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l-type doubling of the kl = −1 levels in the microwave spectrum of the C4v molecule BrF5
JOURNAL
OF MOLECULAR
/-Type
SPECTROSCOPY
Doubling
60,
18-30
(1976)
of the k/=---l Levels in the Microwave of the Cqa Molecule BrF,
Spectrum
I’. N. BRIER AND S. R. JONES Department
of Ckemislry,
Tke University, Munckesfer
1M13 9PL,
En&and
AND J. G. BAKER Sclrustev Laboratory,
The University, Manchester
Ml3 YPL, England
Measurements are reported for the J 3 + 4, 4 + 5, and 5 + 6 transitions of BrFS in the excited vibrational states vb(B1) = 1 and vg(E) = 1. These two states are nearly degenerate and an unusually strong Coriolis interaction perturbs both excited state spectra. New expressions are obtained for the E-species absorption frequencies which are valid in a strong Coriolis resonance situation. The analysis of the E-state spectrum has provided the first experimental observation of the doubling of the kl = - 1 levels predicted for molecules with Ceu symmetry. INTRODUCTION
In two earlier papers concerning measurements of the ground state microwave spectrum of BrF6 (1,Z) we reported the first experimental observation of the K-type doubling effect predicted for molecules possessing a fourfold symmetry axis (3). Further examples of K-type doubling in Cd8molecules have now been reported (4). It was pointed out by de Heer (5) as long ago as 1951 that in a singly excited state of a degenerate vibration, such molecules should also exhibit a second unique feature in their rotational spectrum, namely, an I-t?pe doubling of the kl = -1 levels in addition to the normal Z-type doubling of kl = + 1 states. The basis of this effect is that the four ro-vibrational states with j k 1 = 111 = 1 span E X E = d 1 + .42 + BI+ Bz in C4V symmetry. The usual Z-doubling effect splits the RI = +l states into separate A1 and At levels, and the extra I-doubling splits the kl = -1 states into a & and Rz pair. The Z-doubling of k1 = -1 states has been discussed in more detail by other authors (6-8). Following Cartwright and Mills (7), we will distinguish the two kinds of Z-doubling by writing the doubling constants involved as q+ and q- (but omitting the subscript t signifying quantities associated with a doubly degenerate vibrational state). In this paper we report the spectrum of BrFs in the excited vibrational states es(&) = 1 and Q(E) = 1. An accidental near-degeneracy of v5 and vg produces a strong perturbation of both excited state spectra through a Coriolis resonance interaction. This causes difficulties in the assignment of the spectra, particularly the E-state spectrum, which are already complex through the presence of the two isotopic species 7gBrFb and 81BrF6 plus considerable quadrupole structure. Our main purpose in this 18 Copyright All rights
0
1976
by Academic
of reproduction
Press.
in any form
Inc. reserved.
I-DOUBLING
OF THE kl = -
19
1 LEVELS IN BrFa
paper is to establish an assignment of the vg(E) = 1 spectrum and hence to report the first experimental observation of q--doubling. An exact matrix treatment of the Coriolis resonance with the aid of this assignment, and the calculation of various vibrationrotation parameters for BrFS, is in progress and will be the subject of a separate communication. EXPERIMENTAL
PROCEDURE
Spectra of the J 4 + 5 (30 GHz) and J 5 --+ 6 (36 GHz) transitions were recorded on a Hewlett-Packard 8460A spectrometer, and the J 3 + 4 (24 GHz) transition plus a repeat measurement of J 4 -+ 5 were recorded in this laboratory on a conventional 33 kHz Stark-modulated spectrometer with a phase-lock frequency track system. Problems associated with the stability of BrFb, even when using an all-metal vacuum system, were overcome by the use of a simple flow technique. A sample of BrF6 stored in a stainless-steel cylinder at approximately one-quarter atmosphere pressure was continuously pumped through the Stark cell (which was cooled to 200 K with solid COz) via a needle valve to regulate the pressure. The sample of BrF6 was supplied commercially by Air Products Limited and used without further purification. THEORY
Expressions for the frequencies of rotational transitions of CqV molecules in the absence of any accidental resonances have already been given by Kupecek (9), including the case of a singly excited degenerate vibrational state. The Kupecek formulas include the effect of the off-diagonal Z-resonance terms (7) of the type Ak = f2, AZ = f2 (@ interactions) and Ak = ~2, AZ = r2 (9- interactions). For the two pairs of originally degenerate states kZ = + 1 and kZ = - 1, these interactions produce the two Z-doubling effects described earlier. With the exception of these special cases, the effect of the Z-resonance interaction terms may usually be calculated using secondorder perturbation theory. Thus, for transitions for which kZ # fl, Kupecek gives the following results (9). YJ,K = 2&(J -~
+ 1) - 4D.r(J + 1)” - 2Dm(J
(J + 113 4
+ 1)&Z)* + 2~,r(J
(P>’
(q++>”
(kl + l)(Ct - & + rtC,> + (J+l) 4
+ l)(kZ)
W2(kZ
@Z -
1 1 (0
1)&t - Bt - StCt>
+ 1)
(Ct - Bt + rtC,) -
(q+)“(kZ -
1)
6, - & - i-t&) ’
where a subscript t signifies the Q(E) = 1 state of yg and later expressions with a subscript s will signify quantities associated with the ZJ~(&) = 1 state of ~6. When kZ = + 1, the two perturbation theory terms in Eq. (1) involving the parameter q+ are replaced by the Z-doubling term &q+(J + l), and when k2 = - 1, the terms involving q- are replaced by the second Z-doubling term fp(J + 1). Coriolis Resonance To date, all reported symmetric-top molecules
cases of Coriolis resonances in the spectra have involved an Al-E species interaction.
of C30 and Ci, The theory of
20
BRIER,
JONES AND BAKER
CORlOLlS MATRIX FOR A B-E SPLCIES INTERACTIJN
_* R [J,kli
Il,O’,
J.k
z
W,[J,k]
+ A
5
[J,k]l p,k-11%
-R e, k-1$
(Symetrical)
lO,l', J, k-l >
Wt [J. (k-l)!,]
where Wt [J,kd = Et* J (Jtl) + (Ct - Et*) (ke)' - ZCtct (ke) plus higher order terms - see Eq. (1)
WsrJ.kl
[J,kjl
= Bs* J(W)
=
+ (Cs - Bs*) k2 plus higher term
rj(Jt1) - k(k+ljjt
resonances of this type has been given in some detail by Kuczkowski and Lide (10) and di Lauro and Mills (II). Essentially, the state 1zig,zltli, J, k) = j 1, O”, J, K) of the nondegenerate vibrational state is linked by the Coriolis interaction with the two states 10, lr, J, K + 1) and IO, l-l, J, k - 1) of the degenerate vibration. An exact interpretation of the excited-state spectra then requires (in principle) a numerical diagonalization of the resulting 3 X 3 matrices, one for each value of K. In the case of BrF6 there is a resonance between the near-degenerate states v5 = 1 and q = 1 corresponding to a HI-B species interaction. The states which are linked by the interaction (by the Hamiltonian term labeled HQ in (8, Table III)) are now 11, O”, J, K) with IO, l-l, J, k + 1) and 10, lr, J, K - 1). Thus, it is states with the same value of (R + Z) which interact in this case rather than (k - 1) as in A-E interactions. This results in only minor changes to the usual Coriolis interaction matrix (see Table I, in which a superscript star refers to quantities with their contribution from this specific Coriolis interaction omitted. Note also that a constant vibrational energy term has been subtracted from each of the diagonal elements). Approximate
Methods
If the vibrational degeneracy is almost exact and the interaction term RCJ, k]* - h, then an exact numerical diagonalization of the Coriolis matrices will be necessary. This
J-DOUBLING
35 7cO I
OF THE kl = -
21
IN BrFs
35ml I
35 740 I Freq
1 LEVELS
35 820 ,
MHz
FIG. 1. (a) Observed and (b) calculated spectrum of the J 5 + 6 transition of BrFs in the excited vibrational state zig = 1.
