The ν2ν5 band system of H374GeF revisited: Analysis of a high-resolution FTIR spectrum

JOURNAL OF MOLECULAR SPECTROSCOPY

142, lo-23 (1990)

The v2/v5 Band System of H374GeF Revisited: Analysis of a High-Resolution FTIR Spectrum

s. CRADGCK Department of Chemistry University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, ScotIand, U.K.

AND

H. BURGER,

R. EUJEN, M. LITZ,

AND

A.

RAHNER

Anorganische Chemie. FB 9, Universitiit-Gesamthochschule, D-5600 Wuppertal I, Federal Republic of Germany

The FTIR spectrum of monoisotopic Hs74GeF recorded with a resolution of -2.5 X 10e3 cm-’ (fwhm) has been investigated in the region of the Y~/v~band, ~4 873.82345(2) and ~2 873.98095( 1) cm-‘. Strong perturbations were observed, and different models were tested. With an interaction model comprising qj+) and r, resonance within Yeand Coriolis x, y, and (Yresonance between u2and ~5,ultimately 4768 rovibrational lines including 23 perturbation-allowed transitions were fitted to 32 excited state parameters with (T= 1.5 X lo-” cm-‘. In addition, AK = *3 perturbations between vr , K and ~3, (K + 3 ) levels and Q, kl and vg, (kl - 3 ) sublevels were detected and fitted, and likely locations of similar perturbations in other halides H3EX of group IV elements E are predicted. The intensity perturbation M2 j$$, was found to be positive, and a transition moment ratio 1Mz :M51= 0.77 ( 5 ) was determined. In order to derive the equilibrium rotational constants for Hs74GeF, A, = 2.63241(2) and B, = 0.3355664( 8) cm-‘, the v,/v.+band was studied by Doppler-limited FTIR spectroscopy and examined in some detail. Although abundant perturbations of nearly all K and kl levels, respectively, were substantiated, these were shown to be mostly of rotational type and local. About 650 almost unperturbed transitions with S g 40 were selected and fitted to a model complete to quadratic diagonal terms, 6 = 9 X 10m4cm-‘. Effective band origins were determined, up 2123.3031(l) and ~2 2131.0359( 1) cm-‘. o t99o Academic

Press, Inc.

I. INTRODUCTION

The low wavenumber region of the infrared spectrum of the prolate symmetric top H3GeF contains four fundamentals, of which the germyl deformation modes u2(a, ) and us(e) are only about 0.16 cm-’ apart, giving rise to a single strong band. As in other H&LX molecules (I) there is strong Coriolis coupling between these modes, and as a consequence of the closeness of the band centers the effects of this coupling dominate the band structure to an unusual degree. This band system has been studied recently (2) in the infrared at a resolution of 0.06 cm-‘, but this proved to be inadequate to allow the central region of the band to be assigned completely. Furthermore, 40 rotational J + 1 + J lines, J = 4-8, within the v2/u5 band have been measured by millimeter-wave spectroscopy and fitted, c = 0.536 MHz, to some excited state pa0022-2852190 $3.00 0 1990 by Academic

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10 Reu,

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in any form reserved.

THE u2/u5 BAND OF H3GeF

11

rameters; however, these transitions span only a very limited selection of J and K values ( 3 ) . With the availability of instruments having much higher resolution and in the light of considerable accumulated experience in the analysis of interacting band systems in similar molecules, we have attempted a reanalysis of this system. In the course of the investigations, which also included the study of the interacting bands due to v3 and vg reported separately (4), we have been able to improve considerably the precision of the ground state parameters BO, D$, D&, and the J-dependent sextic distortion constants and to derive precise and reliable values for the normally inaccessible A0 and D!.$constants from perturbation-allowed transitions in the v2/ u5 band system. The results reported here obtained from fully resolved, almost Doppler-limited FfIR spectra use these ground state parameters and allow us to define many excited state parameters, including those relating to the Coriolis interaction and the LYresonance between the two interacting vibrational states u2 and v5 as well as the qj+’ and I resonance within u5much more precisely than the earlier study. Nevertheless, the previous results are confirmed as being generally correct, although we are now able to disclose small additional effects due to level crossings, to substantiate weak interactions between the v2/ v3 and us/ Vgrovibrational states occurring for high K values, to include higherorder terms that could not be obtained reliably from the lower-resolution data, and to determine molecular parameters with much greater significance than previously. Furthermore, we present, for the first time, rovibrational data on the vI = 1 and u4 = 1 states obtained from a preliminary analysis of a selected number of almost unperturbed transitions observed in a Doppler-limited FTIR spectrum. II. EXPERIMENT

