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The quadratic potential function and average structure of sulphur dichloride, SCl2, from its microwave spectrum
JOCKNAL
OF MOLECULAR
SPECTROSCOPY
65, 455-473
(1977)
The Quadratic Potential Function and Average Structure of Sulphur Dichloride, SC12, from Its Microwave Spectrum R. WELLINGTON DAVIS AND M. C. L. GEKKY Department oj Chemistry, The University of British Columbia, Vancower, British Columbia VdT lW5 Canada
The microwave spectra of 32S3sC1~ in the ground (000) and vz = 1 excited vibrational (010) states, and of 32S36C187C1 in the (000) state, have been measured. Values of the quadratic potential constants have been determined from the centrifugal distortion constants and the variation of the inertial defect with vibrational state. A partial substitution structure has been evaluated. The potential function has been used to obtain average structures of 3*S36C1~ in the (000) and (010) states. The frequencies of the three fundamental vibrations have been predicted, and agree extremely well with observed values. A comparison the bonding in SC12 and related molecules.
of 32S36C1~ is made of
INTRODUCTION
The microwave
spectra
of triatomic
information
about
a wide variety
centrifugal
distortion
constants,
bond
lengths
and angles,
molecules
of molecular
have
been
constants,
nuclear
quadrupole
and potential
functions.
used
including
coupling
to provide rotational
constants,
In favorable
accurate constants,
dipole moments,
cases,
such as those
of
structures, as well as SOZ (I), 03 (21, OF2 (3), and Se02 (41, average and equilibrium the quadratic and cubic potential constants, have been determined. Though determination
of the average
and
ground-state
the
structure
requires
normal
requires
results
knowledge
rotational
also knowledge
vibration,
There
structure effective which
of the rotational are often
has been one previous
study
of only
constants, difficult
constants
of the microwave
effective
quadrupole
structural
coupling
parameters,
constants
were
molecular
determined.
commonly
quoted
values
force
field
equilibrium
states
of the
dipole However,
for the fundamental
of sulphur
of the ground
measure the centrifugal distortion constants or to refine The Raman and infrared spectra of sulphur dichloride most
in excited
spectrum
et al. (5), in which several low .7 transitions of the 32S3”C12molecule were measured. Values
state
of the
of each
to obtain.
by nlurray constants,
the harmonic
calculation
ground-state
moment,
dichloride,
(000) vibrational rotational
and accurate
no attempt
the molecular structure. have both been observed.
vibrational
55C1
was made
frequencies
to The
are those
of Stammreich
et al. (6), namely,
514, 208, and 535 cm-’ for ~1, ~2, and ~3, respectively.
Several
of workers
have derived
groups
dichloride However,
using these considerable
potential
Copyrigllt All rights
constants
@
frequencies disagreement
in the various
1977 by .\cademic
of reproduction
(6-11)
Press,
in any form
quadratic
and early electron has been found potential
functions.
potential
functions
for sulphur
diffraction structures (12, 13). for the values of the quadratic This is not surprising
since,
with
Inc. reserved.
ISSN
WZZ-2852
456
DAVIS AND GERRY
only three pieces of data available to determine the four potential constants, assumptions were necessary to derive a potential function. 1n addition, a recent study by Savoie and Tremblay (14) of the infrared and Raman spectra of gaseous, liquid, solid, and matrix isolated sulphur dichloride has suggested that the band previously assigned to 0~3at 535 cm-’ (6) was spurious, that in fact wl and w3 were separated by 9 cm-l or less, and that the assignments of wr and w3 were not certain, although polarization measurements and force constant calculations made the choice wa > WI most likely. For these reasons it seemed useful, as the quadratic potential constants can be written explicitly in terms of the quartic centrifugal distortion constants (15), to obtain sufficient data to evaluate a quadratic potential function based solely on microwave results. In the present study rotational transitions of 32S35C1~ in the ground vibrational state (000) have been measured up to _7 = 60 and in the v2 = 1 excited state (010) up to J = 14. Several transitions of 32S35C137Clup to J = 40 have also been measured in the (000) state, enabling a partial substitution structure to be determined. A quadratic potential function has been derived which is consistent with all the available experimental data, including centrifugal distortion constants, vibrational frequencies, and inertial defects. From this the average structures of 32S35C12in the (000) and (010) states have been calculated. EXPERIMENTAL
METHODS
Measurements were made in the frequency region 12.5-40 GHz using a conventional 100 kHz Stark modulated spectrometer having a 3 m X-band cell. The source was a Hewlett-Packard 8400 B Microwave Spectroscopy Source containing an appropriate backward wave oscillator. The estimated accuracy of the measurements was better than ~0.1 MHz. The sample of sulphur dichloride was obtained from Matheson, Coleman and Bell and purified by vacuum line distillation. This procedure was repeated each day before running, primarily to remove the more volatile chlorine formed by decomposition of sulphur dichloride. Although all spectra were obtained with the cell cooled with dry ice, conditioning of the cell and sample decomposition were problems, as was the case in the previous study (5). Flowing the sample was found to be advantageous to obtaining strong signals, but periodically after warming to room temperature the cell was found to attenuate the microwave radiation and it was necessary to disassemble and clean it, as well as to replace the mica windows. Sample pressures employed were typically 5-30 pm. OBSERVED
SPECTRUM
AND ASSIGNMENT
A rigid rotor spectrum was predicted for the s2S3”C12species using the rotational constants and quadrupole coupling constants of Murray et al. (5). Hyperfine patterns were calculated by diagonalizing the coupling Hamiltonian for two quadrupolar nuclei using a general computer program with the coupling scheme J + 11 = F1, F1 + 12 = F, where IL, I, are the nuclear spin vectors, J is the molecular rotational angular momentum, and F is the total angular momentum. When values of the quantum number I, associated with the vector I, were required, the alternative coupling scheme II+ 12 = I, I + J = F was used, with the matrix elements of Flygare and Gwinn (16) being used
MICROWAVE
SPECTRUM
OF SClz
457
to construct the Hamiltonian. This was often necessary for the “2S3”Cl~species where it is required that the total wavefunction (the product of electronic, vibrational, rotational, and nuclear spin functions) be antisymmetric with respect to interchange of the identical chlorine nuclei. The electronic and vibrational wavefunctions are symmetric for both the (000) and (010) states. For the rotational wavefunctions, using the JKGK, notation, with e and o referring to even and odd K, we have symmetric functions when K,K, is ee or oo and antisymmetric for the eo and oe cases. Since the spin of chlorine is 3, the nuclear spin functions are symmetric for I = 3 or 1 and antisymmetric for I = 2 or 0. For the b-type transitions observed only symmetric spin functions need be considered for eo +-+ oe rotational transitions and antisymmetric spin functions for ee ts oo rotational transitions. The latter had rather simple patterns, and were readily recognized by a strong component at the unsplit line position. For the 3?PC1”7Cl species, where the chlorine nuclei are no longer equivalent, all spin functions had to be considered and the observed patterns were necessarily more complex. Using these predictions, additional low J R-branch lines and Q-branch transitions of the series J”,J-~ +-- Jl,J-l, which formed a bandhead at -29.9 GHz, were found. The 111+- OoOand JI+_~ +- Jo,~ ground-state transitions all had vibrational satellites which on the basis of relative intensities were assigned to the (010) state. Only the ee ++ oo transitions of this series were measured, as the low dipole moment (0.36 D (5)) made overlapping of Stark components and zero-field hyperfine components difficult to avoid for the complex eo ++ oe transitions. Additional lines for the excited state were located after the first transitions measured had been fitted using a rigid rotor model. The rotational constants of 32S35C137Cl were first estimated using the effective structure derived for “2S35C12.Values for the quadrupole coupling constants of %35Cl”7Cl were obtained by transforming the results for “?Y”Cl2 (5) to the 3?S35C1:(7Cl inertial axis sy-stern. and assuming that in the bond axis system the 37Cl coupling constants could be obtained by dividing the corresponding 3”C1values by 1.2688 (the ratio of the quadrupole moments of 35Cl and 37Cl) (17). The resulting coupling constants are in Table 1. Several low J transitions were then easily found, although some hyperfine patterns were very complex and so overlapped by Stark components that accurate frequency measurement was difficult. Curiously, the intense J~,J_~ +- J~,J-I Q-branch series had a bandhead at -29.8 GHz, quite close to that of the YPCl2 species. The remainder of the YPCl~ and 3”S3”C137Classignments
were made using the bootstrap
procedure,
now including
cen-
trifugal distortion constants, which has been described earlier (18, 19). The observed hy perfine structure, especially at intermediate values of J, was extremely useful in confirming assignments. An example of the hyperfine structure observed for the 32S3Ui7CI species is also given in Table 1, along with the assignments, relative splittings calculated using the derived quadrupole coupling constants. ANALYSIS
OF THE OBSERVED
intensities,
and
SPECTRA
The “unsplit-line” frequencies of the measured transitions were estimated using the measured hyperfine patterns. Almost all of the measured lines were symmetric and the procedure was thus simplified. The resulting frequencies were then used to calculate the rotational and centrifugal distortion constants. The calculations employed the
458
DAVIS AND GERRY
TABLE 1. A REPRESENTATIVE TRANSITION (Miz) 01’ 3%35C137C1 SHOWINGNUCLEAR Q”ADR”POLE l,YPERFINE STRUCT”RE
14.5
13
5.05
38553.71
38553.73
14.5 17.5
16 16
6.18 6.18
38554.14 38554.27
39554.24
17.5
19
7.32
38554.65
38554.6G
15.5
14
4.43
38558.10
36558.13
14.5 17.5 17.5
15 18 17
5.29 1.34 6.14
38558.54 38558.61 38558.68
38558.67
16.5
18
5.60
38559.07
c
14.5
14
4.54
38559.60
15.5 16.5
17 15
ti.14 5.29
38559.97 3S560 ,119
36560.03
17.5
18
5.49
jS560.51
38560.57
16.5
18
1.3G
38560 .YS
15.5
15
5.73
38564 .Ol
38564 .Ob
15.5 16.5
16 16
5.28 5.44
38564. .i? 38564.52
%5b.I.
16.5
17
6.46
38564 .Y?
38564 .Y3
%l
x
S7C1
“The b
F labels
of
these
Data is given only for of the total intensity.
‘Observed
dvieak “reduced”
but
overlapped
component
--
Hamiltonian
not
x
= -37.85
ad
= -31.61
aa
byperfine those
n = 1.529
Pllz
17 = 1.386
are
the
components
by interfering
.?
blllz
components hyperfinc
0
Stark
same for with
both
rotational
an intensity
IO
levels.
greater
than
1%
components.
observed.
of Watson
(20) in the I’ representation
(21)
:
%=%2+XD+XD’, XR
=
(1)
AP,2 + B&F + Cp,z,
X0 = --A$”
-
A,,p2pz
-
(2) AKP2 -
26Jp2(pbz -
x0’
= H#
+ H.,,@pf + (&
+ H&@> - p,2)[h.,p4
P,2)
s,[Pa(IQ
-
i),2) +
(Pbf -
i);vYJ,
(3)
+ Hda6 + h.,i$2~,2
+ h&z41
+ [h_rp4 + h.r&2~a2 + h.r&](pb2
- PC”).
(4)
In these equations the angular momentum P has components P,, Pa, P,; A, B, C are the rotational constants; AJ, AJR, AK, 65, 8~ are the quartic centrifugal distortion constants; and HJ, HJK, HgJ, HK, hJ, hJK, hi are the sextic distortion constants. The spectra were fit, by a linear least-squares procedure, to the rotational constants and centrifugal distortion constants, using the first-order energy expressions of a semirigid prolate rotor in a rigid rotor basis (22). The parameters
thus obtained were inserted into
MICROWAVE
SPECTRUM OF SClz
459
the complete Hamiltonian and used to calculate the transition frequencies exactly. The difference between these frequencies and the first-order frequencies represented the these were subtracted from the observed frehigher-order distortion contributions; quencies and the resulting values were refit using the first-order expression. The process was repeated until convergence was attained. In all calculations double precision (16 digit) arithmetic was used. Only a partial set of sestic constants could be detemrined for 32S3LC12 and 32S35C137C1 using the available data. For the (010) state of 32S35C1~, where only a small number of low J lines was measured, the centrifugal distortion contributions were assumed to be the same as for the (000) state. These contributions were subtracted from the measured frequencies and a fit was made to three rotational constants. Table 2 contains the frequencies and assignments of the measured transitions, with hype&e structure removed, along with the calculated frequencies and distortion corrections. The values obtained for the rotational constants and distortion constants are given in Table 3. They fitted the observed transitions with rms deviations of 0.047, 0.035, and 0.063 MHz and average deviations of 0.033, 0.021, and 0.047 MHz for the (000) states of ?PClz and 32S35C137C1 and the (010) state of ?S3X12, respectively.
THE HARMONIC
POTENTIAL
FUNCTION
The analysis of the microwave spectrum of sulphur dichloride has yielded two types of data which, within the framework of the small oscillations model, can be directly related to the intramolecular harmonic (quadratic) potential constants. These are the quartic centrifugal distortion constants, which were obtained using the method of the previous section, and the inertial defects in the ground and exited vibrational states, which were obtained from the rotational constants by the methods described below. These two sets of data were combined to obtain accurate potential constants, which were used in turn to predict the average structure Ijowling
the fundamental
vibrational
frequencies
of 32S3”C1:! in the (000) and (010) vibrational
(23) has shown that for a planar
asymmetric
and to calculate
states.
rotor in its equilibrium
con-
figuration there are only four independent quartic distortion constants. In the notation of Wilson and Howard (24) they may be conveniently chosen as 7anaa, 76666, 7cccr, and ~<~b,~b. Furthermore, for a triatomic molecule XV*, having Cz, symmetry, there are three normal vibrations:
two are totally symmetric,
of species Br. For a potential
function
of species Al, and the other is asymmetric,
written
in terms of symmetry
coordinates
there
are four force constants. They may be obtained from the four centrifugal distortion constants via the elements of the inverse potential constant matrix using espressions derived from those of Herberich et al. (15) with Dowling’s equations (13) :
(F-l)LI
=
-
R sin24 cos24 __2
A cot24 - B
~__
B tan?+ - A ‘Tama
A”
+
AR Tbbb5
I?3
+
-
Tcccc
C4
1 (5) ,
ii
1. 2.
