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The microwave spectrum of germyl isocyanate, a quasi-symmetric top
JOURNAL
OF MOLECULAR
SPECTROSCOPY
128,688
1 ( 1988)
The Microwave Spectrum of Germyl Isocyanate, a Quasi-symmetric Top STEPHEN CRADOCK Department of Chemistv, JAMES R. DURIG,
University of Edinburgh, Edinburgh EH9 3JJ, Scotland A. B. MOHAMAD,
AND JOANN F. SULLIVAN
Department of Chemistry, University of South Carolina. Columbia, South Carolina 29208 AND JACEK KOPUT Department of Chemistry, A. Mickiewicz University, Poznan, Poland The microwave spectrum of gennyl isocyanate in the K, P, and R bands (12.4-40.0 GHz) has been investigated using natural isotopic samples and samples containing specific germanium isotopes, mass numbers 72 and 74, and samples containing GeD, groups. The very complex spectrum is analyzed as that of a quasi-symmetric top, in which the skeletal bending motion has an energy maximum at the linear configuration; the height of the maximum is some 339 cm-‘. Many vibrational states of the two-dimensional bend lie close in energy, resulting in strong interactions between rotational levels of different vibrational states. The program used for the analysis has been used previously to account for similar spectra of methyl and silyl isocyanates and methyl isothiocyanate; the behavior of the germyl compound is more like that of the methyl isocyanate than that of the silyl compound, where the height of the maximum is much less. Although we did not include centrifugal distortion operators in the Hamiltonian the program successfully predicts k = 0 line positions in J + 1 + J bunches with J up to 9, using only lines in the J = 3 bunch to define the parameters of the model, which include the height of the hump, the bend angle of the skeleton at the energy minimum (142.18(5)“), the force constant for the bending motion at the minimum (0.1094(7) mdyn A), and the GeN bondlength at equilibrium (1.8257(5) A). The threefold barrier to internal rotation of the GeH3 group at the equilibrium position is about 3 cm-‘, much lower than the value found for methyl isocyanate. The fit to the observations, about 100 lines in the 4 + 3 bunch, is improved by allowing for a variation in the GeN bondlength as the bend angle changes. The quality of the least-squares fit corresponds to an estimated standard deviation for an observation of about 2 MHz, but not ah observed lines can be accounted for precisely, showing that additional interactions are involved that are not yet included in the model. 0 1988 Academic Press, Inc. I. INTRODUCTION
The molecular structures of isocyanates and isothiocyanates have been studied by spectroscopic and diffraction methods for many years, and it has become clear that at least in the gas phase it is necessary to take account of the low-energy, large-amplitude motion corresponding to both the bend at nitrogen and the internal rotation of the NC0 or NCS group against the rest of the molecule if a satisfactory representation of 0022-2852188 $3.00 Copy&ht
0
1988 by Academic Pms,
Inc.
All rights of reproduction in any form mewed.
68
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
69
the spectra or diffraction patterns is to be achieved. For silyl isocyanate, SiHsNCO, an analysis of the microwave spectrum (I) was found to be possible in terms of a symmetric top model, in which the molecule is treated as having a linear skeleton with a two-dimensional bending motion at nitrogen, and the potential for this motion is taken to be anharmonic. However, for methyl isothiocyanate, CH,NCS, the symmetric top model (in a form which treated each vibrational state separately and took account of the interactions between levels belonging to different vibrational states only as contributing to anomalous values of the centrifugal distortion constants, especially DJK) failed to account fully for the observed line positions (2). A complete analysis (3, 4) of the microwave spectrum of methyl isothiocyanate was possible by using a quasisymmetric top model (5) which takes explicit account of the large-amplitude motions. This model was developed from the work of Hougen et al. on the rigid bender model of a triatomic (6). Similar analyses of the microwave spectrum of methyl isocyanate (7, 8) have been reported, and the same quasi-symmetric top model has been used to explain the microwave spectra of a number of other molecules. The Hamiltonian used (5) takes account of overall rotation (three degrees of freedom), the internal rotation, and the bend at nitrogen, making five degrees of freedom in all. All other motions are ignored, it being assumed that they are of small amplitude and not coupled to the low-frequency motions. As a result, the model neglects any possible mixing of the five degrees of freedom included in the model and the higherfrequency modes. A further limitation is that no contributions of small-amplitude motions to centrifugal distortion terms are included, so the accuracy is limited for higher J values. Once the vibrational wavefunctions have been found by a numerical integration procedure, the appropriate rovibrational levels are treated in three symmetry blocks (A,, Al, and E) by a variation method; details will be found in Refs. (3-5, 7, 8). The prime characteristic of quasi-symmetric top molecule spectra in the microwave region is their complexity. This arises mainly because of the large number of vibrational states that are populated at accessible temperatures, because of the small energy gaps between them. Thus for germyl isocyanate there are 15 distinct k = 0 levels below 250 cm-‘, and all these and more give rise to discernible microwave lines, in each case together with lines for all possible k values other than zero. In addition, the spectra are not readily assignable without the aid of predictions from the model, as the very strong essential interactions between levels of different k values prevent the recognition of subspectra due to particular “vibrational states,” as was possible for silyl isocyanate (I). Nevertheless, with the aid of the model program we have been able to assign the spectra and to refine some structural and potential constants for germyl isocyanate, which now joins the methyl and silyl analogs as a classic example of a quasi-symmetric top. We find that germyl isocyanate lies between the methyl and silyl compounds in terms of the height of the central hump in its bending potential function, which is about 339 cm-‘, compared with about 928 cm-’ for the methyl compound and about 30 cm-] for the silyl. It is thus rather similar to methyl isothiocyanate (2-4) where the hump is about 200 cm-‘; both silyl (9) and germyl (10) isothiocyanates have strictly linear skeletons, though each has a low-frequency, large-amplitude bending mode.
70
CRADOCK
ET AL.
The microwave spectrum of germyl isocyanate has been briefly reported before (I I), and some structural parameters have been derived from an analysis of the spectra of several isotopic species. The analysis reported here confirms the essential correctness of the earlier results, but provides slightly modified values for some parameters, partly because of different assumptions about unrefined bondlengths, and partly because of a different assignment of the true vibrational origin of each J bunch. The structure found is very similar to that determined by the analysis of electron diffraction patterns (12) and not very different from that found in the solid state by X-ray methods (13). II. EXPERIMENTAL
DETAILS
Samples of germyl isocyanate with normal isotopic composition (five isotopes of germanium, mass numbers and percentages 70, 20.52%; 72, 27.43%; 73, 7.76%; 74, 36.54%; 76, 7.76%) or with only a single Ge isotope (mass numbers 72 and 74) were prepared in a vacuum system by passing an appropriate sample of germyl bromide over solid silver cyanate (14) and were purified by trap-to-trap or cold-column fractional distillation. Monoisotopic germyl bromide was prepared from GeOz via GeH4 and GeH3Cl. Deuterium-substituted samples were prepared via GeD4 in the same way. Samples were stored at dry-ice temperature after preparation, and spectra were also run at reduced temperature to minimize sample decomposition in the spectrometer. Microwave spectra were obtained using a Hewlett-Packard 8460A microwave spectrometer, using backward-wave oscillators as tunable sources of radiation in the K, P, and R bands (12.4-40.0 GHz). This allowed the study of the J + 1 + J u-type Rbranch transitions with J in the range 3 to 9. III. SPECTRUM
AND ASSIGNMENTS
The spectrum consists of “main bunches” separated by some 3.66 GHz, each containing most of the u-type R-branch lines expected for one of the (J + 1) + J transitions. In addition, as first noted in the spectrum of methyl isothiocyanate (2), there are lines between the main bunches that appear to follow roughly the pattern expected for the K structure of the spectrum of a symmetric top but with a ridiculously large value of DJK, in this case about 6 MHz. The J and K assignments of these lines can be checked by observing the Stark lobes at low Stark voltages, and these are indeed consistent with the values suggested by the pattern. However, the patterns are actually not sufficiently regular to be properly explained in this way, and even the quasi-symmetric top model used for the analysis here fails to account for the line positions in detail. We may attribute this failure to the combination of deficiencies in the model and truly accidental perturbations of the levels concerned, either by levels not included in our analysis or by levels that are included by mechanisms not taken account of in the Hamiltonian. A typical main bunch and some of its associated outlying lines are illustrated in the survey spectrum shown in Fig. 1. The levels of a quasi-symmetric top can be described in either of two ways, depending on whether we consider it to be best treated as a symmetric top molecule (for which the two vibrational degrees of freedom in the model are the two degenerate components of the bending mode at nitrogen) with a very anharmonic potential function that means that the “reference configuration” with a linear skeleton is significantly higher
71
GERMYL ISOCYANATE MICROWAVE SPECTRUM
22.0
21.5
22.5
&Hz)
FIG. 1. The J = 6 + 5 bunch of 74GeHjNC0, showing the vibrational origin va), three lines (k = 1,2. 3) of the (u, I) = (0, 0) series extending to low frequency, labeled by k, and some of the u = I. k = 0 lines to
higherfrequency.labeledby (u,I).
in energy than the equilibrium structure, or as a bent molecule whose bending motion at nitrogen, together with the internal rotation about the single bond to nitrogen, is of such large amplitude that even molecules in the ground vibrational state may depart quite far from the equilibrium configuration. In the first case our quantum numbers would be vlo and Ilo (hereafter referred to as v and 1 for brevity), the vibrational and vibrational angular momentum quantum numbers for the two-dimensional bending mode yIo of the linear skeleton, together with J and k, the quantum numbers for overall angular momentum and for the component of this angular momentum about the axis coinciding with the linear skeleton. Due to vibration-rotation interactions the sign of the product kl is significant. In the second case the vibrational quantum number is Q, with a second quantum number m for the internal rotation, and there is only one strict quantum number J for overall angular momentum, though we are entitled, as for any prolate near symmetric top, to use a component k, about the axis of least moment of inertia as a pseudo-quantum number. Again, due to torsionrotation interactions, the sign of the product mk, is significant. The two notations are related (2, 15) as of course they must be; the essential equations are vb =
(v -
m=l-k.
