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A vibrational assignment for tungsten hexachloride
147
NOTES Combining becomes
Eqs.
(14) and (16), the least-squares
(J’T’TPT’T
fitting of the combination-difference
J)-‘J’T’TPT’TO
plots
= X.
(17)
Which is seen to be formally equivalent to Eq. (4). It is not exactly equivalent since, in the application of the transformation T, some data points may be dropped; for example, R(0) cannot be used in the upper-state combination difference. Perhaps the biggest problem in the analysis of a real spectrum is that perturbations may not be noticed and the observed frequencies may contain systematic errors which will show up in the rotational constants. Typically, the perturbations are expected to occur in the excited state and if the ground state constants are determined by combination differences they will not be affected by unrecognized perturbations in the excited state. However, the frequency sums in the matrix C in Eq. (11) do not fix the lower state constants; in the present case, (R(J
-
1) + P(J
+ 1) = Z(vo + 2(B’
B” + 20”)
+ B” + GD”)J(J
+ 1) -
2(0’
-
D”)J2(J
(13)
+ l)“,;
and these coefficients fix, in effect, the differences between the lower and the upper-state constants. We conclude, therefore that, if the rotational constants are fitted by least squares to the observed frequencies of just those lines which form the ground-state combination differences, the estimates of the rotational constants are the same as those found from analysis of combination differences. We thank Dr. G. Herzberg for valuable discussions and Mrs. C. Smith for assistance with the computations. This work was supported by Air Force Office of Scientific Research Grant 570-67. REFERENCES 1. G. HERZBERG, “Infrared and Raman Spectra, Van Nostrand, New York, 1945. 2. J. L. GRIGGS, JR., K. N. RAO, L. II. JONES ANL) R. M. POTTER, J. Mol. &e&y. (1967). 3. N. &LUND, lrkiv Fysik 30, 377 (1966). 4. J. OVEREND AND B. CRAWFORD, JR., L. Symposium ture, Columbus, 1961. 5. H. C. ALLEN, JR., _*NDP. C. CROSS, “Molecular
on Spectroscopy Vib-rotors,”
22, 383
and Molecular
p. 168. Wiley,
Struc-
New York,
1963. 6. Ref. (1) p. 390. $folecular
Spectroscopy
Laborafory,
Depatkrrlenl
oj Chemislry
CHRIS W. BROWN AND JOHN OVEREND
University of Minnesota .lfinneapolis, Minnesota, 55455 Received ,4pril S, 1967
A Vibrational
Assignment
for
Tungsten
Hexachloride
Two infrared active fundamental modes of WCle(Oh) were observed in solution-phase spectra, and were used together with six observed combination bands to deduce values for all six fundamental modes. Vibrational
data seem to be unavailable
for the tungsten
hexachloride
molecule
which is
148
NOTES TABLE
I
OBSERVED INFRARED ABSORPTION BANDS OF WCls Solvent (cm-‘)
_.....__
Cs,
CCL
1023 w 770 w 676 w
._ _
570 w 500 VW 470 w __
406 381 367 262
-215 vvw lfi5 vs
~-
IN SOLUTION
Assignment CsH,
~. Impurity
w m vs vw
165 vs
380 m SIX vs 262 VW
(WOCI,)
VI + YJ VP+ YB Ya + K 3VP Y? + Y4 WOCla impurity; (Y, + uf,)? WOClr impltrity Q impllrity YY - “8
165 vs
y1
known to possess octahedral symmetry in the vapor (1) and solid (2) phases. ilu interest in its t,hermodynamic properties’ prompted the present study of it.s infrared and Raman spect r:~.Useful infrared spectra of the solid and solution phases were obtained but, the Raman stlldy failed because WCl, is a highly absorbing material throughout t,he frequency range of Ltaman excitation available t,o us; only a doubtful indicat,ion of a band near 400 cm-’ assignable to Ye , the t,otally symmetric stretching mode, was obtained from several attempts 0 with laser excitation (He-Ne emitting 70 milliwatts at 6328 A) and with mercury-arc escitat ion (4358 A). Beckman IR 9 and IR 11 instruments were used to obtain the infrared spect ~‘a;wavellumber values quoted are probably better than