JOURNAL OF RAMAN SPECTROSCOPY, VOL. 17, 329-334 (1986)
Raman Spectra of Orthorhombic Sulfur at 40 K
Pierre D. Harvey and Ian S. Butler*
Department of Chemistry, Otto Maass Building, McGill University, 801 Sherbrooke St. West, Montreal, Quebec,
Canada H3A 2K6
High-quality Raman spectra of orthorhombic sulfur (S,) have been recorded at 40 K employing multiscanning
conditions. Assignments are proposed for the many new features detected, especially binary and ternary overtones
and combinations of the S S stretching and S-S-S bending vibrations. The anharmonicities of these particular
modes are shown to be fairly small.
INTRODUCTION
In the absence of resonance effects, overtone and combination vibrational bands are usually considered to be
too weak to be observed with a conventional Raman
spectrometer. However, with the development of fully
computerized instruments, the acquisition and quality
of Raman spectra have vastly improved. For instance,
we were recently able to obtain excellent spectra of the
first overtone and combination regions of the Re-CO
bending and CO stretching modes of Re,(CO),,, at low
temperature.'
We now report a similar low-temperature (40K)
Raman study of orthorhombic sulfur (S8). Although
there have been numerous investigations of the vibrational spectra of S8,2-17few authors, apart from Scott et
al.,1 3 have seriously attempted to assign the overtone
and combination bands in the IR spectrum, while these
features have eluded detection in the Raman spectrum.
Our investigation was also performed in an effort to
obtain some information on the anharmonicities of the
S-S stretching and S-S-S bending vibrations and to help
us in an analysis of the vibrational spectra of some
transition metal organometallacyclosulfanes, Cp2MS,
(Cp = q-C5H5;M = Ti, Zr, Hf, Mo, W; n = 2-5)," containing cyclic MS, rings.
of the shoulders being evaluated from the first-derivative
spectra.
RESULTS AND DISCUSSION
~
Orthorhombic S, crystallizes in the Fddd( 0:;) space
group with four molecules per unit cell located at C2
sites." Gauthier and Debeau17 have reported the polarized Raman and IR spectra of a single crystal at ca 30 K
and have assigned the symmetry species for all the
internal and external vibrational modes. We shall make
extensive use of these assignments in our subsequent
analysis of the Raman overtones and combinations
observed in the present work.
Orthorhombic sulfur adopts the familiar cyclic S8 Ddd
crown configuration and its 18 normal modes span the
2a,+ b l + b,+2e1+3e2+2e, representations. The correlation diagram for the isolated molecule, the C2 site
symmetry and the D2hfactor group for the vibrational,
librational and translational modes is shown in Table
1. It is clear that, in the solid state, the IR-active only
Table 1. Correlation diagram for the internal modes of orthorhombic sulfur (S,)"
EXPERIMENTAL
Orthorhombic sulfur (Anachemia Co) was purified by
slow sublimation (140 "C, lop3Torr). The yellow polycrystalline powder was introduced into a Pyrex capillary,
sealed and then mounted on a Cryodyne Cyrocooler
(Cryogenics Technology, Model 21) for the variabletemperature measurements (*1 K). The Raman spectra
were recorded on an Instruments S.A. Ramanor spectrometer equipped with a Jobin-Yvon U-1000 1.0-m
double monochromator coupled to a Columbia Data
Products minicomputer using Instruments S.A. software.
The excitation source was the 514.5-nm green line of a
Spectra-Physics Model 164 argon-ion laser (ca 200 mW
at the sample). The spectra were calibrated against the
emission lines of a standard neon lamp and the peak
positions were accurate to k0.2 cm-' with the positions
*Author to whom correspondence should be addressed.
0377-0486/86/040329-06$05.00
@ 1986 by John Wiley & Sons, Ltd
~~~~~~
Molecular
symmetry
Site
symmetry
Factor
group
D4d
c*
Dm
The librational and translational modes (bath a + 2 b under C, site
symmetry) transform as ag + b , , +26,, +2b3, +a, + b , , +2bz, +
2b,, under D,, factor group symmetry. The accoustic modes are
b , , +b,, +b,, in the translations.
a
Received 20 June 1985
330
P. D. HARVEY AND I. S . BUTLER
450
400
350
300
250
150
200
100
50
WAVENUMBERS
Figure 1. Raman spectrum of S, a t 40K (500-10cm-’ region).
