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Microwave spectrum of the C4v molecule IF5 in the excited vibrational states v5(B1) = 1 and v9(E) = 1
JOURNAL
OF MOLECULAR
SPECTROSCOPY
85,
109- 119 (1981)
Microwave Spectrum of the Cdv Molecule IF, in the Excited Vibrational States v5(B,) = 1 and v,(E) = 1 Analysis
of the v5-vg Coriolis
Resonance
B. BALIKCI AND P. N. BRIER Department
of Chemistry,
The University, Manchester
Ml3 9PL, England
Measurements of the microwave spectrum of the C,, molecule IF, in the excited vibrational states u5(B,) = 1 and v,(E) = 1 are reported for the transitions J4 -+ 5, 5 -+ 6, 6 + 7, 8 + 9, and 9 + 10 (27-55 GHz). The Coriolis resonance interaction between these two states is analyzed by diagonalization of Hamiltonian matrices of dimension 3 X (2J + 1) in which all (A/,Ak) = (+2. ?2)(q+), (T2, ?2)(q-1. and (0, +4)(&J interactions are included as off-diagonal terms in addition to the uj = 1 ++ ug = 1, I, = *1(&J Coriolis interaction. In the ug = 1 state spectra, the BIB, I-doubling of the kl = - 1 transitions and A,IA, splittings of the kl = -3 transitions and BIB, splittings of the kl = +3 transitions, all enhanced by the Coriolis resonance, have been observed and measured. Least-squares refined rovibrational parameters for the uj = 1 and ug = 1 states are reported and a preliminary value for the rotational constant C9 has been obtained.
INTRODUCTION
The ground-state rotational spectrum of IF, was first detected and briefly reported by Bradley et al. (1). More recently, an extensive set of measurements between 140 and 212 GHz was reported by Truchetet et al. (2) for transitions up to 539 + 40 from which the K-type doubling constant R6 was measured and greatly improved ground-state rotational parameters were derived. The groundstate molecular structure of IF, has been deduced from a joint analysis of these rotational parameters and electron diffraction data (3, 4). Several infrared and Raman studies of IF, have been reported which are summarized in the paper by Osborne et al. (5). In all the XF, (X = I, Br, Cl) molecules, there has been no direct spectroscopic observation of the B, species mode Ye. In the case of BrF,, a value of v5 has been deduced from an analysis of the Coriolis resonance between v5and v,(E) in the microwave spectrum (6). This showed v5 to be more than 45 cm-l lower in frequency than a force constant calculation estimate for this quantity (7). For IF, a similar calculation predicts v5 - 257 cm-’ and by analogy it is to be expected that the true value will be nearer 210 cm-’ approximately. This lower value is supported by a thermodynamic estimate of v5 - 180 + 20 cm-l by Osborne et al. (5). Hence the microwave spectrum of IF, in excited vibrational states was expected to closely parallel that of BrF, with the most intense vibrational satellites corresponding to the first excited states of the two lowest vibrational fundamentals, v5 (-200 cm-‘, B,) and vg (189 cm-l, E) and with a strong Coriolis interaction between the two states. This has indeed proved to be the case. 109
0022-2852/81/010109-11$02.00/O Copyright
0 1981 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
110
BALIKCI AND BRIER EXPERIMENTAL
DETAILS
The measurements were made on a continuously flowing sample of IFS in a conventional X-band Stark cell (HP 8425B) cooled to -20°C. The cooling was provided by a flow of cold nitrogen gas around the cell, boiled off from liquid Nz. For this purpose, the Stark cell was enclosed in a loosely fitting tubular plastic bag and thermally insulated, and the cold gas injected at the center of the tube and directed outward toward both ends of the cell. Thermocouple elements were used to monitor the cell temperature and their signals used in an automatic thermostat system coupled to the cartridge heater which boiled off the gas. This could be preset to any desired low temperature and the whole system provides a most convenient variable temperature cooling arrangement. Measurements up to 38 GHz (56 --, 7) were performed on an HP 8460A spectrometer. Above 40 GHz, the measurements were carried out on a video spec-
FORM OF THE HAMILTONIAN MATRIX FOR A .5,-ESPECIES INTERACTION IN Cav SYMMETRY "t
=
1
at
=
-1
Ys
=
1
Vt
1
tt
=
+l
4+
R6 -2
=
Rb -1
q+
St
q+
R St
R(
R St
0
R
9-
St.
__-_Rst__
2-
q+
q-
I
3 -3
1 q-
St
R6 -2
R
R6 -1
St
R6 O
-Rst
I ,--_
--
-Rst) -R
2 (Symmetrical)
q+
m--q
I St-RSt -St I
3
1
3 -2
R6 R6
-1
I
R6
0
2 3
FIG. 1. Vibration-rotation energy matrix for the u,(B,) = 1, u,(E) = 1 Coriolis interaction. Numerals indicate the values of k for the diagonal elements. Broken lines indicate the usual 3 x 3 Coriolis submatrices. The matrix elements take their usual standard forms (6,8, IO, I I). All nonzero matrix elements satisfy the symmetry rule -Ak + At + 2Au, = 4p, p = 0, 2 1, rtr2 etc. (13). (In C,, symmetry for which AuB = 0, this reduces to the more familiar result -Ok + A/ = 3~).
MICROWAVE SPECTRUM OF IF,
111
FIG. 2. Part of the observed and calculated u,(E) = 1 spectrum for the 56 -+ 7 transition of IF,. The observed spectrum was recorded on an HP 8460A spectrometer under relatively fast survey conditions. Only one group ofkl = - 1transitions are shown. The other group are unshifted by the resonance and are found amongst the outer hyperfine components of the ground-state spectrum at -38230 MHz.
trometer system using OK1 47V12 (43-51 GHz) and 55Vll (52-58 GHz) klystrons as sources together with 33-kHz Stark modulation detection. Radiofrequency markers were generated from the beat signal between the mm-wave klystron and a harmonic of an X-band klystron, the latter phase-locked to a harmonic of a 200- to 400-MHz reference signal generated from an HP 8660B frequency synthesizer. The signal-to-noise ratio of the spectrum in a single sweep of the sawtooth scan was poor and absorption frequency measurements from the oscilloscope were correspondingly difficult. To improve the quality of the observed spectrum and also to obtain a permanent record of the spectrum, albeit in small frequency segments, successive video scans were accumulated and averaged on a Northern Scientific NS513 digital memory oscilloscope. The radio-markers (l- to S-MHz spacing) were first amplitude-discriminated and then pulse-shaped and the leading edge of the first pulse used to trigger successive spectral accumulations. The second pulse was added to the spectrum signal and appeared as an adjustable reference marker in the averaged spectrum. Typically 50- 150 scans were averaged in this way using a IO-msec time constant, and the final averaged result output to a chart recorder. The reported absorption frequencies are mean values of pairs of measurements made with frequency scans in opposite directions since small extrapolations were made from the reference marker pulse position to the exact absorption band centers. Tests with theJ3 + 4 transition of OCS at 4865 1.60 MHz showed that frequencies measured in this way should be accurate to better than 0.1 MHz.
