetric stretch and the square root of the mass of the group SX,, and between the frequencies of the SOS bend and the square root of the mass of the group SX,. DISCUSSION
We suggest that the previous assignments which attribute similar frequencies to v, and v, cannot be correct for the following reason: in the asymmetric stretching Table 2. Vibrational frequenciesof the SOS bridging group
ww2
ScO,Cl, S,O,ClF H,S,O, HS,O,F HS,O,Cl K‘zScO, Na,S,O, S,O,(CH& SF,OSF,
323 298 313 328 325 310* 321 346 329 256
814 760 802 809 794 803 800 805 770 808
157 147 154 155 140 148 (lL-5,
* Previously we assigned the S-O-S symmetric stretch in HS,O,Cl at 289 cm-‘. In view of the present correlationit appears better to reassign this vibration at the frequency 310 cm-l and to attribute the band at 289 cm-’ to the S-OH wag.
mode V~ the amplitude of the motions of the heavy SX, groups is small while the amplitude of the motion of the relatively light oxygen atom is large; the vibration can be approximately described as an oscillation of the oxygen atom between the heavy SX, groups; thus this vibrational mode would be expected to have a relatively high frequency. In contrast in the symmetric stretch, vs, the amplitude of the motions of the heavy SX, groups is large while that of the oxygen atom is small. Consequently this vibration would be expected to have a frequency considerably lower than that of v,. The bending mode vb presumably has a lower frequency than vs; it is often found for an angular X0X group that v,/vb N 2. Our assignments for v8, v, and vb for all of those molecules for which satisfactory experimental data are available are shown in Table 2. The values for the disulphuryl halides, halogenodisulphurio acids and disulphuric acid are taken from our previous publications [l-3]. SIMON and WAGNER’S assignment of v, for the disulphate ion [7] seems reasonable as the lines at 818 and 800 cm-r occur strongly in the infra-red spectra of the sodium and potassium salts, respectively. We prefer however to assign the relatively strong bands at 346 cm-l (Na,S,O,) and 321 cm-l
Characteristic vibrational frequencies of the SOS group
743
(K&,0,) in the Raman spectra to the SOS symmetric stretch rather than the frequencies of 741 and 743 cm-l, which seem too close to the frequencies of the asymmetric mode to be due to the symmetric stretch. Neither the infrared nor the Raman spectrum was investigated at sufficiently low frequencies to detect a line at approximately 150 cm-l which we consider as appropriate for the frequency of Y*. In the Raman spectrum of methane-s~phoni~ anhydride SIMON and KRIE~SMA~N [8] assigned the lines at 617 and 661 cm-i, respectively to the asymmetric and symmetric SOS stretches. There is a strong band in the infra-red spectrum [9] at 790 cm-l which is to be compared with the line in SIMONand KRIEGSMANET’SRaman spectrum at 799 cm-l. Although they assign the latter to an asymmetric C-S stretch we suggest that this is the frequency of Y,, and we also prefer to assign Y, at one of the lower frequencies 303 or 356 cm- l. measurements have not been made at sufficiently low frequencies for the bend to be observed, In the Raman spectrum of SF,OSF, [lo] there is a relatively strong polarized line at 256 cm-l which we assign to the SOS symmetric stretch, and a strong line in the infra-red spectrum at 808 cm-l which is observed very weakly in the Raman spectrum and can probably be assigned to Y,. The low-frequency SOS bend has not been observed directly but a frequency of 125 cm-l can be estimated from combination bands. In every case the line attributed to Y, is weak and depolarized in the Raman spectrum but strong in the infra-red, while the line assigned to Y, is strong and polarized in the Raman spectrum but weak in the infra-red spectrum. It is evident that Y, and yb should decrease in frequency with increasing mass of the group SX, while Y, should be relatively inde~ndent of the mass of SX,. Fig. 1 shows that there is, in fact, a linear correlation between the frequency that we have assigned to v, and ill lt2, the square root of the mass of SX, (or the mean mass of SX, where the masses of the two groups attached to the central oxygen atom are different). There is also a similar approximately linear relationship between the frequency of the bending mode and _&P’s which is also shown in Fig. 1. If the SX,OSX, molecule is treated as a simple triatomi~ species YOY, and a simple valence force field is assumed, stretching and bending force constants, k,, and d, may be calculated from the three SOS frequencies [ll]. They are shown in Table 3. For the S20,2- ion k,, was also calculated from the observed angle of 124’ [12]. The observed frequency Y, and the bending force constant d were calculated from the angle and the observed frequencies v, and Ye assuming that d is very small compared with k,,. In the calculation of the force constants for these molecules the masses of the groups involved were used without modification. GOUBEAU [ 131 has suggested that some reduction of the mass of a polyatomic group is appropriate because of deformations in the group when it vibrates. It is found in the present case (see Table 3), [9] E. A. ROBINSON and V. SILBERBERQ. Xkpublished results (1962). L. H. CROSS, P. GOGGIN, H. 3%. ROBERTS and L. A. WOODWARD. Personal communication
[IO]
(1962). G. HERZBERG, Molecular Spectra and Molecular Structure Vol. II, p. 169. Van Nostrand, New York (1945). 1121 H. LYNTON and M. R. TRUTER, J. Chern. Sot. 5112 (1960). 1131 J. GOTTBEAU,Andes real sot. espan. fts. y q&n. (~~ad~~d) Ser. B, 45, 807 (1949).