was the situation found for PFI BHa for which A = 0.83 cm-’ (10). Ingeneral, however, there are too many unknown parameters in the Coriolis matrix and although the diagonalization may be mathematically exact, some assumptions and approximations regarding the quantities in the matrix will have to be made.
3
37 960
c
38 olo’
38460
FIG. 2a. Observed spectrum of the J 5 + 6 transition of BrF5 in the excited vibrational state ZJB@) = 1. Lines identified by the values of the quantity RI.
22
BRIER,
JONES AND BAKER
At the other extreme, if the interaction is very weak and R[J, K]h << A, a secondorder perturbation theory expansion of the Coriolis matrix will be valid. This is a commonly reported situation (12-14) and it is well known that in this case the resonance makes large contributions of opposite signs to the ar constants of the interacting states, with the contribution to the a! of the nondegenerate vibrational state being twice that of the degenerate state. The Coriolis interaction also makes a large contribution to qfor a B-E resonance with q+ unaffected. In addition, as will be demonstrated below, only one component of the q- doublet is affected by the interaction (10, II). We emphasize that these effects are the usual Coriolis contributions to the constants o( and q, but made unusually large by the (weak) resonance. Thus, for a resonance between vb(B1) and v9(E) of BrFS we expect the following general features in the microwave spectrum. The vibrational satellites corresponding to the states ~6 = 1 and 2’9= 1 will be on opposite sides of the ground-state spectrum with the B1 satellites to the low-frequency side if A is negative, and shifted twice as far as the E-species satellites. The E-state spectrum will contain the usual q+ doublets, but the so-far unobserved q- doublets will exhibit anomalously large splitting (“giant” Z-doubling) due to the resonance, with one component unperturbed and left behind nearer the ground-state spectrum. A much more difficult situation arises if the resonance is not weak. In this case the Coriolis interaction will produce further perturbations in the excited-state spectra which may make assignments extremely difficult. As stated earlier, the presence of two isotopic species of BrF6 plus the quadrupole structure plus the fact that transitions of moderately high J-values have been measured, in the presence of a moderately strong Coriolis interaction, lead to very complex excited state spectra (see Figs. la and 2a). Numerical diagonalization of the Coriolis matrices is not possible until some assignments have been made and some preliminary values of the various parameters estimated fairly closely. Sarka et al. (15,16) have shown that for resonance interactions of moderate strength, a higher-order algebraic expansion of the Coriolis matrices will provide useful energy level expressions, particularly for the nondegenerate vibrational state levels. These results have been verified and extended in the present work. The method of approximation consists in arranging the cubic equation for the roots of the Coriolis matrix in a form suitable for successive algebraic iteration (continued fractions). For the z’5(Br) = 1 satellites it is not difficult to show that the leading higher-order terms in such an expansion produce effective anomalous contributions to the centrifugal distortion constants DJ, DJK, and DK. It is usual to retain only the vibrational energy difference, A, for the diagonal elements of the Coriolis matrix, but including the rigid rotor terms also, and retaining the distinction between the rotational constants B,*, B,*, and C,, Ct, the following results are obtained for the effective constants in the B1 satellite spectrum.
(2)
(C,- Bt*+ 2CtTt) -_
A
(3)
DJK = DJK(8)* _ SR” A3
A(6B - 3%) + (C, - B,* + C,{J” 2R2
R2
1 3
(4)
Z-DOUBLING OF THE kl = - 1 LEVELS IN BrFs
23
where 6B = B,* - Bt*, 6C = C, - Ct and we have assumed q-* = 0 (see below). The above results are also valid for an A-E resonance for any symmetric top molecule if the sign of ct is changed throughout. At this level of approximation, therefore, the B-species spectrum should fit the usual symmetric-top formulas, but with anomalous values of the rotational and centrifugal distortion constants. For reasons to be explained shortly, it is not possible to derive closed algebraic expressions valid for the E-species levels when the Coriolis interaction is of moderate strength. The exception to this statement is the case of the kZ = - 1 levels. The Coriolis matrix (Table I) for k = 0, involving the E-state levels 1k, Z) = 11, - 1) and 1- 1, l), may be factored into a 2 X 2 plus a 1 X 1 matrix by transforming to the symmetrized basis set ?Erk = (( 1, -1) f 1-1, 1))/2* (10-12). In this one case, the following expressions are a good approximation for the frequencies of the q- doublets. v+(J) = ZB;t(J
+ 1) + higher-order
v-(J)
+ 1) - 4D_,‘(J + l)“,
= 2B,(J
terms,
(5) (6)
where Bt+ = Bt* + $q-*, B,
(Ct - Bt* + 2Cti-t)
1 -* = Bt* - 2q
A
1,
(7)
(8) (9)
The above expressions demonstrate the result quoted earlier that only one of the qdoublet components is affected by the Coriolis resonance. We see also that the effective doubling constant q- - 2R2/A. These results correspond to the usual selection rules for Cl8 symmetry B1 C) Bz, + t--) - or 9k t) e*. Expressions similar to those quoted by Sarka et al. (15) for the kZ # -1 levels were found inadequate to reproduce the observed spectra of BrF6. Application of the continued fraction method shows that this is due to the presence of a series of Z-resonance terms. For the (~2, F2) interaction, the leading term is of the form (15) --
R2 2
0
A2
[J, kZ][J, kZ + 11 4(kZ + l)(Ct - Bt* + C&j
As noted by Sarka (15), the above expression for these terms if
will only be an adequate
R2/A((cJ, kZ][J, kZ + 1-J)”<< 4(kZ + 1) (C, - Bt* + C,[t).