Conditions: excitation, 514.5 nm (200 mW at sample); slits, 65 pm;
one scan at 2 s point-’ (0.2 crW1 steps); no smoothing or baseline
correction.
(2e, + b2)and inactive ( b , )modes of the free s8 molecule
could now become active in the Raman. Figure 1 shows
the Raman spectrum of s8 at 40 K in the 500-10 cm-’
region. The proposed assignments of the fundamentals
are given in Table 2 in accord with earlier work. The
crystal vibrational symmetries for each of the fundamental components (ag, b , , b,, and h 3 g ) from Ref. 17
have been added.
Even though the 6 , + b,+2e, fundamentals are Raman
active in the crystal, they are less intense than the 2a, +
3e2+2e, modes. Moreover, we found that the relative
intensities of the bands vary as a, = e2= e3> b, = el > b l .
This sequence can also be expected to obtain for the
overtones and combinations. Consequently, both
molecular and crystal symmetry selection rules have to
be taken into account when making the assignments.
The appropriate selection rules for the binary overtones
and combinations of S8 { D4d;
are given in Table 3.
WI
740
720
700
FR1
64:
(Xi7
62C
5,0
C
400
380
36C
340
320
300
28fl
W A V E N U MBERS
Figure 2.
580 cm-’;
(200mW
(0.3 cm-l
Raman spectra of S, at 40 K: (a) 960-800 cm-’; (b) 750(c) 410-260 cm-’ region. Conditions: excitation, 514.5 nm
a t sample); slits, 100pm; three scans a t 2 s point-’
steps); nine-point smoothing, no baseline correction.
First harmonics
The overtone and combination bands in this region are
too weak to be observed under normal conditions but
they can be detected by co-adding spectra (Fig. 2 ) . Our
proposed assignments are listed in Table 2. The most
intense series of overtones and combinations (950-
830 cm-’) are less than or equal to the intensity of the
b, mode (417 cm-I); the other series are approximately
20% of this intensity.
Table 3 also presents the calculated frequencies for
the various overtones and combinations. Only those
Table 2. Moleculara and crystallographicbselection rules for the binary combinations and
overtones of orthorhombic sulfur (S,)‘
a,
a2
bl
62
el
e2
e3
a,
a2
b,
b2
e,
e2
e3
A,
A2
A,
81
82
€1
€2
€3
82
4
€1
€2
€3
A2
€3
€3
A1
(A, +A2 + €2)
€2
€1
€1
A1
€2
(€1
+ €3)
(A, +A2 + 8, + 8 2 )
(8,
+B2+€2)
(€1
+ €3)
(A, +A* + € 2 )
For Dddsymmetry.
bFor D,, symmetry. From Ref. 19, the selection rules are: uxu=g(R), g xg=g(R), u x g = u ( l R ) ,
b, xb2=b,, b2xb,=bl,
6 , xb3=b2. Note that no IR-active component of a fundamental can
combine with a Raman-active component to give a Raman-active combination.
From Ref. 20.The binary overtones of non-degenerate modes follow the same selection rules
as the combinations. For overtones of degenerate modes, the selection rules are: ( e , ) 2 = ( e 3 ) 2 =
A, + E2; ( e2)’=A1 + 81 + 8 2 .