[ll]
744
R. J. GILLESPIE and E. A. ROBINSON
300
)O
SOS sym stretch.
3! cm-’
SOS
bend,
cm-’
Fig. 1. Dependence of SOS vibrational frequencies on the mass of the SX, group in SX,OSX, molecules
(4 1.
SF,OSF,, S,O,(CH,),, SF,OSF,,
(b) :: 7. H&&O,.
2. szo,cl,, 3. S,O,ClF, 4. HS,O,Cl, 8. K&&O,, 9. Na,S,O,. 2. S,O,Cl,, 3. S,O,ClF, 4. H&O&l,
5. HS,O,F, 5. S20,F2,
6. H&O,, 6. HS,O,F,
Table 3. Force constants and bond angles calculated from the spectroscopic data by a simple valence force field treatment Molecule %0&l, S205F2 s,o,clF H&20, HS,O,F HS,O,Cl K2S20, * Na&&O,* (CH,),S,O,* SF,OSF, S20,Fs W20, Na2S20,
k,,
x 10-S
d x 1O-5
2.8 3.3 3.5 3.1 3.0 3.1 3.0 3.1 2.8 3.1 3.1 3.4$ 3.5:
0.09 0.08 0.08 0.08 0.07 0.08 0.09 0.10 0.10 0.06 0.05t 0.08: 0.09:
* vb was not observed but was assumed equal to VJl2. t Calculated by allowing for reduced SO,F group by GOUBEAU’S method [ 131. $ Calculated using the observed S-O-S
mass angle.
of
Characteristic vibrational frequencies of the SOS group
745
that modification of the mass as Goubeau suggests actually makes very little difference in the value of the S-O force constant obtained for the bridging bonds. For example in the case of S,O,F, GOUBEAU’S treatment results in a value of 3.1 x lo5 compared with 3.3 x 105 when the masses are used without modification. In any case, since the S-O-S bonds are found to be relatively weak compared to the other bonds in the molecule the effect considered by GOUBEAU would be expected to be of minor importance. SIEBERT [14] quotes a value of 4.27 x lo5 dyn cm-l for the stretching force constant of a single S-O bond obtained from his empirical “product rule”, while SIMON and KRIEGSMANN [15] prefer a value of 3.5 x lo5 dyn cm-l. In their treatment of the disulphate ion SIMON and WAGNER [7] obtained a value of 3.36 x lo5 dyn cm-l for k,, and concluded that this indicates a bond order of less than unity for the S-O-S bonds. In a recent paper [IS], however, we criticize these values for the force constant of a single SO bond and show that there is a linear relationship between log k,, and log rso, (rso is the observed SO bond length). A value of k,, = 2.7 x lo5 dyn cm-l is deduced for an SO single bond by extrapolation to the probable SO single-bond length of 1.70 A. Thus the values for the force constants of the S-O-S bonds derived in this paper combined with our value for the force constant of an SO single bond suggest that S-O-S bonds have an order that is slightly greater, not less than, unity. On the basis of the log k,,- log rso relationship we predict a bond length of 1.65 A for the S-O-S bonds in the disulphate ion from the observed force constant. The length of these bonds has been found to be 1.645 A [12]. Our conclusion that the order of the S-O-S bonds is slightly greater than unity is also in accord with the observed bond angle of 124’ [12]. As a consequence of the tetrahedral arrangement of four electron pairs in the valency shell and the greater repulsions between lone pairs than between bond pairs the bond angle between two single bonds at an oxygen atom is invariably found to be slightly smaller than the tetrahedral angle of 109” [17]. The larger angle of 124” observed in the disulphate ion indicates that the O-S bonds are interacting with each other more strongly than would be expected if they are single bonds. Since double bonds