-
-
2;72i 4.11) 2.14) V.14) V,l)J 2,161
61
0, 21 2( 2( 31 4, Ul 4,
121 I,( 11, 12( 13( 10, 13, 16( 16( 16, 16, 16, 171 1st 18,
-
-
-
-
20( 20( 21( 21, 211 221 22i 221 23( 24, 251 25( 25( 26, 26( 261 27( 28( 29( 2Y( 30( 30( 30( 31, 31,
2oi
91 10,
-
-
7( 81 9( lO(
-
71
- ii - ii
-
31 2) 3) 2) 5) -
1.17) 5,13) 3.17) 2.18) 211 1.21) 21 I 5.17) 21, 5.161 22( 4.79) 221 6.16) 221 6.17) 23, 3.21) 23i 0.17) 231 4.20) 241 4.20) 25( 9.22) 261 6.201 26( 5.21) 26 I b.21) 271 3.25) 271 4.291 27i 5.23) 281 5.23) 291 5.24) 30, 7.210 30, 5.26) 31( 8.23) 31( 8.24) 31, 6.26) 32f B..7V 32~ 8.25)
171 171 17( 171 1Si 19, 1st
16i
14,
14,
101
2.
01 2) 1, 2)
1. 3) 0. 91 1, 3) 0. 41 0. 6) 1, 5) 1. 7) 2. 6) 3. 5) 1. 71 1. 81 1. 9) 2. 8) 0,lO) 1.11) 3. 91 4. 8) u, 8) 1.121 1.13) 5. 8) 1.15) 5.10 5,12) 3.13) 2.14) 6.12) U.l(o 3.15) 2,191 6.19) 6.15) 5.16) 7,151 7.14) 4.18) 7.16) 5.17) 5.19) 5-19) 7.19) 6.20) 7.18) 4.22) 5.21) 6.20) 6.22) 6.23) 8.21) 6.23) 9.22) 9.21) 7,23) 9.23) 9,221
0. 0. 1. 0.
state) -
ROTATIONAL
vibrational
2. 01 -
:: :;
(ground
1. 2. 1. 1. 5) 2. 4) 81 0. 8) 8, 1, 7) 81 2. 6) Pi 2. 61 9, 2. 7) 101 2. 8) 1. 91 loi 1. 9) 121 1.10) 121 2.101 12, 3. 91 131 3.11) 131 2.111
32S35C12
TABLE
17044.19 12688.11 35091.60 26527.86 37291.67 14573.30 33615.87 351u3.10 17881.46 31828.24 35128.01, 15253.30 -14560.68 30370.45 29983.31 29930.u2 29137.68 30046.23 31088.97 13435.39 -1738U.21( -13429.93 32406.93 3427U.37 -31552.96 39766.13 -14808.74 -13908.38 12849.70 -14716.81 -33960.09 15710.32 12067.07 -36110.07 -16553.83 -16216.57 12753.01 -35509.10 -35535.71 27017.12 -29835.67 179BZ.OY 39379.69 27800.80 -12501.47 14795.95 -12691.58 28319.52 36337.36 17932.92 28694.74 36136.75 -14652.50 34598.95 -33867.00 -33872.19 16668.24 -28158.19 -28166.70
TRANSITIONS
(Hz)
17044.19 12688.08 35091.50 26527.77 37291.62 19573.35 33615.84 35143.12 17881.35 31828.19 35128.06 15253.36 -1U560.69 30370.50 29903.35 29930.53 29837.70 30096.25 31088.96 13035.28 -17384.22 -13u29.91 32806.96 3Ui71.36 -31552.98 39766.13 -14808.70 -13908.38 12849.73 -14716.82 -33460.17 15710.32 12867.06 -36110.06 -16553.M -16216.64 12753.05 -35509.10 -35535.72 27811.13 -29835.68 17982.02 34379.72 27800.89 -12501.43 111795.94 -12691.63 28319.50 36337.35 17932.92 2869U.77 36136.72 -14652.52 3U598.95 -33866.96 -33872.14 16668.23 -28158.11 -28166.68
OF S"LPH"R
-0.10 -0.09 -1.77 -0.01 -1.64 -0.10 -1.011 0.05 -0.54 0.12 -3.28 -4.52 1.95 1. 31 1.65 1.60 -10.12 -6.01 -0.52 -16.20 2.16 0.15 -3.09 -7.03 17.99 -20.12 -5.26 -9.29 5.12 10.68 22.36 -25.55 24.86 97.93 -15.11 -17.97 -55.49 25.32 25.62 -6.95 7.98 -65.03 -159.28 -78.94 -54.89 -131.99 -51.'95 102.47 -79.02 -119.05 -207.84 -255.82 -80.96 -170.63 -10.98 -10.82' -1811.59 -1t9.64 -44.37
DICllLORIDE
0.03 0.10 0.09 0.05 -0.05 0.03 -0.02 0.11 0.05 -0.02 -0.06 0.01 -0.05 -0.04 -0.11 -0.02 -0.02 0.01 0.11 -0.02 -0.02 -0.03 0.01 0.02 -0.00 -0.09 -0.00 -0.03 0.01 0.00 0.00 0.01 -0.01 0.03 0.01 -O.OU 0.04 0.01 -0.01 0.01 0.02 -0.03 -0.09 -0.04 0.01 0.05 0.02 0.01 0.00 -0.03 0.03 0.02 -0.00 -0.01) 0.00 0.01 -0.08 -0.02
0.00
-2
2( 3( 4, 5( B‘, at 9, lO( '101 14(
II II 2, 0) I. 2) 1. 3) 1. 5) 2. 6) 0. 8) 2. 7) 2, 8) 1. 9) 2.12)
11 1. 2, 1.
1,010~
33i 6.27) 33( 6,28) 3U( 8.27) 34, 6.29) 3Ul 8.26) 35( 7.29) 351 Y.27) 35, 7,281 36( 9.28) 37( 7.31) 381 7.32) 39( 8.31) 39( J,31) 39( 9.30) 39( 8.32) 40(10,30) 40(10,31) U2( d.34) 93l10.33) 43(10,34) 43( 8.35) U3f 8.361 44( 9;36j 44, 9.35) 46( 9.38) Qb( 3.37) 47(11.36) U7( 9.39) 47( 3.38) 48(10,38) UB(lU.39) 5O(lU,40) 50(111.41) 51(10.~1) 56f11.46) 56(11,45) 57(14,43) 57(11,45) 57(11,46] 58(14,45) 59(12,Y7) 59l12.48) 6Oll4.47) 60112.48) 6Ot12.49)
32S35C12 (gmund
-
-
21 2( 3f 4( 4( 8( 71 91 101 lot 141
0,
0, 0, 21 1. 1) 1, 31 0. '0 0. 4) 1. 7) 1. 7) 1. 8) 1, 9) 0.10) 1,13)
0.
32, 7.26) 32, 7.25) 331 9,2U) 331 7.26) 33( 9.25) 3U, 8.26) 34(10,24) 3U( 8.27) 35(10,25) 36( R,ZR) 37( 8,ZY) 3R( 9.30) 38f10.28, 38(10,29) 38( 9.29) 39(11.29) 39(11,28) 41( 9.33) 42,11,32) 42(11,31) 42( 9.34) 42, 9.33, 43ilO;33) 43(10,3U) 45(10.35) "5(10,36, 46(12,35) 46,10.36) 46(10,37) u7,11,37, 47(11,36) u9,11,39, UY(11.38, 50(11,40, 55112,431 55(12,410 56,15.42, 56,13,"(1) 56f13.43) 57,15,U2) 'X(13,46) 58f13.45) 59(15,94, 59(13,U7) 59113.46)
state1
-
vibrational
state)
17158.90 12813.97 35456.89 37666.03 14705.97 35214.68 30697.11 3u900.00 30299.14 30234.66 30225.48 34532.63
31414.74 28529.79 -16653.32 34u29.35 -16631.11 14852.58 -35876.C3 15381.94 -30172.3" 26923.09 32997.62 13003.43 -12873.02 -12861.39 12816.52 -32184.lU -32185.13 ?1591.85 [email protected] -14918.62 37984.19 37162.20 16697.03 16792.23 28823.14 29027.53 -16974.70 34954.22 352U9.19 14550.75 14518.69 26635.54 26565.42 32755.91 36412.35 36462.65 -34605.95 16059.53 1605U.Ul -28944.96 -28017.72 28006.35 -17483.10 34052.96 3U036.27
(continued)
17150.82 12813.91 35456.83 37666.1U 14706.01 35214.67 30697.1U 39980.02 30299.11 30239.69 30225.52 31t532.55
31414.78 28529.711 -16653.32 311$29.37 -16631.10 14852.58 -35876.02 15382.OU -30172.23 26923.07 32997.62 13003.46 -12873.00 -12861.UO 12816.51 -32184.24 -32185.15 31591.76 -11191".87 -7U918.65 37988.11 37X2.1.8 16697.04 16792.26 28823.10 29027.50 -1697e.73 3495u.25 35249.20 111550.78 14518.73 26635.54 26565.42 32755.99 36412.32 36462.66 -34W5.96 16059.54 16054.111 -25944.90 2RC17.70 28006.32 -171t83.19 34053.00 34036.27
-0.11 -0.09 -1.77 -1.6" -0.10 0.05 1.32 -3.28 1.65 1.60 -6.01 -7.03
-313.uu -2rrT.73 -118.28 -276.29 -119.06 -260.67 -29.61 -277.61 -72.19 -397.30 -392.99 -356.76 -215.65 -216.26 -348.18 -108.67 -108.61 -550.46 -289.32 -280.06 -627.8(1 -582.86 -515.61 -521,91 -660.03 -674.74 -365.33 -737.81 -759.d9 -646.RU -644.01 -822.33 -815.61 -918.19 -1208.95 -1215.69 -468.92 -1066.87 -1066.08 -580.21 -1307.84 -1305.96 -815.62 -1U36.90 -1434.011
-0iOS 0.01 -0.03 -0.02 0.03 -0.03 -0.011 0.08
0.06 0.06 -0.11
0.08
0.05 -0.00 -0.02 -0.01 0.00 -0.01 -0.10 -0.11 0.02 -0.00 -0.09 -0.02 0.01 0.01 0.70 0.02 0.09 0.04 0.03 0.08 0.02 -0.01 -0.03 0.09 0.03 0.03 -0.03 -0.01 -0.03 -0.04 -0.00 0.00 -0.08 0.03 -0.01 0.01 -0.01 0.00 -0.06 0.02 0.03 o.ov -0.04 -0.00
-0.04
E *
8
5
M
8
MICROWAVE
SPECTRUM
Distortion Correction
Calculntcd Frequency
E, 9, 10, I,( 12, 111, 15, 16, 17, 19, 22, 22, 22, 23, 23, 23, 24, 26, 26, 27, 27, 28, 28( 30, 31, 31,
35, 35, 35, 36, 36, 37, 37, 39, 39, 39, 39, 110, uo,
R (F-‘)r:!
=
-
E 9 10 11 12 14 15 16 16 16 21 21 21 22 22 22 23 25 25 26 26 27 27 29 30
6.26) 6.27) 8,28) b.30) 7.30) 7.29) 9.29) 9.28) 9.30) 9.31) 7.33) 7.32) 8.32) 8.33)
-
30 34 34 34 35 35 36 3h 38 38 38 38 39 39
9.26) 9.25) 7,271 9.271 6.26) 0,26) 0.271 0.29) 0.29) 9.30) 9.31) 9,313 9.301
COSTS
R(tan
sin24
4
-
cot
4)
-
2d cot
-
De".
-0.05 -0.01 -0.02 0.07 0.01 -0.01 -0.01 0.01 -0.03 0.03
1.34 1.74 1.79 1.31 0.08 -5.65 -1O.bA -17.u9
30324.67 29897.90 29778.20 3oc31.09 30712.70 33545.54 35768.35 38559.35 -16OOQ.22 13899.20 -13477."3 -13041.79 15504.53 -32496.02 -32531.58 15316.50 -27005.30 -1569U.4, -15845.03 -35007.11 -34995.36 -29471.70 -29452.27 30536.30 -12655.18 12663.06 -15122.20 -15147.86 35707.95 16144.67 16735.50 -28871.53 -28871.30 -17651.92 -11660.11 33832.47 35523.78 13806.36 13603.09
30324.62 29897.89 29778.18 30031.16 30712.71 335s5.53 35768.34 38559.36 -16009.25 13894.23 -,31177."U -13041.75 15504.54 -32'495.98 -32531.56 15316.52 -27005.38 -1569U.40 -15845.02 -35007.09 -3U995.32 -29471.72 -29952.33 30936.25 -12655.17 12663.09 -15122.,8 -15147.811 35707.97 161911.68 16735.47 -28879.54 -28871.30 -17651.92 -17660.11 33832.47 35523.78 13806.35 13603.10
1. 7) 1. 8) 1. 9) 1.10) 1.11) 1.13) l.lQ) 1.15) 5.12) Q.lU) 6.15) 6.16) 5.77) 7.16) 7.75) 5.17) 7,161 7.19) 7.181 8.18) 8.791 8,193 8,201 6.23) 6,22) 7.23)
2, 6) 2. 7) 2, 8) 1. 9) 2.10) 2.12) 2.13) i,lU) U.13) 3.17) 5.18) 5.17) 4.18) b.17) b.18) 4.20) b,19) 6.20) b.21) 7.21) 7.20) 7.22) 7,21) 5.26) 7.25)
461
OF SCln
-7.30 -25.69 -26.58 -30.52 -88.87 11.42 11.85 -62.01 -5.86 -08.03 -45.75 7.20 6.98 -17.11 -17.51 -165.74 -101.16 -172.70 -1U3.36 -1112.42 -292.54 -282.51 -302.06 -99.69 -99.84 -193.33 -192.91 -414.49 -478.78 -382.95 -373.35
-0.01 -0.01 0.01 0.01)
0.02 0.02 -0.06 0.01 0.01 0.02 0.04 -0.02 -0.06 -0.05 0.01 0.03 0.02 0.02 0.02 0.01 -0.03 -0.01 0.00 0.00 0.00 -0.00 0.00 -0.01 0.01
@ raaaa
A”
2(2Y A(tan
4
-
cot
4)
+
2B
+
tan
Rmx [ mx1 . B3
2rnlr
(F+)33 = - 2~
1 + __
sin2+
z
fj3
AB(tan Tbbbb
-
4
-
C4
cot
4)
1 (7) (8)
Tcccc )
Here R = r'X lO_**/2/z, with r the X-Y bond length; 4 is one-half the bond angle; M is the molecular weight with M = mx + 2m Y. With Planck’s constant h in erg seconds and r in angstroms the force constants F 11, FIZ, F22, and F33, obtained by inverting the matrix calculated above, are in dyne cm-l. They are defined as Fll = f7 + frr, F22 = jJr2, FIZ= 2ijTm/r, and F33= jr- jyr. Though strictly Eqs. (S)-(8) apply only for the equilibrium values of the various molecular constants, a good approximation can be obtained using effective ground-state values. To obtain the potential constant matrix using Eqs. (S)-(8), the four distortion constants 7,,,,, Tbbbb, 7cceo and 7abab must first be calculated from the experimental distortion constants. Watson (20) has shown that a set of five “determinable” distortion Constants, T,,,,, Tbbbb, 7cccc, ?-I, and 72, may be calculated as linear combinations of our experimental quartic constants A J, AJir, AK, 6~, 6~ using the relations summarized in
462
DAVIS AND GERRY
TAHLt. 3.