Experimental details are as in Ref. (4). The isotopic purity of H3GeF was 98.9% 74Ge. The width of weak lines (fwhm) was found to be close to 2.5 X 10e3 cm-’ ; the wavenumber accuracy of the calibrated spectra was estimated to be on the order of 2 X 10e4 cm-‘. The FTIR spectrometer has been described in detail elsewhere (5). III. THEORETICAL

MODEL

The ground state constants up to sextic terms for the Jdependent parameters and the purely K-dependent terms A0 and 0% as given by Eq. ( 1) in Ref. (4) were fixed in the data refinement to the reported values (4). These were determined from ground state combination differences (gscd) measured within the v3, Sf6band. A0 and 0% followed from 23 normally forbidden, but perturbation-allowed lines of v2, v5 associated with the A( k - I) = f3 level crossings denoted A-F in the upper state reduced energy level diagram shown in Fig. 1. Refinement of the whole body of data including the perturbation-allowed lines converged to A0 and D$ values which are consistent within one standard deviation with those reported, Table I. The model adopted to determine u2, v5 excited state parameters is (with the exception of r<) the same as that employed in the ~3, v6 analysis. It comprises diagonal elements of the energy matrix up to sextic terms as in the ground state and in addition the kldependent terms, complete up to fourth order in the Oka classification (6), Ar, vlJJ( J + 1) , qtJc2, q.,.,J2( J + 1)2, qLIKJ(J + 1) k2, and q1d4 as given in Ref. ( 4). Consistently

12

CRADOCK ET AL.

-1

t

02 (J+l) 2 E-B,J(J+lI+D,J

kl:5 kl=-6

kl=L

kl=-5 kl-3 K-L kl=2 kl=l+ K=3 kl-4 kl=-1 kl=O kl=l_ kl:-3

kl=-2

K=2 K-1 K=O

FIG. 1. Reduced upper state energy level diagram of the u2 = 1 states (straight lines denoted by their K values) and uj = 1 states (kl > 0: full dots and kl S 0: open circles, denoted by their kl values). J-dependent changes of character are evident for K = 2 * kl = - 1 and K = 1 ++ kl = 0, these are identified on the right and the left side of the diagram. The encircled crossings denoted A-F are associated with observable perturbation-allowed lines.

the off-diagonal elements [ Wz,5 + W&J(J + 1)], -f [q:f) + q:+jJJ(J + 1 )], ifi@, and 2(2K + l)[rs + r:J(J + l)] account for Coriolis x, y, 41(+), (Y, and r resonance, respectively; see Ref. (4, Eqs. 4-7) for details. Some higher-order terms, 1)2, &‘J(J+ I), and Wf,(2K+. 1) were tested but not found to e.g. qt(+jJJJ2(J+ be significant. So far the’ v2/v5 and us/Vgbands were assumed to be independent of each other. Systematic and opposite, J-dependent displacements of K = 15 and 16 transitions of v3 had indicated the possibility of interactions with the respective K - 3 levels of v2 (4). The supposed AK = 23 interaction between v2 and 19 has now been unambiguously substantiated (Fig. 2). The v2/v5 interaction model was extended to include, for the relevant transitions, a AK = k3 interaction ( 7) given by

13

THE YJY~ BAND OF H&&F TABLE I Ground State Parameters of H374GeF (cm-‘) This work

From Ref. (4)

A0

2.606 779(7)

2.606 790(5)

0; x 105

1.649(21)

1.675(15)

6Q

0.333 951 99(6)

0; x 107 o&

2.851 3(4)

x 106

4.408 7(11)

Hi x 1014

(u2

=

-9.5(6)

H&

x 1011

1.133(27)

H&

x 1010

1.28(4)

1, u3 = 0, J, KIH(uz = 0,

= Wg’[J(J+

1) - K(Kf

v3

=

1,

J, K+ 3)

1)]“2[J(J+

1) - (Ka X

[J(J+

l)(K+

2)]“2

I) - (K+ 2)(K&

3)]“*.