repel each other considerably more strongly than single bonds the larger bond angle in the disulphate ion implies some double-bond character in the S-O-S bonds. The double-bond character arises from a tendency for oxygen to delocalize its lone-pair electrons into 3d orbitals on sulphur [17]. CRUICKSHAKK[18] has ascribed the large bond angle in the disulphate ion and related molecules to electrostatic repulsion between the SO,- groups. He then assumes that the approximately 120” bond angle at oxygen implies sp2 hybridization leaving a single p-orbital available for double bonding with sulphur. However neutral molecules containing S-O-S groups, e.g. polymeric SO,, and similar POP and SiOSi groups, have equally large bond angles at oxygen which cannot be [14] H. SIEBERT, 2. anorg. Chem. 275, 225 (1954). [15] A. SIMON and H. KRIEGSMANN, 2. physik. Chem. 204, 369 (1955). [16] R. J. GILLESPIE and E. A. ROBINSON, Can. J. Chem. To be published. [17] R. J. GILLESPIE, J. Am. Chem. Sot. 82, 5978 (1960). [18] D. W. J. CRUICKSRANK, J. Chem. Sot. 5486 (1961).
746
R. J. GILLESPIEand E. A. ROBINSON
ascribed to electrostatic repulsion between negative groups. Our point of view is that the strong repulsions between the electron pairs in the filled shell of the oxygen atom result in a strong tendency for them to delocalize into vacant orbitals such as the 3d-orbitals on adjacent S, P or Si atoms. This gives rise to double-bond character in the S-O-S, P-O-P and Si-0-Si bonds and the resulting increased repulsion between these bonds results in the observed large bond angles [17]. Acknowledgement-We assistance.
thank the National
Research Council of Canada for generous financial
PergamonPressLtd. Printedin NorthernIreland
Acta, 1063, Vol. 19, pp. 741 to 740.
Characteristic vibrational frequencies of the SOSgroup R. J. GILLESPIE Department,of Chemistry, MeMaster University, Hamilton, Ontario and E. 8. ROBINSON Department of Chemistry, University of Toronto, Toronto, Ontario (Received 29 August 1962)
Abst~t-The ~si~ment of frequenciesfor the three vibrations of the SOS groups in molecules of the type X,SOSX, is discussed. It is shown that 8 consistent assignment can be given for all ten molecules of this type for which data are available. This assignment gives reasonable values of force constants in a simple valence force-fieldcalculation. It is shown that there are linear relationshipsbetween the frequenciesof the symmetrical stretching and bending modes of the SOS group and the square-root of the mass of the groups SX, attached to the oxygen atom. WE HAVE recently proposed assignments for the Raman spectra of the disulphuryl 150, 300 halides S205X2, (I), in which we attributed frequencies of approximately and 800 cm-l to the bend, Q, symmetric stretch, vs, and asymmetric stretch, v,, respectively, of the SOS group [l]. We have subsequently shown that these vibrations in disulphuric acid, H&&O,, chlorodisulphuri~ acid, HS,O,Cl, and ~uorodisulphuric acid, HS,O,F, may be assigned essentiahy the same frequencies [2, 31.
Other workers have assigned somewhat in Table 1. Table
S,O,Cls SsO$s S,O,(CH& H&%0,
K&%0, N@sO 7 [1] [2] [3] [4] [5] [6] [7]
different frequencies
to v8and vb as is shown
1. Previous assignmentsfor vibrations of the SOS group V,
VE
vb
Method
773 818
716 731
486 488
R R
661 806
617 732
-
800 793
743 346
321 741
R I.R.