f2 cm-l. Commercial WCl, was dissolved in CS, , the residue was discarded and t.he filt,raie was evaporated to recover the WC& . This was heated at 250°C in a stream of dry chlorine for several hc~urs. WOCl, sublimed out of the hot zone.2 The black, less-volatile productj did not give the S-ray pattern published for WCl, (2) until it had heen recrystallized from carbon tetrachloride; it. is another polymorph of WC16 The infrared absorption data are collected in Table I which includes bands due to WO(% which was present in small amount. in the best. WC16 sample. Of the six fundament,al vibrnt ional modes only two, ~3 aud vp , are infrared act,ive (S). They- are assigned to the two ver? st rang absorpt,ion bands at 367 and 165 cm-l, and the remaining modes must, in the absence of I:amatl data, be assigned using the observed combination bands. Only eight binary sum IINI ion tones are infrared allowed and we mav turn to the several complete assignments for me! al hexaflllorides for guidance on t,he relative intensities of t,hese combination bands i4 ). The (Y, + Q) and (~2 + Q) are invariably prominent in the spectra of those hesafluorides with notldegerlerate electronic ground states and we may, with confidence. assign the two highest frcc!uency bands at 770 and 676 cm-l to (ul + Q) and (~2 + ~a), respectively. The
LWr th:tllk 1)r. H. Prophet for sllggesting this st~ldy. ‘:We :ire itldebt,ed t,o Mr. H. W. Ititln for obtaining and interpretillp p:~~tcsrl~s of this
mxl.erial
and
of the WC’lr sxmples.
the S-r:+?-
powdrr
149
NOTES TABLE
II
VIBR.~TION.~L ASSIGNMENT FOR WC16 Mode
cm-l
n (atu)
408
v2
(ed
312 3G7 165 206 97
U (fiY) v4 (fiu) vj (f28) YG(ft.)
reverse assignment is ruled out by the fact that Ye is higher in wavenumber than Ye for all hexafluorides and hexachloride anions XCl”,- (5). Values of 408 and 312 cm-1 may be derived for ~1and YZ The (~1 + ~4) is infrared allowed and should appear near 573 cm-1 but, because (~3 + Ye) is invariably much more intense we prefer to assign this band to (Y, + Ye) and so derive a value of 206 cm-l for ZJ~ The remaining, prominent combination band at 470 cm-1 is satisfactorily assigned to (~2 + Ye). This may be involved in a Fermi interaction with the overtone 3va which is the best assignment
for the very weak band observed
For the hexafluorides est observed
at 500 cm-l.
(~2 + ~6) is always intense and, in some cases, it provides
combination
band. By comparison
we may use an empirical factor of 1.5, the approximate ing modes, gion. The
Cl and ygF/YE “, ~4’ /VA (~2 +
Y@) should
to predict
215 cm-’
a 2.mm thickness
that. ~6 for WC16 should be in the 90-100 cm-l
absorption
of a saturated
Ye to be approximately
re-
by the
bands and the wing of the intense IQband.
solution
on the wing of the intense ~4 band;
(4)
value of the ratios for the other bend-
then appear near 400 cm- I, but this region is obscured
presence of an impurit,y band, solvent However,
the strong-
wit.h WF, for which Ye is near 134 cm-’
of WC16 in CS? showed a shoulder,
this may be assigned
97 cm-*. Table II summarized
the complete
to (~2 -
near
~6) which gives
vibrational
assignment.
ACKNOWLEDGMENTS This work was supported
by JANAF
Thermochemical
Tables Contract
AF04
(611)-11201.
REFERENCES 1. K. V. G. EWENS AND M. W. LISTER, Trans. Faraday Sot. 34,1358 (1938). 2. J. A. A. KETELAAR AND G. W. OOSTERHAUT, Rec. Trav. Chim. 62, 167 (1943). S. G. HERZBERG, “Infrared and Raman Spectra,” p. 122. Van Nostrand, Princeton, New Jersey, 1945. 4. B. WEINSTXK AND G. L. GOODMAN, Advczn. Chem. Phvs. 9,169 (1965). 5. K. NAKAMOTO, “Infrared Spectra of Inorganic and Coordination Compounds,” p. 119. Wiley, New York, 1963. Chemical Physics Research Laboratory, The Dow Chemical Co., Midland, Michigan 48640 Received November 25, 1967
J. C. EVANS AND G. Y-S. Lo
NOTES Combining becomes
Eqs.