(1)

A similar perturbation traceable for the kl = - 13 and - 14 sublevels of v5 which may interact with the respective kl = - 16 and - 17 sublevels of Vgwas treated analogously. IV. DESCRIPTION

OF THE SPECTRUM

The general appearance of the v2/ us band has been described previously (2). The low-K Q branches of v2 most affected by the strong Coriolis x, y resonance [with reportedly positive intensity perturbation (M2 &MS > 0) (S)] are weak, difficult to detect, and J-degraded to high wavenumber. Beginning with the clustered QQs branch they are increasingly J-degraded to low wavenumber and well resolved for K 9 7. The spread oQ3 branch can be followed over more than 2 cm-’ and shows, due to the change of attached vibrational character with increasing J, an irregular intensity pattern. As was pointed out previously (2), the band center near 875 cm-’ is particularly dense, while the regions ~862 and >890 cm-’ which comprise the ‘Q&J”) and ‘pQK(J”) branches with K B 3 and the attached AJ = f 1 lines are regular and straightforward to assign (see below). The ‘QK and RQKbranches are throughout degraded to the low and high wavenumber, respectively-the Coriolis x, y perturbation overriding by far any effect of (Y:. As usual, Al A2 splittings are observed for the kl = 1 sublevel, but also the nominal K = 3 levels of u2 and the kl = -2 sublevels of v5 reveal splittings which exceed the resolution threshold. These splittings are illustrated in Fig. 3 and give a fair impression where the crossings A-C, Fig. 1, which involve the 1, (A, for odd J’) and 1_ components (A, for even J’) of the kl = 1 sublevel, occur. Such a case (A in Fig. 1) which gives rise to perturbation-allowed lines is shown in Fig. 1 of Ref. (4). Crossing B is evident from the gap in the RQ$branch of v5, Fig. 4, which is more compressed than the other low-K Q branches of v5 as the attached kl = l- sublevel is unaffected by Coriolis x, y perturbation.

14

CRADOCK ET AL.

-1

E(v,~.J=~o,K)-B~IJ+~)

15cZO

-c

-16 18-

l&00-

-15

-c I

.-.

.-.-.-

1300TL

18 L

17-.-.-.-.-.-.-lL

IL

.-.

k 17' .

.

I .

.

I. -.I!.-

l

'*O"

I

<

-18'

-10 -9

13

_ w36x _v---

-

FIG. 2. Display of reduced upper state energies of v2, ~3, v5, and v6 for J = 20. The framed portions illustrate where AK = k3 perturbations come to resonance.

15

THE vz/v5 BAND OF H@eF

lo-3,-l

1 B

50 A

0

%

20 i 200 100 lo-

0

__________-____-2 -0 00 l-

o

00000

0

0 0 o_-___-_---------

0

0

.

l* 0. av~o.____________-_-__ l 00000 .

00

00

00

.

0.2 0

.

.

.

.

.

.

.

l**e*

000000000000

.

0

l

.

.

0.5 -

0.1 - I J’=lO

.

o

0

5-

fc

.

.

I

I

I

I

I

I

I

I

I

15

20

25

30

35

10

L5

50

55

b

1

RG. 3. Display of A,& splittings of levels reached by transitions of the nominal ‘Q3 branch occurring at 86 I cm-* (open circles) and oQr branch found at 874 cm-r (fitll dots) and attached A.! = + 1 lines, respectively. A, B, and C refer to the level crossings associated with perturbation-allowed lines shown in Fig. 1, the arrows denoting the observed splitting with respect to the normally allowed and perturbation-allowed line. The broken line corresponds to the experimental resolution. Note that the kl = -2 and K = 3 upper states reveal J- and symmetrydependent changes of character. V. ASSIGNMENT