(10) approximation
(11)
Using the electron diffraction structural data for BrF6 (17), plus an estimate of ft from an approximate harmonic force field (I), we find (C, - Bt* + C,ct) - -2000 MHz. It will be seen shortly that the condition expressed in Eq. (11) does not hold for BrF6 even for low values of J. In this situation there are many terms comparable in magnitude to that in Eq. (10) produced by the iteration method and it is not possible to write convenient analytic expressions for the E-state energy levels correct even to only the second step of iteration. The consequence of this is to produce an effect on the E-state
24
BRIER, JONES .4XD BAKER
energy levels and spectrum entirely analogous to that of a strong I-resonance. Thus, lines with the same value of (k + I) are pushed apart in the spectrum, those with the lowest value of (K + Z) being aflected the most, and the y- doublets being the estreme example of the effect. Although useful algebraic expressions cannot be obtained in the above circumstances for the E-state levels, a numerical application of the iteration method does produce rapid convergence and provides a simple method for calculating the appearance of the E-state spectrum. Again assuming q-* = 0, the E-state energies for kl # 1 are given by the iteration method as E’“’ = B,*J(J
+ 1) + (C, - R,*)(kz)2 - 2CJlkl + %.J*J(J
+ l)hl
J(J + l)(R2 - l)(n+)”
J”(J + l)"(q+)z + 16(k1 - 1) (C, - E3,* - CL<,) -
8(c1 - 1st’ - c&t)
and
1
(12)
R2 [J, kZ + l] -l, E@) = EC”) + ;[I, where the quantities A’ = -[A
KI] 1 - Al
DJ*, DJK* are neglected
6’
(13)
in E(O) and
+ 2(C, - B,* + CtT,) @I) + (C, - B,*) + GBJ(J + 1) + (X - SB)(kZ)2] + [E+l) IY = -4(kZ + l)(Ct - Bt* + C,{,) + [IS’-‘)
- E(O)].
- E’0’],
(14) (15)
RESULTS
BrF, has several low-frequency vibrational modes (18) which are espected to have sufficient population of their first excited states at 200 K to produce observable rotational spectra. The most intense vibrational satellites are expected for the Q(E) = 240 cm-‘, v6(B1) and vs(Bt) = 312 cm-’ modes. The v6 frequency has never been measured experimentally despite its being symmetry allowed in the Raman effect. Only an estimated value -275 cm-’ is available from an approximate force field calculation (1, 18). Initial searches for vibrational satellites in the microwave spectrum of BrF6 were completely unsuccessful due to the fact that the two most intense groups of such lines are shifted a long way in frequency from the ground-state spectrum (-1400 and 700 MHz at J 5 -+ 6, for example). These large shifts in the ratio - 2 : 1 are indicative of a Coriolis resonance effect. Since the larger shift is to the low-frequency side of the ground-state spectrum, the nondegenerate vibrational mode involved in the resonance must have a lower frequency than the degenerate mode with which it is coupled. The latter is certainly VI)(E) = 240 cm-’ (the next E-species mode is at 415 cm-‘). It is probable, therefore, that vg is coupled with the unobserved v~, which must have a frequency 7240 cm-l. Figures la and 2a show the two observed satellite spectra for the J 5 + 6 transition. We will now discuss the detailed assignments of these two spectra plus those corresponding to the J 3 + 4 and J 4 -+ 5 transitions.
2.5
Spectrum of BrF6 in the Q,(B~) = 1 State The Br-state satellite spectra do indeed fit the usual symmetric-top expression but with anomalous effective values of the rotational constant and the centrifugal distortion constants [Eqs. (2))(4)]. Table II lists the values of these constants which gave best agreement with the observed spectra. They predict the measured absorption frequencies with less than 1 MHz differences. The calculated spectrum for the J 5 + 6 transition is shown in Fig. lb. We note that the successful reproduction of the observed intensities using the B-species nuclear spin statistical weights of Table III proves that the resonance is a B-E species interaction, as previously surmised. Since the resonance contributions to DJ and DJK dominate the total effective values of these constants (Table II), by making the approximations DJ - 4R4/A3, DJK - -8R4/A3, and B, - B. + 2R2/A, we may estimate separately the quantities R and A. (In a weak resonance situation, one can only deduce the ratio R2/A.) The values are R - 3000 MHz and A - - 7 cm-‘. From Table II we see in fact that DJR is only approximately equal to -20~.
BRIER,
26
JONES AND BAKER
Spectrum of BrFs ira the zjy(E) = 1 State The Q(E) = 1 satellite spectrum (Fig. 2a) is much more complex than that of the Br-species state and very extensive (a total spread of - 1200 MHz at _75 -+ 6). According to our earlier estimates of R and A from the B-state spectrum, the separation of the p- doublets should be -24R2/A G 1200 MHz. Thus we expect that the lowest-frequency lines of the E-state spectrum, which are close to the last observed line of the ground-state spectrum on the high-frequency side (see Fig. 2a), should be the unperturbed quadrupole components of the ++ transition of the p- doublet, the $- components being at the other extreme of the E-state spectrum. Confirmation of this assignment is obtained from the known characteristic quadrupole structure associated with each value of K and also by the distinctive Stark effects exhibited for lines with kl = 0, kl = fl, kZ # 0, f 1. (Despite the added complexity of the spectra, the quadrupole structure was of great help in obtaining initial assignments.) Due to the very large effective p doubling constant, the q- doublets require very high Stark fields to modulate them TAaLE
'VALUES ,iF THE PARAKETEKS
USE"
IV
IN THE CALCilLATlliN ilF THE
ViBRATIONAL
STATE
v9 (E)
=
SPECTRUM("'
71)
B'BrF5
Urrs
Gt
3 2w.14
3 103.30
%’
3 1111.6!,
3 o'J?i.:o
li.002
UJ
U.U66
2.78
q+
(Ct-Ut*+ CtTt) t
(Ct-Bt
Ctrt)
2.75
-1 4Y3.U
-1 485.0
-700.n
-7OU.U
-I).lii
6
-0.ll5
-279.2
eqi)
PRELIMINARY
VALIJLS FOR SOME
-233.5
UERIVED
CUN:TANTS
R
3 300.0
t
h
-6.7
f
Ct
2 ooo.fl
it
-0.20
in units
(b)
2OU.U I).3
t
200.0
t_
0.02
-14.1
+
0.5
of Liz except
,?(cmm') and
i,B
(a) All quantities
OF BrF5
Tt (dmension-
less).
(b) These withIn
values
are the same
tile quoted
errors.
for botn
isotopic
species
of BrF5
1
OF THE
Z-DOUBLING
kl = - 1 LEVELS IN BrFs
37670
37730
37810
, ,, 137790
37930
37870
'?'dA
-
A
m--+--f-38M0
37960
27
38150
38L60
FIG. 2b. Calculated spectrum of the J 5 ---f 6 transition of BrFb in the excited vibrational state Q(E) = 1 using the values of the constants in Table IV.
fully (Fig. 2a). Although the q+ doublets were detected at low Stark fields, they show close Stark lobes and incomplete modulation. We note that the *1BrF6#+ components of the q- doublet are overlapped by the ground-state spectrum and were not detected. The K = 0 lines should have a pure second-order Stark effect requiring still higher Stark fields to modulate them fully. For this reason the K = 0 line-s were not observed in either the ground-state spectrum or the Q,(&) = 1 satellite spectrum. Their appearance in the v,(E) = 1 spectrum is due to the Coriolis interaction mixing the states kZ = 0 and kZ = -2, hence giving some first-order character to their Stark splitting. This type of effect has been noted before (10). A complete assignment and analysis of the E-state spectrum requires the application of the iteration expressions given in Eqs. (12) and (13). To do this, values of the param-
3
37EcQ
Freq (MHZ)
2
2
38 000
385x
FIG. 3. Spectrum of the .7 5 -P 6 transition of n’BrF6 in the excited vibrational state Q(E) = 1 omitting the quadrupole hype&e structure. Lines identified by the values of the quantity 1(kI + 1) 1.