(14) and (16), the least-squares
(J’T’TPT’T
fitting of the combination-difference
J)-‘J’T’TPT’TO
plots
= X.
(17)
Which is seen to be formally equivalent to Eq. (4). It is not exactly equivalent since, in the application of the transformation T, some data points may be dropped; for example, R(0) cannot be used in the upper-state combination difference. Perhaps the biggest problem in the analysis of a real spectrum is that perturbations may not be noticed and the observed frequencies may contain systematic errors which will show up in the rotational constants. Typically, the perturbations are expected to occur in the excited state and if the ground state constants are determined by combination differences they will not be affected by unrecognized perturbations in the excited state. However, the frequency sums in the matrix C in Eq. (11) do not fix the lower state constants; in the present case, (R(J
-
1) + P(J
+ 1) = Z(vo + 2(B’
B” + 20”)
+ B” + GD”)J(J
+ 1) -
2(0’
-
D”)J2(J
(13)
+ l)“,;
and these coefficients fix, in effect, the differences between the lower and the upper-state constants. We conclude, therefore that, if the rotational constants are fitted by least squares to the observed frequencies of just those lines which form the ground-state combination differences, the estimates of the rotational constants are the same as those found from analysis of combination differences. We thank Dr. G. Herzberg for valuable discussions and Mrs. C. Smith for assistance with the computations. This work was supported by Air Force Office of Scientific Research Grant 570-67. REFERENCES 1. G. HERZBERG, “Infrared and Raman Spectra, Van Nostrand, New York, 1945. 2. J. L. GRIGGS, JR., K. N. RAO, L. II. JONES ANL) R. M. POTTER, J. Mol. &e&y. (1967). 3. N. &LUND, lrkiv Fysik 30, 377 (1966). 4. J. OVEREND AND B. CRAWFORD, JR., L. Symposium ture, Columbus, 1961. 5. H. C. ALLEN, JR., _*NDP. C. CROSS, “Molecular
on Spectroscopy Vib-rotors,”
22, 383
and Molecular
p. 168. Wiley,
Struc-
New York,
1963. 6. Ref. (1) p. 390. $folecular
Spectroscopy
Laborafory,
Depatkrrlenl
oj Chemislry
CHRIS W. BROWN AND JOHN OVEREND
University of Minnesota .lfinneapolis, Minnesota, 55455 Received ,4pril S, 1967
A Vibrational
Assignment
for
Tungsten
Hexachloride
Two infrared active fundamental modes of WCle(Oh) were observed in solution-phase spectra, and were used together with six observed combination bands to deduce values for all six fundamental modes. Vibrational
data seem to be unavailable
for the tungsten
hexachloride
molecule
which is
148
NOTES TABLE
I
OBSERVED INFRARED ABSORPTION BANDS OF WCls Solvent (cm-‘)
_.....__
Cs,
CCL
1023 w 770 w 676 w
._ _
570 w 500 VW 470 w __
406 381 367 262
-215 vvw lfi5 vs
~-
IN SOLUTION
Assignment CsH,
~. Impurity
w m vs vw
165 vs
380 m SIX vs 262 VW
(WOCI,)
VI + YJ VP+ YB Ya + K 3VP Y? + Y4 WOCla impurity; (Y, + uf,)? WOClr impltrity Q impllrity YY - “8
165 vs
y1
known to possess octahedral symmetry in the vapor (1) and solid (2) phases. ilu interest in its t,hermodynamic properties’ prompted the present study of it.s infrared and Raman spect r:~.Useful infrared spectra of the solid and solution phases were obtained but, the Raman stlldy failed because WCl, is a highly absorbing material throughout t,he frequency range of Ltaman excitation available t,o us; only a doubtful indicat,ion of a band near 400 cm-’ assignable to Ye , the t,otally symmetric stretching mode, was obtained from several attempts 0 with laser excitation (He-Ne emitting 70 milliwatts at 6328 A) and with mercury-arc escitat ion (4358 A). Beckman IR 9 and IR 11 instruments were used to obtain the infrared spect ~‘a;wavellumber values quoted are probably better than f2 cm-l. Commercial WCl, was dissolved in CS, , the