112
BALIKCI AND BRIER TABLE I Observed and Calculated Absorption Frequencies kica'd)
Fca)
~(c&G)(~~~)
m-(C)
kf,
-3-
13/z
27 041.54
-0.17
-3+
13/Z
27 041.54
to.02
1-
1312
27 123.33
for IF,, u,(E) = I
F
u(obs)
err
3-
11/z
27 144.12
-0.18
3+
11/2
27 144.12
-0.24
to.53
-1+
712
27 324.03
-0.40
-545
1+
13/Z
27 100.54
+0.12
-1-
312
26 902.12
-0.07
1+
11/E
27 105.63
tQ.21
-2
13/Z
27 038.61
+0.27
-3-
712
27 105.63
-0.24
0
1312
27 141.07
to.07
-3+
712
27 105.63
-0.06
2
13/Z
27 088.41
to.20
1-
512
27 149.67
to.55
4
13/Z
27 025.09
to.02
1-
312
27 135.01
to.57
4
11/2
27 179.88
-0.06
-1+
1312
27 296.77
-0.46
0
11/Z
27 136.2
to.07
3+
13/Z
27 060.37
-0.05
0
912
27 148.63
tO.20
3-
13/Z
27 060.37
tO.02
4
512
27 025.09
-0.50
-1-
13/Z
26 890.55
-0.06
0
312
27 159.06
-0.29
-1+
11/z
27 302.23
-0.20
-2
312
27 030.64
~3.62
-1-
11/z
26 895.81
to.01
-J56 1+
1512
32 537.91
to.18
-1-
912
32 292.62
to.32
-3+
13/Z
32 509.58
to.43
3+
712
32 522.30
-0.40
-3-
13/Z
32 509.58
-0.04
3-
712
32 522.30
-0.21
5
11/Z
32 601.57
-0.10
-1'
712
32 7p9.98
-0.28
1-
11/z
32 574.50
-!I.08
-1-
712
32 292.62
-0.35
512
32 283.37
-0.05
1512
32 526.47
tO.01
1512
32 478.01
to.00
1512
32 460.85
to.08
15/Z
32 436.91
-0.05
-4
1312
32 545.12
-0.40
-2
1312
32 455.72
-0.06
-4
11/z 9/2
32 465.96 32 532.43
to.35
-3+
11/z
32 522.30
to.59
-1-
-3-
11/z
32 522.30
to.12
2
-3-
7/Z
32 483.01
to.29
4
-1+
15/Z
32 761.86
to.19
-4
-1-
15/2
32 274.35
-0.03
-2
-1+
1312
32 763.86
to.06
-1-
13/Z
32 276.52
to.03
3-
11/Z 11/z
32 561.30 32 561.30
-0.39
-2
-0.57
3+
-0.03
-5
11/z
32 600.22
tO.07
4
712
32 497.90
to.20
-it
11/z
32 772.29
to.02
2
J/2
32 545.12
to.07
-1-
11/2
32 284.93
-0.04
-2
J/2
32 455.72
-0.21
3-
912
32 549.40
-0.32
2
512
32 526.47
to.20
3+
912
32 549.40
-0.50
-2
512
32 436.91
to.24
912
32 549.40
-0.17
1-
17/Z
38 010.85
+0.30
-1-
13/Z
37 664.19
to.00
5
17/Z
37 897.24
Co.06
-1'
11/z
38 237.51
+0.14
-5
J6*7
MICROWAVE
SPECTRUM
TABLE
ka
F
u(obs)
err
113
OF IF,
I-Conrinued
ke
u(obs)
F
err
1+
1512
37 980.49
-0.11
-1-
11/2
37 670.12
-3+
1512
37 899.69
NJ.55
3+
9l2
37 960.41
-0.21
-3-
15/2
37 899.69
-0.49
3-
912
37 960.41
to.23
to.29
-3+
13/2
37 909.98
to.59
-1-
912
37 670.66
-0.27
-3-
13/2
37 909.98
-0.45
-1+
7l2
38 231.76
-0.11
1-
13/2
38 017.64
t0.61
3‘
712
37 937.07
co.28
1+
1312
37 986.75
to.23
3+
712
37 937.07
-0.18
5
13/2
37 996.35
-0.15
-1-
-0.25
-3-
11/2
37 905.85
-0.09
-2
712 1l/2
37 664.19 37 823.15
to.02
1+
11/2
37 992.21
-0.05
-4
17/2
37 883.24
-0.03
5
912
37 922.87
-0.12
4
1712
37 920.86
-0.06
1-
712
38 017.64
-0.01
2
17/2
37 965.66
to.10
5
7/2
37 866.05
to.03
-2
15/2
37 834.31
to.00
-3+
712
37 866.05
to.69
-4
1512
37 934.72
to.17
-3-
712
37 866.05
-0.36
0
1512
38 052.62
to.12
-5
1712
37 881.40
+0.13
4
1512
37 971.91
HI.01
-1-
1712
37 657.63
to.33
-6
1312
38 013.52
-0.19
3-
17/2
37 943.07
to.36
6
1312
38 013.52
t0.69
3+
1712
37 943.07
-0.10
0
1312
38 057.86
tO.04
-1+
1512
38 225.44
-0.19
2
13/2
37 983.68
-0.02
-5
1512
37 963.21
to.07
4
1312
37 985.72
to.28
3-
1512
37 970.32
to.22
-4
11/2
37 934.72
-0.08
3+
1512
37 970.32
-0.22
0
11/2
38 064.60
-0.23
-1‘
15/2
37 657.63
-0.47
2
912
37 980.49
-0.03
-1+
13/2
38 231.76
+0.10
0
912
38 068.27
to.05
3+
1312
37 980.49
-0.15
-2
912
37 838.26
-0.25
3-
13/2
37 980.49
+0.29
6
7/2
37 823.15
+0.17
13/2
37 980.49
-0.41
-4
712
37 866.05
-0.06
-3+
19/2
48 671.48
to.32
-5
1712
48 764.12
to.16
-3-
19/2
48 674.46
-0.17
-1-
1712
48 427.02
-0.13
1
77/2
48 886.98
to.31
3-
15/Z
48 840.36
-0.24
-3+
17/2
48 677.68
to.14
3+
1512
48 842.28
-0.57
-3-
17/2
48 680.47
-0.54
-5
15/2
48 757.13
tO.40
-3+
1512
48 677.68
+0.13
-1-
1512
48 431.10
to.29
-3-
1512
48 680.47
-0.56
3+
13/2
48 836.44
-0.29
-3+
13/2
48 671.48
to.30
3-
13/P
48 834.55
to.12
-3-
13/2
48 674.46
-0.21
-5
13/2
48 736.03
to.18
1+
13/2
48 891.65
to.05
-1-
13/z
48 431.57
-0.39 -0.16
-5
584
21/2
48 824.51
-0.27
11/2
48 824.51
-5
21/2
48 715.59
-0.01
-2
21/E
48 570.45
tO.14
-1-
21/2
48 423.80
-0.11
-2
19/2
48 575.17
to.19
3-
1912
48 834.55
to.23
4
1712
48 831.72
-0.07
3+
19/z
48 836.44
-0.15
-2
1712
48 579.72
tO.ll
3+
3+
114
BALIKCI TABLE
ka.