11)/2
(14 (lb)
The rotational quantum number k translates directly to k,. The analysis of the spectrum of silyl isocyanate was published (I) using the “symmetric top” formalism, but the reports on the spectra of methyl isocyanate (7, 8) and methyl isothiocyanate (3, 4) used the bent molecule formalism. Nevertheless, we here use the “symmetric top” quantum numbers to denote the various vibrational states; the “translation” may be performed using the equations above. One advantage of the symmetric top description is that it emphasizes the occurrence of lines in fairly close clusters in the higherfrequency portions of each bunch, as may be seen in Fig. 1; these are assigned to the various k lines for a particular vibrational state on the symmetric top model, but are apparently chance coincidences on the bent molecule model. For the lower vibrational levels, where the effects of the essential perturbations between the various vibrational states are large, the lines due to different k levels are far apart, and either formalism may be used. It must be noted that the distinction between the two notations is purely one of viewpoint; either provides an equally valid description of the levels and the
72
CRADOCK
ET AL.
spectra. The inadequacy of the previous (2) treatment of the methyl isothiocyanate problem stems from the failure to include the essential and chance interactions between energy levels, not from the choice of notation. The relationship between the two formalisms has been explored in some detail recently (15). The Stark effect is of limited use in assigning the spectra; we can distinguish the k = 0 lines as usual as those lines having a slow second-order Stark effect. They appear only at Stark voltages of more than 100 V/cm. The Z-doublet lines with I = 1, k = 1, and kl positive have a characteristic Stark behavior, showing Stark lobes to high or low frequency, with a somewhat faster second-order Stark effect, appearing at voltages of 20 V/cm or so. All other lines have a very rapid first-order Stark effect, appearing at voltages of less than 10 V/cm; we find no pairs of lines with a very fast Stark effect giving lobes between the zero-field lines due to splitting caused by the barrier to internal rotation, as were observed for methyl isocyanate (8). Because we have not been able to observe bunches with very low Jwe see no discrete structure due to nitrogen quadrupole coupling. The lines in the lowest bunch (J 4 + 3) were somewhat broad (of the order of 2 MHz for k = 0 lines and more ir higher k lines). There was no sign of any splitting like that illustrated (8) for the k = 3 line of methyl isocyanate, and we were unable to use quadrupole splittings to aid assignments. The assignments reported below were made on the basis of identification of k = 0 lines and I-doublet lines from their Stark effects (see above), which allowed use of the skeletal bending-torsion-rotation Hamiltonian to define the potential function, using reasonable bondlengths to begin with. The equilibrium bond angle was defined on the basis of the I-doublet separation, as in the earlier report (II) (which used only this separation and the bunch separation, giving rotation constants B - C and B + C, respectively, for a number of isotopic species). The model Hamiltonian was then used to predict the positions of other lines for the lowest observed J bunch (J = 4 + 3) for which the effects of the neglect of centrifugal distortion and other interactions should be minimized. Most of the expected lines could be assigned, though there was inevitably some overlapping because of the density of lines in the main bunches. Unfortunately, as mentioned above, the lines found between the main bunches, for which assignments were easy to make and where no overlapping occurred, proved to be impossible to fit precisely, discrepancies of 100 MHz or more being found in some cases. Finally, the structural and potential parameters found by least-squares refinement for the 74GeH3 isotopic species were used to predict the spectra of 72GeH3 and 74GeD3 species, the accuracy of the fit of calculated and observed frequencies of the k = 0 lines confirming the consistency of the structure (Table I). It was also found that the parameters fitted only to line positions for the J = 4 + 3 bunch were adequate to predict the positions of k = 0 lines at least for J bunches up to J = 10 + 9; for other k values there were as expected increasing deviations from the predicted line positions as J and k increased, but these deviations could not be simply explained by use of a single term of the form D.&J + l)k2. The analysis of higher bunches will therefore have to await the availability of a higher-order model, and the present analysis must be regarded as preliminary in this respect, though we hope it is based on a correct assignment, and we are confident that it leads to a reasonable description of the structure and the potential function.
GERMYL ISOCYANATE MICROWAVE SPECTRUM
13
TABLE I Observed and Calculated k = 0 Line Positions/MHz in the J = 6 + 5 Bunch for Three Isotopic Species of Germyl isocyanate
“GeH3NCO
74GeH3NC0
74Ge03NC0
ohs
22105.62
21937.26
21222
talc
22104.09
21936.17
21225.49
ohs
22 178.80
22009.61
21290
talc
22178.75
22010.01
21292 98
ohs
22467.2
22295.94
21546
caic
22467.04
22296.06
21552.41
Level (v.!z) 0.0
2.2
6.6
Note:
observed
spectra.
frequencies
and are only
for the GeD3
approximate
species
(estimated
are taken
precision
t
from
survey
5 MHz).
IV. MODEL HAMILTONIAN
The definitions of molecular coordinates and the axis system are as used for methyl isocyanate (7, 8), and all the analysis reported here used the same model as this earlier work. A full description of the model program is given in Refs. (7, 8) and further references therein and does not need repetition here. Basically, the zero-order Hamiltonian H!btb,,contains the appropriate quadratic products of the five momentum operators corresponding to the five degrees of freedom involved, plus a potential function V(p, T) defining the variation of potential energy with the GeNC bending coordinate p and the torsional coordinate T. The energy levels and wavefunctions are calculated variationally. The basis set consists of products of symmetric top rotational wavefunctions, free internal rotor torsional wavefunctions, and vibrational wavefunctions obtained by numerical integration over the one-dimensional bending potential. The results were found to be rather insensitive to the number of points used in the numerical integration, and thus in the definition of the vibrational wavefunctions, presumably because any deficiencies in the basis functions were accommodated in the subsequent variation procedure. V. RESULTS
About 15 lines were assigned in the J = 4 + 3 bunch, of which 63 were fitted to some 9.5 lines predicted by the model, the others being too far from the calculated positions to be included. The final standard deviation, for an observation of unit weight, was 1.9 MHz with six refining parameters. While this is not a good fit by comparison with other microwave problems, it is comparable to the results achieved using the present model for other molecules (3, 8).
CRADOCK
74
ET AL.
The model program contained several variables, which are listed in Table II. Only a portion of these proved to be refinable; the situation is similar to that encountered in the definition of the structure of a symmetric top molecule from the single observable B rotation constant. The NC0 group geometry was assumed to be linear, with r(N=C) = 1.199 A, r(C=O) = 1.174 A, as found for silyl isocyanate (I) and assumed for Structure I of methyl isocyanate (8). The HGeN bond angle was fixed so as to achieve consistency between the observed and calculated k = 0 line positions for the GeD3 isotopic species, as mentioned above. The GeN bondlength and the equilibrium angle at nitrogen were refined and were well determined. The GeNC bending potential function was assumed to be of the form (quadratic + Lorentzian hump), as found for silyl isocyanate, methyl isocyanate, and methyl isothiocyanate, and required two parameters, H, the height of the hump, andf; the restoring force constant at the equilibrium angle, as well as the value of the bond angle at equilibrium. All these potential parameters were refined. One very important parameter was the leading term x in the power series expressing the variation in the GeN bondlength with p, rGeN=r’+x(p-p,).
- *.
(2)
This was well determined. The parameters 6 and y, representing the tilt of the GeH3 group and the bend of the NC0 group away from the linear configuration, can be treated as the coefficients of (p - pe) in a power series expansion and are related to the zero-order coefficients
TABLE II Model Parameters
Parameter
Value
(this
r(GeN)/x
1.8257(5)
r(GeH)/B. r(N=C)/B.
work)
Microwavea
E.LIb
X-rayc
1.826(15)
1.831(4)
1.856(6)
1.500 fixed
1.52019)
1.532(6)
1.28-1.35
1.199 fixed
1.168(27)
1.190(7)
1.161(g)
r(c-0)/X
1.174 fixed
1.182(20)
1.182(7)
1.185(9)
<(HGeN)/deg
108.15
108.3(20)
110 fixed
101,113
fixed
<(GeNC)/deg
142.18(5)
143.2(34)
141.3(3)
147.0(6)
<(NCO)/deg
180.0 fixodd
180.0 fixed
180.0 fixed
173.8(8)
GeH3
0.0 fixedd
3(2)
0. fixed
not defined
tilt/deg
x(GeN)/x
rad-’
x(N=C)/X
rad-’
H/cm-’ flmdyn Vg’/crn
Notes:
0.019(3) 0.0 fixedd 338.7(20)
A -1
0.1094(7) rad -1 W(2)
a) Reference
(11), b) Reference
d) see text for estimated
limits
(12). c) solid on these
phase
parameters.
at 178 K, Reference
(13).