The assignment of lines was facilitated by the use of the program KILO (9) with the parameters found in the earlier study (2). The upper state reduced energy level diagram, Fig. 1, showed the expected J values of crossings that could involve r and (Y resonances and hence the values for which the perturbations should be most intense; however, the diagram does not predict the perturbed line positions because the ( Ak - Al) = +3 coupling parameters were not considered in that model. It was found that in every case the J value of maximum interaction was correctly predicted. A list of predicted line positions from KILO (9) guided the early stages of assignment, and several subbands were quickly identified. Assignments were checked in all cases with gscd, which proved to be a powerful tool. Due to the quality of the gscd a line could be accepted or rejected with confidence in almost all cases. For low K values, the expected quality of agreement was of the order of 0.1 X 10e3 cm-’ or better, and this expectation was found to be justified in practice. When a sufficient body of lines unperturbed by r and CY resonance had been assigned, refinements of upper state parameters using MILL1 (9) were superseded by an “infinite chain” program (IO), with which further line positions were predicted by a bootstrapping procedure. The chain program enabled us to treat first the I resonance and later the cr resonance as will be described separately below. Ultimately all the expected

16

CRADOCK ET AL.

LO I

876.7

I

I

876.9

I

I

8771 cri'

I

J I

8773

q

I

15

50 I

1

877.5

FIG. 4.Theoretical and experimental spectrum of H374GeF in the region of the RQobranch. Note the near J = 28 related to the level crossing B in Fig. 1.A: simulated spectrum; B: experimental spectrum.

gap

resonances were identified and assigned, and perturbation-allowed transitions were predicted with the same program. With the exception of ‘PO( 13) (see Fig. 1 in Ref. (4)) these were all weak, but they enabled us to determine the ground state parameters A0 and 0% as described earlier (4). VI. DATA FIT AND RESULTS

A total of 4768 individual lines, of which 23 were perturbation-allowed transitions, were subjected to the data reduction procedure. These lines spanned J” and K” values s62 and 615 for v2 and 658 and $19 for v5, respectively. Most of them were unitweighted, while about 10% which were obviously blended were given a weight of 0.1. Those lines which belonged to unresolved Ai A2 doublets with 0.4 X 10e3 cm-’ < Av(Ai&) < 2.5 X lop3 cm-’ were treated as two lines, each assigned a weight of 0.2. Their inclusion is responsible for a considerable fraction of the rms deviation of the fit. Lines reaching the levels affected by AK = 3 perturbations with v3 and vg (see below) and differing more than 0.6 X 10e3 cm-’ from their predicted position were given zero weight. The initially used 3 X 3 model was stepwise extended to include the (Yand r resonance parameters and the J( J + 1) dependence of the latter. Since the vibrational character of a K, kl series changes in a complex fashion at least for low K values, assignments to the dominating V, I character had to be adjusted during refinement. Information related to the parameters r5, r<, and a$,< comes mostly from the lowK levels, and since these are strongly mixed up, correlation of these parameters is