a
33 1
RAMAN SPECTRA OF ORTHORHOMBIC SULFUR AT 40 K
Table 3. Raman frequencies and assignments for S, at 40 K
Raman freauencies (cm-’)
(+05cm-’)
Calculated frequencies (cm-’)
( + I cm-’)
-Au (cm-’)
( + I cm-’)
951 .O
946.5
936.0
951 .O
946.5
0.0
0
1.5
0.5
2.0
1 .o
0
0.5
0
907.0
F“
882.5
{E
933.0
932.0
907.5
931
.O
931.O
882.0
873.0
849.0
872.5
852.0
833.0
{ E::
{Z
718.5
713.1
694.7
71 1.5
692.5
685.5
{::;::
K::
{:;:::
665.5
657.0
656.8
634.3
625.1
633.5
{:z
G::
625.5
594.2
557.0
594.0
557.0
551 .O
552.0
551.5
552.5
527.0
503.0
502.8
551 .O
527.0
502.5
1 .o
-0.5
0.5
3.0
1 .o
-0.5
2.9
0.1
1.6
2.2
0.3
1.3
2.1
3.1
1.4
2.4
-0.2
0.8
-0.4
1.1
2.1
0.2
0
0.9
-0.1
0
1
1.5
2.5
0
0.5
0.3
I
I
:::q
Molecular symmetry
Crystal symmetry
(Dad)
(Dm1
a1
e3
a9
a, + bl,
ag+b1,+b2,+b39
b2g + b3g
ag + b3,
bl, + bzg
a,
a,
e3
b19
e2
el f e 3
el + e 3
a1 +e2
a1 + e2
a1 +e2
a, + b3,
ag + blg + bZg+ b3,
a1 +ez
a1+e2
blg+b2,+b3,
el
a9
a1
a9
a1
bl 9
el +e3
a,+b1,
el + e 3
a, +bl,
b, +a2
+ e,
a,+bi/
a1
a,
e2
bzg + 639
e2
ag +bl,
el +e3
a, +btg
elf e 3
b*g + b3g
ag + 61, + 6 2 , + b3,
el + e 3
ag + b2, + b,,
el + e 3
bl + b2, + b3,
83
e2
b39
e3
a,
Al + a2+4+ b,
b2, + b3gb
a, +A2+ b, +B2
a,+bl,
el + e 3
a, +big +b3g
A1+a2+t/,+b2
b2, + b3gb
el +e3
bl g + b2,
el +e3
e9
A, +a,+& +b2
b2, + b3gb
a, +A2+ 6,+ X
Comments
e3
Mol. forbidden
,
475.5
474.5
471 .O
470.0
S-S stretch
463.5
M1’ol
432.0
41 7.0
415.5
390.0
I
371.5
354.5
399.0
390.8
{
z::
372.2
354.2
356.2
399.0
0.8
0.9
1.9
0.7
-0.3
1.7
0
1.4
2.4
332
P. D. HARVEY AND I. S. BUTLER
~
~
Table 3 (continued)
Raman frequencies (cm
(*0.5 cm-')
321.5
I)
Assignments
Calculated frequencies (cm-')
(tl em-')
v4+v9
v2
+v,
304.5
{
323.6
306.2
307.2
x2
288.0
277.0
251.4
247.6
237.6
220.2
21 5.8
197.6
188.4
183.8
158.8
156.6
153.2
149.6
1
113
%+'9
V8 +US
289.0
279.8
-Av (cm-I)
Molecular symmetry
(*I cm-')
(Dad)
2.1
1.7
2.7
1.7
1.9
1 .o
2.8
Comments
e2
e2
82
a, +A2+ bl +4
a, +A2+ b, +b2
el + e 3
a, +A2+ b, +a2
vi1
e3
u4
v2
b2
a1
v6
el
V0
e2
S-S-S
69.2+46.2
v9+31.8
58.6+57.1
(58.6+54.4
115.4
112.8
115.7
113
2.4
-0.2
2.7
0
bending
a, + bl + b3,
S-S-S
e2
v9
81 .O
79.2
69.2
65.4
58.6
57.1
54.4
46.2
42.4
38.8
bending
Liberations
a, + b2,
f
b3,
Translation
b2, + b,,
The crossed molecular symmetries mean that they do not correlate with the crystal symmetries (see Table 1).
The remaining components a2 and b2 are inactive and infrared active, respectively, for the isolated molecule so that such assignment is
highly improbable in the Raman spectra of solid S,.
a
bands for which Av=vc,,c-u,b5 is between -1 and
+3 cm-' are included. These limits were chosen by taking
into account the intrinsic experimental uncertainties
(k0.5 cm-') for the negative limit, and so there would
be at least one possibility for each observed band within
the positive limit. The molecularly forbidden transitions
are neglected unless they are the only possibility. The
molecular and crystallographic symmetries for each of
the assigned transitions are listed and compared. They
must obey to the correlation diagram of Fig. 1. Some of
them have many components, i.e. a, + a,+ b, + b2 for the
molecular symmetries, but have only one crystallographic species. In other words, some of them do not
correlate and must be removed (see footnote a, Table
3 ) . This will result in some occasions when the assigned
transitions are unlikely in the Raman spectra (see footnote b, Table 3). It should also be mentioned that the
observed frequencies which have been assigned to only
one possible overtone or combination possess ug and/or
b,, crystallographic symmetry (except for one case). For
the others, both ag and b,, appear with or without other
components.