R + I.R. R + I.R.
R. R. R. H. A. P. A.
Reference GERDINC and LINDEN[4] SIPAON and LEHMANN [S] SIMON and KRIECBMANN [S] GI@UI%REand SAVOIE[6]
SIMONand WAGNEX.[7] SIMONand WAGNER[7]
J. GILLESPIE and E, A. ROBINSON,Co?%.J. Chem. 39, 2179 (1961). 3. GILLESPIE and E. A. ROBINSON,Can. J, Chem. 40, 658 (1962). J. GILLESPIE and E. A. ROBINSON, Can. J. Chem. 40,676 (1962). GERDINC and A. C. LINDEN, Rec. Truv. Chim. 61, 735 (1942). SIMON and H. A. LEHMANN, 2. Anoyq. Chem. 311, 224 (1961). A. GIG&RE and R. &VOTE, Can. J. Ghem. 38, 2467 (1960). SIMON and H. WAGNER, 2. Anorg. Chem. 311, 102 (1961). [S] A. SIMON and H. KRIEGSMANN, Chem. Ber. 89, 2378 (1956). 741
742
R. J. GILLESPIE and E. A. ROBINSON
The purpose of this paper is to show: (i) that the three characteristic vibrations of the SOS group in all of the molecules of the type X,SOSX, that have been studied can be assigned in a way which is consistent with our new assignments for these vibrations in the disulphuryl halides; (ii) that these assignments lead to reasonable values of the force constants and SOS bond angles; (iii) that there are linear relationships between the frequencies of the SOS symmetric stretch and the square root of the mass of the group SX,, and between the frequencies of the SOS bend and the square root of the mass of the group SX,. DISCUSSION
We suggest that the previous assignments which attribute similar frequencies to v, and v, cannot be correct for the following reason: in the asymmetric stretching Table 2. Vibrational frequenciesof the SOS bridging group
ww2
ScO,Cl, S,O,ClF H,S,O, HS,O,F HS,O,Cl K‘zScO, Na,S,O, S,O,(CH& SF,OSF,
323 298 313 328 325 310* 321 346 329 256
814 760 802 809 794 803 800 805 770 808
157 147 154 155 140 148 (lL-5,
* Previously we assigned the S-O-S symmetric stretch in HS,O,Cl at 289 cm-‘. In view of the present correlationit appears better to reassign this vibration at the frequency 310 cm-l and to attribute the band at 289 cm-’ to the S-OH wag.
mode V~ the amplitude of the motions of the heavy SX, groups is small while the amplitude of the motion of the relatively light oxygen atom is large; the vibration can be approximately described as an oscillation of the oxygen atom between the heavy SX, groups; thus this vibrational mode would be expected to have a relatively high frequency. In contrast in the symmetric stretch, vs, the amplitude of the motions of the heavy SX, groups is large while that of the oxygen atom is small. Consequently this vibration would be expected to have a frequency considerably lower than that of v,. The bending mode vb presumably has a lower frequency than vs; it is often found for an angular X0X group that v,/vb N 2. Our assignments for v8, v, and vb for all of those molecules for which satisfactory experimental data are available are shown in Table 2. The values for the disulphuryl halides, halogenodisulphurio acids and disulphuric acid are taken from our previous publications [l-3]. SIMON and WAGNER’S assignment of v, for the disulphate ion [7] seems reasonable as the lines at 818 and 800 cm-r occur strongly in the infra-red spectra of the sodium and potassium salts, respectively. We prefer however to assign the relatively strong bands at 346 cm-l (Na,S,O,) and 321 cm-l
Characteristic vibrational frequencies of the SOS group
743