THE vz/us BAND OF H3GeF

17

expectedly high; e.g., r5 and Q$< rf~0.998. Accordingly, reasonable predictions of their values are required in order to achieve convergence of the fit. This was eventually reached with u = 0.146 X 10m3 cm-‘, differences between observed and calculated positions of unit-weighted lines not exceeding -0.3 X 10m3 cm-i except for the high-/ lines attached to the K = 12 and 13 levels of v2 and the kl = - 13 and - 14 sublevels of v5. These revealed systematic, - J6-dependent shifts opposite to those of the respective (K, kl) +3, -3 levels of v3and vgreported previously ( 4)) the smaller Boltzmann factor and hence lower intensity and poorer observability of the latter being kept in mind. The relative energies of ~2, v5, ~3, and vg levels are evident from Fig. 2, and the local character of the AK = +3 perturbations becomes understandable. Although both v2 and v5 and v3 and v6 levels are coupled by Coriolis x, y resonance, the levels in question affected by AK = +3 perturbations are almost purely v2 and v5 in character; thus, the two perturbations represented by WE3 and Ws3 are fairly, but not fully independent. The model employed to fit jointly the transitions of ~2, ~3, v5, and v6 associated with the perturbation was a truncated chain comprising (K, )k - II) -3, K, ( k - 11 and(K, Ik-1))+31evelsofv2andv5connectedtoK, Ik-Il,(K, (k-11)+3and (K, Ik-1~)+6levelsofugandv~,withrestrictionto 11 SKS 14and-15Skl S - 12 respectively. The v2/v5 parameters were fixed to those of model 2, with & = 0, and similarly model 2 of Ref. (4) was chosen, with r6 fixed to zero. This procedure is justified by the full equivalence of the simpler models 2 and the extended models 3 for the levels under consideration. Table II displays the excited state parameters obtained with three different models. Model 1, consistent with that employed in (2)) is clearly inadequate with regard to the quality of the data, the significance of the omitted ( Ak - Al) = +3 perturbations and the importance of higher order terms. On the other hand, it was fully satisfactory for the medium-resolution (0.06 cm-‘) data which had been fitted with g = 8.4 X 1O-3 cm-‘; thus the quality of the reported fit (2) was limited by the data and not by the model. The intermediate model 2, which differs from the final model 3 only in that the LY resonance parameter LYE< is fixed to zero, is comparable to model 3 except that it does not account in a satisfactory fashion for the shifts associated with two crossings, those of the levels kl = 1+ with K = 3 around J’ = 46 (C in Fig. 1) and those of the level kl = 0 with kl = -3 near J’ = 59, (obs - talc) values amounting to - +5 X 10P3. Otherwise models 2 and 3 are equivalent, although some highly correlated parameters are entirely different. Note in particular the changes of 95J and vljK, their sum being invariant, as was already pointed out in the v3/vg analysis (4). A similar correlation and fluctuation of their values had been established for the v3 and pg parameters, too (4), and the explanation that the Hamiltonian is not unique (11, 12) is also taken up here. The “extracted” high-J and -K lines of v2/ v5combined with those of v3/ vg attached by the AK = 53 interaction were fitted with u = 0.25 X lop3 cm-‘, which may be compared with the values u = 0.73 X lop3 cm-’ for the same transitions when the WK+3 parameters are fixed to zero. More significant than the improvement of the (r value is, however, the drop of the (obs - talc) values from f4.5 X 10e3 cm-’ to +0.3

18

CRADOCK ET AL. TA3LE II Parameters of the uz = 1 and us = 1 Excited States of H3%eF (cm-’ ) 1

mdel

“;

873.824

(~-A,)xlo~ (B,-B,,)rlU4

-5.678

(D”-o”)xlo’ .J J

66(E)

873.QsO

95(11)

-11.398

l(l9)

9.777

5.536

4(19)

-5.769

2(17)

5

(Ol-0$x10 (H;-HJo)xlo

-0.033

4(20)

O.Ofix

(H;,-H~)x10

873.823

“< = 1 873.980

958(15)

U’(21)

873.980

951(11)

6(5)

9.777

‘(7)

-11.394

l(4)

5.553

3(3)

-5.770

9(7)

0.046

5.564l 92(28)

0.048

Z(7)

-0.033

3(7)

Q’(l5)

-0.034

6(5)

0.047

l(10)

-0.008

3(H)

-O.lU

3(6)

-0.w

E(8)

-0.143

6(4)

-0.036

5(7)

0.063

6(10)

-0.033

‘(4)

E(7)

-0.034

02(29)

11

O.Ofix

1.70(4)

10

b

1.661(17)

-3.5(29) -0.221

-8.9(Q)

s’s(e)

-0.222

0.063 -11.4(11)

-0.756(17)

0.33(3)

-2.36(6)

n5dplo’0

l&7(26)

-0.737(12)

0.330(24)

1.673(13)

-3.4(21)

-9.‘(l)

052 5(13)

-0.222

-5.23(3)

-6.61(3)

-1.261(E)

-1.275(12)

WIOQ

4.059(12)

-&l(8)

qs*)xlO4

3.629

0117)

3.724

(*)Jxlo9

-8.6(6, 3(6)

3.723

-3.730(M)

45

r5x104

4.859

4.889(6)

0.314

“2.5 $,X10

7

0.314

573(5)

-8.234

-8.636(22)

l(30)

7.41(4)

of

-l.l’(lO) 528 3(6)

0.314

O(29)

data

4768 1.605

4760 0.2M

528 2(4)

-8.357(4)

O.OflX

“2”;5x104

6(5)

-3.632(22)

-0.76(14)

A09 5

052 O(l0)

1.058(25)

4.024(17)

%&O’O

Zl(10)

O.Ofix

-0.322(4)

rl#o6

= 1

-11.392

3(9)

873.823

“.