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
75
by the reasonable requirement that both tilt and bend are zero in the configuration with the GeNC group linear (3, 8). In fact, both were found to be zero, within a small standard deviation (of the order of 0.2”) so we have fixed each at zero in the final refinements. Note that this conflicts with the conclusion of the earlier report on the microwave spectrum (11) that the tilt was about 3”. The F’sparameters represent the torsional potential hindering internal rotation of the GeH3 group in the bent configuration. The form of the potential function is assumed to be V& T) = V&p) - l/2 V&)cos 37 - - * * ) (3) where V, is expanded as a power series in (p - p,). The effect of the V’Jterm in the potential is to allow mixing, and hence perturbation, of levels whose torsional quantum numbers m differ by 3; in the spectrum this manifests itself mainly as a splitting of lines corresponding to the levels where m = 3 (a systematic effect, observed for methyl isocyanate, where I’, is of the order of 20 cm-’ (8)) and as a shift, which may be very large, of lines which are due to levels which happen to lie very close to another where the m values differ by 3. This is an accidental effect, as the exact energies of the levels depend on the whole set of potential and structural constants. As mentioned above, no lines showing the characteristic splitting expected for lines due to levels with m = 3 were found in our spectra, suggesting that I’, was much smaller than for methyl isocyanate. At first, the assignment of lines was attempted with all the V3 constants set to zero. This allowed an extension of the assignment, and when almost all lines expected in the bunch had been assigned the coefficient of (p - pe), V:“, was allowed to refine. This improved the fit considerably, and the final value (Table II) is welldefined at about 5 cm-‘. As we assume that the barrier to internal rotation is zero at the linear configuration this implies that the barrier at the equilibrium bend angle, I’:“), is equal to I’:“. pe, or about 3 cm-‘. Thus it is much smaller than the value of about 20 cm-’ found for methyl isocyanate (8) but this is to be expected in view of the much greater length of the GeN bond. The observed line positions are listed in Table III for the J = 4 + 3 bunch, together with assignments of quantum numbers (v, 1; k) (the sign of the product kl is indicated as the sign of k) and the symmetry of the lower level involved (A,, AZ, or E) and the calculated line position in each case. As mentioned above, the least-squares fit used only these frequencies directly; Table I shows how well the k = 0 lines of some of the lowest vibrational states of the 72GeH3 and 74GeD3 species in a higher J bunch are fitted by the refined structure. The final parameter set (including those parameters which could not be refined) is listed in Table II, with the earlier microwave (1 I), electron diffraction (12) and X-ray (13) results where appropriate. We have also investigated the possible effects of centrifugal distortion terms of the form 0.J2(J + 1)2 by measuring the line positions for the (0, 0; 0) transitions for all J bunches up to J = 10 + 9. These should be unaffected by the strong essential interactions, and as expected form a well-behaved pattern following the symmetric top formula v$ = 2BJ- 4DJJ3, (4) where J is the higher J value involved. The DJ constant for the ground vibrational state (v, I) = (0,O) has the fairly small value of 1.55 kHz, so the k = 0 lines for higher
CRADOCK
76
ET AL.
TABLE III
Observed and Calculated Line Positions/MHz for the J = 4 + 3 Bunch of “GeHSNC0 (v.ll;k) 003A 203A 403A 402E 202 002E 401E 511 400 311 201E 510E 111 512 200 5 l-l OOlE 310 312 000 511 313 422 421E 423E 110 3 l-l 420E 112 222A 223E 221E 4 2-l 220E 311 4 2-l 2 2-l 113E 332 331E 532 4 2-3 531E 533A 330A 530A 11-l
Syme
E
A2 A2 A2
A2 E A2 E E E A2 A1 E A
E E E
A At E A E E E
E
Mobs) 14215 14330 14362 14420.3 14428.3 14435.6 14470.7 14485.5 14468.7 14520.6 14544.1 14546.2 14556.5 14561.0 14574.0 14574.0 14577.1 14605.0 14615.6 14625.1 14633.2 14643.3 14643.3 14646.5 14647.5 14647.3 14650.2 14651.6 14655.3 146595 14662.6 14663.8 14664.1 14673.0 14676.3 14665.3 14689.5 14699.0 14698.5 14701.5 14704.6 14705.5 14706.2 14706.2 14711.4 14711.4 14713.8
v(calc) 14192.5 14254.8 14316.4 14415.6 14429.9 14406.5 14471.4 14476.7 14491.0 14523.2 14541.7 145569 14557.3 14559.6 14576.6 14574.1 14571.2 146076 14613.0 14624.5 14626.1 14643.3 14644.9 14647.1 14647.7 146466 14650.4 14653.8 14653.9 146597 146633 14665.0 146652 14673.6 14674.3 14681.9 14692.0 14696.0 14699.7 14703.6 14705.9 14704.1 14707.8 14708.7 14710.5 14712.0 14713.8
Wtt 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(v,&;k) 111 53-l 2 2-2 33-l 732 731E 3 3-2 5 3-3 443E 442 441A 3 3-3 11-2 2 2-3 440E 44-l 4 4-2 643E 642 641A 4 4-3 6 4-2 553E 552 551E 550 5 5-l 5 5-2 5 5-3 753 751E 750 3 l-3 563A 662 561E 660A 5 6-l 5 6-2 363 362 773 772 171A 170 363 382 11-3
Sym’
w(obs)
w(calc)
Al E E E E
14713.9 14719.5 14719.5 14719.5 14729.6 14729.6 14733.0 14737.0 14745.0 14749.7 14749.7 14754.5 14754.5 14754.5 14755.7 14760.0 14770.2 14774.0 14774.0 14774.0 14761.0 14786.0 14604.0 14804.0 14805.5 148087 14811.8 148160 14821.0 148420 148420 14642.0 14843.0 14859.5 14861.5 14861.5 14663.9 14666.0 14869.0 14906.0 14908.0 14921.2 14921.2 14921.2 14921.2 14979.5 14979.5 15040.0
14710.5 14717.6 14719.0 14720.3 14727.7 14726.3 14733.4 14735.2 14747.0 14748.7 14751.8 14752.2 14754.9 14755.3 14756.3 14762.2 14770.2 14771.5 14772.2 14773.7 14780.5 14783.7 14801.5 148026 148040 14808.5 14812.5 14817.2 14823.0 148402 14641.7 14843.3 146390 148569 14860.7 14662.3 14664.3 14666.8 14869.2 14910.1 14910.4 14920.3 14921.0 14921.6 14923.0 14982.5 14982.7 15018.3
E A E A A E E A E E A A E A E E E E E E
E E A E E E E E A E
Wtb 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
i I
1 1 1
1 1 1
i 1 1 0
1 1 1 1
1 1 1 1 1 1 1 1 0 0 0
Note: a) symmetry of lower level (A indicates both Al and A2 components) b) weight of transition in least-squares fit.
J bunches could have been used in the least-squares fit, as the centrifugal distortion contributes shifts of less than 10 MHz to the line positions for the highest J value observed. We have chosen not to do so, as the calculation takes much longer for higher J values, but we have confirmed that the program successfully predicts line positions to within a few MHz for k = 0 transitions as far as the J = 10 + 9 bunch, except for the (v, 1) = (1, 1) and (3, 1) vibrational states, for which DJ is much larger (see below). The measured k = 0 line positions are shown in Table IV. Where no entry is given the line position was not measured precisely, but in all the bunches studied the same essential pattern of k = 0 lines was present.
GERMYL
ISOCYANATE
MICROWAVE
77
SPECTRUM
TABLE IV Measured VA
2.0
4.0
1.1
3.1
5.1
3
14625.1
14574.0
14488.7
146473
14605.0
14548.1
4
18281.43
18216.88
18111.2
18305.56
182508
5
21937.26
21858.7
21733.08
21961.07
218930
6
25592.84 29248.34
v,L
32908.6
6
32903.37 36558.10
36438.2
2.2
4.2
3
21820.8
29091.8
29263.0
29147.2
9
=
J"=
for 74GeH3NCO/MHz
0.0
=
J'=
k = 0 Line Positions
14673.0
365506
36416.8
3.3
4.4
5.5
6.6
14711.4
147557
14808.7
14863.9
18341.55
18319.50
18389.41
18444.87
18511.0
18580.18
22009.61
21983.2
22067.03
22133.6
22212.8
22295.94
29421.85
2951047
29616.33
29727.14
a
33013.1
32973.2
33099.0
33198.5
33317.8
33442.5
9
366808
366363
36776.1
36886.6
37019.1
37157.5
2934543
The potential function describing the bending motion of the GeNCO chain has a minimum at a bond angle GeNC of 142.2”, very close to that found in the electron diffraction study (12) 141.3(3)“, but rather different from the value found in the crystal (13), 147”. The GeN bondlength is also very close to the electron diffraction value; the differences in the bondlength and bond angle at nitrogen between the Xray structure and the present results may well be due to intermolecular interactions in the solid. The barrier (hump) at linearity of the GeNCO chain is about 339 cm-‘. The potential function is illustrated in cross section in Fig. 2, which also shows the positions of some of the lower vibrational levels, whose energies relative to that of the ground state are listed in Table V, together with the effective rotation constants B and centrifugal distortion constants DJ derived from the k = 0 lines of the spectra by use of the symmetric top formula Eq. (4). It is clear that the centrifugal distortion constants show behavior similar to that observed for silyl isocyanate (I), in that the lowest levels in each set have anomalous contributions due to the anharmonic motion, but the higher levels have more normal DJ values. The anomalous contributions are distinctly larger for the germyl compound, but this is to be expected in view of the greater height of the hump. VI. COMPARISON
WITH
OTHER
QUASI-SYMMETRIC
TOP
MOLECULES
We may compare the present results with those for other isocyanates and related molecules using the criteria suggested in Ref. (15). A correlation parameter, -rn, which
78
CRADOCK
ET AL.