2x
BRIER,
JONES
ASD
BAKER
eters Bt*, Ct, 6U, 6C, R, A, 11, y+, and (I-* are needed. Inspection of the iteration expressions and Eqs. (2)-(S) shows that it is simpler to use the quantities (C, - N1* + C,{,) and (C, - R 1* - C,[J instead of C1, ct as independent variables. Certain combinations of the above parameters are available from the measured effective constants H,, DJ, and DJK of the B1-species spectrum [Eqs. (2)-(-l)]. In addition, the analysis of three sets of q- doublet frequencies (J 3 -+ 1, 4 + 5, and 5 + 6) using Eqs. (S)-(9) produces values of the quantities B tf, Bt-, and DJ’. We now assume we may neglect the quantities DJ(4*, DJ(t)* and the corresponding DJK parameters. This may be justified by noting that the measured value of DJ’ (Eq. 9) is within 1 kHz of the value obtained for DJ (Eq. 3). To proceed further we must also assume y-* = 0. This approximation was made by Kuczkowski and Lide (10) in the analysis of the Coriolis resonance in I’Fa BH3. For clarity, terms involving y-* have in fact been omitted from all the equations presented in this paper. (The value of q+ is obtained directly from the Q+ doublet separations.) With the above approximations, we then have measured values for six combinations of the above eight parameters. By assuming values for (C, - Bt* + CJ,) and (C, - Bt* - C&J, the iteration expressions for the E-state spectrum Eqs. (12)-(S) may be evaluated (three to four cycles being sufficient) and the appearance of the calculated and observed spectra compared. By var)-ing the assumed initial values of (C, - Bt* + CJJ and (C, - Bt* - C,(,) it is possible to obtain close agreement between calculation and experiment. The spectrum is highly sensitive to the value of the first of the above pair of parameters due to the large value of R2/A with which it is combined, and it is therefore well determined. The value of (c’, - Ht* - CJ,) is not well determined. The ql,r* term in Do) was included only at the later stages of the above procedure to obtain the final optimum frequency fit to the observed spectrum. The values of the various parameters which gave best agreement with experiment are listed in Table IV. The calculated spectrum for the J 5 --, 6 transition is shown in Fig. 2b. It can be seen that there is good overall agreement between esperiment and calculation, calculated absorption frequencies typically being within -0.6 MHz of their measured values. Figure 3 shows the J 5 --+ 6 E-state spectrum schematically for one isotopic species only and with the quadrupole structure omitted. This demonstrates clearly the “l-resonance” type of effect which determines the general appearance of the whole spectrum. We note that if the more usual approximations are made that B,* = Bt* and C, = Ct, final differences between calculated and observed absorption frequencies are increased up to 5 MHz for the higher K transitions. The calculated spectrum then appears to bear little relation to the measured spectrum despite being fundamentally correct.
CONCLUSIONS
The measurements and assignment of the spectrum of BrF6 in the first excited state of one of its E-species vibrations has provided the first ervperimental observation of the doubling of kZ = -1 levels predicted for molecules with Cd, symmetry. The spectrum of the measured E-species state is strongly perturbed by a Coriolis resonance interaction with a nearby nondegenerate vibrational level. It has been shown that this resonance is of a B-E species type and that the B-species mode involved is
I-DOUBLING OF THE kl = - 1 LEVELS IN BrF6
29
almost certainly ~g(Br). Due to the B-species nature of the interacting state, the major effect on the E-species satellite spectrum, as far as the present study is concerned, was the extremely large value of the q- doubling constant which it produced. The analysis of the &-species vibrational satellites was straightforward since the spectrum fitted the usual symmetric-top formula but with anomalous values of the rotational and centrifugal distortion constants. However, the E-species satellites could not be analyzed in such a simple manner. A method of analysis has been developed, based on an existing approximate treatment of Coriolis resonances, which involves numerical evaluation of an iteration expression. Values for all but two of the parameters in this expression are obtained from the measured constants of the &species satellite spectrum plus an analysis of the kZ = -1 lines of the E-species spectrum. The latter lines are a special case for which sufficiently accurate closed algebraic expressions can be obtained for the absorption frequencies. Trial and error variation of the remaining pair of parameters produced close agreement between calculated and measured spectra. A further interesting result of the analysis of the E-species satellites was the value of A = ys - vt = -6.7 cm-l. This provides us with an accurate estimate of the frequency of vb(Bi) = 233 cm-‘. As explained earlier, ~6 has not been previously observed by any other spectroscopic method. Finally, we note that the agreement between the calculated and observed spectrum of the E-species state is not yet perfect. The major discrepancy occurs for the kZ = -3 lines in the J 5 -+ 6 transition. It is not apparent in the spectra for the lower J transitions. Also, the q+ doublet splitting deviates from a simple (J + 1) dependence. Since the Coriolis interaction mixes the kl = 1 and kl = -3 levels, these two effects are most certainly interdependent. A more exact matrix diagonalization treatment of the interaction is now in progress, using the present results as a starting point. Initial results show that only certain combinations of parameters are independently determinable, as one might expect, and that the effects concerning the 61 = -3 and kZ = 1 levels can be accounted for in this treatment. ACKNOWLEDGMENTS It is a pleasure to thank Professor I. M. Mills, Reading University, for the use of the HP846OA spectrometer, and Dr. A. G. Robiette for his assistance with the operation of that instrument. One of us (S. R. J.) would like to thank Brasenose College, Oxford University, for the award of a Hulme Senior Scholarship. RECEIVED:
July 28, 1975 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
R. H BRADLEY,P. N. BRIER, ANDM. J. Wrrrrrrz, J. Mol. Spectrosc. 44, 536 (1972). S. R. JONES,P. N. BEIER, D. M. BROOKBANKS, ANDJ. G. BAKER, J. Mol. Spectrosc. 47,351 (1973). G. AXAT ANDL. HENRY, J. Phys. Radium 21, 728 (1960). R. JUREK, P. SUZEAU,J. CHANUSSOT,ANDJ. P. CHAMPION,J. Phys. 35, 533 (1974). J. DE HEER, Phys. Rev. 83, 741 (1951). M. L. GRENIER-BESSON, J. Phys. Radium 21, 535 (1960). G. J. CARTWRIGHTANDI. M. MILLS, J. Mol. Spectrosc. 34, 415 (1970). T. OKA, J. Chem. Phys. 47, 5410 (1967). P. KUPECEK,J. Phys. Radium 25, 831 (1964). R. L. KUCZKOWSKIANDD. R. LIDE, J. Chem. Phys. 46, 357 (1967).