432(29)

I!&06

no.

3

1

6(10)

-8.8(16)

(A?)5

Y, i

-0.174

14

(ll~pl~K)xlo

llodel

Y1 = 1

5(M)

O.OfiX 6

(o;r-oJOr)xlo

I+101

9.642

Model 2 Yq = 1

Yp = 1

-2.50(4) 4768 0.146

X 10 -3 for the most displaced lines experimentally accessible upon consideration of the AK = +-3 interactions, PPIS(J”) and QR13(J”), JQ 46. The relative signs of the parameters We’ and Wg3 are correlated with those of the appropriate other al/e interaction constants. The signs were determined to be opposite and their values are given in Table II. Lists of observed and calculated wavenumbers and correlation coefficients have been deposited as supplementary material.’ The band contour shown in Fig. 4 was obtained with a transition moment ratio 1MS ( : 1A& ( = 0.77( 5). A positive intensity perturbation M2 {&kfS (13) is deduced ’ Lists of observed and calculated wavenumbers and correlation coefficients (70 pp.) have been deposited in the Editorial Office of the Journal of Molecular Spectroscopy and may be obtained from Fachinformationszentrum Karkruhe, D-75 14 Eggenstein-Leopoldshafen, West Germany, on submission of the names of the authors, the literature reference, and the registry number IRD-10038.

19

THE v~/Y~ BAND OF H,GeF

unambiguously. This sign agrees with that of ab initio calculations (8) but could not be determined in the previous study (2). In effect, the positive sign of the intensity perturbation enhances the intensity of ‘R and RP lines of us extending to the band center at the expense of a depletion of ‘P and RR lines developing towards the wings. Thus it gives the uz/v5 band of H3GeF its pronounced central intensity maximum (see Fig. 1 of Ref. (2)). We note that the ( MS I : I M2 ( ratio is considerably larger in H3GeF than in the heavier halides (I), and we point out its (probably fortuitous) consistency with that of ab initio calculations, 0.77, Ref. (8). VII. THE v, = 1 AND u4 = 1 STATES

Any thorough rovibrational analysis of H3GeF is unsatisfactory as long as almost nothing is known about the stretching vibrations vl ( al) and v4(e) located near 2120 and 2 130 cm-‘, respectively. Inconsistent band origins of v1and u4, 2 118.9 and 2 128.6 cm -’ (IS) and 2120.6 and 2131.7 cm-’ (16), have been obtained from mediumresolution IR studies employing a grating spectrometer, the v4 band origin following from a polynomial fit of QK peaks (15,27). Furthermore, (ArZ)4 = -0.140 and (A0 - A4) = 19 X 10S3 cm-’ have been deduced (17). We have recorded an almost Doppler-limited spectrum of H374GeF in the v1/u4 region with an optical resolution of 2.7 X 10e3 cm-’ and an experimental linewidth (fwhm) of 3.5 X low3 cm-’ employing the same interferometer as for the v2/u5 study. As mentioned previously, the v1/ v4 band is abundantly perturbed by overtones and combination bands involving v2, ~3, v5, and v6 quanta and apparently “of discouraging complexity” (4). Table III summarizes the perttubers whose vibrational wavenumbers do not differ more than a70 cm-’ from either up or vi. The perturber wavenumbers were determined from those of the fundamentals with corrections for anharmonicity obtained from an ab initio calculation of the anharmonic force field ( 14). Interestingly, there is only one single perturber (3~3) below vI and v4, and in agreement with the experimental spectrum the AK = - 1 systems of v4 appear much more regular than those with AK = + 1. Evidently ‘Qs to ‘Qg branches are almost unperturbed while ‘Qlo to ‘Q18 reveal J-dependent irregularities. The structure of the latter is affected by an interaction which is typical of rotational type. The perturber is presumably 3v3, TABLE III Possible Perturber9 of the u1 = 1 and uq = 1 Rovibrational States (cm

3v3

2053

“I’ +2”;

2157

v 2 +2”‘2 6

2158

“2+2”;

2156

“‘lt2”‘2 5 6

2159

v~+u;~+v;’

2203

~3+v;~+v;~

2203

“2+“3+“;l

2202

aPerturber

wavenumbers

and ab rnlt~o

calculated

anharmoniclty

from up values

constants

from Ref.