BOO-
540-
480-
420-
180-
0
0
I
I 10
I
I 20
I
I 30
,
I 40
I
I 50
I
I 60
FIG. 2. Refined potential curve for bending of GeH3NC0 at nitrogen, with J = 0, k = 0 levels below 250 cm-‘. The levels are labeled by values of u and I in the form vl.
compares the energies of the (v, I) = (2n + 1, 1) and (2n + 2,0) levels above the (2~2, 0) level, where n is the bending quantum number Q, appropriate to the bent molecule formalism (see Section III), is defined in terms of the symmetric top labeling of levels as -rn=1-4
E(u=2n+ 1,1= l;k= l,J= l)-E(2n,O;O,O) E(2n+2,0;0,0)-E(2n,O;O,O) [
1.
The correlation parameter for the ground vibrational state is y. = 0.85, compared with 0.9 1 for methyl isocyanate and -0.24 for silyl isocyanate. Germyl isocyanate is thus much nearer the “bent molecule” limit (where ye is + 1) than the silyl compound, but not so close as the methyl compound. Unlike methyl isothiocyanate, germyl isocyanate does not become much closer to the linear limiting case (for which y is - 1) in the first and second excited bending states, for which the correlation parameters are -yl = 0.78 and y2 = 0.62. The pattern of k = 0 lines due to the successive excited bending states of germyl isocyanate in which there is no torsional excitation (no vibrational angular momentum
79
GERMYL ISOCYANATE MICROWAVE SPECTRUM TABLE V Calculated Energies G of k = 0 Levels and Effective Rotation Constants B of 74GeH3NC0 state
Notes.
G/cm-’
0.0
0.0
1828.1 1
1828.217(l)
20 47(3)
1,’
5.7
1829.28
1831 566(3)
22.8
1832 51
1834.192(l)
3,3
507
1637 35
1838.986(
4.4
89.0
1843 32
1844.539(Z)
1.05(l)
2.0
92 1
1822.36
1821.351(7)
-2 79(4)
3.1
98.9
1624.86
1826495(Z)
28.28(3)
4.2
118.6
1830 70
1831.996(2)
0.91(Z)
5,5
137.3
1850.06
1851.134(4)
0.89(3)
0.80(l) 094(l)
1)
(1838.981
5.3
150.0
1838.19
4.0
178.3
1811.39
1811.12(2)
0.4(3)
5.1
187.8
1819.05
181861(l)
2.9(l)
6,4
192.1
1846.43
6.6
195 1
1857 31
includes
calculated calculated
from
1.55(l)
2.2
(0,O). which
B(obs)
DJ/kHz
B(calc)/MHzB(obs)/MHz
(V.L)
all k=O levels
itself
difference
from
the bending
and DJ are derived J=3 to J=9.
calculated
lies 46 2 cm -’
energy
above
(for J-3); vibrational
from
The B(obs)
k=O line is apparently
1858 056(Z)
hidden
to lie less than the potentlal B(calc)
value
= %(
wavefunction
the observed
above
G is the
+), (see text),
line positions
for the state
by the stronger
200 cm-’
mmimum
in J bunches
(5.3) is uncertain
because
k=O line due to the state
the
(3,3).
1 in the symmetric top model) is shown in Fig. 3, using the calculated values of the rotation constants B. It is clear that germyl isocyanate is much more like methyl isocyanate in its behavior than the silyl compound, for which the bending excited states have larger effective B values than the ground state, or methyl isothiocyanate, where the pattern of k = 0 lines reverses (see Fig. 4 of Ref. (15)). We have confirmed that the present model allows us to calculate reliable values for the rotation constants B and the Z-doubling constant qlo for germyl isocyanate as half the expectation values of the sum and difference of the xx and yy terms of the inverse moment of inertia matrix, as for other quasi-symmetric tops (15). Some calculated values of half the sum are shown in Table IV, together with the B values derived from the spectra, and the I-doubling constants calculated for the first few levels with I = 1 are shown in Table VI together with the effective values of qlo derived from the ldoublet lines of the spectra. As the isotopic variation of such quantities is of some interest we have included observed and calculated values for all three isotopic species.
80
CRADOCK
ET AL.
I
2
3
4
“b
FIG. 3. Variation of B values for levels with I= 0 and u = 0, 2, 4, or 6, corresponding to ub = 0, 1, 2, or 3 with m = 0 in the bent molecule notation, for methyl, silyl, and germyl isocyanates and methyl and silyl isothiocyanates.
VII. CONCLUSIONS
We have confirmed that the quasi-symmetric top model provides an adequate basis the description of the microwave spectrum of germyl isocyanate, as for the methyl and silyl analogs. The spectra allow us to refine effective B rotation constants and OJ centrifugal constants, and the program developed to express the quasi-symmetric top model makes it possible to define two structural parameters (GeN bondlength and the equilibrium bond angle at nitrogen) and three potential parameters, the height of the hump at linearity of the GeNCO chain (which is assumed to be Lorentzian), the force constant for the GeNC bending motion, and the height of the threefold barrier to internal rotation at the equilibrium bond angle. The variation of the GeN bondlength with the bend angle is also defined, but the tilt of the GeH3 group and the bend of the NC0 chain are too small to be defined and are set at zero. The structural and potential constants found from a single J bunch in the spectrum of the 74GeH3 species can be used to predict the spectra of other isotopic species, showing that the assumptions made in respect of unrefined structural parameters (GeH, NC, and CO bondlengths, HGeN bond angle) are sensible. The magnitude of the hump, 339 cm-‘, is intermediate between the values found for methyl and silyl isocyanates, as is the force constant for the bending motion. We are currently investigating the far-infrared spectrum of monoisotopic samples of germyl isocyanate at Doppler-limited resolution, and we hope to be able to use the model program to assign lines and features in the two bands (due to Av = 1 and 2 transitions (16)) observed previously (I 7). We have already established that the model for
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
81
TABLE VI Observed
state
and Calculated
(v.9,)
CSIC
(3.1) ohs call2
(5.1) obs talc
Note: observed
with
k!L=+l.
values
calculated
Constants,
qlo/MHz
74GeHsNC0
“GeH3NCO
(1.1) obs
in spectra:
I-Doubling
74GeD3NC0
19.9
i 9.68
19.33
19.45
19.16
19.16
19.6
19.17
19.44
19.16
i 8.90
i a.88
la.8
18.46
1a.67
i 8.70
i a.45
i 8.40
are derived values
from
the separation
are ‘/~(~p~~>-~~~~>)
of k-do&M
lines
for levels
see Ref.(l4).
program with the present parameter set predicts the Av = 2 transitions near 100 cm-‘, as observed in the Raman spectrum of the gas (17). ACKNOWLEDGMENTS Financial support from the National Science Foundation (USA) through Grant CHE-79-20763 is gratefully acknowledged; S.C. and J.R.D. acknowledge support from NATO in the form of a Collaborative Research Grant No. 140/82.
RECEIVED:
July 24, 1987 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16. 17.
J. A. DUCKETT, A. G. ROBIETTE,AND I. M. MILL.S, J. Mol. Specfrosc. 62, 19-33 (1976). S. CRADOCK, J. Mol. Spectrosc. 92, 170-183 (1982). J. KOPUT, .I. Mol. Spectrosc. 118, 189-207 (1986). M. KREGLEWSKI, Chem. Phys. Left. 112,275-278 (1984). A. WIERZBICKI, J. KOPUT, AND M. KREGLEWSKI,J. Mol. Spectrosc. 99, 102-l 15 (1983). J. T. HOUGEN, P. R. BUNKER, AND J. W. C. JOHNS, J. Mol. Spectrosc. 34, 136-l 72 (1970). J. KOPUT, J. Mol. Spectrosc. 106, 12-2 1 (1984). J. KOPUT, J. Mol. Specfrosc. 115, 131-146 (1986). D. R. JENKINS,R. KEWLEY, AND T. M. SUGDEN, Trans. Faraday SOC.58, 1284-1290 (1962). J. R. DURIG, Y. S. LI, AND J. F. SULLIVAN, J. Chem. Phys. 71, 1041-1049 (1979). J. R. DURIG, J. F. SULLIVAN, Y. S. LI, AND A. B. MOHAMAD, J. Mol. Struct. 79, 235-238 (1982). J. D. MURDOCH, D. W. H. RANKIN, AND B. BEAGLEY, J. Mol. Struct. 31,291-299 (1976). M. J. BARROW, E. A. V. EBSWORTH, AND M. M. HARDING, J. Chem. Sot., Dalton Trans., 1838-1844 ( 1980). T. N. SRIVASTAVA, J. E. GRIFFITHS,AND M. ONYSZCHUK, Canad. J. Chem. 40,739-744 (1962). J. KOPUT, J. Mol. Specfrosc. 118, 448-458 (1986). S. CRAD~CK AND D. C. J. SKEA, J. Chem. Sot., Faraday Trans. 2 76, 860-871 (1980). J. R. DURIG AND J. F. SULLIVAN, unpublished observations.