A
RO’I’ATIOUAI. CONSTANTS’ AND CENTRI,U;AI. COUSTAN’I’SU,li SIILI’IIUR DICIILORIDE
g:rO”“J vibrational state
14613.5968
IIISTOIITION
(0101
vibrational state
(53) I,
14732.830
(10)
14490.169
(21)
”
291O.8702
(11)
?918.3174
(341
2841.1929
(47)
C
‘243lJ.6943
(10)
2126.lfliZ
(341
2371.963.1
(35)
x 103 *J AJL: x 102
-1.4604
AK 65 %
1.3249
(251
,T
(3iI
,:
Y 10’
1.3802:
x 104
3.3968
(50)
x 103
n.927
11-1)
(70)
1.239 -1.440
r?
1.357
/a
3.168 3.62
iiJK x 10’ “KJ
-2.56
* 107
3.55
x 101 “J * IO’ h JK
C(:entrifugnl
-5.0 2.7
distortion
assumed
to bc
the
same a5 for
the
ground
(13) (13) (2) (35) 121)
(68) (1.15) (2.21 11.01
state.
Table 4. The harmonic force constants of the A1 vibrations (Fll, F12, F2.J can now be obtained directly from +ranaa, Tbbbb, and 7cece using Eqs. (s)-(7). Though the force constants still depend on the validity of the planar assumption, they have usually been found to give good values, to within 5% or better of the corresponding vibration frequencies, even for the very light molecules Hz0 (2.5) and H2S (26). The force constant for the B1 vibration (F& is much more difficult to evaluate. By Eq. (8) it is related to T&b, which is not one of Watson’s determinable parameters. It can be estimated in a variety of ways (25, 27-29) from 71 and/or 72 using Dowling’s planar relations (23), which are also given in Table 4. Because of vibrational effects the values of T&b thus obtained vary widely, depending on the method used to determine them. Consequently the derived value of F33 is rather uncertain, and the prediction of the B1 fundamental frequency is usually much worse than those of the A1 fundamentals. Table 5 contains the five determinable parameters of 32S35C12 in its ground vibrational state, calculated from the experimental distortion constants by the equations of Table 4, part a. The Constants roana, Tbbbb, rcecc, and 71 were obtained directly. To evaluate 72, on the other hand, the rotational constants A’, B’, C’ were necessary; these are the rotational constants of Kivelson and Wilson (30) and are related to the experimental rotational constants by A’ = A -
16R,,
B’ = B + 16&(/l’
-
C’)/(B’
- C’),
C’ = C -
- B’)/(B’
- C’).
16&(A
(9)
MICROWAVE
SPECTRUM
OF SC12
463
The constant R, = - (~AJ f ~b,&,/32 is defined by Nielson (31). T&c was obtained sufficiently accurately from the planar relations and ground-state values for the rotational constants. The resulting values are also in Table 5, and are evidently very close to the Watson values A, B, C, in Table 3. Four different methods were used to calculate T&b in 32S35C12.These were: (i) from the value of rl and all the planar relations; (ii) from the value of 7~ and all the planar relations; (iii) from the planar relations for Taabb, T,~,,, Tb&, and Tbbee and simultaneous solution of the equations for 71 and 72; (iv) from the planar relations for 7aabb, T,,~,., 7aaco and Tb&c and simultaneous solution of the equations for ~1 and 72. The results and their uncertainties are also in Table 5. There is clearly a wide variation between the values calculated, and because of the nebulous nature of the vibrational effects it is virtually impossible to decide which value is the most accurate. The problem of choosing the correct value for T&b has been considered by several authors. Watson (20) pointed out that in the equilibrium configuration i-2 = CeT1 + (-4, + %)7,,,,. In the nonequilibrium a “planarity defect,”
configuration AT, by
(10)
this clearly is invalid,
AT = rcccc -
C(Q -
&)/(A
and Kirchhoff
(27) defined
+ B)].
(11)
This should provide some indication of the degree of breakdown of the planarity conditions. It has been calculated for x?S35Cla as (-4.5 =I=3.2) X lCV5 MHz, essentially TABLE
3.
Evaluation T
aaao
Tbbbb TCCCC ,I
=
4.
of
RELltTIONSHIPS
Watson’s
determinable
-4(AJ
+ A.,R
=
-.$(A,,
+ ?SJi
=
-4(A
=
!jabb
J
-
+ ?A,,,
RETWEEti CRNTRIII~G~~~. PISTORTION
parameters
(I’
?A,,) =
-J(A
,h
with 1~ =
+ 3AJ3
(X1-R’-C’)/(B’-C’I
relationsb
incnc=‘bcbc
=
123/ 0
representation)
+ A,)
J(?si,,
I’lonnr
COSSTANTS ’
+
Xii
-
“A,,)
+ r
(B’+C’) __ 1 (B’-C’I
1
464
DAVIS AND GERRY
a.
b.
Watson’s
Llcterminablc
x lo+’
-4.9899
f
0.003?
‘bbbb
x 10+3
-8.017
f
0.011
7 cccc
* lof3
-2.582
+ 0.011
fl
x 10+2
4.251
+_ 0.015
x2
x 10-1
5.88GG
c 0.042
Kivelson-Nilson
Rotational
14h13.5973
B’
2920.8586
r 0.0011
C’
2430.7054
_+ 0.0010
Values
of
baby
using
by
Value
x 103
-5.982
(ii]
-5.80
i. 0.22
(iii)
-6.89
+ O.tiS
(iv)
-6.02
i
Distortion
Constants
T&b
x IO2
‘bbcc
’
%Yandard Methods
CT2 is
Mcthodsb
(i)
T’aacc
b
x rOm5)
Different
Method
d.
Ek 0.0052
Rg = -2.9220
Obtained
in
Evaluated
lo3
c
Constants
A’
(obtained
C,
Parameters
T aaaa
0.20
0.22
Using
the
4.292
* 0.030
-4.365
A 0.008
1.592
x lo2
Planar
Relations
k 0.021
ermrs. are
described
in
the
text.
W%z’.
indeterminate, and so is of little use here. It should be noted as well that the difference in the values of r&b obtained from methods (i) and (ii) is given by (28) : Bralab
=
[(A
+
BIPClA7.
(12)
This too is indeterminate. Yamada and Winnewisser (28) have also shown that the planarity defect is only one of several factors defining the breakdown of the planarity relations. In any case knowledge of the existence of these factors still does not solve the basic problem of choosing the correct value of r&b. In an attempt to obtain a further measure of the effects of vibration on both the measured and calculated distortion constants, another fit to the experimental data was carried out. This time the planarity relations were used to eliminate one of the five distortion constants, and a iit was made to four constants, chosen to be raaaa, 7F,bbb, Toabb, and Taba&.The fit was again a first-order fit in a rigid rotor basis, and the rotational constants used in the planarity relations were the effective ground-state constants obtained earlier. As no account was taken of sextic distortion contributions, only transitions having J < 25 were used in the fit. The rms deviation was 0.055 MHz with
MICROWAVE
SPECTRUM
OF SClz
465
an average deviation of 0.044 MHz. The results of this fit (Fit II) are compared to those of the previous analysis (Fit I) in Table 6. In a further analysis (Fit 111) a tit to the four distortion constants Tanaa, ,-b,,bb, raabb, rabub Was made with a Value for the rotational constant C’ being obtained from the relation l/C’ = l/A’+ l/B’. These results are also reported in Table 6. Here the rms deviation between the observed and calculated frequencies was 0.049 MHz with an average deviation of 0.041 MHz. Excellent agreement is observed for the directly determinable spectroscopic constants A’, B’, C’, raaoa, and rbbbb. The agreement iS 1eSSSatisfactory for T,,,~ and raabb which have been compared using the planar conditions (see Table 4) and is very poor for ‘T&bThe large discrepancies between the values for rob0b obtained by various methods make its further use undesirable. The three force constants of the symmetric vibrations (Fir, FIB, and EBB)were calculated using the values of raaaa, 76666, and T,,,~ in Table 5 in Eqs. (5)-(7). The results are in Table 7. The rotational constants used were the effective ground-state constants A, B, c. The uncertainties given have been calculated assuming the errors in raaaa, Tbbbb, rcccc to be those given in Table 5 and the errors in the rotational constants to be the differences between the observed effective ground-state values and the values calculated from the average moments of inertia of the next section. The latter errors are several orders of magnitude larger than the experimental uncertainties and are responsible for the major part of the uncertainties quoted for the potential constants Err, FrB, and Fz2. These uncertainties should, however, give some indication of the model error. The corresponding vibration frequencies, wr and ~2, were then calculated, and are also given in Table 7 in comparison with experimental values of Savoie and Tremblay (14).
DAVIS
466 TABLE 7.
AND
GERRY
QUADRATIC POTENTIAL CONSTANTS AND RELATED PARAMETERS
-__ Potential
Derived
Value
FII
x 1O-5
2.913
?z 0.090
PI2
x 10-3
9.258
i- 0.55
F22 x 1O-4
2.624
f
F3? Y 1O-5
2.421
cent
*(OOOP
,WO) aaaa
dyne
0.021
II II
Observed
Value
’
=cccc Tab*
x lo3 x 103
0.0006
lo3
0.x.313
-4.9899
-4.9899
f
-8.0173
-8.0173
f
0.010s
-2.5823
-2.5829
f
0.0105
0.0032
a.
-6.7280 514.8
f
wi
206.9
+ 4
ZlP
w3
523.8
f
525 .sa
Wl
8
518.0aJc
5
aw1(%37C1,)
7.0
SkQ(34S35C12)
7.6
Sw,(3’S37C12)
6.1
6.0
aW3(3%35C12)
8.9
9.0
(Cz3)
Units
0.3086
0.8306
x lo1
‘bbbb
(513)
cm-’ ,I
0.5220
A2 A
Units
i- 0.01
Value Predicted from above force constants
Parameter
T
--
Constant
7sc 10
2
0.324
i- 0.003
2
0.676
-
e,(oon)
%atrix.
distortion
‘Liquid. ‘Reference 114). d Several values are Tables 5 and 6.
0.003
given
in
and C(O1”’ parts.
arc
sums of
vibrational
and centrifugal
f Obtained using Watson’s rotational constants A,B,C. Strictly the calculated values should be compared with inertial defects from Rivelson-Wilson constants, such as are given in Table 5 for the ground vibrational state.
(Somewhat different values have been obtained by other workers (6, 7, 32)). Though the calculated uncertainties in WI and wz to some extent neglect effects of zero point rather small, nevertheless vibrations in applying Eqs. (S)-(7), and are consequently the excellent agreement with the experimental values suggests that they are quite reasonable. Because of the range in experimental values for Taba?,it was not used to calculate the & force constant Fz3. Instead this force constant was calculated from a value of 03 obtained using inertial defect data. To obtain these inertial defects the measured rotational constants of all isotopic species and vibrational states were converted to principal moments of inertia. The resulting values, including the inertial defects, are in Table 8. The fact that the ground-state inertial defects are small positive numbers essentially independent of isotopic species is consistent with the planar structure of the molecule.
MICROWAVE
SPECTRUM
467
OF SClz
The experimentally determined inertial defect is the sum of vibrational, centrifugal, and electronic contributions, of which the vibrational contribution is by far the largest. The vibrational contributions to the inertial defects of %““C12 in the (000) and (010) vibrational states depend only upon the harmonic part of the potential function (9, 33) and are given by the following equations (4) :
A, = AVi,,(o’“)- AVi,,WW= 4K Here j-13and {23 (strictly {13@)and {23((z))are Coriolis coupling coefficients, and the factor K = h/8& has the value 16.85763 amu AZ cm-‘. Note that in Eq. (14) AZ is the dijerence between the ground and first excited state inertial defects. The centrifugal contribution is given by Acent = - 7&zh[(3r,‘/4C’)
+ (Ib’/B’)
+ (1,‘/2A’)],
(15)
where I,‘, Ib’, I,’ are principal moments of inertia obtained from A’, B’, C’, respectively; Acent will be assumed to be independent of vibrational state to the present accuracy. Finally, the electronic contribution is probably of the order of our experimental errors (9) and will be ignored. TARLE 8.
INERTIAL PARAMETERS=OF SULPHUR DIa,LORIDE
_3%3%x?
3%35C137CI
Ground vibrational state
rffective _.
Values-
IV a
34.58279
(I,!’