(K&,0,) in the Raman spectra to the SOS symmetric stretch rather than the frequencies of 741 and 743 cm-l, which seem too close to the frequencies of the asymmetric mode to be due to the symmetric stretch. Neither the infrared nor the Raman spectrum was investigated at sufficiently low frequencies to detect a line at approximately 150 cm-l which we consider as appropriate for the frequency of Y*. In the Raman spectrum of methane-s~phoni~ anhydride SIMON and KRIE~SMA~N [8] assigned the lines at 617 and 661 cm-i, respectively to the asymmetric and symmetric SOS stretches. There is a strong band in the infra-red spectrum [9] at 790 cm-l which is to be compared with the line in SIMONand KRIEGSMANET’SRaman spectrum at 799 cm-l. Although they assign the latter to an asymmetric C-S stretch we suggest that this is the frequency of Y,, and we also prefer to assign Y, at one of the lower frequencies 303 or 356 cm- l. measurements have not been made at sufficiently low frequencies for the bend to be observed, In the Raman spectrum of SF,OSF, [lo] there is a relatively strong polarized line at 256 cm-l which we assign to the SOS symmetric stretch, and a strong line in the infra-red spectrum at 808 cm-l which is observed very weakly in the Raman spectrum and can probably be assigned to Y,. The low-frequency SOS bend has not been observed directly but a frequency of 125 cm-l can be estimated from combination bands. In every case the line attributed to Y, is weak and depolarized in the Raman spectrum but strong in the infra-red, while the line assigned to Y, is strong and polarized in the Raman spectrum but weak in the infra-red spectrum. It is evident that Y, and yb should decrease in frequency with increasing mass of the group SX, while Y, should be relatively inde~ndent of the mass of SX,. Fig. 1 shows that there is, in fact, a linear correlation between the frequency that we have assigned to v, and ill lt2, the square root of the mass of SX, (or the mean mass of SX, where the masses of the two groups attached to the central oxygen atom are different). There is also a similar approximately linear relationship between the frequency of the bending mode and _&P’s which is also shown in Fig. 1. If the SX,OSX, molecule is treated as a simple triatomi~ species YOY, and a simple valence force field is assumed, stretching and bending force constants, k,, and d, may be calculated from the three SOS frequencies [ll]. They are shown in Table 3. For the S20,2- ion k,, was also calculated from the observed angle of 124’ [12]. The observed frequency Y, and the bending force constant d were calculated from the angle and the observed frequencies v, and Ye assuming that d is very small compared with k,,. In the calculation of the force constants for these molecules the masses of the groups involved were used without modification. GOUBEAU [ 131 has suggested that some reduction of the mass of a polyatomic group is appropriate because of deformations in the group when it vibrates. It is found in the present case (see Table 3), [9] E. A. ROBINSON and V. SILBERBERQ. Xkpublished results (1962). L. H. CROSS, P. GOGGIN, H. 3%. ROBERTS and L. A. WOODWARD. Personal communication
[IO]
(1962). G. HERZBERG, Molecular Spectra and Molecular Structure Vol. II, p. 169. Van Nostrand, New York (1945). 1121 H. LYNTON and M. R. TRUTER, J. Chern. Sot. 5112 (1960). 1131 J. GOTTBEAU,Andes real sot. espan. fts. y q&n. (~~ad~~d) Ser. B, 45, 807 (1949).
[ll]
744
R. J. GILLESPIE and E. A. ROBINSON
300
)O
SOS sym stretch.
3! cm-’
SOS
bend,
cm-’
Fig. 1. Dependence of SOS vibrational frequencies on the mass of the SX, group in SX,OSX, molecules
(4 1.
SF,OSF,, S,O,(CH,),, SF,OSF,,
(b) :: 7. H&&O,.
2. szo,cl,, 3. S,O,ClF, 4. HS,O,Cl, 8. K&&O,, 9. Na,S,O,. 2. S,O,Cl,, 3. S,O,ClF, 4. H&O&l,
5. HS,O,F, 5. S20,F2,
6. H&O,, 6. HS,O,F,
Table 3. Force constants and bond angles calculated from the spectroscopic data by a simple valence force field treatment Molecule %0&l, S205F2 s,o,clF H&20, HS,O,F HS,O,Cl K2S20, * Na&&O,* (CH,),S,O,* SF,OSF, S20,Fs W20, Na2S20,
k,,
x 10-S
d x 1O-5
2.8 3.3 3.5 3.1 3.0 3.1 3.0 3.1 2.8 3.1 3.1 3.4$ 3.5:
0.09 0.08 0.08 0.08 0.07 0.08 0.09 0.10 0.10 0.06 0.05t 0.08: 0.09:
* vb was not observed but was assumed equal to VJl2. t Calculated by allowing for reduced SO,F group by GOUBEAU’S method [ 131. $ Calculated using the observed S-O-S
mass angle.