OF MOLECULAR
SPECTROSCOPY
128,688
1 ( 1988)
The Microwave Spectrum of Germyl Isocyanate, a Quasi-symmetric Top STEPHEN CRADOCK Department of Chemistv, JAMES R. DURIG,
University of Edinburgh, Edinburgh EH9 3JJ, Scotland A. B. MOHAMAD,
AND JOANN F. SULLIVAN
Department of Chemistry, University of South Carolina. Columbia, South Carolina 29208 AND JACEK KOPUT Department of Chemistry, A. Mickiewicz University, Poznan, Poland The microwave spectrum of gennyl isocyanate in the K, P, and R bands (12.4-40.0 GHz) has been investigated using natural isotopic samples and samples containing specific germanium isotopes, mass numbers 72 and 74, and samples containing GeD, groups. The very complex spectrum is analyzed as that of a quasi-symmetric top, in which the skeletal bending motion has an energy maximum at the linear configuration; the height of the maximum is some 339 cm-‘. Many vibrational states of the two-dimensional bend lie close in energy, resulting in strong interactions between rotational levels of different vibrational states. The program used for the analysis has been used previously to account for similar spectra of methyl and silyl isocyanates and methyl isothiocyanate; the behavior of the germyl compound is more like that of the methyl isocyanate than that of the silyl compound, where the height of the maximum is much less. Although we did not include centrifugal distortion operators in the Hamiltonian the program successfully predicts k = 0 line positions in J + 1 + J bunches with J up to 9, using only lines in the J = 3 bunch to define the parameters of the model, which include the height of the hump, the bend angle of the skeleton at the energy minimum (142.18(5)“), the force constant for the bending motion at the minimum (0.1094(7) mdyn A), and the GeN bondlength at equilibrium (1.8257(5) A). The threefold barrier to internal rotation of the GeH3 group at the equilibrium position is about 3 cm-‘, much lower than the value found for methyl isocyanate. The fit to the observations, about 100 lines in the 4 + 3 bunch, is improved by allowing for a variation in the GeN bondlength as the bend angle changes. The quality of the least-squares fit corresponds to an estimated standard deviation for an observation of about 2 MHz, but not ah observed lines can be accounted for precisely, showing that additional interactions are involved that are not yet included in the model. 0 1988 Academic Press, Inc. I. INTRODUCTION
The molecular structures of isocyanates and isothiocyanates have been studied by spectroscopic and diffraction methods for many years, and it has become clear that at least in the gas phase it is necessary to take account of the low-energy, large-amplitude motion corresponding to both the bend at nitrogen and the internal rotation of the NC0 or NCS group against the rest of the molecule if a satisfactory representation of 0022-2852188 $3.00 Copy&ht
0
1988 by Academic Pms,
Inc.
All rights of reproduction in any form mewed.
68
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
69
the spectra or diffraction patterns is to be achieved. For silyl isocyanate, SiHsNCO, an analysis of the microwave spectrum (I) was found to be possible in terms of a symmetric top model, in which the molecule is treated as having a linear skeleton with a two-dimensional bending motion at nitrogen, and the potential for this motion is taken to be anharmonic. However, for methyl isothiocyanate, CH,NCS, the symmetric top model (in a form which treated each vibrational state separately and took account of the interactions between levels belonging to different vibrational states only as contributing to anomalous values of the centrifugal distortion constants, especially DJK) failed to account fully for the observed line positions (2). A complete analysis (3, 4) of the microwave spectrum of methyl isothiocyanate was possible by using a quasisymmetric top model (5) which takes explicit account of the large-amplitude motions. This model was developed from the work of Hougen et al. on the rigid bender model of a triatomic (6). Similar analyses of the microwave spectrum of methyl isocyanate (7, 8) have been reported, and the same quasi-symmetric top model has been used to explain the microwave spectra of a number of other molecules. The Hamiltonian used (5) takes account of overall rotation (three degrees of freedom), the internal rotation, and the bend at nitrogen, making five degrees of freedom in all. All other motions are ignored, it being assumed that they are of small amplitude and not coupled to the low-frequency motions. As a result, the model neglects any possible mixing of the five degrees of freedom included in the model and the higherfrequency modes. A further limitation is that no contributions of small-amplitude motions to centrifugal distortion terms are included, so the accuracy is limited for higher J values. Once the vibrational wavefunctions have been found by a numerical integration procedure, the appropriate rovibrational levels are treated in three symmetry blocks (A,, Al, and E) by a variation method; details will be found in Refs. (3-5, 7, 8). The prime characteristic of quasi-symmetric top molecule spectra in the microwave region is their complexity. This arises mainly because of the large number of vibrational states that are populated at accessible temperatures, because of the small energy gaps between them. Thus for germyl isocyanate there are 15 distinct k = 0 levels below 250 cm-‘, and all these and more give rise to discernible microwave lines, in each case together with lines for all possible k values other than zero. In addition, the spectra are not readily assignable without the aid of predictions from the model, as the very strong essential interactions between levels of different k values prevent the recognition of subspectra due to particular “vibrational states,” as was possible for silyl isocyanate (I). Nevertheless, with the aid of the model program we have been able to assign the spectra and to refine some structural and potential constants for germyl isocyanate, which now joins the methyl and silyl analogs as a classic example of a quasi-symmetric top. We find that germyl isocyanate lies between the methyl and silyl compounds in terms of the height of the central hump in its bending potential function, which is about 339 cm-‘, compared with about 928 cm-’ for the methyl compound and about 30 cm-] for the silyl. It is thus rather similar to methyl isothiocyanate (2-4) where the hump is about 200 cm-‘; both silyl (9) and germyl (10) isothiocyanates have strictly linear skeletons, though each has a low-frequency, large-amplitude bending mode.
70
CRADOCK
ET AL.
The microwave spectrum of germyl isocyanate has been briefly reported before (I I), and some structural parameters have been derived from an analysis of the spectra of several isotopic species. The analysis reported here confirms the essential correctness of the earlier results, but provides slightly modified values for some parameters, partly because of different assumptions about unrefined bondlengths, and partly because of a different assignment of the true vibrational origin of each J bunch. The structure found is very similar to that determined by the analysis of electron diffraction patterns (12) and not very different from that found in the solid state by X-ray methods (13). II. EXPERIMENTAL
DETAILS
Samples of germyl isocyanate with normal isotopic composition (five isotopes of germanium, mass numbers and percentages 70, 20.52%; 72, 27.43%; 73, 7.76%; 74, 36.54%; 76, 7.76%) or with only a single Ge isotope (mass numbers 72 and 74) were prepared in a vacuum system by passing an appropriate sample of germyl bromide over solid silver cyanate (14) and were purified by trap-to-trap or cold-column fractional distillation. Monoisotopic germyl bromide was prepared from GeOz via GeH4 and GeH3Cl. Deuterium-substituted samples were prepared via GeD4 in the same way. Samples were stored at dry-ice temperature after preparation, and spectra were also run at reduced temperature to minimize sample decomposition in the spectrometer. Microwave spectra were obtained using a Hewlett-Packard 8460A microwave spectrometer, using backward-wave oscillators as tunable sources of radiation in the K, P, and R bands (12.4-40.0 GHz). This allowed the study of the J + 1 + J u-type Rbranch transitions with J in the range 3 to 9. III. SPECTRUM
AND ASSIGNMENTS
The spectrum consists of “main bunches” separated by some 3.66 GHz, each containing most of the u-type R-branch lines expected for one of the (J + 1) + J transitions. In addition, as first noted in the spectrum of methyl isothiocyanate (2), there are lines between the main bunches that appear to follow roughly the pattern expected for the K structure of the spectrum of a symmetric top but with a ridiculously large value of DJK, in this case about 6 MHz. The J and K assignments of these lines can be checked by observing the Stark lobes at low Stark voltages, and these are indeed consistent with the values suggested by the pattern. However, the patterns are actually not sufficiently regular to be properly explained in this way, and even the quasi-symmetric top model used for the analysis here fails to account for the line positions in detail. We may attribute this failure to the combination of deficiencies in the model and truly accidental perturbations of the levels concerned, either by levels not included in our analysis or by levels that are included by mechanisms not taken account of in the Hamiltonian. A typical main bunch and some of its associated outlying lines are illustrated in the survey spectrum shown in Fig. 1. The levels of a quasi-symmetric top can be described in either of two ways, depending on whether we consider it to be best treated as a symmetric top molecule (for which the two vibrational degrees of freedom in the model are the two degenerate components of the bending mode at nitrogen) with a very anharmonic potential function that means that the “reference configuration” with a linear skeleton is significantly higher
71
GERMYL ISOCYANATE MICROWAVE SPECTRUM
22.0
21.5
22.5
&Hz)
FIG. 1. The J = 6 + 5 bunch of 74GeHjNC0, showing the vibrational origin va), three lines (k = 1,2. 3) of the (u, I) = (0, 0) series extending to low frequency, labeled by k, and some of the u = I. k = 0 lines to
higherfrequency.labeledby (u,I).
in energy than the equilibrium structure, or as a bent molecule whose bending motion at nitrogen, together with the internal rotation about the single bond to nitrogen, is of such large amplitude that even molecules in the ground vibrational state may depart quite far from the equilibrium configuration. In the first case our quantum numbers would be vlo and Ilo (hereafter referred to as v and 1 for brevity), the vibrational and vibrational angular momentum quantum numbers for the two-dimensional bending mode yIo of the linear skeleton, together with J and k, the quantum numbers for overall angular momentum and for the component of this angular momentum about the axis coinciding with the linear skeleton. Due to vibration-rotation interactions the sign of the product kl is significant. In the second case the vibrational quantum number is Q, with a second quantum number m for the internal rotation, and there is only one strict quantum number J for overall angular momentum, though we are entitled, as for any prolate near symmetric top, to use a component k, about the axis of least moment of inertia as a pseudo-quantum number. Again, due to torsionrotation interactions, the sign of the product mk, is significant. The two notations are related (2, 15) as of course they must be; the essential equations are vb =
(v -
m=l-k.