34.3fl291
I \’ b
173.02344
(7)
173.17479
(10)
177.87564
I” c
207.91549
(9)
2118.3n895
(30)
215.06357
(32)
,z”
0.30926
(11)
0.831?5
(35)
n.31n56
(44)
34.7366
gAll b
parameters
are
in
173.Rlh6
XX .0466
208.4068
n.on14
n.0013
a.m.“.
i?;
=
Tc -
Ib -
Ia
(2)
34.87737
34 .S889
173.3Cl86
the
conversion
factor
is
505379
are uncertainties in units of the last Nlrmbers in parentheses They reflect the uncertainties in the rotational constants.
@:
ground vibrational state
(010) vibrational state
a.m.“.
significant
i’
Pllz. figures.
(5) (30)
468
DAVIS AND GERRY
To use AZ to obtain w3 it is first necessary to calculate the Coriolis coupling constant {23; this was done using the equations of Meal and Polo (34) for an XY2 molecule: (i-13)~
=
[A,
(i-23Y
=
1 -
-
FII/(G-~)II]/(XI
-
As),
(16) (17)
(!T13Y,
where Xi = 4?r2c2w?are the roots of the A1 block of the secular equation 1FG - AE 1 = 0 (35). An expression for (G-‘)rr is given by Polo (36). It was calculated by an iterative method using first the effective structural parameters and later the average parameters, all of which are discussed in the next section. The value of Frr from Table 7 was used to obtain ({~a)~ and ({~3)~. These together with A2 calculated from Table 8 were then used in Eq. (14) to evaluate w3 and hence F33. Table 7 contains in all a summary of the derived quadratic potential constants along with the predicted and, where appropriate, observed values of the distortion constants, vibrational fundamentals, inertial defects, and Coriolis coupling coefficients. The calculated inertial defects A@O”)and A(OlO)are the sum of vibrational and centrifugal parts. The frequency of ~3, like 01 and 02, is in remarkable agreement with the measured frequency of Savoie and Tremblay (14). As indicated earlier, the quoted uncertainties in the calculated frequencies to some extent ignore zero point vibrational effects, but the agreement with experimental values confirms that the approximation is good. The predicted and observed vibrational isotope shifts of the symmetric isotopic species also agree extremely well, except perhaps for the shift observed for wr between 24S35C12and “2S35C12.This was apparently, however, the least accurately measured shift (14), and the quoted experimental uncertainties are f 1 cm- l. Finally, F33 was used to calculate rabab from Eq. (8) ; again a very reasonable value was found. MOLECULAR
STRUCTURE
OF SULPHUR DICHLORIDE
The CZ” symmetry of sulphur dichloride has been well established from previous electron diffraction (12, 13) and microwave results (5). The electron diffraction results were rather inaccurate, however, and the previous microwave results permitted the determination of effective structural parameters only. In the present work we have sufficient data to determine effective, partial substitution, and average structures for sulphur dichloride. The inertial parameters of the various SC12 species are collected in Table 8. These parameters have been derived using the rotational constants of Table 3. The effective structural parameters, ~0 and 00, are easily calculated using the ground-state moments of inertia of the %36C12 species. Because the inertial defect is nonzero, slightly different results are obtained when the three possible pairs of moments I,, Ib; I,, I,; and 15, Tc are used. These are all presented in Table 9. The mean effective structure is identical to that derived by Murray et al. (5). A partial substitution structure for sulphur dichloride has also been obtained. Kraitchman’s equations (37, 38) were used to estimate the coordinates of chlorine. The center-of-mass condition, 2; mibi = 0, yielded the b coordinate of sulphur ; its a coordinate is zero by symmetry. Again three possible structures can be calculated. These are also presented in Table 9 and are seen to be more self-consistent than the effective parameters.
MICROWAVE
SPECTRUM
469
OF SClz
Finally, the physically well-defined average structures of 32S35C12 have been found in both the (000) and (010) vibrational states. These average structures have been defined by Oka (39) and by Herschbach and Laurie (40). For a Czll triatomic molecule like SC12 they are obtained in general in any vibrational state using the following equations : (2v1 +
I,* = I,” + 3K
1) sin2X + (2v:! + 1) cos”X
(2213+ 1)(1,/I,) +
Wl
(2~1 + 1) cos2X +
Ib* = Isv + 3K C
I,” = T,v + 3K
w3
Wl
w2
(2~1 + 1)
(2% + 1) +
(2% + 1)
W2
w3
-
+
(202
+
1)
Wl”>
.r232 (Jz(w32
-
wz2)
W12 -
(2v3
(19)
(332 r132
wl(w32
(18)
1
W2
(22’1+ 1) [
w3
+
(-Ql
--a
(2~ +@I) sin2X + (2% + l)(IblIJ
1> 1,
+
{I32
1) 1
+
w&Q2 - WI”)
w22
(232
wa(w32- W?“)
II
)
(20)
where I,* and IOU are the average and effective moments of inertia, respectively, in the vibrational state in question, and K = (1z/Wc) has been evaluated earlier. The parameter X is determined from the equation
cos2x+ X23(Ib/le)~cosx+ rz.32- (IJIJ
= 0.
(21)
470
DAVIS
AND
GERRY
Here 123 is negative by convention (41). To use Eq. (20) in any vibrational state it is necessary in general that (wt - W) and (WQ- ~2) be fairly large. This is not the case here, since wr - 03. However, for the (000) and (010) states the equation is valid, since factors of (~3 - WI) all cancel. The resulting average moments of inertia and their corresponding inertial defects are presented in Table 8. The inertial defects are effectively zero in both vibrational states, as required. The average bond lengths and angles, obtained using various pairs of principal moments, are given for both vibrational states in Table 9. In both cases the bond lengths and angles calculated using different pairs are very consistent. As might be expected for different states of a bending vibration, the average bond length is essentially independent of vibrational state while the average bond angle is slightly larger in the excited state. These variations reflect the anharmonicity of the vibration. DISCUSSION
The harmonic force field obtained in this work has been obtained using solely microwave data. Two questions concerning it should be answered. First, does this potential function represent an improvement on results previously obtained? Second, is a combination of microwave and vibrational data likely to result in a useful refinement of the potential function? In Table 10 the present potential function is compared with that of Savoie and Tremblay (14) and that of Oka and Morino (9). The constants of Savoie and Tremblay, which are based on the most recent and most comprehensive vibrational data, are in better agreement with the present results than any previously derived potential function (6-11). Those of Oka and Morino differ slightly more but resemble closely those of other previous workers, who because of lack of data made the constraint Frr = F33. These latter results are based on the vibrational frequencies of Stammreich et al. (6). Also given in Table 10 are values predicted for the vibrational fundamentals, Coriolis coupling constants, centrifugal distortion constants, and inertial defects ; they were obtained using the corresponding potential function and the ground-state average structure. The table demonstrates that while all three potential functions provide good predictions of the fundamental vibration frequencies, only the present results account satisfactorily also for the observed values of the centrifugal distortion constants and inertial defects. The excellent agreement between the value of F33 derived here and that based on the most recent vibrational data is especially reassuring as it, being the only element of the B, matrix, is the element most easily determined from vibrational data. The good agreement between the observed and our calculated vibrational frequencies tends also to confirm our estimated error limits both for these frequencies and also the force constants and Coriolis coupling constants. This is in spite of the fact that we have neglected anharmonicity, especially in applying Eqs. (5)-(g). It is clear from the variation of the average structures with vibrational state that such anharmonicity is nonzero. However, we believe it is probably negligible in evaluating the force field; this is to be expected because of the large masses of the atoms in the molecule. Finally, since the differences between observed and calculated vibration frequencies are also less than the shifts observed upon a change of phase from liquid to solid (14), and since the observed isotopic shifts are well accounted for (Table 7), we conclude that a combination of presently available microwave and infrared data would not meaningfully refine the present potential function. Measurement of the microwave spectra of the
MICROWAVE
SPECTRUM OF SCla
471
(100) and (001) excited vibrational states should help, for, since these vibrations have very similar frequencies, they will be affected by a strong Coriolis resonance. Because of this the inertial defects in these two states are very sensitive to the difference wp - wl, which could now be accurately evaluated. Indeed, this difference may be sufficiently small that it could be observed direct2y (as a vibrational transition) in the millimeter wave spectrum. Unfortunately the weakness of these spectra and the low populations of these states make such observations rather difficult. The various bond lengths, r&Cl), determined in the present work are compared to earlier values, and to corresponding values in related molecules, in Table 11. Clearly the present values are more accurate than the earlier electron diffraction values, but of similar accuracy to that of Murray et al. (5). Except for NSCI, for which unusual properties can be anticipated, the S-Cl bond lengths are very similar for all molecules shown and are close to the sum of Pauling’s single bond radii (2.03 A) (53). Thus for SC12 in particular this bond is apparently a single bond, and, because of the similar electronegativities of the two atoms, should be strongly covalent. Further evidence for the bond character comes from the 35Cl quadrupole coupling constant along the bond, X,,, which is also given in Table 11, along with those of the related molecules. The largest of these values (-90 MHz) occurs for SC& itself; it TAULE I,,: COCII'ARISON OF PRESE.WDERIVE"CONSTAWS IVITHTIIOSE OF PREVIOUSWORKERSAND EXPERIMENTAL DATA
Savoic and Trenblay (14)
Oka and Horino (9) ____~
1.913
(YU)’
1.641 -0.029
0.0926 (55) 0.2024 (21)
U.3U3 2.433
2.421 (in)
dyne Cm-I II
2.52 -U."55
,I
lU.3U5 2.52
I,
-4.99u
-,1 .&l
-3.97
-.I.YYU(3))' hUlZ
-8.017
-8.22
-8.52
-8.017 (11)
"
-2.582
-2.88
-3.04
-1.ss2 (II)
"
0.324 (3)
11.415
U.4JU
0.676 (3)
0.585
0.560
515 (8) 107 (4)
517.1 211
514 ?UY
51B.U' 211
524 (5)
525.3
53s
515.5
Cl.3086 0.8306
0.190 0.736
U.187 U.714
0 .5UJ.i 0.5313
11.5120
0.446
0.427
0 .5?'11
O.OOOG
0 .noo6
n .ixm
--
“Numbers in parentheses figures .
are
one
-
standard
deviation
in
units
of
the
last
significant
u,I II :L.III.". xi,I II
472
has been cahxlated by Murray et al. (5) assuming it to be the principal value of the quadrupole tensor, and by us using our improved structure. It is quite close to that of 110 MHz), which provides strong evidence for covalent single bond the Cl atom (-character. The other components, perpendicular to the bond, are very similar, suggesting only slight asymmetry to the bond. Furthermore, were there considerable ionic or rcharacter to the bond a value much lower in absolute value would be anticipated. This has been used for SiH,Cl (17) and SiH&l~ (54) to indicate considerable back bonding from Cl to the d orbitals of Si; we conclude that such back bonding is negligible in sulphur dichloride. ACKNOWLEDGMENTS This work was supported by the National Research Council of Canada. We thank Professor N. L. Paddock for the sample of sulphur dichloride, and Professor T. L. Weatherly for sending us his results prior to publication. RECEIVED:
January
6, 1977 REFERENCES
1. Y. MORIXO, Y. KIKUCHI,S. SAITO,ANDE. HIEOTA,J. Mol. Spectrosc.13,9.5 (1964). 2. F. TANAKA AND Y. MORINO, J. Mol. Spectrosc. 33, 538 (1970).
MICROWAVE
SPECTRUM
OF SClz
473
3. Y. MORINO AND S. SAITO,J. Mol. Spectrosc. 19, 435 (1966). 4. H. TAKEO, E. HIROTA, ANDY. MOR~XO,J. Mol. Spectrosc. 34, 370 (1970). j. J. L. MURRAY, W. A. LITTLE, JR., Q. WILLIAMS, AND T. L. WEATHERLY, J. Chem. Phys. 65, 985 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 21. 25. 26. 27. 28. 29. 30. 31. 32. 33. 31. 3j. 36. 37. 38. 39. 40. 41. ?Z. 43. I-!. 4X 46. 47. 48. 49. 50. il. 52. 53. 54.