The first series (950-830 cm-') contains overtones and
combinations of the S-S stretching modes. The vibra-
tional analysis shows that possibily four overtones are
observed: 2v,, 2v,, 2vI0 and 2v3 with the latter being the
most intense where v 3 = p , (inactive for the free Sg
molecule). The other overtones appear as weaker
shoulders in the spectra. The associated Av values are
2vl, 0; 2v5, 1.0 (average of three components); 2v10,
-0.5; and 2v3, 1 cm-' These values are within the experimental error and so no accurate mechanical anharmonicity terms can be deduced. However, if we consider Av
to be in the range 0-2cmP1 (taking into account the
uncertaincy in the frequencies), we can estimate the
anharmonicity values from Eqn (1):
where
v!+O
=w i
+ Xi1
and vfCo and v;+O are the observed values (in cm-') of
the first overtone and fundamental of the ith vibration,
respectively, w i is the frequency of the harmonic oscillator and X i i is the binary anharmonic term. We obtain
Xii (where i = 1, 2, 5 , 6 , 8, 10,11) in the range from 0
to -1 cm-'. The S-S stretching and S-S-S bendingvibrations are therefore highly harmonic.
333
RAMAN SPECTRA OF ORTHORHOMBIC SULFUR AT 40K
Table 4. Raman spectrum of SBat 40 K in the 1450-1250 cm-'
region
Observed
frequency
(cm-')
Assignments
1444.5
1422.5
1404
2.5
0.2
1411.5
1405.2
1 .a
1.2
1406.2
1391.Q
1377.5
2.2
4.0
3.0
v7x2+v3
1376.7
1357.3
2.2
3.3
v, +v5+v,
vg x 2 +v,
1356.5
1346.7
2.5
1.2
v,x2+v5
1347.2
1322.5
2.2
2.0
1323
1303.1
1280.5
1273.6
2.5
3.1
-0.2
2.6
i
{
x3
1450
1400
1350
1300
1250
v,x2+v5
v1 X2+v10
i
v1 + V 7 + " 1 0
1374.5
WAVENUMBERS
Figure 3. Raman spectrum of Ss at 40 K (1500-1200cm-' region).
Conditions: excitation, 514.5 nm (200 mW a t sample); slits, 250 km;
60 scans a t 4 s point-' (0.5cm-' steps); 25-point smoothing,
baseline corrected.
v,x3
v5 x 2 f v ,
1387.0
~
v7+v5+v10
1354
1345
{
{
i
v5+u10+v3
The 800-500cm-' region shows many bands and
shoulders which are due chiefly to combinations between
one S-S stretching mode with one S-S-S deformation
mode (it appears that a shoulder at 502.5 cm-' can be
also assigned to 2ul,, the first overtone of the highest
energy bending mode). The 410-260 cm-' region contains bands that are essentially due to overtone and
combination modes of two S-S-S bending modes and
these bands are of comparable intensity to those in the
800-500 cm-' region bands.
Second harminics
Under our experimental conditions, the intensities of
the first harmonic overtones and combinations are ca
1% of the intensity of the fundamentals. This implies
that the second harmonic bands will be approximately
0.01% of the intensity of fundamentals. Many scans will
therefore be required in order to observe these extremely
weak features. The ternary combinations of the S-S
stretching modes are expected to lie between 1425
(maximum allowed values) and 1270 cm-' (minimum
allowed values). Figure 3 shows the Raman spectrum
of solid S8 at 4 0 K in the 1500-1200cm-1 region. This
spectrum represents the co-addition of 60 scans and took
about 32 h to accumulate. Even under these conditions
the bands are still weak, necessitating baseline correction
and 25-point smoothing in order to produce a reasonable
spectrum. The observed bands are reproducible as a
function of the number of scans (20, 40 and 60).
Moreover, their reliability is confirmed by the absence
of any band below the lower limit (1270 cm-') and only
one band appearing above the higher limit (1425 cm-')
expected if the bands are indeed due to second harmonics.