11)/2
(14 (lb)
The rotational quantum number k translates directly to k,. The analysis of the spectrum of silyl isocyanate was published (I) using the “symmetric top” formalism, but the reports on the spectra of methyl isocyanate (7, 8) and methyl isothiocyanate (3, 4) used the bent molecule formalism. Nevertheless, we here use the “symmetric top” quantum numbers to denote the various vibrational states; the “translation” may be performed using the equations above. One advantage of the symmetric top description is that it emphasizes the occurrence of lines in fairly close clusters in the higherfrequency portions of each bunch, as may be seen in Fig. 1; these are assigned to the various k lines for a particular vibrational state on the symmetric top model, but are apparently chance coincidences on the bent molecule model. For the lower vibrational levels, where the effects of the essential perturbations between the various vibrational states are large, the lines due to different k levels are far apart, and either formalism may be used. It must be noted that the distinction between the two notations is purely one of viewpoint; either provides an equally valid description of the levels and the
72
CRADOCK
ET AL.
spectra. The inadequacy of the previous (2) treatment of the methyl isothiocyanate problem stems from the failure to include the essential and chance interactions between energy levels, not from the choice of notation. The relationship between the two formalisms has been explored in some detail recently (15). The Stark effect is of limited use in assigning the spectra; we can distinguish the k = 0 lines as usual as those lines having a slow second-order Stark effect. They appear only at Stark voltages of more than 100 V/cm. The Z-doublet lines with I = 1, k = 1, and kl positive have a characteristic Stark behavior, showing Stark lobes to high or low frequency, with a somewhat faster second-order Stark effect, appearing at voltages of 20 V/cm or so. All other lines have a very rapid first-order Stark effect, appearing at voltages of less than 10 V/cm; we find no pairs of lines with a very fast Stark effect giving lobes between the zero-field lines due to splitting caused by the barrier to internal rotation, as were observed for methyl isocyanate (8). Because we have not been able to observe bunches with very low Jwe see no discrete structure due to nitrogen quadrupole coupling. The lines in the lowest bunch (J 4 + 3) were somewhat broad (of the order of 2 MHz for k = 0 lines and more ir higher k lines). There was no sign of any splitting like that illustrated (8) for the k = 3 line of methyl isocyanate, and we were unable to use quadrupole splittings to aid assignments. The assignments reported below were made on the basis of identification of k = 0 lines and I-doublet lines from their Stark effects (see above), which allowed use of the skeletal bending-torsion-rotation Hamiltonian to define the potential function, using reasonable bondlengths to begin with. The equilibrium bond angle was defined on the basis of the I-doublet separation, as in the earlier report (II) (which used only this separation and the bunch separation, giving rotation constants B - C and B + C, respectively, for a number of isotopic species). The model Hamiltonian was then used to predict the positions of other lines for the lowest observed J bunch (J = 4 + 3) for which the effects of the neglect of centrifugal distortion and other interactions should be minimized. Most of the expected lines could be assigned, though there was inevitably some overlapping because of the density of lines in the main bunches. Unfortunately, as mentioned above, the lines found between the main bunches, for which assignments were easy to make and where no overlapping occurred, proved to be impossible to fit precisely, discrepancies of 100 MHz or more being found in some cases. Finally, the structural and potential parameters found by least-squares refinement for the 74GeH3 isotopic species were used to predict the spectra of 72GeH3 and 74GeD3 species, the accuracy of the fit of calculated and observed frequencies of the k = 0 lines confirming the consistency of the structure (Table I). It was also found that the parameters fitted only to line positions for the J = 4 + 3 bunch were adequate to predict the positions of k = 0 lines at least for J bunches up to J = 10 + 9; for other k values there were as expected increasing deviations from the predicted line positions as J and k increased, but these deviations could not be simply explained by use of a single term of the form D.&J + l)k2. The analysis of higher bunches will therefore have to await the availability of a higher-order model, and the present analysis must be regarded as preliminary in this respect, though we hope it is based on a correct assignment, and we are confident that it leads to a reasonable description of the structure and the potential function.
GERMYL ISOCYANATE MICROWAVE SPECTRUM
13
TABLE I Observed and Calculated k = 0 Line Positions/MHz in the J = 6 + 5 Bunch for Three Isotopic Species of Germyl isocyanate
“GeH3NCO
74GeH3NC0
74Ge03NC0
ohs
22105.62
21937.26
21222
talc
22104.09
21936.17
21225.49
ohs
22 178.80
22009.61
21290
talc
22178.75
22010.01
21292 98
ohs
22467.2
22295.94
21546
caic
22467.04
22296.06
21552.41
Level (v.!z) 0.0
2.2
6.6
Note:
observed
spectra.
frequencies
and are only
for the GeD3
approximate
species
(estimated
are taken
precision
t
from
survey
5 MHz).
IV. MODEL HAMILTONIAN
The definitions of molecular coordinates and the axis system are as used for methyl isocyanate (7, 8), and all the analysis reported here used the same model as this earlier work. A full description of the model program is given in Refs. (7, 8) and further references therein and does not need repetition here. Basically, the zero-order Hamiltonian H!btb,,contains the appropriate quadratic products of the five momentum operators corresponding to the five degrees of freedom involved, plus a potential function V(p, T) defining the variation of potential energy with the GeNC bending coordinate p and the torsional coordinate T. The energy levels and wavefunctions are calculated variationally. The basis set consists of products of symmetric top rotational wavefunctions, free internal rotor torsional wavefunctions, and vibrational wavefunctions obtained by numerical integration over the one-dimensional bending potential. The results were found to be rather insensitive to the number of points used in the numerical integration, and thus in the definition of the vibrational wavefunctions, presumably because any deficiencies in the basis functions were accommodated in the subsequent variation procedure. V. RESULTS
About 15 lines were assigned in the J = 4 + 3 bunch, of which 63 were fitted to some 9.5 lines predicted by the model, the others being too far from the calculated positions to be included. The final standard deviation, for an observation of unit weight, was 1.9 MHz with six refining parameters. While this is not a good fit by comparison with other microwave problems, it is comparable to the results achieved using the present model for other molecules (3, 8).
CRADOCK
74
ET AL.
The model program contained several variables, which are listed in Table II. Only a portion of these proved to be refinable; the situation is similar to that encountered in the definition of the structure of a symmetric top molecule from the single observable B rotation constant. The NC0 group geometry was assumed to be linear, with r(N=C) = 1.199 A, r(C=O) = 1.174 A, as found for silyl isocyanate (I) and assumed for Structure I of methyl isocyanate (8). The HGeN bond angle was fixed so as to achieve consistency between the observed and calculated k = 0 line positions for the GeD3 isotopic species, as mentioned above. The GeN bondlength and the equilibrium angle at nitrogen were refined and were well determined. The GeNC bending potential function was assumed to be of the form (quadratic + Lorentzian hump), as found for silyl isocyanate, methyl isocyanate, and methyl isothiocyanate, and required two parameters, H, the height of the hump, andf; the restoring force constant at the equilibrium angle, as well as the value of the bond angle at equilibrium. All these potential parameters were refined. One very important parameter was the leading term x in the power series expressing the variation in the GeN bondlength with p, rGeN=r’+x(p-p,).
- *.
(2)
This was well determined. The parameters 6 and y, representing the tilt of the GeH3 group and the bend of the NC0 group away from the linear configuration, can be treated as the coefficients of (p - pe) in a power series expansion and are related to the zero-order coefficients
TABLE II Model Parameters
Parameter
Value
(this
r(GeN)/x
1.8257(5)
r(GeH)/B. r(N=C)/B.
work)
Microwavea
E.LIb
X-rayc
1.826(15)
1.831(4)
1.856(6)
1.500 fixed
1.52019)
1.532(6)
1.28-1.35
1.199 fixed
1.168(27)
1.190(7)
1.161(g)
r(c-0)/X
1.174 fixed
1.182(20)
1.182(7)
1.185(9)
<(HGeN)/deg
108.15
108.3(20)
110 fixed
101,113
fixed
<(GeNC)/deg
142.18(5)
143.2(34)
141.3(3)
147.0(6)
<(NCO)/deg
180.0 fixodd
180.0 fixed
180.0 fixed
173.8(8)
GeH3
0.0 fixedd
3(2)
0. fixed
not defined
tilt/deg
x(GeN)/x
rad-’
x(N=C)/X
rad-’
H/cm-’ flmdyn Vg’/crn
Notes:
0.019(3) 0.0 fixedd 338.7(20)
A -1
0.1094(7) rad -1 W(2)
a) Reference
(11), b) Reference
d) see text for estimated
limits
(12). c) solid on these
phase
parameters.
at 178 K, Reference
(13).