(1976). H. STAMMREICH, F. FORNERIS,ANDK. SONE,J. Gem. Phys. 23,972 (1955). J. M. BARROW, J. Phys. Chem. 59, 987 (1955). K. VENKATESWARLU ANDP. THIRUGNANASAMB~NDAM, Z. Phys. Chem. Abt. B 212, 138 (1959). T. OKA ANDY. MORIXO, J. Mol. Spectrosc. 8, 9 (1962). K. VENKATESWARLU ANDR. THIRUGNANASAMBANDAM, Indian J. Pure Appl. Phys. 1, 377 (1963). P. THIRUGNANASAMBANDAM AND S. MOHAN, J. &hem. Phys. 61, 470 (1974). I). P. STEVENSON AXD J. Y. BEACH, J. Am. Chem. Sot. 60, 2872 (1938). K. J. PALMER,J. Am. Chem. Sot. 60, 2360 (1938). R. SAVOIEANDJ. TREMBLAY,Can. J. Spectrosc. 17, 73 (1972). (:. E. HERBERICH,R. H. JACKSON,ANDD. J. MILLEN, J. Chem. Sot. A 336 (1966). W. H. FLYGARE AND W. D. GWINN, J. Chem. Phys. 36, 787 (1962). W. GORDYANY 1~. 1;. COOK, “Microwave Molecular Spectra,” Wiley-Interscience, New York, 1970. RI. C. L. GERRY, J. Mol. Spcctrosc. 45, 71 (1973). R. W. DAVIS ANDM. C. L. GERRY, J. Mol. Spectrosc. 57, 118 (1975). J. K. G. WATSON,J. Chem. Phys. 46, 1935 (1967). G. W. KING, R. M. HAINER, ANDP. C. CROSS,J. Chem. Phys. IL27 (1943). I’. HELMINGER,R. L. COOK, ANDF. C. DELUCIA, J. Mol. Spectrosc. 40, 123 (1971). J. M. DOWLING,J. Mol. Spedrosc. 6, 550 (1961). E. B. WILSON, JR. ANDJ. B. HOWARD,J. Chem. Phys. 4, 260 (1936). K. L. COOK, F. C. DELUCIA, ANDP. HELMINGER,J. Mol. Spectrosc. 53, 62 (1974). R. L. Coors, F. C. DELUCIA, AP;DP. HELMINGER,J. Mol. Strwt. 28, 237 (1975). IV. H. KIRCHHOFF,J. Mol. Spectrosc. 41, 333 (1972). K. YAMADA AND M. WINNEWISSER, 2. Nutwforsch. Teil A 31, 131 (1976). R. L. COOK, F. C. DELUCIA, ANDP. HELMIXGER,J. Mol. Spectrosc. 41, 123 (1972). D. KIVELSONANDE. B. WILSON, JR., J. Chem. Phys. 20, 1575 (1972). H. H. NIELSEN, Rev. Mod. Phys. 23, 90 (1951). I. R. BEATTIE AND H. CHUDZYNSK.~,J. Chem. Sot. A 984 (1967). I). R. HERSCHBACHAND V. W. LAURIE, J. Chew Phys. 40, 3142( 1964). J. H. MEAL AND S. R. POLO, J. Chem. Phys. 24, 1126 (1956). E. B. WILSON, JR., J. C. DECIUS, AXI) P. C. CROSS, “Molecular Vibrations,” McGraw-Hill, New York, 1955. S. R. POLO, J. Chrm. Phys. 24, 1133 (1956). J. KRAITCHMAN,Am. J. Phys. 21, 17 (1953). C. C. COSTAIN, J. Chem. Phys. 29, 864 (1958). ‘I’. OKA, J. Phys. SOL.Japan 15, 2274 (1960). I). R. HERSCH~ACR AND V. W. LAURIE, J. Chem. Phys. 37, 1687 (1962). K. T. CWNG AND P. M. PARKER, J. Chem. Phys. 43, 3869 (1965). B. BEAGLEY, G. H. EIDERSLEY, D. P. BROWN, AND D. TOMLINSON, Traits. Faraday Sot. 65, 2300 (1969). H. 0. HOOPERANDP. J. BRAY, J. Chem. Phys. 33, 334 (1960). A. GUARNIERI, 2. Naturforsch. Teil A 25, 18 (1970). T. BEPPU, E. HIROTA, AND Y. MORINO, J. Mol. Spectrosc. 36, 386 (1970). W. C. EYKEN AND K. HEDRERG,J. Chem. Phys. 58, 2195 (1973). I. HARGITTAI,Acta Chim. Acad. Sci. Hung. 60, 231 (1969). P. J. BRAY, J. Chem. Phys. 23, 703 (1955). C. W. HOLT ANDM. C. L. GERRY, Chem. Phys. Lett. 9,621 (1971). M. HARGITTAIANDI. HARGITTAI,J. Chem. Phys. 59, 2513 (1973). U. P. VAN EIJC~, A. J. KORTHOF,ANDZ. C. MYLHOFF,J. Mol. Stnrd. 24, 222 (197.5). R. KEWLEY, K. S. R. MURTY, AND T. M. SUGDEN, Trans. Faraday Sot. 56, 1732 (1960). L. PAULING, “The Nature of the Chemical Bond,” Cornell Univ. Press, Ithaca, N. Y., 1960. R. W. DAVIS ANP M. C. L. GERRY, 1. Mol. Specfrosc. 60, 117 (1976).
OF MOLECULAR
SPECTROSCOPY
65, 455-473
(1977)
The Quadratic Potential Function and Average Structure of Sulphur Dichloride, SC12, from Its Microwave Spectrum R. WELLINGTON DAVIS AND M. C. L. GEKKY Department oj Chemistry, The University of British Columbia, Vancower, British Columbia VdT lW5 Canada
The microwave spectra of 32S3sC1~ in the ground (000) and vz = 1 excited vibrational (010) states, and of 32S36C187C1 in the (000) state, have been measured. Values of the quadratic potential constants have been determined from the centrifugal distortion constants and the variation of the inertial defect with vibrational state. A partial substitution structure has been evaluated. The potential function has been used to obtain average structures of 3*S36C1~ in the (000) and (010) states. The frequencies of the three fundamental vibrations have been predicted, and agree extremely well with observed values. A comparison the bonding in SC12 and related molecules.
of 32S36C1~ is made of
INTRODUCTION
The microwave
spectra
of triatomic
information
about
a wide variety
centrifugal
distortion
constants,
bond
lengths
and angles,
molecules
of molecular
have
been
constants,
nuclear
quadrupole
and potential
functions.
used
including
coupling
to provide rotational
constants,
In favorable
accurate constants,
dipole moments,
cases,
such as those
of
structures, as well as SOZ (I), 03 (21, OF2 (3), and Se02 (41, average and equilibrium the quadratic and cubic potential constants, have been determined. Though determination
of the average
and
ground-state
the
structure
requires
normal
requires
results
knowledge
rotational
also knowledge
vibration,
There
structure effective which
of the rotational are often
has been one previous
study
of only
constants, difficult
constants
of the microwave
effective
quadrupole
structural
coupling
parameters,
constants
were
molecular
determined.
commonly
quoted
values
force
field
equilibrium
states
of the
dipole However,
for the fundamental
of sulphur
of the ground
measure the centrifugal distortion constants or to refine The Raman and infrared spectra of sulphur dichloride most
in excited
spectrum
et al. (5), in which several low .7 transitions of the 32S3”C12molecule were measured. Values
state
of the
of each
to obtain.
by nlurray constants,
the harmonic
calculation
ground-state
moment,
dichloride,
(000) vibrational rotational
and accurate
no attempt
the molecular structure. have both been observed.
vibrational
55C1
was made
frequencies
to The
are those
of Stammreich
et al. (6), namely,
514, 208, and 535 cm-’ for ~1, ~2, and ~3, respectively.
Several
of workers
have derived
groups
dichloride However,
using these considerable
potential
Copyrigllt All rights
constants
@
frequencies disagreement
in the various
1977 by .\cademic
of reproduction
(6-11)
Press,
in any form
quadratic
and early electron has been found potential
functions.
potential
functions
for sulphur
diffraction structures (12, 13). for the values of the quadratic This is not surprising
since,
with
Inc. reserved.
ISSN
WZZ-2852
456
DAVIS AND GERRY
only three pieces of data available to determine the four potential constants, assumptions were necessary to derive a potential function. 1n addition, a recent study by Savoie and Tremblay (14) of the infrared and Raman spectra of gaseous, liquid, solid, and matrix isolated sulphur dichloride has suggested that the band previously assigned to 0~3at 535 cm-’ (6) was spurious, that in fact wl and w3 were separated by 9 cm-l or less, and that the assignments of wr and w3 were not certain, although polarization measurements and force constant calculations made the choice wa > WI most likely. For these reasons it seemed useful, as the quadratic potential constants can be written explicitly in terms of the quartic centrifugal distortion constants (15), to obtain sufficient data to evaluate a quadratic potential function based solely on microwave results. In the present study rotational transitions of 32S35C1~ in the ground vibrational state (000) have been measured up to _7 = 60 and in the v2 = 1 excited state (010) up to J = 14. Several transitions of 32S35C137Clup to J = 40 have also been measured in the (000) state, enabling a partial substitution structure to be determined. A quadratic potential function has been derived which is consistent with all the available experimental data, including centrifugal distortion constants, vibrational frequencies, and inertial defects. From this the average structures of 32S35C12in the (000) and (010) states have been calculated. EXPERIMENTAL
METHODS
Measurements were made in the frequency region 12.5-40 GHz using a conventional 100 kHz Stark modulated spectrometer having a 3 m X-band cell. The source was a Hewlett-Packard 8400 B Microwave Spectroscopy Source containing an appropriate backward wave oscillator. The estimated accuracy of the measurements was better than ~0.1 MHz. The sample of sulphur dichloride was obtained from Matheson, Coleman and Bell and purified by vacuum line distillation. This procedure was repeated each day before running, primarily to remove the more volatile chlorine formed by decomposition of sulphur dichloride. Although all spectra were obtained with the cell cooled with dry ice, conditioning of the cell and sample decomposition were problems, as was the case in the previous study (5). Flowing the sample was found to be advantageous to obtaining strong signals, but periodically after warming to room temperature the cell was found to attenuate the microwave radiation and it was necessary to disassemble and clean it, as well as to replace the mica windows. Sample pressures employed were typically 5-30 pm. OBSERVED
SPECTRUM
AND ASSIGNMENT
A rigid rotor spectrum was predicted for the s2S3”C12species using the rotational constants and quadrupole coupling constants of Murray et al. (5). Hyperfine patterns were calculated by diagonalizing the coupling Hamiltonian for two quadrupolar nuclei using a general computer program with the coupling scheme J + 11 = F1, F1 + 12 = F, where IL, I, are the nuclear spin vectors, J is the molecular rotational angular momentum, and F is the total angular momentum. When values of the quantum number I, associated with the vector I, were required, the alternative coupling scheme II+ 12 = I, I + J = F was used, with the matrix elements of Flygare and Gwinn (16) being used
MICROWAVE
SPECTRUM
OF SClz
457
to construct the Hamiltonian. This was often necessary for the “2S3”Cl~species where it is required that the total wavefunction (the product of electronic, vibrational, rotational, and nuclear spin functions) be antisymmetric with respect to interchange of the identical chlorine nuclei. The electronic and vibrational wavefunctions are symmetric for both the (000) and (010) states. For the rotational wavefunctions, using the JKGK, notation, with e and o referring to even and odd K, we have symmetric functions when K,K, is ee or oo and antisymmetric for the eo and oe cases. Since the spin of chlorine is 3, the nuclear spin functions are symmetric for I = 3 or 1 and antisymmetric for I = 2 or 0. For the b-type transitions observed only symmetric spin functions need be considered for eo +-+ oe rotational transitions and antisymmetric spin functions for ee ts oo rotational transitions. The latter had rather simple patterns, and were readily recognized by a strong component at the unsplit line position. For the 3?PC1”7Cl species, where the chlorine nuclei are no longer equivalent, all spin functions had to be considered and the observed patterns were necessarily more complex. Using these predictions, additional low J R-branch lines and Q-branch transitions of the series J”,J-~ +-- Jl,J-l, which formed a bandhead at -29.9 GHz, were found. The 111+- OoOand JI+_~ +- Jo,~ ground-state transitions all had vibrational satellites which on the basis of relative intensities were assigned to the (010) state. Only the ee ++ oo transitions of this series were measured, as the low dipole moment (0.36 D (5)) made overlapping of Stark components and zero-field hyperfine components difficult to avoid for the complex eo ++ oe transitions. Additional lines for the excited state were located after the first transitions measured had been fitted using a rigid rotor model. The rotational constants of 32S35C137Cl were first estimated using the effective structure derived for “2S35C12.Values for the quadrupole coupling constants of %35Cl”7Cl were obtained by transforming the results for “?Y”Cl2 (5) to the 3?S35C1:(7Cl inertial axis sy-stern. and assuming that in the bond axis system the 37Cl coupling constants could be obtained by dividing the corresponding 3”C1values by 1.2688 (the ratio of the quadrupole moments of 35Cl and 37Cl) (17). The resulting coupling constants are in Table 1. Several low J transitions were then easily found, although some hyperfine patterns were very complex and so overlapped by Stark components that accurate frequency measurement was difficult. Curiously, the intense J~,J_~ +- J~,J-I Q-branch series had a bandhead at -29.8 GHz, quite close to that of the YPCl2 species. The remainder of the YPCl~ and 3”S3”C137Classignments
were made using the bootstrap
procedure,
now including
cen-
trifugal distortion constants, which has been described earlier (18, 19). The observed hy perfine structure, especially at intermediate values of J, was extremely useful in confirming assignments. An example of the hyperfine structure observed for the 32S3Ui7CI species is also given in Table 1, along with the assignments, relative splittings calculated using the derived quadrupole coupling constants. ANALYSIS
OF THE OBSERVED
intensities,
and
SPECTRA
The “unsplit-line” frequencies of the measured transitions were estimated using the measured hyperfine patterns. Almost all of the measured lines were symmetric and the procedure was thus simplified. The resulting frequencies were then used to calculate the rotational and centrifugal distortion constants. The calculations employed the
458
DAVIS AND GERRY
TABLE 1. A REPRESENTATIVE TRANSITION (Miz) 01’ 3%35C137C1 SHOWINGNUCLEAR Q”ADR”POLE l,YPERFINE STRUCT”RE
14.5
13
5.05
38553.71
38553.73
14.5 17.5
16 16
6.18 6.18
38554.14 38554.27
39554.24
17.5
19
7.32
38554.65
38554.6G
15.5
14
4.43
38558.10
36558.13
14.5 17.5 17.5
15 18 17
5.29 1.34 6.14
38558.54 38558.61 38558.68
38558.67
16.5
18
5.60
38559.07
c
14.5
14
4.54
38559.60
15.5 16.5
17 15
ti.14 5.29
38559.97 3S560 ,119
36560.03
17.5
18
5.49
jS560.51
38560.57
16.5
18
1.3G
38560 .YS
15.5
15
5.73
38564 .Ol
38564 .Ob
15.5 16.5
16 16
5.28 5.44
38564. .i? 38564.52
%5b.I.
16.5
17
6.46
38564 .Y?
38564 .Y3
%l
x
S7C1
“The b
F labels
of
these
Data is given only for of the total intensity.
‘Observed
dvieak “reduced”
but
overlapped
component
--
Hamiltonian
not
x
= -37.85
ad
= -31.61
aa
byperfine those
n = 1.529
Pllz
17 = 1.386
are
the
components
by interfering
.?
blllz
components hyperfinc
0
Stark
same for with
both
rotational
an intensity
IO
levels.
greater
than
1%
components.
observed.
of Watson
(20) in the I’ representation
(21)
:
%=%2+XD+XD’, XR
=
(1)
AP,2 + B&F + Cp,z,
X0 = --A$”
-
A,,p2pz
-
(2) AKP2 -
26Jp2(pbz -
x0’
= H#
+ H.,,@pf + (&
+ H&@> - p,2)[h.,p4
P,2)
s,[Pa(IQ
-
i),2) +
(Pbf -
i);vYJ,
(3)
+ Hda6 + h.,i$2~,2
+ h&z41
+ [h_rp4 + h.r&2~a2 + h.r&](pb2
- PC”).