BRIER, JONES AND BAKER
30
J. Mol. SpectrOSC. 21, 386 (1966). Y. MORINO AND C. HIROSE, J. Mol. Spectrosc. 24, 204 (1967). C. MATSUMURA, E. HIROTA, T. OI;A, AND Y. MORINO, J. Mol. Spectrosc. 9, 366 (1962) M. J. WHITTLE, A. P. Cos, AND C. ROBERTS, J. Mo1. Spectrosc. 40, 580 (1971). K. SARKA, J. Mol. Spectrosc. 41, 233 (1972). K. SARKA, D. PAPOUSE~, AND K. NARAHARI RAO, J. Mol. Speclrosc. 37, 1 (1971). A. G. ROBIETTE, R. H. BRADLEY, AND P. N. BRIER, C’llenz. Cownztn. 23, 1.567 (1971). G. M. BEGUN, W. H. FLETCHER, AND D. F. SMITH, J. C/rem. Pk_vs. 42, 2236 (1965). P. SUZEAU, R. JUREX, AND J. CHANUSSOT, C. R. Acad. Sci. Paris, B 276, 777 (1973).
11. C. DI LAUaO AND I. M. MILLS,
12. 13. II. 15. Id. 17. 18. 19.
OF MOLECULAR
/-Type
SPECTROSCOPY
Doubling
60,
18-30
(1976)
of the k/=---l Levels in the Microwave of the Cqa Molecule BrF,
Spectrum
I’. N. BRIER AND S. R. JONES Department
of Ckemislry,
Tke University, Munckesfer
1M13 9PL,
En&and
AND J. G. BAKER Sclrustev Laboratory,
The University, Manchester
Ml3 YPL, England
Measurements are reported for the J 3 + 4, 4 + 5, and 5 + 6 transitions of BrFS in the excited vibrational states vb(B1) = 1 and vg(E) = 1. These two states are nearly degenerate and an unusually strong Coriolis interaction perturbs both excited state spectra. New expressions are obtained for the E-species absorption frequencies which are valid in a strong Coriolis resonance situation. The analysis of the E-state spectrum has provided the first experimental observation of the doubling of the kl = - 1 levels predicted for molecules with Ceu symmetry. INTRODUCTION
In two earlier papers concerning measurements of the ground state microwave spectrum of BrF6 (1,Z) we reported the first experimental observation of the K-type doubling effect predicted for molecules possessing a fourfold symmetry axis (3). Further examples of K-type doubling in Cd8molecules have now been reported (4). It was pointed out by de Heer (5) as long ago as 1951 that in a singly excited state of a degenerate vibration, such molecules should also exhibit a second unique feature in their rotational spectrum, namely, an I-t?pe doubling of the kl = -1 levels in addition to the normal Z-type doubling of kl = + 1 states. The basis of this effect is that the four ro-vibrational states with j k 1 = 111 = 1 span E X E = d 1 + .42 + BI+ Bz in C4V symmetry. The usual Z-doubling effect splits the RI = +l states into separate A1 and At levels, and the extra I-doubling splits the kl = -1 states into a & and Rz pair. The Z-doubling of k1 = -1 states has been discussed in more detail by other authors (6-8). Following Cartwright and Mills (7), we will distinguish the two kinds of Z-doubling by writing the doubling constants involved as q+ and q- (but omitting the subscript t signifying quantities associated with a doubly degenerate vibrational state). In this paper we report the spectrum of BrFs in the excited vibrational states es(&) = 1 and Q(E) = 1. An accidental near-degeneracy of v5 and vg produces a strong perturbation of both excited state spectra through a Coriolis resonance interaction. This causes difficulties in the assignment of the spectra, particularly the E-state spectrum, which are already complex through the presence of the two isotopic species 7gBrFb and 81BrF6 plus considerable quadrupole structure. Our main purpose in this 18 Copyright All rights
0
1976
by Academic
of reproduction
Press.
in any form
Inc. reserved.
I-DOUBLING
OF THE kl = -
19
1 LEVELS IN BrFa
paper is to establish an assignment of the vg(E) = 1 spectrum and hence to report the first experimental observation of q--doubling. An exact matrix treatment of the Coriolis resonance with the aid of this assignment, and the calculation of various vibrationrotation parameters for BrFS, is in progress and will be the subject of a separate communication. EXPERIMENTAL
PROCEDURE
Spectra of the J 4 + 5 (30 GHz) and J 5 --+ 6 (36 GHz) transitions were recorded on a Hewlett-Packard 8460A spectrometer, and the J 3 + 4 (24 GHz) transition plus a repeat measurement of J 4 -+ 5 were recorded in this laboratory on a conventional 33 kHz Stark-modulated spectrometer with a phase-lock frequency track system. Problems associated with the stability of BrFb, even when using an all-metal vacuum system, were overcome by the use of a simple flow technique. A sample of BrF6 stored in a stainless-steel cylinder at approximately one-quarter atmosphere pressure was continuously pumped through the Stark cell (which was cooled to 200 K with solid COz) via a needle valve to regulate the pressure. The sample of BrF6 was supplied commercially by Air Products Limited and used without further purification. THEORY
Expressions for the frequencies of rotational transitions of CqV molecules in the absence of any accidental resonances have already been given by Kupecek (9), including the case of a singly excited degenerate vibrational state. The Kupecek formulas include the effect of the off-diagonal Z-resonance terms (7) of the type Ak = f2, AZ = f2 (@ interactions) and Ak = ~2, AZ = r2 (9- interactions). For the two pairs of originally degenerate states kZ = + 1 and kZ = - 1, these interactions produce the two Z-doubling effects described earlier. With the exception of these special cases, the effect of the Z-resonance interaction terms may usually be calculated using secondorder perturbation theory. Thus, for transitions for which kZ # fl, Kupecek gives the following results (9). YJ,K = 2&(J -~
+ 1) - 4D.r(J + 1)” - 2Dm(J
(J + 113 4
+ 1)&Z)* + 2~,r(J
(P>’
(q++>”
(kl + l)(Ct - & + rtC,> + (J+l) 4
+ l)(kZ)
W2(kZ
@Z -
1 1 (0
1)&t - Bt - StCt>
+ 1)
(Ct - Bt + rtC,) -
(q+)“(kZ -
1)
6, - & - i-t&) ’
where a subscript t signifies the Q(E) = 1 state of yg and later expressions with a subscript s will signify quantities associated with the ZJ~(&) = 1 state of ~6. When kZ = + 1, the two perturbation theory terms in Eq. (1) involving the parameter q+ are replaced by the Z-doubling term &q+(J + l), and when k2 = - 1, the terms involving q- are replaced by the second Z-doubling term fp(J + 1). Coriolis Resonance To date, all reported symmetric-top molecules
cases of Coriolis resonances in the spectra have involved an Al-E species interaction.