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
75
by the reasonable requirement that both tilt and bend are zero in the configuration with the GeNC group linear (3, 8). In fact, both were found to be zero, within a small standard deviation (of the order of 0.2”) so we have fixed each at zero in the final refinements. Note that this conflicts with the conclusion of the earlier report on the microwave spectrum (11) that the tilt was about 3”. The F’sparameters represent the torsional potential hindering internal rotation of the GeH3 group in the bent configuration. The form of the potential function is assumed to be V& T) = V&p) - l/2 V&)cos 37 - - * * ) (3) where V, is expanded as a power series in (p - p,). The effect of the V’Jterm in the potential is to allow mixing, and hence perturbation, of levels whose torsional quantum numbers m differ by 3; in the spectrum this manifests itself mainly as a splitting of lines corresponding to the levels where m = 3 (a systematic effect, observed for methyl isocyanate, where I’, is of the order of 20 cm-’ (8)) and as a shift, which may be very large, of lines which are due to levels which happen to lie very close to another where the m values differ by 3. This is an accidental effect, as the exact energies of the levels depend on the whole set of potential and structural constants. As mentioned above, no lines showing the characteristic splitting expected for lines due to levels with m = 3 were found in our spectra, suggesting that I’, was much smaller than for methyl isocyanate. At first, the assignment of lines was attempted with all the V3 constants set to zero. This allowed an extension of the assignment, and when almost all lines expected in the bunch had been assigned the coefficient of (p - pe), V:“, was allowed to refine. This improved the fit considerably, and the final value (Table II) is welldefined at about 5 cm-‘. As we assume that the barrier to internal rotation is zero at the linear configuration this implies that the barrier at the equilibrium bend angle, I’:“), is equal to I’:“. pe, or about 3 cm-‘. Thus it is much smaller than the value of about 20 cm-’ found for methyl isocyanate (8) but this is to be expected in view of the much greater length of the GeN bond. The observed line positions are listed in Table III for the J = 4 + 3 bunch, together with assignments of quantum numbers (v, 1; k) (the sign of the product kl is indicated as the sign of k) and the symmetry of the lower level involved (A,, AZ, or E) and the calculated line position in each case. As mentioned above, the least-squares fit used only these frequencies directly; Table I shows how well the k = 0 lines of some of the lowest vibrational states of the 72GeH3 and 74GeD3 species in a higher J bunch are fitted by the refined structure. The final parameter set (including those parameters which could not be refined) is listed in Table II, with the earlier microwave (1 I), electron diffraction (12) and X-ray (13) results where appropriate. We have also investigated the possible effects of centrifugal distortion terms of the form 0.J2(J + 1)2 by measuring the line positions for the (0, 0; 0) transitions for all J bunches up to J = 10 + 9. These should be unaffected by the strong essential interactions, and as expected form a well-behaved pattern following the symmetric top formula v$ = 2BJ- 4DJJ3, (4) where J is the higher J value involved. The DJ constant for the ground vibrational state (v, I) = (0,O) has the fairly small value of 1.55 kHz, so the k = 0 lines for higher
CRADOCK
76
ET AL.
TABLE III
Observed and Calculated Line Positions/MHz for the J = 4 + 3 Bunch of “GeHSNC0 (v.ll;k) 003A 203A 403A 402E 202 002E 401E 511 400 311 201E 510E 111 512 200 5 l-l OOlE 310 312 000 511 313 422 421E 423E 110 3 l-l 420E 112 222A 223E 221E 4 2-l 220E 311 4 2-l 2 2-l 113E 332 331E 532 4 2-3 531E 533A 330A 530A 11-l
Syme
E
A2 A2 A2
A2 E A2 E E E A2 A1 E A
E E E
A At E A E E E
E
Mobs) 14215 14330 14362 14420.3 14428.3 14435.6 14470.7 14485.5 14468.7 14520.6 14544.1 14546.2 14556.5 14561.0 14574.0 14574.0 14577.1 14605.0 14615.6 14625.1 14633.2 14643.3 14643.3 14646.5 14647.5 14647.3 14650.2 14651.6 14655.3 146595 14662.6 14663.8 14664.1 14673.0 14676.3 14665.3 14689.5 14699.0 14698.5 14701.5 14704.6 14705.5 14706.2 14706.2 14711.4 14711.4 14713.8
v(calc) 14192.5 14254.8 14316.4 14415.6 14429.9 14406.5 14471.4 14476.7 14491.0 14523.2 14541.7 145569 14557.3 14559.6 14576.6 14574.1 14571.2 146076 14613.0 14624.5 14626.1 14643.3 14644.9 14647.1 14647.7 146466 14650.4 14653.8 14653.9 146597 146633 14665.0 146652 14673.6 14674.3 14681.9 14692.0 14696.0 14699.7 14703.6 14705.9 14704.1 14707.8 14708.7 14710.5 14712.0 14713.8
Wtt 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(v,&;k) 111 53-l 2 2-2 33-l 732 731E 3 3-2 5 3-3 443E 442 441A 3 3-3 11-2 2 2-3 440E 44-l 4 4-2 643E 642 641A 4 4-3 6 4-2 553E 552 551E 550 5 5-l 5 5-2 5 5-3 753 751E 750 3 l-3 563A 662 561E 660A 5 6-l 5 6-2 363 362 773 772 171A 170 363 382 11-3
Sym’
w(obs)
w(calc)
Al E E E E
14713.9 14719.5 14719.5 14719.5 14729.6 14729.6 14733.0 14737.0 14745.0 14749.7 14749.7 14754.5 14754.5 14754.5 14755.7 14760.0 14770.2 14774.0 14774.0 14774.0 14761.0 14786.0 14604.0 14804.0 14805.5 148087 14811.8 148160 14821.0 148420 148420 14642.0 14843.0 14859.5 14861.5 14861.5 14663.9 14666.0 14869.0 14906.0 14908.0 14921.2 14921.2 14921.2 14921.2 14979.5 14979.5 15040.0
14710.5 14717.6 14719.0 14720.3 14727.7 14726.3 14733.4 14735.2 14747.0 14748.7 14751.8 14752.2 14754.9 14755.3 14756.3 14762.2 14770.2 14771.5 14772.2 14773.7 14780.5 14783.7 14801.5 148026 148040 14808.5 14812.5 14817.2 14823.0 148402 14641.7 14843.3 146390 148569 14860.7 14662.3 14664.3 14666.8 14869.2 14910.1 14910.4 14920.3 14921.0 14921.6 14923.0 14982.5 14982.7 15018.3
E A E A A E E A E E A A E A E E E E E E
E E A E E E E E A E
Wtb 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
i I
1 1 1
1 1 1
i 1 1 0
1 1 1 1
1 1 1 1 1 1 1 1 0 0 0
Note: a) symmetry of lower level (A indicates both Al and A2 components) b) weight of transition in least-squares fit.
J bunches could have been used in the least-squares fit, as the centrifugal distortion contributes shifts of less than 10 MHz to the line positions for the highest J value observed. We have chosen not to do so, as the calculation takes much longer for higher J values, but we have confirmed that the program successfully predicts line positions to within a few MHz for k = 0 transitions as far as the J = 10 + 9 bunch, except for the (v, 1) = (1, 1) and (3, 1) vibrational states, for which DJ is much larger (see below). The measured k = 0 line positions are shown in Table IV. Where no entry is given the line position was not measured precisely, but in all the bunches studied the same essential pattern of k = 0 lines was present.
GERMYL
ISOCYANATE
MICROWAVE
77
SPECTRUM
TABLE IV Measured VA
2.0
4.0
1.1
3.1
5.1
3
14625.1
14574.0
14488.7
146473
14605.0
14548.1
4
18281.43
18216.88
18111.2
18305.56
182508
5
21937.26
21858.7
21733.08
21961.07
218930
6
25592.84 29248.34
v,L
32908.6
6
32903.37 36558.10
36438.2
2.2
4.2
3
21820.8
29091.8
29263.0
29147.2
9
=
J"=
for 74GeH3NCO/MHz
0.0
=
J'=
k = 0 Line Positions
14673.0
365506
36416.8
3.3
4.4
5.5
6.6
14711.4
147557
14808.7
14863.9
18341.55
18319.50
18389.41
18444.87
18511.0
18580.18
22009.61
21983.2
22067.03
22133.6
22212.8
22295.94
29421.85
2951047
29616.33
29727.14
a
33013.1
32973.2
33099.0
33198.5
33317.8
33442.5
9
366808
366363
36776.1
36886.6
37019.1
37157.5
2934543
The potential function describing the bending motion of the GeNCO chain has a minimum at a bond angle GeNC of 142.2”, very close to that found in the electron diffraction study (12) 141.3(3)“, but rather different from the value found in the crystal (13), 147”. The GeN bondlength is also very close to the electron diffraction value; the differences in the bondlength and bond angle at nitrogen between the Xray structure and the present results may well be due to intermolecular interactions in the solid. The barrier (hump) at linearity of the GeNCO chain is about 339 cm-‘. The potential function is illustrated in cross section in Fig. 2, which also shows the positions of some of the lower vibrational levels, whose energies relative to that of the ground state are listed in Table V, together with the effective rotation constants B and centrifugal distortion constants DJ derived from the k = 0 lines of the spectra by use of the symmetric top formula Eq. (4). It is clear that the centrifugal distortion constants show behavior similar to that observed for silyl isocyanate (I), in that the lowest levels in each set have anomalous contributions due to the anharmonic motion, but the higher levels have more normal DJ values. The anomalous contributions are distinctly larger for the germyl compound, but this is to be expected in view of the greater height of the hump. VI. COMPARISON
WITH
OTHER
QUASI-SYMMETRIC
TOP
MOLECULES
We may compare the present results with those for other isocyanates and related molecules using the criteria suggested in Ref. (15). A correlation parameter, -rn, which
78
CRADOCK
ET AL.