F
v(obs)
AND BRIER I-Continued
err
ke
F
v(obs)
err
-5
19/2
48 752.42
to.31
-6
15/2
48 779.47
-0.41
-1-
19/2
48 423.80
to.07
-2
15/2
48 581.80
-0.11
3-
1712
48 840.36
-0.18
-2
13/2
48 579.72
-0.43
3+
1712
48 842.28
-0.51
-2
lll2
48 572.90
-0.19
-0.10
J9+10 9
23/2
54 136.00
to.10
7
13/2
54 163.54
-7
2312
54 143.97
-0.00
-5
1312
54 115.79
to.21
-3-
2312
54 046.79
to.36
-1-
1312
53 813.54
-0.12
-3+
23/2
54 040.96
+0.10
a
23/2
54 156.86
-0.21
-3-
2112
54 055.21
~I.07
-4
2312
54 093.89
-0.29
-3+
2112
54 049.90
+0.30
-2
2312
53 937.61
to.20
9
1912
54 248.54
+0.23
-6
2312
54 136.00
to.08
-3+
19/2
54 055.21
+0.51
-4
2112
54 110.32
-0.18
-3+
1712
54 055.21
-0.13
-a
2112
54 216.51
to.01
-7
1512
54 171.29
+0.02
-2
2112
53 940.20
-0.36
5
1512
54 236.79
to.55
-6
2112
54 174.21
+0.12
5
1312
54 213.92
-0.32
-4
1912
54 117.15
-0.39
9
1312
54 110.60
to.11
4
1912
54 264.96
-0.28
7
2312
54 177.74
+o.Ol
-a
1912
54 236.79
to.24
-1-
2312
53 809.57
-0.31
a
1912
54 246.53
to.54
-5
2112
54 147.21
tD.16
-4
1712
54 115.79
-0.33
-1-
21/2
53 809.57
+0.16
a
15/2
54 191.09
to.31
-5
19/2
54 156.86
+0.27
-4
15/2
54 107.38
+O.lO
-1-
19/2
53 all.64
-0.41
-2
15/2
53 944.95
-0.42
-5
1712
54 152.59
to.07
-4
13/i: 54 092.04
-0.15
-1‘
1712
53 815.07
-0.01
a
1312
54 137.65
+0.04
-5
1512
54 137.65
-0.23
-2
1312
53 940.20
to.19
OBSERVED AND CALCULATED ABSORPTION FREQUENCIES FOR IF5. (v5(a,) = 1) 54-5 2
1312
27 556.88
to.04
4
912
27 670.53
+O.lD
2
11/2
27 591.39
+0.05
0
912
27 581.68
tD.15
2
912
27 603.91
-0.16
0
712
27 596.41
to.19
4
1312
27 505.97
+0.29
4
512
27 505.97
-0.25
0
1312
27 573.47
-0.10
0
5/2
27 602.28
+0.32
4
11/2
27 660.65
to.07
0
312
27 591.55
-0.28
0
1112
27 568.72
-0.37
3
1312
27 535.77
tD.14
2
15/2
33 079.86
-0.23
4
712
33 068.68
-0.12
2
1112
33 108.33
-0.23
4
5/2
33 012.71
+o.oo
MICROWAVE
ke
SPECTRUM
u(obs)
err
g/2
33 108.33
-0.31
5
5/2
33 079.86
to.00
1
15/2
33 090.55
to.35
3
F
ke
115
OF IF,
v(obs)
err
15/2
33 025.70
+o.lO
15/2
33 087.69
to.03
1512
33 067.25
+0.09
F
1512
33 049.23
to.16
1
1312
33 090.01
to.23
13/2
33 087.02
+0.09
5
13/2
33 160.96
to.08
13/2
33 133.67
to.03
5
11/2
33 179.32
+0.03
11/2
33 148.92
-0.13
3
11/2
33 125.42
to.01
9/2
33 120.45
to.28
3
5/2
33 051.74
+0.04
7/2
33 108.43
-0.36
-J6+7
2
17/2
38 599.45
-0.06
4
11/2
38 630.48
-0.21
15/2
38 665.33
-0.03
4
912
38 600.57
to.08
9/2
38 614.27
-0.31
4
712
38 562.41
to.13
7/2
38 601.10
-0.55
5
17/2
38 564.36
tO.05
17/2
38 579.45
tO.06
3
17/2
38 591.05
to.00
17/2
38 605.99
to.02
1
17/2
38 604.36
to.05
15/2
38 630.48
to.01
1
15/2
38 605.15
to.03
15/2
38 603.40
-0.07
3
1312
38 628.91
to.20
13/2
38 644.10
to.06
5
13/Z
38 663.84
+0.12
13/2
38 608.87
-0.09
3
11/z
38 624.22
-0.04
(a)
Ak
(b)
Measured frequencies (MHz) accurate to ? 0.1 MHz
(c)
Err
= =
0, AF
=
tl transitions only
v(obs) -
v(calc). Frequencies calculated with the values
of the parameters given in the first column of Table II. (d)
Superscripts + and - refer to transitions involving $* and $-. Assignments are based on R6 ) 0, qi > 0, qG* < 0.