The vibrational analysis is presented in Table 4. The
fundamental frequencies used are averages of the
observed crystallographic components (for 250 pm slits,
resolution 2-3 cm-I): ul = 475.0, u, = 470.5, u5 = 465.2,
u,o= 441.0 and 432.0 and u j = 416.3 cm-'. The Au limits
1320.5
1300.0
1280.5
1271.0
hv (cm-')
(11.5cm-')
1425.0
1410.7
V'
v1 +v7+u5
1410.5
Calculated
frequency
(cm-')
(*l.Ocm-')
~10x3
v3 X 2 + v,
vl0 X2+v,
v,X2+vlo
Comments
v l O = ~cm-'
1
v10=432cm-'
vl,=441 cm-'
v l o = ~ cm-'
l
vlo=441 cm-'
u10=432 cm-'
cm-'
V,,=UI
(-1 to +4 cm-') were again chosen bearing in mind the
criteria already mentioned. The crystallographic symmetries could not be taken into account because of this
relatively poor resolution. On the other hand, the
molecular symmetry selection rules for ternary combinations show that only five of 35 possible combinations
are molecularly forbidden, i.e. they should be very weak
and so are not considered in the assignments.
The Av values are larger for the second than for the
first harmonics. These Au values represent, of course, a
triple contribution of the anharmonicity terms. For the
three possible S-S stretching second overtones given in
Table 3, Av=2.5 ( ~ U I ) 1.0
, (3v7) and 2.5 cm-' ( 3 ~ ~ ~ ) .
The anharmonicity terms can be deduced from Eqn (7)
by
Again, the Xii values cannot be evaluated accurately;
however, they lie in the range 0 to -1 cm-', in good
agreement with the values obtained from the first harmonics. Attempts to detect other ternary overtones and
combinations under same experimental conditions
proved unsuccessful.
Acknowledgements
This research was generously supported by operating grants from
NSERC (Canada) and FCAC (Quibec). P.D.H. thanks McGill University and NSERC (Canada) for graduate assistantships.
334
P. D. HARVEY AND I . S. BUTLER
REFERENCES
1. P. D. Harvey and I. S . Butler, Can. J. Chem. 63, 1510.
2. D. W. Scott and J. P. McCullough, J. Mol. Spectrosc. 6, 372
(1961).
3. R. B. Barnes, Phys. Rev. 39, 5790 (1932).
4. P. Krishnamurti, lndian J. Phys. 5, 105 (1930).
5. C. S. Verkateswaran, Proc. lndian Acad. SCi. 4A. 345,414 (1936).
6. S. C. Sirkar and J. Gupta, lndian J. Phys. 10, 473 (1936).
7. K. Venkateswarhu, Proc. lndian Acad. Sci. 12A, 453 (1940).
8. R. Norris. Proc. lndianAcad. Sci. 13A,291 (1941);16A287 (1942).
9. H. Gerding and R. Westrik, Recl. Trav. Chim. Pays-Bas. 62, 68
(1943).
10. H. J. Bernstein and J. Powling. J. Chem. Phys. 18, 1018 (1950).
11. G. M. Barrow, J. Chem. Phys. 21, 219 (1953).
12. V. D. Neff and T. H. Walnut, J. Chem. Phys. 35, 1723 (1961).
13. D. W. Scott, J. P.McCullough and F. H. Kruse, J. Mol. Spectrosc.
13, 313 (1964).
14. G. A. Ozin, J. Chem. SOC.A 116 (1969).
15. A. Anderson and Y. T. Loh, Can. J. Chem. 47, 879 (1969).
16. V. S. Grorelik, L. T. Kaldeava and M. M. Sushinski. Sov. Phys.
Solid State 12, 2648 (1971).
17. G. Gauthier and M. Debeau, Spectrochim. Acta. PartA 30,1193
(1974).
18. I. S. Butler, P. D. Harvey, J. M. McCall and A. Shaver, J. Raman
Spectrosc., in press.
19. J. C. Abrahams, Acta Crystallogr. 8. 661 (1955).
20. G. Herzberg, lnfrared and Raman Spectra of Polyatomic
Molecules. Van Nostrand Reinhold, New York (1945).