of C30 and Ci, The theory of
20
BRIER,
JONES AND BAKER
CORlOLlS MATRIX FOR A B-E SPLCIES INTERACTIJN
_* R [J,kli
Il,O’,
J.k
z
W,[J,k]
+ A
5
[J,k]l p,k-11%
-R e, k-1$
(Symetrical)
lO,l', J, k-l >
Wt [J. (k-l)!,]
where Wt [J,kd = Et* J (Jtl) + (Ct - Et*) (ke)' - ZCtct (ke) plus higher order terms - see Eq. (1)
WsrJ.kl
[J,kjl
= Bs* J(W)
=
+ (Cs - Bs*) k2 plus higher term
rj(Jt1) - k(k+ljjt
resonances of this type has been given in some detail by Kuczkowski and Lide (10) and di Lauro and Mills (II). Essentially, the state 1zig,zltli, J, k) = j 1, O”, J, K) of the nondegenerate vibrational state is linked by the Coriolis interaction with the two states 10, lr, J, K + 1) and IO, l-l, J, k - 1) of the degenerate vibration. An exact interpretation of the excited-state spectra then requires (in principle) a numerical diagonalization of the resulting 3 X 3 matrices, one for each value of K. In the case of BrF6 there is a resonance between the near-degenerate states v5 = 1 and q = 1 corresponding to a HI-B species interaction. The states which are linked by the interaction (by the Hamiltonian term labeled HQ in (8, Table III)) are now 11, O”, J, K) with IO, l-l, J, k + 1) and 10, lr, J, K - 1). Thus, it is states with the same value of (R + Z) which interact in this case rather than (k - 1) as in A-E interactions. This results in only minor changes to the usual Coriolis interaction matrix (see Table I, in which a superscript star refers to quantities with their contribution from this specific Coriolis interaction omitted. Note also that a constant vibrational energy term has been subtracted from each of the diagonal elements). Approximate
Methods
If the vibrational degeneracy is almost exact and the interaction term RCJ, k]* - h, then an exact numerical diagonalization of the Coriolis matrices will be necessary. This
J-DOUBLING
35 7cO I
OF THE kl = -
21
IN BrFs
35ml I
35 740 I Freq
1 LEVELS
35 820 ,
MHz
FIG. 1. (a) Observed and (b) calculated spectrum of the J 5 + 6 transition of BrFs in the excited vibrational state zig = 1.
was the situation found for PFI BHa for which A = 0.83 cm-’ (10). Ingeneral, however, there are too many unknown parameters in the Coriolis matrix and although the diagonalization may be mathematically exact, some assumptions and approximations regarding the quantities in the matrix will have to be made.
3
37 960
c
38 olo’
38460
FIG. 2a. Observed spectrum of the J 5 + 6 transition of BrF5 in the excited vibrational state ZJB@) = 1. Lines identified by the values of the quantity RI.
22
BRIER,
JONES AND BAKER
At the other extreme, if the interaction is very weak and R[J, K]h << A, a secondorder perturbation theory expansion of the Coriolis matrix will be valid. This is a commonly reported situation (12-14) and it is well known that in this case the resonance makes large contributions of opposite signs to the ar constants of the interacting states, with the contribution to the a! of the nondegenerate vibrational state being twice that of the degenerate state. The Coriolis interaction also makes a large contribution to qfor a B-E resonance with q+ unaffected. In addition, as will be demonstrated below, only one component of the q- doublet is affected by the interaction (10, II). We emphasize that these effects are the usual Coriolis contributions to the constants o( and q, but made unusually large by the (weak) resonance. Thus, for a resonance between vb(B1) and v9(E) of BrFS we expect the following general features in the microwave spectrum. The vibrational satellites corresponding to the states ~6 = 1 and 2’9= 1 will be on opposite sides of the ground-state spectrum with the B1 satellites to the low-frequency side if A is negative, and shifted twice as far as the E-species satellites. The E-state spectrum will contain the usual q+ doublets, but the so-far unobserved q- doublets will exhibit anomalously large splitting (“giant” Z-doubling) due to the resonance, with one component unperturbed and left behind nearer the ground-state spectrum. A much more difficult situation arises if the resonance is not weak. In this case the Coriolis interaction will produce further perturbations in the excited-state spectra which may make assignments extremely difficult. As stated earlier, the presence of two isotopic species of BrF6 plus the quadrupole structure plus the fact that transitions of moderately high J-values have been measured, in the presence of a moderately strong Coriolis interaction, lead to very complex excited state spectra (see Figs. la and 2a). Numerical diagonalization of the Coriolis matrices is not possible until some assignments have been made and some preliminary values of the various parameters estimated fairly closely. Sarka et al. (15,16) have shown that for resonance interactions of moderate strength, a higher-order algebraic expansion of the Coriolis matrices will provide useful energy level expressions, particularly for the nondegenerate vibrational state levels. These results have been verified and extended in the present work. The method of approximation consists in arranging the cubic equation for the roots of the Coriolis matrix in a form suitable for successive algebraic iteration (continued fractions). For the z’5(Br) = 1 satellites it is not difficult to show that the leading higher-order terms in such an expansion produce effective anomalous contributions to the centrifugal distortion constants DJ, DJK, and DK. It is usual to retain only the vibrational energy difference, A, for the diagonal elements of the Coriolis matrix, but including the rigid rotor terms also, and retaining the distinction between the rotational constants B,*, B,*, and C,, Ct, the following results are obtained for the effective constants in the B1 satellite spectrum.
(2)
(C,- Bt*+ 2CtTt) -_
A
(3)
DJK = DJK(8)* _ SR” A3
A(6B - 3%) + (C, - B,* + C,{J” 2R2
R2
1 3
(4)
Z-DOUBLING OF THE kl = - 1 LEVELS IN BrFs
23
where 6B = B,* - Bt*, 6C = C, - Ct and we have assumed q-* = 0 (see below). The above results are also valid for an A-E resonance for any symmetric top molecule if the sign of ct is changed throughout. At this level of approximation, therefore, the B-species spectrum should fit the usual symmetric-top formulas, but with anomalous values of the rotational and centrifugal distortion constants. For reasons to be explained shortly, it is not possible to derive closed algebraic expressions valid for the E-species levels when the Coriolis interaction is of moderate strength. The exception to this statement is the case of the kZ = - 1 levels. The Coriolis matrix (Table I) for k = 0, involving the E-state levels 1k, Z) = 11, - 1) and 1- 1, l), may be factored into a 2 X 2 plus a 1 X 1 matrix by transforming to the symmetrized basis set ?Erk = (( 1, -1) f 1-1, 1))/2* (10-12). In this one case, the following expressions are a good approximation for the frequencies of the q- doublets. v+(J) = ZB;t(J
+ 1) + higher-order
v-(J)
+ 1) - 4D_,‘(J + l)“,
= 2B,(J
terms,
(5) (6)
where Bt+ = Bt* + $q-*, B,
(Ct - Bt* + 2Cti-t)
1 -* = Bt* - 2q
A
1,
(7)
(8) (9)
The above expressions demonstrate the result quoted earlier that only one of the qdoublet components is affected by the Coriolis resonance. We see also that the effective doubling constant q- - 2R2/A. These results correspond to the usual selection rules for Cl8 symmetry B1 C) Bz, + t--) - or 9k t) e*. Expressions similar to those quoted by Sarka et al. (15) for the kZ # -1 levels were found inadequate to reproduce the observed spectra of BrF6. Application of the continued fraction method shows that this is due to the presence of a series of Z-resonance terms. For the (~2, F2) interaction, the leading term is of the form (15) --
R2 2
0
A2
[J, kZ][J, kZ + 11 4(kZ + l)(Ct - Bt* + C&j
As noted by Sarka (15), the above expression for these terms if
will only be an adequate
R2/A((cJ, kZ][J, kZ + 1-J)”<< 4(kZ + 1) (C, - Bt* + C,[t).