THEORY
The theory of a Coriolis B,-E species interaction in Gel, symmetry has been given in our previous papers on BrF, (6,8,9). The only difference in the present work is that we have made more exact calculations of the rotational energy levels in the v,(B,) = 1 and u,(E) = 1 vibrational states by setting up and diagonalizing Hamiltonian matrices of dimension 3 x (25 + I) in a harmonic oscillatorsymmetric-top 1us, VI’,J,k) basis (actually factored into smaller submatrices of A, B, and E species symmetries). This allows us to include all the (Al,Ak) = (2,2)(q+), (2, -2)(q-), and (0,4)(&) interactions as off-diagonal elements as well as the U, = I t, ut = 1, 1, = k 1(R,,) Coriolis interaction term. The form of the resulting matrix is shown in Fig. 1. These matrices were set up and diagonalized for each quadrupole hyperfine component separately with both first- and second-order quadrupole energy contributions included in the diagonal terms. As in the case of BrF,, the centrifugal distortion constants DJ, D JK, and R, for both excited states
116
BALIKCI AND BRIER
FIG. 3. The calculated v,(E) = 1 spectrum for the J8 + 9 transition showing the two pairs of A,/A, and B,/B, doublings and splittings in the IF, spectrum. Note the discontinuities in the frequency scale above 48,500 MHz and below 49,100 MHz. This contraction of the spectrum omits the k/ = -2 transitions at 48,570 MHz and the kl = +2 transitions at 49,000 MHz.
were constrained to be zero.
at their ground-state
values and the constant r)tJ was constrained
RESULTS
The work of Truchetet et al. (2) on the ground-state spectrum of IF5 produced precise values for all the ground-state rotational parameters except for the quadrupole coupling constant esQ (due to the collapse of the hyperfine structure at the high J transitions studied by these authors). Therefore, before embarking on the study of the excited vibrational state spectrum, a series of absorption frequency measurements were made for the stronger and nonoverlapped hyperfine transitions of the ground-state spectrum from J3 + 4 through to 56 --, 7 on HP 8460A spectrometer in order to obtain an improved value for esQ. A least-squares refinement to a total of 88 data, constraining the centrifugal distortion constants DJ, DJK, and R6 to the values reported in Ref. (2), and including both first- and second-order contributions to the quadrupole splitting, gave the following results for B0 and esQ. B0 = 2727.4226 ‘_’0.0010 MHz (Ref. (2), 2727.4217 + 0.0010 MHz), and eqQ = 1069.07 ? 0.4 MHz (Ref. (2), 1067 5 10 MHz), all errors corresponding to one standard deviation. Frequency scans above and below the ground-state transitions revealed two groups of vibrational satellites. The group to the low-frequency side had a complex structure typical of an E-species excited state, while the group to the highfrequency side closely resembled the ground-state spectrum and corresponds therefore to a nondegenerate vibrational state. The large shifts of the excited state lines from the ground-state transitions in a 2:l ratio (6) indicate a Coriolis resonance interaction between the two vibrational states involved. In analogy with BrF, (6) and our previous discussion of the vibrational frequencies of IFS, we assign the two sets of satellites to the v,(E) = 1 and the 05(B1) = 1 states. Since
MICROWAVE
SPECTRUM TABLE
OF IF,
117
II
Refined Parameters for IF,
v5 - Y9
t546 380.
R5,9
3 134.1
B5*
(150.)
2 728.25 (0.9)
Cg + (Cc), - Bg* Cg - (Wg
(27 000.)
2 722.18 (1.8)
l
B9
- Bg*
_* Q9 Q; eqQ c5 - c9
III
II
I
t544 450.
+505 800.
3 122.8
2 900.
2 722.3
2 724.9
2 728.2
2 726.9
(1.8)
-1 132.8
-1 131.5
-470.58 (1.4)
-474.6
-480.8
-1 133.3
-4.91 (1.9) 2.26 1 067.0 3.0
(0.03) (1.5) (9.)
-5.04
-7.62
2.27
2.28
1 066.95
1 066.91
1.2
(FIXED)
-1.2
(FIXED)
(FIXED)
DERIVED QUANTITIES c9 Fy 9,9 v5
1 926.3
(0.8)
1 924.45
1 920.76
-0.17 (0.02) 207.2
(0.9)
REFINEMENT II
C5 - Cg CONSTRAINED TO 1.2 MHz AS ESTIMATED FROM 79/81 BrF5 DATA
REFINEMENT III
R5 g ADDITIONALLY CONSTRAINED TO 2900 MHz TO MAKE Bg* < Bo AS IN BrF5
All quantities in MHz except v5 (cm-') and r:,g (dimensionless). Quoted errors represent 2.5 standard deviations.