(this work (14).

“I’ +2”;2

and Ref.

2159

(4))

‘)

20

CRADOCK ET AL.

which is itself involved in a higher-order Coriolis resonance with 2~~ + vd’ similar to that reported for v3 and Vg(4). Since the perturbation of the kl < -8 sublevels is mainly of Al = Ak = -+I type, the subband origins, i.e., the lines with J N K, are almost unshifted and, together with the -8 B kl C -6 series and complemented by the first two to five lines of the ‘PI to ‘P6, R&, and RRI series, form a body of data from which the major effective v4 parameters, Table IV, may be derived. Judging from the sharpness of the attached QQ branches, the 0 s KS 5 levels of vl are apparently rotationally unperturbed, except for K = 2, which is weakly affected by a Coriolis X, y interaction with u4. From the appropriate Q(P, R) lines with Jd 30, effective values were derived for the parameters v?, a:, cyf, and W14, Table IV. Inspection of Table III suggests that any anharmonic perturbation of vl, i.e., by 3v3 and vf’ + 2ui*, should be global at least for the K values under consideration here, and due to the substantial energy separation of the vibrational levels involved, we expect that such global effects are absorbed by, and not of major influence on, the effective v1 parameters quoted in Table IV. The results of the full rovibrational analysis of the v1/v4 band ongoing in our laboratories will be reported after completion. VIII. DISCUSSION

The present analysis of the v2/v5 band employing a high-resolution FT spectrum updates the information on the fundamental vibrations of H374GeF significantly. Together with the preceeding analysis of the r+/& band (4) and the preliminary results on vi / v4, the major rovibrational parameters of the most abundant isotopic variety of H3GeF are now available, Table V, and they may be both compared with the results of an ab initio calculation ( 14) and used to determine equilibrium rotational constants from their ground state values. It should be noted that the c$ values originating from the ab initio calculations do not contain contributions from the vl /u4, v2/v5, and v3/ 5 Coriolis X, y resonances. We note that the signs and orders of magnitude of exper-

TABLE IV Parameters of the v, = 1 and u., = I States of H374GeF from Analysis of Selected, Essentially Unperturbed Lines (cm-‘)” v1 = 1 2123.303

“0

15(10)

x 10'

-2.371

l(7)

(6” - rlo) x lo4

-1.352

3130)

(A, - A&

” =I 2131.034 -1.711 0.104(5) -0.147

(Ai*),

-1.686(30)

n4K x 105 6.01(3)

Wl 4 x 103

655

No. of data

9.0

0 x 104 state

933(Z)

3.10(6)

“4J x lo6

'Ground

94(11) 6(8)

constants

Of Table

I wereemployed.

21

THE v2/vS BAND OF H3GeF TABLE V Equilibrium Rotational Constants and Vibration-Rotation

Interaction Constants of H374GeF (cm-‘)

Experimental.

From abioitlo

this work

harmonic

Ref

and

(4) 779(7)

fxld.

Ref.