(4)
In these equations the angular momentum P has components P,, Pa, P,; A, B, C are the rotational constants; AJ, AJR, AK, 65, 8~ are the quartic centrifugal distortion constants; and HJ, HJK, HgJ, HK, hJ, hJK, hi are the sextic distortion constants. The spectra were fit, by a linear least-squares procedure, to the rotational constants and centrifugal distortion constants, using the first-order energy expressions of a semirigid prolate rotor in a rigid rotor basis (22). The parameters
thus obtained were inserted into
MICROWAVE
SPECTRUM OF SClz
459
the complete Hamiltonian and used to calculate the transition frequencies exactly. The difference between these frequencies and the first-order frequencies represented the these were subtracted from the observed frehigher-order distortion contributions; quencies and the resulting values were refit using the first-order expression. The process was repeated until convergence was attained. In all calculations double precision (16 digit) arithmetic was used. Only a partial set of sestic constants could be detemrined for 32S3LC12 and 32S35C137C1 using the available data. For the (010) state of 32S35C1~, where only a small number of low J lines was measured, the centrifugal distortion contributions were assumed to be the same as for the (000) state. These contributions were subtracted from the measured frequencies and a fit was made to three rotational constants. Table 2 contains the frequencies and assignments of the measured transitions, with hype&e structure removed, along with the calculated frequencies and distortion corrections. The values obtained for the rotational constants and distortion constants are given in Table 3. They fitted the observed transitions with rms deviations of 0.047, 0.035, and 0.063 MHz and average deviations of 0.033, 0.021, and 0.047 MHz for the (000) states of ?PClz and 32S35C137C1 and the (010) state of ?S3X12, respectively.
THE HARMONIC
POTENTIAL
FUNCTION
The analysis of the microwave spectrum of sulphur dichloride has yielded two types of data which, within the framework of the small oscillations model, can be directly related to the intramolecular harmonic (quadratic) potential constants. These are the quartic centrifugal distortion constants, which were obtained using the method of the previous section, and the inertial defects in the ground and exited vibrational states, which were obtained from the rotational constants by the methods described below. These two sets of data were combined to obtain accurate potential constants, which were used in turn to predict the average structure Ijowling
the fundamental
vibrational
frequencies
of 32S3”C1:! in the (000) and (010) vibrational
(23) has shown that for a planar
asymmetric
and to calculate
states.
rotor in its equilibrium
con-
figuration there are only four independent quartic distortion constants. In the notation of Wilson and Howard (24) they may be conveniently chosen as 7anaa, 76666, 7cccr, and ~<~b,~b. Furthermore, for a triatomic molecule XV*, having Cz, symmetry, there are three normal vibrations:
two are totally symmetric,
of species Br. For a potential
function
of species Al, and the other is asymmetric,
written
in terms of symmetry
coordinates
there
are four force constants. They may be obtained from the four centrifugal distortion constants via the elements of the inverse potential constant matrix using espressions derived from those of Herberich et al. (15) with Dowling’s equations (13) :
(F-l)LI
=
-
R sin24 cos24 __2
A cot24 - B
~__
B tan?+ - A ‘Tama
A”
+
AR Tbbb5
I?3
+
-
Tcccc
C4
1 (5) ,
ii
1. 2.
-
-
2;72i 4.11) 2.14) V.14) V,l)J 2,161
61
0, 21 2( 2( 31 4, Ul 4,
121 I,( 11, 12( 13( 10, 13, 16( 16( 16, 16, 16, 171 1st 18,
-
-
-
-
20( 20( 21( 21, 211 221 22i 221 23( 24, 251 25( 25( 26, 26( 261 27( 28( 29( 2Y( 30( 30( 30( 31, 31,
2oi
91 10,
-
-
7( 81 9( lO(
-
71
- ii - ii
-
31 2) 3) 2) 5) -
1.17) 5,13) 3.17) 2.18) 211 1.21) 21 I 5.17) 21, 5.161 22( 4.79) 221 6.16) 221 6.17) 23, 3.21) 23i 0.17) 231 4.20) 241 4.20) 25( 9.22) 261 6.201 26( 5.21) 26 I b.21) 271 3.25) 271 4.291 27i 5.23) 281 5.23) 291 5.24) 30, 7.210 30, 5.26) 31( 8.23) 31( 8.24) 31, 6.26) 32f B..7V 32~ 8.25)
171 171 17( 171 1Si 19, 1st
16i
14,
14,
101
2.
01 2) 1, 2)
1. 3) 0. 91 1, 3) 0. 41 0. 6) 1, 5) 1. 7) 2. 6) 3. 5) 1. 71 1. 81 1. 9) 2. 8) 0,lO) 1.11) 3. 91 4. 8) u, 8) 1.121 1.13) 5. 8) 1.15) 5.10 5,12) 3.13) 2.14) 6.12) U.l(o 3.15) 2,191 6.19) 6.15) 5.16) 7,151 7.14) 4.18) 7.16) 5.17) 5.19) 5-19) 7.19) 6.20) 7.18) 4.22) 5.21) 6.20) 6.22) 6.23) 8.21) 6.23) 9.22) 9.21) 7,23) 9.23) 9,221
0. 0. 1. 0.
state) -
ROTATIONAL
vibrational
2. 01 -
:: :;
(ground
1. 2. 1. 1. 5) 2. 4) 81 0. 8) 8, 1, 7) 81 2. 6) Pi 2. 61 9, 2. 7) 101 2. 8) 1. 91 loi 1. 9) 121 1.10) 121 2.101 12, 3. 91 131 3.11) 131 2.111
32S35C12
TABLE
17044.19 12688.11 35091.60 26527.86 37291.67 14573.30 33615.87 351u3.10 17881.46 31828.24 35128.01, 15253.30 -14560.68 30370.45 29983.31 29930.u2 29137.68 30046.23 31088.97 13435.39 -1738U.21( -13429.93 32406.93 3427U.37 -31552.96 39766.13 -14808.74 -13908.38 12849.70 -14716.81 -33960.09 15710.32 12067.07 -36110.07 -16553.83 -16216.57 12753.01 -35509.10 -35535.71 27017.12 -29835.67 179BZ.OY 39379.69 27800.80 -12501.47 14795.95 -12691.58 28319.52 36337.36 17932.92 28694.74 36136.75 -14652.50 34598.95 -33867.00 -33872.19 16668.24 -28158.19 -28166.70
TRANSITIONS
(Hz)
17044.19 12688.08 35091.50 26527.77 37291.62 19573.35 33615.84 35143.12 17881.35 31828.19 35128.06 15253.36 -1U560.69 30370.50 29903.35 29930.53 29837.70 30096.25 31088.96 13035.28 -17384.22 -13u29.91 32806.96 3Ui71.36 -31552.98 39766.13 -14808.70 -13908.38 12849.73 -14716.82 -33460.17 15710.32 12867.06 -36110.06 -16553.M -16216.64 12753.05 -35509.10 -35535.72 27811.13 -29835.68 17982.02 34379.72 27800.89 -12501.43 111795.94 -12691.63 28319.50 36337.35 17932.92 2869U.77 36136.72 -14652.52 3U598.95 -33866.96 -33872.14 16668.23 -28158.11 -28166.68
OF S"LPH"R
-0.10 -0.09 -1.77 -0.01 -1.64 -0.10 -1.011 0.05 -0.54 0.12 -3.28 -4.52 1.95 1. 31 1.65 1.60 -10.12 -6.01 -0.52 -16.20 2.16 0.15 -3.09 -7.03 17.99 -20.12 -5.26 -9.29 5.12 10.68 22.36 -25.55 24.86 97.93 -15.11 -17.97 -55.49 25.32 25.62 -6.95 7.98 -65.03 -159.28 -78.94 -54.89 -131.99 -51.'95 102.47 -79.02 -119.05 -207.84 -255.82 -80.96 -170.63 -10.98 -10.82' -1811.59 -1t9.64 -44.37
DICllLORIDE
0.03 0.10 0.09 0.05 -0.05 0.03 -0.02 0.11 0.05 -0.02 -0.06 0.01 -0.05 -0.04 -0.11 -0.02 -0.02 0.01 0.11 -0.02 -0.02 -0.03 0.01 0.02 -0.00 -0.09 -0.00 -0.03 0.01 0.00 0.00 0.01 -0.01 0.03 0.01 -O.OU 0.04 0.01 -0.01 0.01 0.02 -0.03 -0.09 -0.04 0.01 0.05 0.02 0.01 0.00 -0.03 0.03 0.02 -0.00 -0.01) 0.00 0.01 -0.08 -0.02
0.00
-2
2( 3( 4, 5( B‘, at 9, lO( '101 14(
II II 2, 0) I. 2) 1. 3) 1. 5) 2. 6) 0. 8) 2. 7) 2, 8) 1. 9) 2.12)
11 1. 2, 1.
1,010~
33i 6.27) 33( 6,28) 3U( 8.27) 34, 6.29) 3Ul 8.26) 35( 7.29) 351 Y.27) 35, 7,281 36( 9.28) 37( 7.31) 381 7.32) 39( 8.31) 39( J,31) 39( 9.30) 39( 8.32) 40(10,30) 40(10,31) U2( d.34) 93l10.33) 43(10,34) 43( 8.35) U3f 8.361 44( 9;36j 44, 9.35) 46( 9.38) Qb( 3.37) 47(11.36) U7( 9.39) 47( 3.38) 48(10,38) UB(lU.39) 5O(lU,40) 50(111.41) 51(10.~1) 56f11.46) 56(11,45) 57(14,43) 57(11,45) 57(11,46] 58(14,45) 59(12,Y7) 59l12.48) 6Oll4.47) 60112.48) 6Ot12.49)
32S35C12 (gmund
-
-
21 2( 3f 4( 4( 8( 71 91 101 lot 141
0,
0, 0, 21 1. 1) 1, 31 0. '0 0. 4) 1. 7) 1. 7) 1. 8) 1, 9) 0.10) 1,13)
0.
32, 7.26) 32, 7.25) 331 9,2U) 331 7.26) 33( 9.25) 3U, 8.26) 34(10,24) 3U( 8.27) 35(10,25) 36( R,ZR) 37( 8,ZY) 3R( 9.30) 38f10.28, 38(10,29) 38( 9.29) 39(11.29) 39(11,28) 41( 9.33) 42,11,32) 42(11,31) 42( 9.34) 42, 9.33, 43ilO;33) 43(10,3U) 45(10.35) "5(10,36, 46(12,35) 46,10.36) 46(10,37) u7,11,37, 47(11,36) u9,11,39, UY(11.38, 50(11,40, 55112,431 55(12,410 56,15.42, 56,13,"(1) 56f13.43) 57,15,U2) 'X(13,46) 58f13.45) 59(15,94, 59(13,U7) 59113.46)
state1
-
vibrational
state)
17158.90 12813.97 35456.89 37666.03 14705.97 35214.68 30697.11 3u900.00 30299.14 30234.66 30225.48 34532.63
31414.74 28529.79 -16653.32 34u29.35 -16631.11 14852.58 -35876.C3 15381.94 -30172.3" 26923.09 32997.62 13003.43 -12873.02 -12861.39 12816.52 -32184.lU -32185.13 ?1591.85 [email protected] -14918.62 37984.19 37162.20 16697.03 16792.23 28823.14 29027.53 -16974.70 34954.22 352U9.19 14550.75 14518.69 26635.54 26565.42 32755.91 36412.35 36462.65 -34605.95 16059.53 1605U.Ul -28944.96 -28017.72 28006.35 -17483.10 34052.96 3U036.27
(continued)
17150.82 12813.91 35456.83 37666.1U 14706.01 35214.67 30697.1U 39980.02 30299.11 30239.69 30225.52 31t532.55
31414.78 28529.711 -16653.32 311$29.37 -16631.10 14852.58 -35876.02 15382.OU -30172.23 26923.07 32997.62 13003.46 -12873.00 -12861.UO 12816.51 -32184.24 -32185.15 31591.76 -11191".87 -7U918.65 37988.11 37X2.1.8 16697.04 16792.26 28823.10 29027.50 -1697e.73 3495u.25 35249.20 111550.78 14518.73 26635.54 26565.42 32755.99 36412.32 36462.66 -34W5.96 16059.54 16054.111 -25944.90 2RC17.70 28006.32 -171t83.19 34053.00 34036.27
-0.11 -0.09 -1.77 -1.6" -0.10 0.05 1.32 -3.28 1.65 1.60 -6.01 -7.03
-313.uu -2rrT.73 -118.28 -276.29 -119.06 -260.67 -29.61 -277.61 -72.19 -397.30 -392.99 -356.76 -215.65 -216.26 -348.18 -108.67 -108.61 -550.46 -289.32 -280.06 -627.8(1 -582.86 -515.61 -521,91 -660.03 -674.74 -365.33 -737.81 -759.d9 -646.RU -644.01 -822.33 -815.61 -918.19 -1208.95 -1215.69 -468.92 -1066.87 -1066.08 -580.21 -1307.84 -1305.96 -815.62 -1U36.90 -1434.011
-0iOS 0.01 -0.03 -0.02 0.03 -0.03 -0.011 0.08
0.06 0.06 -0.11
0.08
0.05 -0.00 -0.02 -0.01 0.00 -0.01 -0.10 -0.11 0.02 -0.00 -0.09 -0.02 0.01 0.01 0.70 0.02 0.09 0.04 0.03 0.08 0.02 -0.01 -0.03 0.09 0.03 0.03 -0.03 -0.01 -0.03 -0.04 -0.00 0.00 -0.08 0.03 -0.01 0.01 -0.01 0.00 -0.06 0.02 0.03 o.ov -0.04 -0.00
-0.04
E *
8
5
M
8
MICROWAVE
SPECTRUM
Distortion Correction
Calculntcd Frequency
E, 9, 10, I,( 12, 111, 15, 16, 17, 19, 22, 22, 22, 23, 23, 23, 24, 26, 26, 27, 27, 28, 28( 30, 31, 31,
35, 35, 35, 36, 36, 37, 37, 39, 39, 39, 39, 110, uo,
R (F-‘)r:!