the latter are to the high-frequency side of the ground-state spectrum then, for IF 5, Q(B~) > v,(E). An approximate value for the quantity 2R$,/A - 35 (where A = ug - vg) could immediately be obtained from the gross shifts (6) and combined with a theoretical estimate of 1R,,, 1 - 3010 2 100 MHz (using a force constant calculation of 1i& 1 - 0.78) gives A = vg - ug - + 17 cm-l. The accidental vibrational degeneracy of v5 and vg in IF, is therefore much less close than in BrF, (A - -6.8 cm-‘). The observed transitions in both excited state spectra were readily assigned from theoretical predictions of the spectrum using initial estimates of the rovibrational parameters involved in the energy matrix of Fig. 1. Figure 2 shows part of the measured v,(E) = 1 spectrum for the 56 + 7 transition together with the calculated spectrum. Table I lists all the observed frequencies and their assignments. In-Fig. 3 we show the two pairs of AI/A, and B,/B, doublings and splittings observable in the v,(E) = 1 spectrum of IF, for the 58 + 9 transition at 48.8 GHz (calculated spectrum). The CJ+doubling of the kl = + 1 transitions is the wellknown consequence of the (Ak,Al) = (2,2) interaction linking the originally
118
BALIKCI
AND BRIER
degenerate pair of states 9: (kf = + 1). The q- doubling of the I/$ (kl = - 1) transitions is similarly due to the nonzero (2, -2) interaction, but enhanced into a case of giant l-doubling by the further (Coriolis) interaction between the $7 (kl = - 1) and $I~(k = 0) states (6). In addition to the above, there is an AJA, splitting of the kl = -3 transitions caused by the Coriolis interaction linking the I/$ (kl = -3) levels with the I-doubled (q+) I,!$ (kl = + 1) levels via the intermediate I,!J~’ (kl = 2) st a t es. (The (2, -2)qinteraction which links these levels directly has a much smaller effect). Finally, there is a B,/B, splitting of the kf = +3 transitions caused by the (2,2)q+ coupling between the IJF (kl = +3) and the giant I-doubled JIT (kl = -1) levels. The major interaction here is between the Coriolis perturbed +; (kl = - 1) states with the $J; (kl = 1-3) states due to an accidental near degeneracy and avoided crossing of these states estimated to be in the region Jl I- 13. This causes a further shift of the +; (kl = - 1) transitions in addition to the kl = +3 splittings. At J8 + 9 the calculated kl = -3 splittings are 3.5 MHz approximately and the kf = +3 splittings 2.3 MHz. DISCUSSION
A least-squares refinement of the rovibrational parameters involved in the vg-vg Coriolis resonance gave the results listed in the first column of Table II. The refinement proved stable but the least-squares minimum is not deep and well defined. The probable errors are therefore conservatively quoted as 2.5 standard deviations. These errors are comparable to those reported for BrF, (8, 9) when allowance is made for the stronger Coriolis resonance in the latter case. Not shown in Table II are the results of refining separate values for eqQ@) and eqQct) which gave 1066.3 (1.5) and 1067.6 (2.0) MHz, respectively, with negligible changes in any of the other parameter values. For BrF, it was found that 2a$ + I$ = 6.85 MHz whereas for IF, we find 3.54 MHz, i.e., approximately one-half the BrF, value. In view of the large error associated with C, - C,,, we therefore carried out a second refinement (see Table II) constraining this quantity to one-half the BrF, result. This produced changes in the values of the other parameters which are typically less than one-quarter of the corresponding standard deviations of the original calculation (except for C, + (C& - B; and C, - (C& - B,* which changed by approximately one and three standard deviations, respectively). These changes are not significant. A further feature of the original refinement is that it gives a value of Bg*greater than the ground-state constant B. (a$ - -0.8 + 0.4 MHz) whereas the reverse was the case for both isotopes of BrF, (CX~- + 1.1 2 0.3 MHz) (12). The vibrational frequencies of BrF, and IF, are such that, at least for the nonresonant, hnmonic contributions to (Yeand ag (both (Yeand cyB),one would not expect such a reversal of sign. It is, of course, difficult to make any predictions concerning the differences expected between the anharmonic contributions to the a-constants. We did make a final refinement for IFS, therefore, constraining R5,9 to a value (2900 MHz) which gives a result for (wg* approximately half the BrF, result (Table II). In terms of the original theoretical estimate for R,,g (3010 ? 100 MHz) there is nothing to choose between this value and the refinement result (3134 2 60 MHz). However, the parameter values from this refinement differ from the original refinement results
119
MICROWAVE SPECTRUM OF IF,
by four standard deviations typically and are therefore of marginal credibility. For all three sets of rovibrational parameters in Table II, we deduce a value for the rotational constant C, in the region 1920- 1925 MHz which differs significantly from the preferred prediction of Heenan and Robiette (4) (C, - C, = 1945 +- 10 MHz) from a combined refinement of electron diffraction data and the microwave measurement of BO, even allowing for the probable differences between Cg and Co/C,. We make no further comments on the present refinements or the detailed molecular structure of IF,. It is hoped that rovibrational parameters of considerably improved precision may be obtained with the aid of additional experimental data for the Jll --;, 12 and/or 512 + 13 transitions at 65 and 70 GHz, respectively. Absorption frequencies of the kl = - 1 and kl = +3 lines for these transitions are expected to show splittings and shifts of several hundred megahertz due to the near accidental degeneracy and avoided crossing of the I,!J;(kl = - 1) and I/J; (kl = +3) levels presently predicted to occur at almost exactly J = 12. Absorption frequency measurements for transitions involving these states should provide data particularly sensitive to the magnitudes of the rovibrational parameters of the Coriolis resonance. This effect is entirely analogous to the situation reported for BrF, (9) at J = 8 except, in that case, the negative value of A = vg - vg leads to an avoided crossing of the I/I: (kf = - 1) and I,!J[(kl = +3) levels. A klystron source for the region 65-75 GHz will be available to us in the near future and it is hoped to report these important measurements at a later date. ACKNOWLEDGMENTS It is a pleasure to thank Professor I. M. Mills, Reading University for the use of the HP 8460A spectrometer and Dr. J. G. Baker, Schuster Laboratory, Manchester University for the use of the millimeter wave equipment. We should also like to thank Dr. J. G. Smith, Newcastle University for his help and encouragement in attempts to measure the IF, spectrum at 70 GHz using a source modulation spectrometer and harmonic generation. One of us (B.B.) would like to thank the Government of Turkey, Ministry of Education for financial support during the period of this research. RECEIVED:
February
28, 1980 REFERENCES
1. R. H. BRADLEY,P. N. BRIER, AND M. J. WHITTLE, C/rem. Phys. Lert. 11, 192-193 (1971). 2. F. TRUCHETET,R. JUREK, AND J. CHANUSSOT,Canad. J. Phys. 56, 601-609 (1978). 3. A. G. ROBIETTE, R. H. BRADLEY, AND P. N. BRIER, f. C&m. Sot. D 1567-1568 (1971). 4. R. K. HEENAN AND
A. G. ROBIETTE,J. Mol. Struct. 55, 191-197 (1979).
5. D. W. OSBORNE,F. SCHREINER,AND H. SELIG, .I. Chem. Phys. 54, 3790-3798 (1971). 6. P. N. BRIER, S. R. JONES, AND J. G. BAKER, J. Mol. Spectrosc. 60, 18-30 (1976). 7. G. M. BEGUN, W. H. FLETCHER, AND D. F. SMITH. J. Chem. Phys. 42, 2236-2242 (1965). 8. P. N. BRIER, S. R. JONES. J. G. BAKER, AND C. GHEORGHIOU,J. Mol. Spectrosc. 64, 415-428 (1977). 9. C. GHEORGHIOU,P. N. BRIER, J. G. BAKER, AND S. R. JONES, J. Mol. Spectrosc. (1978). IO. C. DI LAURO AND I. M. MILLS, J. Mol. Spectrosc. 21, 386-413 (1966). II. G. J. CARTWRIGHTAND I. M. MILLS, J. Mol. Spectrosc. 34, 415-439 (1970). 12. P. N. BRIER. Unpublished improved refinements of the BrF, data.