(10) approximation
(11)
Using the electron diffraction structural data for BrF6 (17), plus an estimate of ft from an approximate harmonic force field (I), we find (C, - Bt* + C,ct) - -2000 MHz. It will be seen shortly that the condition expressed in Eq. (11) does not hold for BrF6 even for low values of J. In this situation there are many terms comparable in magnitude to that in Eq. (10) produced by the iteration method and it is not possible to write convenient analytic expressions for the E-state energy levels correct even to only the second step of iteration. The consequence of this is to produce an effect on the E-state
24
BRIER, JONES .4XD BAKER
energy levels and spectrum entirely analogous to that of a strong I-resonance. Thus, lines with the same value of (k + I) are pushed apart in the spectrum, those with the lowest value of (K + Z) being aflected the most, and the y- doublets being the estreme example of the effect. Although useful algebraic expressions cannot be obtained in the above circumstances for the E-state levels, a numerical application of the iteration method does produce rapid convergence and provides a simple method for calculating the appearance of the E-state spectrum. Again assuming q-* = 0, the E-state energies for kl # 1 are given by the iteration method as E’“’ = B,*J(J
+ 1) + (C, - R,*)(kz)2 - 2CJlkl + %.J*J(J
+ l)hl
J(J + l)(R2 - l)(n+)”
J”(J + l)"(q+)z + 16(k1 - 1) (C, - E3,* - CL<,) -
8(c1 - 1st’ - c&t)
and
1
(12)
R2 [J, kZ + l] -l, E@) = EC”) + ;[I, where the quantities A’ = -[A
KI] 1 - Al
DJ*, DJK* are neglected
6’
(13)
in E(O) and
+ 2(C, - B,* + CtT,) @I) + (C, - B,*) + GBJ(J + 1) + (X - SB)(kZ)2] + [E+l) IY = -4(kZ + l)(Ct - Bt* + C,{,) + [IS’-‘)
- E(O)].
- E’0’],
(14) (15)
RESULTS
BrF, has several low-frequency vibrational modes (18) which are espected to have sufficient population of their first excited states at 200 K to produce observable rotational spectra. The most intense vibrational satellites are expected for the Q(E) = 240 cm-‘, v6(B1) and vs(Bt) = 312 cm-’ modes. The v6 frequency has never been measured experimentally despite its being symmetry allowed in the Raman effect. Only an estimated value -275 cm-’ is available from an approximate force field calculation (1, 18). Initial searches for vibrational satellites in the microwave spectrum of BrF6 were completely unsuccessful due to the fact that the two most intense groups of such lines are shifted a long way in frequency from the ground-state spectrum (-1400 and 700 MHz at J 5 -+ 6, for example). These large shifts in the ratio - 2 : 1 are indicative of a Coriolis resonance effect. Since the larger shift is to the low-frequency side of the ground-state spectrum, the nondegenerate vibrational mode involved in the resonance must have a lower frequency than the degenerate mode with which it is coupled. The latter is certainly VI)(E) = 240 cm-’ (the next E-species mode is at 415 cm-‘). It is probable, therefore, that vg is coupled with the unobserved v~, which must have a frequency 7240 cm-l. Figures la and 2a show the two observed satellite spectra for the J 5 + 6 transition. We will now discuss the detailed assignments of these two spectra plus those corresponding to the J 3 + 4 and J 4 -+ 5 transitions.
2.5
Spectrum of BrF6 in the Q,(B~) = 1 State The Br-state satellite spectra do indeed fit the usual symmetric-top expression but with anomalous effective values of the rotational constant and the centrifugal distortion constants [Eqs. (2))(4)]. Table II lists the values of these constants which gave best agreement with the observed spectra. They predict the measured absorption frequencies with less than 1 MHz differences. The calculated spectrum for the J 5 + 6 transition is shown in Fig. lb. We note that the successful reproduction of the observed intensities using the B-species nuclear spin statistical weights of Table III proves that the resonance is a B-E species interaction, as previously surmised. Since the resonance contributions to DJ and DJK dominate the total effective values of these constants (Table II), by making the approximations DJ - 4R4/A3, DJK - -8R4/A3, and B, - B. + 2R2/A, we may estimate separately the quantities R and A. (In a weak resonance situation, one can only deduce the ratio R2/A.) The values are R - 3000 MHz and A - - 7 cm-‘. From Table II we see in fact that DJR is only approximately equal to -20~.
BRIER,
26
JONES AND BAKER
Spectrum of BrFs ira the zjy(E) = 1 State The Q(E) = 1 satellite spectrum (Fig. 2a) is much more complex than that of the Br-species state and very extensive (a total spread of - 1200 MHz at _75 -+ 6). According to our earlier estimates of R and A from the B-state spectrum, the separation of the p- doublets should be -24R2/A G 1200 MHz. Thus we expect that the lowest-frequency lines of the E-state spectrum, which are close to the last observed line of the ground-state spectrum on the high-frequency side (see Fig. 2a), should be the unperturbed quadrupole components of the ++ transition of the p- doublet, the $- components being at the other extreme of the E-state spectrum. Confirmation of this assignment is obtained from the known characteristic quadrupole structure associated with each value of K and also by the distinctive Stark effects exhibited for lines with kl = 0, kl = fl, kZ # 0, f 1. (Despite the added complexity of the spectra, the quadrupole structure was of great help in obtaining initial assignments.) Due to the very large effective p doubling constant, the q- doublets require very high Stark fields to modulate them TAaLE
'VALUES ,iF THE PARAKETEKS
USE"
IV
IN THE CALCilLATlliN ilF THE
ViBRATIONAL
STATE
v9 (E)
=
SPECTRUM("'
71)
B'BrF5
Urrs
Gt
3 2w.14
3 103.30
%’
3 1111.6!,
3 o'J?i.:o
li.002
UJ
U.U66
2.78
q+
(Ct-Ut*+ CtTt) t
(Ct-Bt
Ctrt)
2.75
-1 4Y3.U
-1 485.0
-700.n
-7OU.U
-I).lii
6
-0.ll5
-279.2
eqi)
PRELIMINARY
VALIJLS FOR SOME
-233.5
UERIVED
CUN:TANTS
R
3 300.0
t
h
-6.7
f
Ct
2 ooo.fl
it
-0.20
in units
(b)
2OU.U I).3
t
200.0
t_
0.02
-14.1
+
0.5
of Liz except
,?(cmm') and
i,B
(a) All quantities
OF BrF5
Tt (dmension-
less).