residue was discarded and t.he filt,raie was evaporated to recover the WC& . This was heated at 250°C in a stream of dry chlorine for several hc~urs. WOCl, sublimed out of the hot zone.2 The black, less-volatile productj did not give the S-ray pattern published for WCl, (2) until it had heen recrystallized from carbon tetrachloride; it. is another polymorph of WC16 The infrared absorption data are collected in Table I which includes bands due to WO(% which was present in small amount. in the best. WC16 sample. Of the six fundament,al vibrnt ional modes only two, ~3 aud vp , are infrared act,ive (S). They- are assigned to the two ver? st rang absorpt,ion bands at 367 and 165 cm-l, and the remaining modes must, in the absence of I:amatl data, be assigned using the observed combination bands. Only eight binary sum IINI ion tones are infrared allowed and we mav turn to the several complete assignments for me! al hexaflllorides for guidance on t,he relative intensities of t,hese combination bands i4 ). The (Y, + Q) and (~2 + Q) are invariably prominent in the spectra of those hesafluorides with notldegerlerate electronic ground states and we may, with confidence. assign the two highest frcc!uency bands at 770 and 676 cm-l to (ul + Q) and (~2 + ~a), respectively. The
LWr th:tllk 1)r. H. Prophet for sllggesting this st~ldy. ‘:We :ire itldebt,ed t,o Mr. H. W. Ititln for obtaining and interpretillp p:~~tcsrl~s of this
mxl.erial
and
of the WC’lr sxmples.
the S-r:+?-
powdrr
149
NOTES TABLE
II
VIBR.~TION.~L ASSIGNMENT FOR WC16 Mode
cm-l
n (atu)
408
v2
(ed
312 3G7 165 206 97
U (fiY) v4 (fiu) vj (f28) YG(ft.)
reverse assignment is ruled out by the fact that Ye is higher in wavenumber than Ye for all hexafluorides and hexachloride anions XCl”,- (5). Values of 408 and 312 cm-1 may be derived for ~1and YZ The (~1 + ~4) is infrared allowed and should appear near 573 cm-1 but, because (~3 + Ye) is invariably much more intense we prefer to assign this band to (Y, + Ye) and so derive a value of 206 cm-l for ZJ~ The remaining, prominent combination band at 470 cm-1 is satisfactorily assigned to (~2 + Ye). This may be involved in a Fermi interaction with the overtone 3va which is the best assignment
for the very weak band observed
For the hexafluorides est observed
at 500 cm-l.
(~2 + ~6) is always intense and, in some cases, it provides
combination
band. By comparison
we may use an empirical factor of 1.5, the approximate ing modes, gion. The
Cl and ygF/YE “, ~4’ /VA (~2 +
Y@) should
to predict
215 cm-’
a 2.mm thickness
that. ~6 for WC16 should be in the 90-100 cm-l
absorption
of a saturated
Ye to be approximately
re-
by the
bands and the wing of the intense IQband.
solution
on the wing of the intense ~4 band;
(4)
value of the ratios for the other bend-
then appear near 400 cm- I, but this region is obscured
presence of an impurit,y band, solvent However,
the strong-
wit.h WF, for which Ye is near 134 cm-’
of WC16 in CS? showed a shoulder,
this may be assigned
97 cm-*. Table II summarized
the complete
to (~2 -
near
~6) which gives
vibrational
assignment.
ACKNOWLEDGMENTS This work was supported
by JANAF
Thermochemical
Tables Contract
AF04
(611)-11201.
REFERENCES 1. K. V. G. EWENS AND M. W. LISTER, Trans. Faraday Sot. 34,1358 (1938). 2. J. A. A. KETELAAR AND G. W. OOSTERHAUT, Rec. Trav. Chim. 62, 167 (1943). S. G. HERZBERG, “Infrared and Raman Spectra,” p. 122. Van Nostrand, Princeton, New Jersey, 1945. 4. B. WEINSTXK AND G. L. GOODMAN, Advczn. Chem. Phvs. 9,169 (1965). 5. K. NAKAMOTO, “Infrared Spectra of Inorganic and Coordination Compounds,” p. 119. Wiley, New York, 1963. Chemical Physics Research Laboratory, The Dow Chemical Co., Midland, Michigan 48640 Received November 25, 1967
J. C. EVANS AND G. Y-S. Lo