=
-
E 9 10 11 12 14 15 16 16 16 21 21 21 22 22 22 23 25 25 26 26 27 27 29 30
6.26) 6.27) 8,28) b.30) 7.30) 7.29) 9.29) 9.28) 9.30) 9.31) 7.33) 7.32) 8.32) 8.33)
-
30 34 34 34 35 35 36 3h 38 38 38 38 39 39
9.26) 9.25) 7,271 9.271 6.26) 0,26) 0.271 0.29) 0.29) 9.30) 9.31) 9,313 9.301
COSTS
R(tan
sin24
4
-
cot
4)
-
2d cot
-
De".
-0.05 -0.01 -0.02 0.07 0.01 -0.01 -0.01 0.01 -0.03 0.03
1.34 1.74 1.79 1.31 0.08 -5.65 -1O.bA -17.u9
30324.67 29897.90 29778.20 3oc31.09 30712.70 33545.54 35768.35 38559.35 -16OOQ.22 13899.20 -13477."3 -13041.79 15504.53 -32496.02 -32531.58 15316.50 -27005.30 -1569U.4, -15845.03 -35007.11 -34995.36 -29471.70 -29452.27 30536.30 -12655.18 12663.06 -15122.20 -15147.86 35707.95 16144.67 16735.50 -28871.53 -28871.30 -17651.92 -11660.11 33832.47 35523.78 13806.36 13603.09
30324.62 29897.89 29778.18 30031.16 30712.71 335s5.53 35768.34 38559.36 -16009.25 13894.23 -,31177."U -13041.75 15504.54 -32'495.98 -32531.56 15316.52 -27005.38 -1569U.40 -15845.02 -35007.09 -3U995.32 -29471.72 -29952.33 30936.25 -12655.17 12663.09 -15122.,8 -15147.811 35707.97 161911.68 16735.47 -28879.54 -28871.30 -17651.92 -17660.11 33832.47 35523.78 13806.35 13603.10
1. 7) 1. 8) 1. 9) 1.10) 1.11) 1.13) l.lQ) 1.15) 5.12) Q.lU) 6.15) 6.16) 5.77) 7.16) 7.75) 5.17) 7,161 7.19) 7.181 8.18) 8.791 8,193 8,201 6.23) 6,22) 7.23)
2, 6) 2. 7) 2, 8) 1. 9) 2.10) 2.12) 2.13) i,lU) U.13) 3.17) 5.18) 5.17) 4.18) b.17) b.18) 4.20) b,19) 6.20) b.21) 7.21) 7.20) 7.22) 7,21) 5.26) 7.25)
461
OF SCln
-7.30 -25.69 -26.58 -30.52 -88.87 11.42 11.85 -62.01 -5.86 -08.03 -45.75 7.20 6.98 -17.11 -17.51 -165.74 -101.16 -172.70 -1U3.36 -1112.42 -292.54 -282.51 -302.06 -99.69 -99.84 -193.33 -192.91 -414.49 -478.78 -382.95 -373.35
-0.01 -0.01 0.01 0.01)
0.02 0.02 -0.06 0.01 0.01 0.02 0.04 -0.02 -0.06 -0.05 0.01 0.03 0.02 0.02 0.02 0.01 -0.03 -0.01 0.00 0.00 0.00 -0.00 0.00 -0.01 0.01
@ raaaa
A”
2(2Y A(tan
4
-
cot
4)
+
2B
+
tan
Rmx [ mx1 . B3
2rnlr
(F+)33 = - 2~
1 + __
sin2+
z
fj3
AB(tan Tbbbb
-
4
-
C4
cot
4)
1 (7) (8)
Tcccc )
Here R = r'X lO_**/2/z, with r the X-Y bond length; 4 is one-half the bond angle; M is the molecular weight with M = mx + 2m Y. With Planck’s constant h in erg seconds and r in angstroms the force constants F 11, FIZ, F22, and F33, obtained by inverting the matrix calculated above, are in dyne cm-l. They are defined as Fll = f7 + frr, F22 = jJr2, FIZ= 2ijTm/r, and F33= jr- jyr. Though strictly Eqs. (S)-(8) apply only for the equilibrium values of the various molecular constants, a good approximation can be obtained using effective ground-state values. To obtain the potential constant matrix using Eqs. (S)-(8), the four distortion constants 7,,,,, Tbbbb, 7cceo and 7abab must first be calculated from the experimental distortion constants. Watson (20) has shown that a set of five “determinable” distortion Constants, T,,,,, Tbbbb, 7cccc, ?-I, and 72, may be calculated as linear combinations of our experimental quartic constants A J, AJir, AK, 6~, 6~ using the relations summarized in
462
DAVIS AND GERRY
TAHLt. 3.
A
RO’I’ATIOUAI. CONSTANTS’ AND CENTRI,U;AI. COUSTAN’I’SU,li SIILI’IIUR DICIILORIDE
g:rO”“J vibrational state
14613.5968
IIISTOIITION
(0101
vibrational state
(53) I,
14732.830
(10)
14490.169
(21)
”
291O.8702
(11)
?918.3174
(341
2841.1929
(47)
C
‘243lJ.6943
(10)
2126.lfliZ
(341
2371.963.1
(35)
x 103 *J AJL: x 102
-1.4604
AK 65 %
1.3249
(251
,T
(3iI
,:
Y 10’
1.3802:
x 104
3.3968
(50)
x 103
n.927
11-1)
(70)
1.239 -1.440
r?
1.357
/a
3.168 3.62
iiJK x 10’ “KJ
-2.56
* 107
3.55
x 101 “J * IO’ h JK
C(:entrifugnl
-5.0 2.7
distortion
assumed
to bc
the
same a5 for
the
ground
(13) (13) (2) (35) 121)
(68) (1.15) (2.21 11.01
state.
Table 4. The harmonic force constants of the A1 vibrations (Fll, F12, F2.J can now be obtained directly from +ranaa, Tbbbb, and 7cece using Eqs. (s)-(7). Though the force constants still depend on the validity of the planar assumption, they have usually been found to give good values, to within 5% or better of the corresponding vibration frequencies, even for the very light molecules Hz0 (2.5) and H2S (26). The force constant for the B1 vibration (F& is much more difficult to evaluate. By Eq. (8) it is related to T&b, which is not one of Watson’s determinable parameters. It can be estimated in a variety of ways (25, 27-29) from 71 and/or 72 using Dowling’s planar relations (23), which are also given in Table 4. Because of vibrational effects the values of T&b thus obtained vary widely, depending on the method used to determine them. Consequently the derived value of F33 is rather uncertain, and the prediction of the B1 fundamental frequency is usually much worse than those of the A1 fundamentals. Table 5 contains the five determinable parameters of 32S35C12 in its ground vibrational state, calculated from the experimental distortion constants by the equations of Table 4, part a. The Constants roana, Tbbbb, rcecc, and 71 were obtained directly. To evaluate 72, on the other hand, the rotational constants A’, B’, C’ were necessary; these are the rotational constants of Kivelson and Wilson (30) and are related to the experimental rotational constants by A’ = A -
16R,,
B’ = B + 16&(/l’
-
C’)/(B’
- C’),
C’ = C -
- B’)/(B’
- C’).
16&(A
(9)
MICROWAVE
SPECTRUM
OF SC12
463
The constant R, = - (~AJ f ~b,&,/32 is defined by Nielson (31). T&c was obtained sufficiently accurately from the planar relations and ground-state values for the rotational constants. The resulting values are also in Table 5, and are evidently very close to the Watson values A, B, C, in Table 3. Four different methods were used to calculate T&b in 32S35C12.These were: (i) from the value of rl and all the planar relations; (ii) from the value of 7~ and all the planar relations; (iii) from the planar relations for Taabb, T,~,,, Tb&, and Tbbee and simultaneous solution of the equations for 71 and 72; (iv) from the planar relations for 7aabb, T,,~,., 7aaco and Tb&c and simultaneous solution of the equations for ~1 and 72. The results and their uncertainties are also in Table 5. There is clearly a wide variation between the values calculated, and because of the nebulous nature of the vibrational effects it is virtually impossible to decide which value is the most accurate. The problem of choosing the correct value for T&b has been considered by several authors. Watson (20) pointed out that in the equilibrium configuration i-2 = CeT1 + (-4, + %)7,,,,. In the nonequilibrium a “planarity defect,”
configuration AT, by
(10)
this clearly is invalid,
AT = rcccc -
C(Q -
&)/(A
and Kirchhoff
(27) defined
+ B)].
(11)
This should provide some indication of the degree of breakdown of the planarity conditions. It has been calculated for x?S35Cla as (-4.5 =I=3.2) X lCV5 MHz, essentially TABLE
3.
Evaluation T
aaao
Tbbbb TCCCC ,I
=
4.
of
RELltTIONSHIPS
Watson’s
determinable
-4(AJ
+ A.,R
=
-.$(A,,
+ ?SJi
=
-4(A
=
!jabb
J
-
+ ?A,,,
RETWEEti CRNTRIII~G~~~. PISTORTION
parameters
(I’
?A,,) =
-J(A
,h
with 1~ =
+ 3AJ3
(X1-R’-C’)/(B’-C’I
relationsb
incnc=‘bcbc
=
123/ 0
representation)
+ A,)
J(?si,,
I’lonnr
COSSTANTS ’
+
Xii
-
“A,,)
+ r
(B’+C’) __ 1 (B’-C’I
1
464
DAVIS AND GERRY
a.
b.
Watson’s
Llcterminablc
x lo+’
-4.9899
f
0.003?
‘bbbb
x 10+3
-8.017
f
0.011
7 cccc
* lof3
-2.582
+ 0.011
fl
x 10+2
4.251
+_ 0.015
x2
x 10-1
5.88GG
c 0.042
Kivelson-Nilson
Rotational
14h13.5973
B’
2920.8586
r 0.0011
C’
2430.7054
_+ 0.0010
Values
of
baby
using
by
Value
x 103
-5.982
(ii]
-5.80
i. 0.22
(iii)
-6.89
+ O.tiS
(iv)
-6.02
i
Distortion
Constants
T&b
x IO2
‘bbcc
’
%Yandard Methods
CT2 is
Mcthodsb
(i)
T’aacc
b
x rOm5)
Different
Method
d.
Ek 0.0052
Rg = -2.9220
Obtained
in
Evaluated
lo3
c
Constants
A’
(obtained
C,
Parameters
T aaaa
0.20
0.22
Using
the
4.292
* 0.030
-4.365
A 0.008
1.592
x lo2
Planar
Relations
k 0.021
ermrs. are
described
in
the
text.
W%z’.
indeterminate, and so is of little use here. It should be noted as well that the difference in the values of r&b obtained from methods (i) and (ii) is given by (28) : Bralab
=
[(A
+
BIPClA7.
(12)
This too is indeterminate. Yamada and Winnewisser (28) have also shown that the planarity defect is only one of several factors defining the breakdown of the planarity relations. In any case knowledge of the existence of these factors still does not solve the basic problem of choosing the correct value of r&b. In an attempt to obtain a further measure of the effects of vibration on both the measured and calculated distortion constants, another fit to the experimental data was carried out. This time the planarity relations were used to eliminate one of the five distortion constants, and a iit was made to four constants, chosen to be raaaa, 7F,bbb, Toabb, and Taba&.The fit was again a first-order fit in a rigid rotor basis, and the rotational constants used in the planarity relations were the effective ground-state constants obtained earlier. As no account was taken of sextic distortion contributions, only transitions having J < 25 were used in the fit. The rms deviation was 0.055 MHz with
MICROWAVE
SPECTRUM
OF SClz
465
an average deviation of 0.044 MHz. The results of this fit (Fit II) are compared to those of the previous analysis (Fit I) in Table 6. In a further analysis (Fit 111) a tit to the four distortion constants Tanaa, ,-b,,bb, raabb, rabub Was made with a Value for the rotational constant C’ being obtained from the relation l/C’ = l/A’+ l/B’. These results are also reported in Table 6. Here the rms deviation between the observed and calculated frequencies was 0.049 MHz with an average deviation of 0.041 MHz. Excellent agreement is observed for the directly determinable spectroscopic constants A’, B’, C’, raaoa, and rbbbb. The agreement iS 1eSSSatisfactory for T,,,~ and raabb which have been compared using the planar conditions (see Table 4) and is very poor for ‘T&bThe large discrepancies between the values for rob0b obtained by various methods make its further use undesirable. The three force constants of the symmetric vibrations (Fir, FIB, and EBB)were calculated using the values of raaaa, 76666, and T,,,~ in Table 5 in Eqs. (5)-(7). The results are in Table 7. The rotational constants used were the effective ground-state constants A, B, c. The uncertainties given have been calculated assuming the errors in raaaa, Tbbbb, rcccc to be those given in Table 5 and the errors in the rotational constants to be the differences between the observed effective ground-state values and the values calculated from the average moments of inertia of the next section. The latter errors are several orders of magnitude larger than the experimental uncertainties and are responsible for the major part of the uncertainties quoted for the potential constants Err, FrB, and Fz2. These uncertainties should, however, give some indication of the model error. The corresponding vibration frequencies, wr and ~2, were then calculated, and are also given in Table 7 in comparison with experimental values of Savoie and Tremblay (14).
DAVIS
466 TABLE 7.
AND
GERRY
QUADRATIC POTENTIAL CONSTANTS AND RELATED PARAMETERS
-__ Potential
Derived
Value
FII
x 1O-5
2.913
?z 0.090
PI2
x 10-3
9.258
i- 0.55
F22 x 1O-4
2.624
f
F3? Y 1O-5
2.421
cent
*(OOOP
,WO) aaaa
dyne
0.021
II II
Observed
Value
’
=cccc Tab*
x lo3 x 103
0.0006
lo3
0.x.313
-4.9899
-4.9899
f
-8.0173
-8.0173
f
0.010s
-2.5823
-2.5829
f
0.0105
0.0032
a.