(b) These withIn
values
are the same
tile quoted
errors.
for botn
isotopic
species
of BrF5
1
OF THE
Z-DOUBLING
kl = - 1 LEVELS IN BrFs
37670
37730
37810
, ,, 137790
37930
37870
'?'dA
-
A
m--+--f-38M0
37960
27
38150
38L60
FIG. 2b. Calculated spectrum of the J 5 ---f 6 transition of BrFb in the excited vibrational state Q(E) = 1 using the values of the constants in Table IV.
fully (Fig. 2a). Although the q+ doublets were detected at low Stark fields, they show close Stark lobes and incomplete modulation. We note that the *1BrF6#+ components of the q- doublet are overlapped by the ground-state spectrum and were not detected. The K = 0 lines should have a pure second-order Stark effect requiring still higher Stark fields to modulate them fully. For this reason the K = 0 line-s were not observed in either the ground-state spectrum or the Q,(&) = 1 satellite spectrum. Their appearance in the v,(E) = 1 spectrum is due to the Coriolis interaction mixing the states kZ = 0 and kZ = -2, hence giving some first-order character to their Stark splitting. This type of effect has been noted before (10). A complete assignment and analysis of the E-state spectrum requires the application of the iteration expressions given in Eqs. (12) and (13). To do this, values of the param-
3
37EcQ
Freq (MHZ)
2
2
38 000
385x
FIG. 3. Spectrum of the .7 5 -P 6 transition of n’BrF6 in the excited vibrational state Q(E) = 1 omitting the quadrupole hype&e structure. Lines identified by the values of the quantity 1(kI + 1) 1.
2x
BRIER,
JONES
ASD
BAKER
eters Bt*, Ct, 6U, 6C, R, A, 11, y+, and (I-* are needed. Inspection of the iteration expressions and Eqs. (2)-(S) shows that it is simpler to use the quantities (C, - N1* + C,{,) and (C, - R 1* - C,[J instead of C1, ct as independent variables. Certain combinations of the above parameters are available from the measured effective constants H,, DJ, and DJK of the B1-species spectrum [Eqs. (2)-(-l)]. In addition, the analysis of three sets of q- doublet frequencies (J 3 -+ 1, 4 + 5, and 5 + 6) using Eqs. (S)-(9) produces values of the quantities B tf, Bt-, and DJ’. We now assume we may neglect the quantities DJ(4*, DJ(t)* and the corresponding DJK parameters. This may be justified by noting that the measured value of DJ’ (Eq. 9) is within 1 kHz of the value obtained for DJ (Eq. 3). To proceed further we must also assume y-* = 0. This approximation was made by Kuczkowski and Lide (10) in the analysis of the Coriolis resonance in I’Fa BH3. For clarity, terms involving y-* have in fact been omitted from all the equations presented in this paper. (The value of q+ is obtained directly from the Q+ doublet separations.) With the above approximations, we then have measured values for six combinations of the above eight parameters. By assuming values for (C, - Bt* + CJ,) and (C, - Bt* - C&J, the iteration expressions for the E-state spectrum Eqs. (12)-(S) may be evaluated (three to four cycles being sufficient) and the appearance of the calculated and observed spectra compared. By var)-ing the assumed initial values of (C, - Bt* + CJJ and (C, - Bt* - C,(,) it is possible to obtain close agreement between calculation and experiment. The spectrum is highly sensitive to the value of the first of the above pair of parameters due to the large value of R2/A with which it is combined, and it is therefore well determined. The value of (c’, - Ht* - CJ,) is not well determined. The ql,r* term in Do) was included only at the later stages of the above procedure to obtain the final optimum frequency fit to the observed spectrum. The values of the various parameters which gave best agreement with experiment are listed in Table IV. The calculated spectrum for the J 5 --, 6 transition is shown in Fig. 2b. It can be seen that there is good overall agreement between esperiment and calculation, calculated absorption frequencies typically being within -0.6 MHz of their measured values. Figure 3 shows the J 5 --+ 6 E-state spectrum schematically for one isotopic species only and with the quadrupole structure omitted. This demonstrates clearly the “l-resonance” type of effect which determines the general appearance of the whole spectrum. We note that if the more usual approximations are made that B,* = Bt* and C, = Ct, final differences between calculated and observed absorption frequencies are increased up to 5 MHz for the higher K transitions. The calculated spectrum then appears to bear little relation to the measured spectrum despite being fundamentally correct.
CONCLUSIONS
The measurements and assignment of the spectrum of BrF6 in the first excited state of one of its E-species vibrations has provided the first ervperimental observation of the doubling of kZ = -1 levels predicted for molecules with Cd, symmetry. The spectrum of the measured E-species state is strongly perturbed by a Coriolis resonance interaction with a nearby nondegenerate vibrational level. It has been shown that this resonance is of a B-E species type and that the B-species mode involved is
I-DOUBLING OF THE kl = - 1 LEVELS IN BrF6
29
almost certainly ~g(Br). Due to the B-species nature of the interacting state, the major effect on the E-species satellite spectrum, as far as the present study is concerned, was the extremely large value of the q- doubling constant which it produced. The analysis of the &-species vibrational satellites was straightforward since the spectrum fitted the usual symmetric-top formula but with anomalous values of the rotational and centrifugal distortion constants. However, the E-species satellites could not be analyzed in such a simple manner. A method of analysis has been developed, based on an existing approximate treatment of Coriolis resonances, which involves numerical evaluation of an iteration expression. Values for all but two of the parameters in this expression are obtained from the measured constants of the &species satellite spectrum plus an analysis of the kZ = -1 lines of the E-species spectrum. The latter lines are a special case for which sufficiently accurate closed algebraic expressions can be obtained for the absorption frequencies. Trial and error variation of the remaining pair of parameters produced close agreement between calculated and measured spectra. A further interesting result of the analysis of the E-species satellites was the value of A = ys - vt = -6.7 cm-l. This provides us with an accurate estimate of the frequency of vb(Bi) = 233 cm-‘. As explained earlier, ~6 has not been previously observed by any other spectroscopic method. Finally, we note that the agreement between the calculated and observed spectrum of the E-species state is not yet perfect. The major discrepancy occurs for the kZ = -3 lines in the J 5 -+ 6 transition. It is not apparent in the spectra for the lower J transitions. Also, the q+ doublet splitting deviates from a simple (J + 1) dependence. Since the Coriolis interaction mixes the kl = 1 and kl = -3 levels, these two effects are most certainly interdependent. A more exact matrix diagonalization treatment of the interaction is now in progress, using the present results as a starting point. Initial results show that only certain combinations of parameters are independently determinable, as one might expect, and that the effects concerning the 61 = -3 and kZ = 1 levels can be accounted for in this treatment. ACKNOWLEDGMENTS It is a pleasure to thank Professor I. M. Mills, Reading University, for the use of the HP846OA spectrometer, and Dr. A. G. Robiette for his assistance with the operation of that instrument. One of us (S. R. J.) would like to thank Brasenose College, Oxford University, for the award of a Hulme Senior Scholarship. RECEIVED:
July 28, 1975 REFERENCES
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