of
Characteristic vibrational frequencies of the SOS group
745
that modification of the mass as Goubeau suggests actually makes very little difference in the value of the S-O force constant obtained for the bridging bonds. For example in the case of S,O,F, GOUBEAU’S treatment results in a value of 3.1 x lo5 compared with 3.3 x 105 when the masses are used without modification. In any case, since the S-O-S bonds are found to be relatively weak compared to the other bonds in the molecule the effect considered by GOUBEAU would be expected to be of minor importance. SIEBERT [14] quotes a value of 4.27 x lo5 dyn cm-l for the stretching force constant of a single S-O bond obtained from his empirical “product rule”, while SIMON and KRIEGSMANN [15] prefer a value of 3.5 x lo5 dyn cm-l. In their treatment of the disulphate ion SIMON and WAGNER [7] obtained a value of 3.36 x lo5 dyn cm-l for k,, and concluded that this indicates a bond order of less than unity for the S-O-S bonds. In a recent paper [IS], however, we criticize these values for the force constant of a single SO bond and show that there is a linear relationship between log k,, and log rso, (rso is the observed SO bond length). A value of k,, = 2.7 x lo5 dyn cm-l is deduced for an SO single bond by extrapolation to the probable SO single-bond length of 1.70 A. Thus the values for the force constants of the S-O-S bonds derived in this paper combined with our value for the force constant of an SO single bond suggest that S-O-S bonds have an order that is slightly greater, not less than, unity. On the basis of the log k,,- log rso relationship we predict a bond length of 1.65 A for the S-O-S bonds in the disulphate ion from the observed force constant. The length of these bonds has been found to be 1.645 A [12]. Our conclusion that the order of the S-O-S bonds is slightly greater than unity is also in accord with the observed bond angle of 124’ [12]. As a consequence of the tetrahedral arrangement of four electron pairs in the valency shell and the greater repulsions between lone pairs than between bond pairs the bond angle between two single bonds at an oxygen atom is invariably found to be slightly smaller than the tetrahedral angle of 109” [17]. The larger angle of 124” observed in the disulphate ion indicates that the O-S bonds are interacting with each other more strongly than would be expected if they are single bonds. Since double bonds repel each other considerably more strongly than single bonds the larger bond angle in the disulphate ion implies some double-bond character in the S-O-S bonds. The double-bond character arises from a tendency for oxygen to delocalize its lone-pair electrons into 3d orbitals on sulphur [17]. CRUICKSHAKK[18] has ascribed the large bond angle in the disulphate ion and related molecules to electrostatic repulsion between the SO,- groups. He then assumes that the approximately 120” bond angle at oxygen implies sp2 hybridization leaving a single p-orbital available for double bonding with sulphur. However neutral molecules containing S-O-S groups, e.g. polymeric SO,, and similar POP and SiOSi groups, have equally large bond angles at oxygen which cannot be [14] H. SIEBERT, 2. anorg. Chem. 275, 225 (1954). [15] A. SIMON and H. KRIEGSMANN, 2. physik. Chem. 204, 369 (1955). [16] R. J. GILLESPIE and E. A. ROBINSON, Can. J. Chem. To be published. [17] R. J. GILLESPIE, J. Am. Chem. Sot. 82, 5978 (1960). [18] D. W. J. CRUICKSRANK, J. Chem. Sot. 5486 (1961).
746
R. J. GILLESPIEand E. A. ROBINSON
ascribed to electrostatic repulsion between negative groups. Our point of view is that the strong repulsions between the electron pairs in the filled shell of the oxygen atom result in a strong tendency for them to delocalize into vacant orbitals such as the 3d-orbitals on adjacent S, P or Si atoms. This gives rise to double-bond character in the S-O-S, P-O-P and Si-0-Si bonds and the resulting increased repulsion between these bonds results in the observed large bond angles [17]. Acknowledgement-We assistance.
thank the National
Research Council of Canada for generous financial