-6.7280 514.8
f
wi
206.9
+ 4
ZlP
w3
523.8
f
525 .sa
Wl
8
518.0aJc
5
aw1(%37C1,)
7.0
SkQ(34S35C12)
7.6
Sw,(3’S37C12)
6.1
6.0
aW3(3%35C12)
8.9
9.0
(Cz3)
Units
0.3086
0.8306
x lo1
‘bbbb
(513)
cm-’ ,I
0.5220
A2 A
Units
i- 0.01
Value Predicted from above force constants
Parameter
T
--
Constant
7sc 10
2
0.324
i- 0.003
2
0.676
-
e,(oon)
%atrix.
distortion
‘Liquid. ‘Reference 114). d Several values are Tables 5 and 6.
0.003
given
in
and C(O1”’ parts.
arc
sums of
vibrational
and centrifugal
f Obtained using Watson’s rotational constants A,B,C. Strictly the calculated values should be compared with inertial defects from Rivelson-Wilson constants, such as are given in Table 5 for the ground vibrational state.
(Somewhat different values have been obtained by other workers (6, 7, 32)). Though the calculated uncertainties in WI and wz to some extent neglect effects of zero point rather small, nevertheless vibrations in applying Eqs. (S)-(7), and are consequently the excellent agreement with the experimental values suggests that they are quite reasonable. Because of the range in experimental values for Taba?,it was not used to calculate the & force constant Fz3. Instead this force constant was calculated from a value of 03 obtained using inertial defect data. To obtain these inertial defects the measured rotational constants of all isotopic species and vibrational states were converted to principal moments of inertia. The resulting values, including the inertial defects, are in Table 8. The fact that the ground-state inertial defects are small positive numbers essentially independent of isotopic species is consistent with the planar structure of the molecule.
MICROWAVE
SPECTRUM
467
OF SClz
The experimentally determined inertial defect is the sum of vibrational, centrifugal, and electronic contributions, of which the vibrational contribution is by far the largest. The vibrational contributions to the inertial defects of %““C12 in the (000) and (010) vibrational states depend only upon the harmonic part of the potential function (9, 33) and are given by the following equations (4) :
A, = AVi,,(o’“)- AVi,,WW= 4K Here j-13and {23 (strictly {13@)and {23((z))are Coriolis coupling coefficients, and the factor K = h/8& has the value 16.85763 amu AZ cm-‘. Note that in Eq. (14) AZ is the dijerence between the ground and first excited state inertial defects. The centrifugal contribution is given by Acent = - 7&zh[(3r,‘/4C’)
+ (Ib’/B’)
+ (1,‘/2A’)],
(15)
where I,‘, Ib’, I,’ are principal moments of inertia obtained from A’, B’, C’, respectively; Acent will be assumed to be independent of vibrational state to the present accuracy. Finally, the electronic contribution is probably of the order of our experimental errors (9) and will be ignored. TARLE 8.
INERTIAL PARAMETERS=OF SULPHUR DIa,LORIDE
_3%3%x?
3%35C137CI
Ground vibrational state
rffective _.
Values-
IV a
34.58279
(I,!’
34.3fl291
I \’ b
173.02344
(7)
173.17479
(10)
177.87564
I” c
207.91549
(9)
2118.3n895
(30)
215.06357
(32)
,z”
0.30926
(11)
0.831?5
(35)
n.31n56
(44)
34.7366
gAll b
parameters
are
in
173.Rlh6
XX .0466
208.4068
n.on14
n.0013
a.m.“.
i?;
=
Tc -
Ib -
Ia
(2)
34.87737
34 .S889
173.3Cl86
the
conversion
factor
is
505379
are uncertainties in units of the last Nlrmbers in parentheses They reflect the uncertainties in the rotational constants.
@:
ground vibrational state
(010) vibrational state
a.m.“.
significant
i’
Pllz. figures.
(5) (30)
468
DAVIS AND GERRY
To use AZ to obtain w3 it is first necessary to calculate the Coriolis coupling constant {23; this was done using the equations of Meal and Polo (34) for an XY2 molecule: (i-13)~
=
[A,
(i-23Y
=
1 -
-
FII/(G-~)II]/(XI
-
As),
(16) (17)
(!T13Y,
where Xi = 4?r2c2w?are the roots of the A1 block of the secular equation 1FG - AE 1 = 0 (35). An expression for (G-‘)rr is given by Polo (36). It was calculated by an iterative method using first the effective structural parameters and later the average parameters, all of which are discussed in the next section. The value of Frr from Table 7 was used to obtain ({~a)~ and ({~3)~. These together with A2 calculated from Table 8 were then used in Eq. (14) to evaluate w3 and hence F33. Table 7 contains in all a summary of the derived quadratic potential constants along with the predicted and, where appropriate, observed values of the distortion constants, vibrational fundamentals, inertial defects, and Coriolis coupling coefficients. The calculated inertial defects A@O”)and A(OlO)are the sum of vibrational and centrifugal parts. The frequency of ~3, like 01 and 02, is in remarkable agreement with the measured frequency of Savoie and Tremblay (14). As indicated earlier, the quoted uncertainties in the calculated frequencies to some extent ignore zero point vibrational effects, but the agreement with experimental values confirms that the approximation is good. The predicted and observed vibrational isotope shifts of the symmetric isotopic species also agree extremely well, except perhaps for the shift observed for wr between 24S35C12and “2S35C12.This was apparently, however, the least accurately measured shift (14), and the quoted experimental uncertainties are f 1 cm- l. Finally, F33 was used to calculate rabab from Eq. (8) ; again a very reasonable value was found. MOLECULAR
STRUCTURE
OF SULPHUR DICHLORIDE
The CZ” symmetry of sulphur dichloride has been well established from previous electron diffraction (12, 13) and microwave results (5). The electron diffraction results were rather inaccurate, however, and the previous microwave results permitted the determination of effective structural parameters only. In the present work we have sufficient data to determine effective, partial substitution, and average structures for sulphur dichloride. The inertial parameters of the various SC12 species are collected in Table 8. These parameters have been derived using the rotational constants of Table 3. The effective structural parameters, ~0 and 00, are easily calculated using the ground-state moments of inertia of the %36C12 species. Because the inertial defect is nonzero, slightly different results are obtained when the three possible pairs of moments I,, Ib; I,, I,; and 15, Tc are used. These are all presented in Table 9. The mean effective structure is identical to that derived by Murray et al. (5). A partial substitution structure for sulphur dichloride has also been obtained. Kraitchman’s equations (37, 38) were used to estimate the coordinates of chlorine. The center-of-mass condition, 2; mibi = 0, yielded the b coordinate of sulphur ; its a coordinate is zero by symmetry. Again three possible structures can be calculated. These are also presented in Table 9 and are seen to be more self-consistent than the effective parameters.
MICROWAVE
SPECTRUM
469
OF SClz
Finally, the physically well-defined average structures of 32S35C12 have been found in both the (000) and (010) vibrational states. These average structures have been defined by Oka (39) and by Herschbach and Laurie (40). For a Czll triatomic molecule like SC12 they are obtained in general in any vibrational state using the following equations : (2v1 +
I,* = I,” + 3K
1) sin2X + (2v:! + 1) cos”X
(2213+ 1)(1,/I,) +
Wl
(2~1 + 1) cos2X +
Ib* = Isv + 3K C
I,” = T,v + 3K
w3
Wl
w2
(2~1 + 1)
(2% + 1) +
(2% + 1)
W2
w3
-
+
(202
+
1)
Wl”>
.r232 (Jz(w32
-
wz2)
W12 -
(2v3
(19)
(332 r132
wl(w32
(18)
1
W2
(22’1+ 1) [
w3
+
(-Ql
--a
(2~ +@I) sin2X + (2% + l)(IblIJ
1> 1,
+
{I32
1) 1
+
w&Q2 - WI”)
w22
(232
wa(w32- W?“)
II
)
(20)
where I,* and IOU are the average and effective moments of inertia, respectively, in the vibrational state in question, and K = (1z/Wc) has been evaluated earlier. The parameter X is determined from the equation
cos2x+ X23(Ib/le)~cosx+ rz.32- (IJIJ
= 0.
(21)
470
DAVIS
AND
GERRY
Here 123 is negative by convention (41). To use Eq. (20) in any vibrational state it is necessary in general that (wt - W) and (WQ- ~2) be fairly large. This is not the case here, since wr - 03. However, for the (000) and (010) states the equation is valid, since factors of (~3 - WI) all cancel. The resulting average moments of inertia and their corresponding inertial defects are presented in Table 8. The inertial defects are effectively zero in both vibrational states, as required. The average bond lengths and angles, obtained using various pairs of principal moments, are given for both vibrational states in Table 9. In both cases the bond lengths and angles calculated using different pairs are very consistent. As might be expected for different states of a bending vibration, the average bond length is essentially independent of vibrational state while the average bond angle is slightly larger in the excited state. These variations reflect the anharmonicity of the vibration. DISCUSSION
The harmonic force field obtained in this work has been obtained using solely microwave data. Two questions concerning it should be answered. First, does this potential function represent an improvement on results previously obtained? Second, is a combination of microwave and vibrational data likely to result in a useful refinement of the potential function? In Table 10 the present potential function is compared with that of Savoie and Tremblay (14) and that of Oka and Morino (9). The constants of Savoie and Tremblay, which are based on the most recent and most comprehensive vibrational data, are in better agreement with the present results than any previously derived potential function (6-11). Those of Oka and Morino differ slightly more but resemble closely those of other previous workers, who because of lack of data made the constraint Frr = F33. These latter results are based on the vibrational frequencies of Stammreich et al. (6). Also given in Table 10 are values predicted for the vibrational fundamentals, Coriolis coupling constants, centrifugal distortion constants, and inertial defects ; they were obtained using the corresponding potential function and the ground-state average structure. The table demonstrates that while all three potential functions provide good predictions of the fundamental vibration frequencies, only the present results account satisfactorily also for the observed values of the centrifugal distortion constants and inertial defects. The excellent agreement between the value of F33 derived here and that based on the most recent vibrational data is especially reassuring as it, being the only element of the B, matrix, is the element most easily determined from vibrational data. The good agreement between the observed and our calculated vibrational frequencies tends also to confirm our estimated error limits both for these frequencies and also the force constants and Coriolis coupling constants. This is in spite of the fact that we have neglected anharmonicity, especially in applying Eqs. (5)-(g). It is clear from the variation of the average structures with vibrational state that such anharmonicity is nonzero. However, we believe it is probably negligible in evaluating the force field; this is to be expected because of the large masses of the atoms in the molecule. Finally, since the differences between observed and calculated vibration frequencies are also less than the shifts observed upon a change of phase from liquid to solid (14), and since the observed isotopic shifts are well accounted for (Table 7), we conclude that a combination of presently available microwave and infrared data would not meaningfully refine the present potential function. Measurement of the microwave spectra of the
MICROWAVE
SPECTRUM OF SCla
471
(100) and (001) excited vibrational states should help, for, since these vibrations have very similar frequencies, they will be affected by a strong Coriolis resonance. Because of this the inertial defects in these two states are very sensitive to the difference wp - wl, which could now be accurately evaluated. Indeed, this difference may be sufficiently small that it could be observed direct2y (as a vibrational transition) in the millimeter wave spectrum. Unfortunately the weakness of these spectra and the low populations of these states make such observations rather difficult. The various bond lengths, r&Cl), determined in the present work are compared to earlier values, and to corresponding values in related molecules, in Table 11. Clearly the present values are more accurate than the earlier electron diffraction values, but of similar accuracy to that of Murray et al. (5). Except for NSCI, for which unusual properties can be anticipated, the S-Cl bond lengths are very similar for all molecules shown and are close to the sum of Pauling’s single bond radii (2.03 A) (53). Thus for SC12 in particular this bond is apparently a single bond, and, because of the similar electronegativities of the two atoms, should be strongly covalent. Further evidence for the bond character comes from the 35Cl quadrupole coupling constant along the bond, X,,, which is also given in Table 11, along with those of the related molecules. The largest of these values (-90 MHz) occurs for SC& itself; it TAULE I,,: COCII'ARISON OF PRESE.WDERIVE"CONSTAWS IVITHTIIOSE OF PREVIOUSWORKERSAND EXPERIMENTAL DATA
Savoic and Trenblay (14)
Oka and Horino (9) ____~
1.913
(YU)’
1.641 -0.029
0.0926 (55) 0.2024 (21)
U.3U3 2.433
2.421 (in)
dyne Cm-I II
2.52 -U."55
,I
lU.3U5 2.52
I,
-4.99u
-,1 .&l
-3.97
-.I.YYU(3))' hUlZ
-8.017
-8.22
-8.52
-8.017 (11)
"
-2.582
-2.88
-3.04
-1.ss2 (II)
"
0.324 (3)
11.415
U.4JU
0.676 (3)
0.585
0.560
515 (8) 107 (4)
517.1 211
514 ?UY
51B.U' 211
524 (5)
525.3
53s
515.5
Cl.3086 0.8306
0.190 0.736
U.187 U.714
0 .5UJ.i 0.5313
11.5120
0.446
0.427
0 .5?'11
O.OOOG
0 .noo6
n .ixm
--
“Numbers in parentheses figures .
are
one
-
standard
deviation
in
units
of
the
last
significant
u,I II :L.III.". xi,I II
472
has been cahxlated by Murray et al. (5) assuming it to be the principal value of the quadrupole tensor, and by us using our improved structure. It is quite close to that of 110 MHz), which provides strong evidence for covalent single bond the Cl atom (-character. The other components, perpendicular to the bond, are very similar, suggesting only slight asymmetry to the bond. Furthermore, were there considerable ionic or rcharacter to the bond a value much lower in absolute value would be anticipated. This has been used for SiH,Cl (17) and SiH&l~ (54) to indicate considerable back bonding from Cl to the d orbitals of Si; we conclude that such back bonding is negligible in sulphur dichloride. ACKNOWLEDGMENTS This work was supported by the National Research Council of Canada. We thank Professor N. L. Paddock for the sample of sulphur dichloride, and Professor T. L. Weatherly for sending us his results prior to publication. RECEIVED:
January
6, 1977 REFERENCES
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MICROWAVE
SPECTRUM
OF SClz
473
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