2.606

2.632 413119)

2.628

7

60

0.333

951 99(6)

0.345

0

Be

0.335

566 4(8)

0.346

4

at x 103

23.711(7)

17.571

+

-9.777

-9.890

at x 103 a:

x 103

a;

7(7)

1.083 4(3) 17.116(8)

1.138 11.624

x 103

11.394

l(4)

9.570

ai x 103

-10.385

4(2)

-7.895

a; x 103

0.135

23(30)

0.059

a;

x 103

0.577

09(7)

0.289

a; x 103

2.297

99(Z)

a; Y 103

-0.010

mt x 103

-0.556

a;

x 103

0.675

1.940

4(S)

-0.027

092(28)

-0.407

75(43

(14)

2 611 0

A0

Ae

x 103

an-

force

0.622

imental and theoretical (Yvalues are consistent, although (Y:, a$, and czz$values differ by 20-30%. The experimental a!, a$, and LYEvalues are surprisingly invariant for the whole H3GeX series, 23.45 -t 0.25, -10.0 + 0.25, and 16.8 f 0.4 X lop3 cm-‘, while (~2 ( 11.4 to 13.1) and cza (-10.4 to - 13.2 X 10M3cm-‘) reveal systematic changes in the series X = F-Cl-Br-I ( 1, 4, 18). These are also accounted for by the ab initio calculations ( 14). This consistency gives credence to the reliability of the u2/ us and v, / v4 rovibrational parameters. As a further test the experimentally available 0°K value, 1.65 (2) X lop5 cm-’ (4), may be compared with the value calculated by means of the Aliev and Watson sum rule (19, 20), D&alc. = 1.679(4) X lop5 cm-‘. This convincing agreement stresses both the capability of the sum rule for the determination of 0°K if high quality rotational analyses are available, and the adequacy of the models employed for this purpose for H374GeF. The consistency of the A0 and 0: values obtained from the fit of the entire body of data and the set of perturbationallowed lines (4), Table I, should be noted, although the marginally smaller standard deviations of the refined values of the present study should be mentioned. The disadvantage of the latter is, however, their correlation with excited state parameters, and therefore we give preference to the values from Ref. (4). The AK = +3 interaction has been elucidated for the first time for the v2/v3 and v5/ Vgrovibrational states of the H3 EX series, although its effects had already been noticed in the study of H3SiF (31). It is most likely that AK = &3 perturbations will

22

CRADOCK ET AL. TABLE VI Predicted Crossings of vz (K), vs (K + 3)/v;’ (/cl), ~a’ (kl - 3)/~;’ (kl), Y:’ (kl + 3) Levels in Monohalides HsEX X=F

lla/

Br

Cl

I

Ref.

-7/12

20/-11117

22/-13/18

23/-15121 (21-30)

Sl

7f-13118

24/-15120

29/-16/21

32/-17/23

(1)

Ge

12/-14/M

27/-15/19

33/-16/20

35/-17/22

(1.4,18)

25/-14/19

33/-N/19

36/-17/21

(1.8)

E=C

Sn "Useful

7/-14/18 K. kl values

are given

in bold

type.

occur in all HjEX- and DjEX-type molecules, although their effects might be signiI%zant only for K, kl values which are not experimentally accessible due to the low population of the attached states. Since lineshifts are expected to increase with - J6, they may become significant even if Wg’ and WE3 are much smaller than in H3GeF. In order to evaluate in general the probabilities of such AK = ?3 interactions, we have calculated the K, kl values close to which the v2 (K) , v3 (K + 3 ) and v$’ (kl), vi’ (kl + 3) crossings occur. For this purpose it is sufficient to express energies by v. + (A0 - Bo)K2 - 2(Ar),kl, and even approximate rovibrational parameters are satisfactory. It is evident from Table VI that, for useful K values, v2/v3 rotational interactions will be important only for the fluorides, while v5/v6 interactions should affect most of the molecules considered, lineshifts being expected in the AK = -1 systems at lower K” than for AK = + 1 transitions. The fluorides, chlorides, and CH3Br should be particularly amenable to these perturbations. We are interested to see whether these predictions can be substantiated by forthcoming experimental work. ACKNOWLEDGMENTS We thank K. Lattner, Giessen, for technical assistance in obtaining the FT spectrum; Dr. L. Halonen, Helsinki, for the computer program; and Professor W. Thiel, Wuppertal, for making ab initio anharmonicity constants available to us. Financial support and a Visiting Professorship to SC. by the Deutsche Forschungsgemeinschafi through SFB 42 are gratefully acknowledged. RECEIVED:

January 4, 1990 REFERENCES

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2. 3. 4. 5. 6. 7.

THE vz/us BAND

OF HJGeF

23

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