13. G. AMAT, H. H. NIELSEN, AND G. TARRAGO,in “Rotation-Vibration cules.” Chap. VI, Dekker, New York, 1971.
72, 282-292
of Polyatomic
Mole-
OF MOLECULAR
SPECTROSCOPY
85,
109- 119 (1981)
Microwave Spectrum of the Cdv Molecule IF, in the Excited Vibrational States v5(B,) = 1 and v,(E) = 1 Analysis
of the v5-vg Coriolis
Resonance
B. BALIKCI AND P. N. BRIER Department
of Chemistry,
The University, Manchester
Ml3 9PL, England
Measurements of the microwave spectrum of the C,, molecule IF, in the excited vibrational states u5(B,) = 1 and v,(E) = 1 are reported for the transitions J4 -+ 5, 5 -+ 6, 6 + 7, 8 + 9, and 9 + 10 (27-55 GHz). The Coriolis resonance interaction between these two states is analyzed by diagonalization of Hamiltonian matrices of dimension 3 X (2J + 1) in which all (A/,Ak) = (+2. ?2)(q+), (T2, ?2)(q-1. and (0, +4)(&J interactions are included as off-diagonal terms in addition to the uj = 1 ++ ug = 1, I, = *1(&J Coriolis interaction. In the ug = 1 state spectra, the BIB, I-doubling of the kl = - 1 transitions and A,IA, splittings of the kl = -3 transitions and BIB, splittings of the kl = +3 transitions, all enhanced by the Coriolis resonance, have been observed and measured. Least-squares refined rovibrational parameters for the uj = 1 and ug = 1 states are reported and a preliminary value for the rotational constant C9 has been obtained.
INTRODUCTION
The ground-state rotational spectrum of IF, was first detected and briefly reported by Bradley et al. (1). More recently, an extensive set of measurements between 140 and 212 GHz was reported by Truchetet et al. (2) for transitions up to 539 + 40 from which the K-type doubling constant R6 was measured and greatly improved ground-state rotational parameters were derived. The groundstate molecular structure of IF, has been deduced from a joint analysis of these rotational parameters and electron diffraction data (3, 4). Several infrared and Raman studies of IF, have been reported which are summarized in the paper by Osborne et al. (5). In all the XF, (X = I, Br, Cl) molecules, there has been no direct spectroscopic observation of the B, species mode Ye. In the case of BrF,, a value of v5 has been deduced from an analysis of the Coriolis resonance between v5and v,(E) in the microwave spectrum (6). This showed v5 to be more than 45 cm-l lower in frequency than a force constant calculation estimate for this quantity (7). For IF, a similar calculation predicts v5 - 257 cm-’ and by analogy it is to be expected that the true value will be nearer 210 cm-’ approximately. This lower value is supported by a thermodynamic estimate of v5 - 180 + 20 cm-l by Osborne et al. (5). Hence the microwave spectrum of IF, in excited vibrational states was expected to closely parallel that of BrF, with the most intense vibrational satellites corresponding to the first excited states of the two lowest vibrational fundamentals, v5 (-200 cm-‘, B,) and vg (189 cm-l, E) and with a strong Coriolis interaction between the two states. This has indeed proved to be the case. 109
0022-2852/81/010109-11$02.00/O Copyright
0 1981 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
110
BALIKCI AND BRIER EXPERIMENTAL
DETAILS
The measurements were made on a continuously flowing sample of IFS in a conventional X-band Stark cell (HP 8425B) cooled to -20°C. The cooling was provided by a flow of cold nitrogen gas around the cell, boiled off from liquid Nz. For this purpose, the Stark cell was enclosed in a loosely fitting tubular plastic bag and thermally insulated, and the cold gas injected at the center of the tube and directed outward toward both ends of the cell. Thermocouple elements were used to monitor the cell temperature and their signals used in an automatic thermostat system coupled to the cartridge heater which boiled off the gas. This could be preset to any desired low temperature and the whole system provides a most convenient variable temperature cooling arrangement. Measurements up to 38 GHz (56 --, 7) were performed on an HP 8460A spectrometer. Above 40 GHz, the measurements were carried out on a video spec-
FORM OF THE HAMILTONIAN MATRIX FOR A .5,-ESPECIES INTERACTION IN Cav SYMMETRY "t
=
1
at
=
-1
Ys
=
1
Vt
1
tt
=
+l
4+
R6 -2
=
Rb -1
q+
St
q+
R St
R(
R St
0
R
9-
St.
__-_Rst__
2-
q+
q-
I
3 -3
1 q-
St
R6 -2
R
R6 -1
St
R6 O
-Rst
I ,--_
--
-Rst) -R
2 (Symmetrical)
q+
m--q
I St-RSt -St I
3
1
3 -2
R6 R6
-1
I
R6
0
2 3
FIG. 1. Vibration-rotation energy matrix for the u,(B,) = 1, u,(E) = 1 Coriolis interaction. Numerals indicate the values of k for the diagonal elements. Broken lines indicate the usual 3 x 3 Coriolis submatrices. The matrix elements take their usual standard forms (6,8, IO, I I). All nonzero matrix elements satisfy the symmetry rule -Ak + At + 2Au, = 4p, p = 0, 2 1, rtr2 etc. (13). (In C,, symmetry for which AuB = 0, this reduces to the more familiar result -Ok + A/ = 3~).
MICROWAVE SPECTRUM OF IF,
111
FIG. 2. Part of the observed and calculated u,(E) = 1 spectrum for the 56 -+ 7 transition of IF,. The observed spectrum was recorded on an HP 8460A spectrometer under relatively fast survey conditions. Only one group ofkl = - 1transitions are shown. The other group are unshifted by the resonance and are found amongst the outer hyperfine components of the ground-state spectrum at -38230 MHz.
trometer system using OK1 47V12 (43-51 GHz) and 55Vll (52-58 GHz) klystrons as sources together with 33-kHz Stark modulation detection. Radiofrequency markers were generated from the beat signal between the mm-wave klystron and a harmonic of an X-band klystron, the latter phase-locked to a harmonic of a 200- to 400-MHz reference signal generated from an HP 8660B frequency synthesizer. The signal-to-noise ratio of the spectrum in a single sweep of the sawtooth scan was poor and absorption frequency measurements from the oscilloscope were correspondingly difficult. To improve the quality of the observed spectrum and also to obtain a permanent record of the spectrum, albeit in small frequency segments, successive video scans were accumulated and averaged on a Northern Scientific NS513 digital memory oscilloscope. The radio-markers (l- to S-MHz spacing) were first amplitude-discriminated and then pulse-shaped and the leading edge of the first pulse used to trigger successive spectral accumulations. The second pulse was added to the spectrum signal and appeared as an adjustable reference marker in the averaged spectrum. Typically 50- 150 scans were averaged in this way using a IO-msec time constant, and the final averaged result output to a chart recorder. The reported absorption frequencies are mean values of pairs of measurements made with frequency scans in opposite directions since small extrapolations were made from the reference marker pulse position to the exact absorption band centers. Tests with theJ3 + 4 transition of OCS at 4865 1.60 MHz showed that frequencies measured in this way should be accurate to better than 0.1 MHz.