BOO-
540-
480-
420-
180-
0
0
I
I 10
I
I 20
I
I 30
,
I 40
I
I 50
I
I 60
FIG. 2. Refined potential curve for bending of GeH3NC0 at nitrogen, with J = 0, k = 0 levels below 250 cm-‘. The levels are labeled by values of u and I in the form vl.
compares the energies of the (v, I) = (2n + 1, 1) and (2n + 2,0) levels above the (2~2, 0) level, where n is the bending quantum number Q, appropriate to the bent molecule formalism (see Section III), is defined in terms of the symmetric top labeling of levels as -rn=1-4
E(u=2n+ 1,1= l;k= l,J= l)-E(2n,O;O,O) E(2n+2,0;0,0)-E(2n,O;O,O) [
1.
The correlation parameter for the ground vibrational state is y. = 0.85, compared with 0.9 1 for methyl isocyanate and -0.24 for silyl isocyanate. Germyl isocyanate is thus much nearer the “bent molecule” limit (where ye is + 1) than the silyl compound, but not so close as the methyl compound. Unlike methyl isothiocyanate, germyl isocyanate does not become much closer to the linear limiting case (for which y is - 1) in the first and second excited bending states, for which the correlation parameters are -yl = 0.78 and y2 = 0.62. The pattern of k = 0 lines due to the successive excited bending states of germyl isocyanate in which there is no torsional excitation (no vibrational angular momentum
79
GERMYL ISOCYANATE MICROWAVE SPECTRUM TABLE V Calculated Energies G of k = 0 Levels and Effective Rotation Constants B of 74GeH3NC0 state
Notes.
G/cm-’
0.0
0.0
1828.1 1
1828.217(l)
20 47(3)
1,’
5.7
1829.28
1831 566(3)
22.8
1832 51
1834.192(l)
3,3
507
1637 35
1838.986(
4.4
89.0
1843 32
1844.539(Z)
1.05(l)
2.0
92 1
1822.36
1821.351(7)
-2 79(4)
3.1
98.9
1624.86
1826495(Z)
28.28(3)
4.2
118.6
1830 70
1831.996(2)
0.91(Z)
5,5
137.3
1850.06
1851.134(4)
0.89(3)
0.80(l) 094(l)
1)
(1838.981
5.3
150.0
1838.19
4.0
178.3
1811.39
1811.12(2)
0.4(3)
5.1
187.8
1819.05
181861(l)
2.9(l)
6,4
192.1
1846.43
6.6
195 1
1857 31
includes
calculated calculated
from
1.55(l)
2.2
(0,O). which
B(obs)
DJ/kHz
B(calc)/MHzB(obs)/MHz
(V.L)
all k=O levels
itself
difference
from
the bending
and DJ are derived J=3 to J=9.
calculated
lies 46 2 cm -’
energy
above
(for J-3); vibrational
from
The B(obs)
k=O line is apparently
1858 056(Z)
hidden
to lie less than the potentlal B(calc)
value
= %(
wavefunction
the observed
above
G is the
+
line positions
for the state
by the stronger
200 cm-’
mmimum
in J bunches
(5.3) is uncertain
because
k=O line due to the state
the
(3,3).
1 in the symmetric top model) is shown in Fig. 3, using the calculated values of the rotation constants B. It is clear that germyl isocyanate is much more like methyl isocyanate in its behavior than the silyl compound, for which the bending excited states have larger effective B values than the ground state, or methyl isothiocyanate, where the pattern of k = 0 lines reverses (see Fig. 4 of Ref. (15)). We have confirmed that the present model allows us to calculate reliable values for the rotation constants B and the Z-doubling constant qlo for germyl isocyanate as half the expectation values of the sum and difference of the xx and yy terms of the inverse moment of inertia matrix, as for other quasi-symmetric tops (15). Some calculated values of half the sum are shown in Table IV, together with the B values derived from the spectra, and the I-doubling constants calculated for the first few levels with I = 1 are shown in Table VI together with the effective values of qlo derived from the ldoublet lines of the spectra. As the isotopic variation of such quantities is of some interest we have included observed and calculated values for all three isotopic species.
80
CRADOCK
ET AL.
I
2
3
4
“b
FIG. 3. Variation of B values for levels with I= 0 and u = 0, 2, 4, or 6, corresponding to ub = 0, 1, 2, or 3 with m = 0 in the bent molecule notation, for methyl, silyl, and germyl isocyanates and methyl and silyl isothiocyanates.
VII. CONCLUSIONS
We have confirmed that the quasi-symmetric top model provides an adequate basis the description of the microwave spectrum of germyl isocyanate, as for the methyl and silyl analogs. The spectra allow us to refine effective B rotation constants and OJ centrifugal constants, and the program developed to express the quasi-symmetric top model makes it possible to define two structural parameters (GeN bondlength and the equilibrium bond angle at nitrogen) and three potential parameters, the height of the hump at linearity of the GeNCO chain (which is assumed to be Lorentzian), the force constant for the GeNC bending motion, and the height of the threefold barrier to internal rotation at the equilibrium bond angle. The variation of the GeN bondlength with the bend angle is also defined, but the tilt of the GeH3 group and the bend of the NC0 chain are too small to be defined and are set at zero. The structural and potential constants found from a single J bunch in the spectrum of the 74GeH3 species can be used to predict the spectra of other isotopic species, showing that the assumptions made in respect of unrefined structural parameters (GeH, NC, and CO bondlengths, HGeN bond angle) are sensible. The magnitude of the hump, 339 cm-‘, is intermediate between the values found for methyl and silyl isocyanates, as is the force constant for the bending motion. We are currently investigating the far-infrared spectrum of monoisotopic samples of germyl isocyanate at Doppler-limited resolution, and we hope to be able to use the model program to assign lines and features in the two bands (due to Av = 1 and 2 transitions (16)) observed previously (I 7). We have already established that the model for
GERMYL
ISOCYANATE
MICROWAVE
SPECTRUM
81
TABLE VI Observed
state
and Calculated
(v.9,)
CSIC
(3.1) ohs call2
(5.1) obs talc
Note: observed
with
k!L=+l.
values
calculated
Constants,
qlo/MHz
74GeHsNC0
“GeH3NCO
(1.1) obs
in spectra:
I-Doubling
74GeD3NC0
19.9
i 9.68
19.33
19.45
19.16
19.16
19.6
19.17
19.44
19.16
i 8.90
i a.88
la.8
18.46
1a.67
i 8.70
i a.45
i 8.40
are derived values
from
the separation
are ‘/~(~p~~>-~~~~>)
of k-do&M
lines
for levels
see Ref.(l4).
program with the present parameter set predicts the Av = 2 transitions near 100 cm-‘, as observed in the Raman spectrum of the gas (17). ACKNOWLEDGMENTS Financial support from the National Science Foundation (USA) through Grant CHE-79-20763 is gratefully acknowledged; S.C. and J.R.D. acknowledge support from NATO in the form of a Collaborative Research Grant No. 140/82.
RECEIVED:
July 24, 1987 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16. 17.
J. A. DUCKETT, A. G. ROBIETTE,AND I. M. MILL.S, J. Mol. Specfrosc. 62, 19-33 (1976). S. CRADOCK, J. Mol. Spectrosc. 92, 170-183 (1982). J. KOPUT, .I. Mol. Spectrosc. 118, 189-207 (1986). M. KREGLEWSKI, Chem. Phys. Left. 112,275-278 (1984). A. WIERZBICKI, J. KOPUT, AND M. KREGLEWSKI,J. Mol. Spectrosc. 99, 102-l 15 (1983). J. T. HOUGEN, P. R. BUNKER, AND J. W. C. JOHNS, J. Mol. Spectrosc. 34, 136-l 72 (1970). J. KOPUT, J. Mol. Spectrosc. 106, 12-2 1 (1984). J. KOPUT, J. Mol. Specfrosc. 115, 131-146 (1986). D. R. JENKINS,R. KEWLEY, AND T. M. SUGDEN, Trans. Faraday SOC.58, 1284-1290 (1962). J. R. DURIG, Y. S. LI, AND J. F. SULLIVAN, J. Chem. Phys. 71, 1041-1049 (1979). J. R. DURIG, J. F. SULLIVAN, Y. S. LI, AND A. B. MOHAMAD, J. Mol. Struct. 79, 235-238 (1982). J. D. MURDOCH, D. W. H. RANKIN, AND B. BEAGLEY, J. Mol. Struct. 31,291-299 (1976). M. J. BARROW, E. A. V. EBSWORTH, AND M. M. HARDING, J. Chem. Sot., Dalton Trans., 1838-1844 ( 1980). T. N. SRIVASTAVA, J. E. GRIFFITHS,AND M. ONYSZCHUK, Canad. J. Chem. 40,739-744 (1962). J. KOPUT, J. Mol. Specfrosc. 118, 448-458 (1986). S. CRAD~CK AND D. C. J. SKEA, J. Chem. Sot., Faraday Trans. 2 76, 860-871 (1980). J. R. DURIG AND J. F. SULLIVAN, unpublished observations.