112
BALIKCI AND BRIER TABLE I Observed and Calculated Absorption Frequencies kica'd)
Fca)
~(c&G)(~~~)
m-(C)
kf,
-3-
13/z
27 041.54
-0.17
-3+
13/Z
27 041.54
to.02
1-
1312
27 123.33
for IF,, u,(E) = I
F
u(obs)
err
3-
11/z
27 144.12
-0.18
3+
11/2
27 144.12
-0.24
to.53
-1+
712
27 324.03
-0.40
-545
1+
13/Z
27 100.54
+0.12
-1-
312
26 902.12
-0.07
1+
11/E
27 105.63
tQ.21
-2
13/Z
27 038.61
+0.27
-3-
712
27 105.63
-0.24
0
1312
27 141.07
to.07
-3+
712
27 105.63
-0.06
2
13/Z
27 088.41
to.20
1-
512
27 149.67
to.55
4
13/Z
27 025.09
to.02
1-
312
27 135.01
to.57
4
11/2
27 179.88
-0.06
-1+
1312
27 296.77
-0.46
0
11/Z
27 136.2
to.07
3+
13/Z
27 060.37
-0.05
0
912
27 148.63
tO.20
3-
13/Z
27 060.37
tO.02
4
512
27 025.09
-0.50
-1-
13/Z
26 890.55
-0.06
0
312
27 159.06
-0.29
-1+
11/z
27 302.23
-0.20
-2
312
27 030.64
~3.62
-1-
11/z
26 895.81
to.01
-J56 1+
1512
32 537.91
to.18
-1-
912
32 292.62
to.32
-3+
13/Z
32 509.58
to.43
3+
712
32 522.30
-0.40
-3-
13/Z
32 509.58
-0.04
3-
712
32 522.30
-0.21
5
11/Z
32 601.57
-0.10
-1'
712
32 7p9.98
-0.28
1-
11/z
32 574.50
-!I.08
-1-
712
32 292.62
-0.35
512
32 283.37
-0.05
1512
32 526.47
tO.01
1512
32 478.01
to.00
1512
32 460.85
to.08
15/Z
32 436.91
-0.05
-4
1312
32 545.12
-0.40
-2
1312
32 455.72
-0.06
-4
11/z 9/2
32 465.96 32 532.43
to.35
-3+
11/z
32 522.30
to.59
-1-
-3-
11/z
32 522.30
to.12
2
-3-
7/Z
32 483.01
to.29
4
-1+
15/Z
32 761.86
to.19
-4
-1-
15/2
32 274.35
-0.03
-2
-1+
1312
32 763.86
to.06
-1-
13/Z
32 276.52
to.03
3-
11/Z 11/z
32 561.30 32 561.30
-0.39
-2
-0.57
3+
-0.03
-5
11/z
32 600.22
tO.07
4
712
32 497.90
to.20
-it
11/z
32 772.29
to.02
2
J/2
32 545.12
to.07
-1-
11/2
32 284.93
-0.04
-2
J/2
32 455.72
-0.21
3-
912
32 549.40
-0.32
2
512
32 526.47
to.20
3+
912
32 549.40
-0.50
-2
512
32 436.91
to.24
912
32 549.40
-0.17
1-
17/Z
38 010.85
+0.30
-1-
13/Z
37 664.19
to.00
5
17/Z
37 897.24
Co.06
-1'
11/z
38 237.51
+0.14
-5
J6*7
MICROWAVE
SPECTRUM
TABLE
ka
F
u(obs)
err
113
OF IF,
I-Conrinued
ke
u(obs)
F
err
1+
1512
37 980.49
-0.11
-1-
11/2
37 670.12
-3+
1512
37 899.69
NJ.55
3+
9l2
37 960.41
-0.21
-3-
15/2
37 899.69
-0.49
3-
912
37 960.41
to.23
to.29
-3+
13/2
37 909.98
to.59
-1-
912
37 670.66
-0.27
-3-
13/2
37 909.98
-0.45
-1+
7l2
38 231.76
-0.11
1-
13/2
38 017.64
t0.61
3‘
712
37 937.07
co.28
1+
1312
37 986.75
to.23
3+
712
37 937.07
-0.18
5
13/2
37 996.35
-0.15
-1-
-0.25
-3-
11/2
37 905.85
-0.09
-2
712 1l/2
37 664.19 37 823.15
to.02
1+
11/2
37 992.21
-0.05
-4
17/2
37 883.24
-0.03
5
912
37 922.87
-0.12
4
1712
37 920.86
-0.06
1-
712
38 017.64
-0.01
2
17/2
37 965.66
to.10
5
7/2
37 866.05
to.03
-2
15/2
37 834.31
to.00
-3+
712
37 866.05
to.69
-4
1512
37 934.72
to.17
-3-
712
37 866.05
-0.36
0
1512
38 052.62
to.12
-5
1712
37 881.40
+0.13
4
1512
37 971.91
HI.01
-1-
1712
37 657.63
to.33
-6
1312
38 013.52
-0.19
3-
17/2
37 943.07
to.36
6
1312
38 013.52
t0.69
3+
1712
37 943.07
-0.10
0
1312
38 057.86
tO.04
-1+
1512
38 225.44
-0.19
2
13/2
37 983.68
-0.02
-5
1512
37 963.21
to.07
4
1312
37 985.72
to.28
3-
1512
37 970.32
to.22
-4
11/2
37 934.72
-0.08
3+
1512
37 970.32
-0.22
0
11/2
38 064.60
-0.23
-1‘
15/2
37 657.63
-0.47
2
912
37 980.49
-0.03
-1+
13/2
38 231.76
+0.10
0
912
38 068.27
to.05
3+
1312
37 980.49
-0.15
-2
912
37 838.26
-0.25
3-
13/2
37 980.49
+0.29
6
7/2
37 823.15
+0.17
13/2
37 980.49
-0.41
-4
712
37 866.05
-0.06
-3+
19/2
48 671.48
to.32
-5
1712
48 764.12
to.16
-3-
19/2
48 674.46
-0.17
-1-
1712
48 427.02
-0.13
1
77/2
48 886.98
to.31
3-
15/Z
48 840.36
-0.24
-3+
17/2
48 677.68
to.14
3+
1512
48 842.28
-0.57
-3-
17/2
48 680.47
-0.54
-5
15/2
48 757.13
tO.40
-3+
1512
48 677.68
+0.13
-1-
1512
48 431.10
to.29
-3-
1512
48 680.47
-0.56
3+
13/2
48 836.44
-0.29
-3+
13/2
48 671.48
to.30
3-
13/P
48 834.55
to.12
-3-
13/2
48 674.46
-0.21
-5
13/2
48 736.03
to.18
1+
13/2
48 891.65
to.05
-1-
13/z
48 431.57
-0.39 -0.16
-5
584
21/2
48 824.51
-0.27
11/2
48 824.51
-5
21/2
48 715.59
-0.01
-2
21/E
48 570.45
tO.14
-1-
21/2
48 423.80
-0.11
-2
19/2
48 575.17
to.19
3-
1912
48 834.55
to.23
4
1712
48 831.72
-0.07
3+
19/z
48 836.44
-0.15
-2
1712
48 579.72
tO.ll
3+
3+
114
BALIKCI TABLE
ka.
F
v(obs)
AND BRIER I-Continued
err
ke
F
v(obs)
err
-5
19/2
48 752.42
to.31
-6
15/2
48 779.47
-0.41
-1-
19/2
48 423.80
to.07
-2
15/2
48 581.80
-0.11
3-
1712
48 840.36
-0.18
-2
13/2
48 579.72
-0.43
3+
1712
48 842.28
-0.51
-2
lll2
48 572.90
-0.19
-0.10
J9+10 9
23/2
54 136.00
to.10
7
13/2
54 163.54
-7
2312
54 143.97
-0.00
-5
1312
54 115.79
to.21
-3-
2312
54 046.79
to.36
-1-
1312
53 813.54
-0.12
-3+
23/2
54 040.96
+0.10
a
23/2
54 156.86
-0.21
-3-
2112
54 055.21
~I.07
-4
2312
54 093.89
-0.29
-3+
2112
54 049.90
+0.30
-2
2312
53 937.61
to.20
9
1912
54 248.54
+0.23
-6
2312
54 136.00
to.08
-3+
19/2
54 055.21
+0.51
-4
2112
54 110.32
-0.18
-3+
1712
54 055.21
-0.13
-a
2112
54 216.51
to.01
-7
1512
54 171.29
+0.02
-2
2112
53 940.20
-0.36
5
1512
54 236.79
to.55
-6
2112
54 174.21
+0.12
5
1312
54 213.92
-0.32
-4
1912
54 117.15
-0.39
9
1312
54 110.60
to.11
4
1912
54 264.96
-0.28
7
2312
54 177.74
+o.Ol
-a
1912
54 236.79
to.24
-1-
2312
53 809.57
-0.31
a
1912
54 246.53
to.54
-5
2112
54 147.21
tD.16
-4
1712
54 115.79
-0.33
-1-
21/2
53 809.57
+0.16
a
15/2
54 191.09
to.31
-5
19/2
54 156.86
+0.27
-4
15/2
54 107.38
+O.lO
-1-
19/2
53 all.64
-0.41
-2
15/2
53 944.95
-0.42
-5
1712
54 152.59
to.07
-4
13/i: 54 092.04
-0.15
-1‘
1712
53 815.07
-0.01
a
1312
54 137.65
+0.04
-5
1512
54 137.65
-0.23
-2
1312
53 940.20
to.19
OBSERVED AND CALCULATED ABSORPTION FREQUENCIES FOR IF5. (v5(a,) = 1) 54-5 2
1312
27 556.88
to.04
4
912
27 670.53
+O.lD
2
11/2
27 591.39
+0.05
0
912
27 581.68
tD.15
2
912
27 603.91
-0.16
0
712
27 596.41
to.19
4
1312
27 505.97
+0.29
4
512
27 505.97
-0.25
0
1312
27 573.47
-0.10
0
5/2
27 602.28
+0.32
4
11/2
27 660.65
to.07
0
312
27 591.55
-0.28
0
1112
27 568.72
-0.37
3
1312
27 535.77
tD.14
2
15/2
33 079.86
-0.23
4
712
33 068.68
-0.12
2
1112
33 108.33
-0.23
4
5/2
33 012.71
+o.oo
MICROWAVE
ke
SPECTRUM
u(obs)
err
g/2
33 108.33
-0.31
5
5/2
33 079.86
to.00
1
15/2
33 090.55
to.35
3
F
ke
115
OF IF,
v(obs)
err
15/2
33 025.70
+o.lO
15/2
33 087.69
to.03
1512
33 067.25
+0.09
F
1512
33 049.23
to.16
1
1312
33 090.01
to.23
13/2
33 087.02
+0.09
5
13/2
33 160.96
to.08
13/2
33 133.67
to.03
5
11/2
33 179.32
+0.03
11/2
33 148.92
-0.13
3
11/2
33 125.42
to.01
9/2
33 120.45
to.28
3
5/2
33 051.74
+0.04
7/2
33 108.43
-0.36
-J6+7
2
17/2
38 599.45
-0.06
4
11/2
38 630.48
-0.21
15/2
38 665.33
-0.03
4
912
38 600.57
to.08
9/2
38 614.27
-0.31
4
712
38 562.41
to.13
7/2
38 601.10
-0.55
5
17/2
38 564.36
tO.05
17/2
38 579.45
tO.06
3
17/2
38 591.05
to.00
17/2
38 605.99
to.02
1
17/2
38 604.36
to.05
15/2
38 630.48
to.01
1
15/2
38 605.15
to.03
15/2
38 603.40
-0.07
3
1312
38 628.91
to.20
13/2
38 644.10
to.06
5
13/Z
38 663.84
+0.12
13/2
38 608.87
-0.09
3
11/z
38 624.22
-0.04
(a)
Ak
(b)
Measured frequencies (MHz) accurate to ? 0.1 MHz
(c)
Err
= =
0, AF
=
tl transitions only
v(obs) -
v(calc). Frequencies calculated with the values
of the parameters given in the first column of Table II. (d)
Superscripts + and - refer to transitions involving $* and $-. Assignments are based on R6 ) 0, qi > 0, qG* < 0.
THEORY
The theory of a Coriolis B,-E species interaction in Gel, symmetry has been given in our previous papers on BrF, (6,8,9). The only difference in the present work is that we have made more exact calculations of the rotational energy levels in the v,(B,) = 1 and u,(E) = 1 vibrational states by setting up and diagonalizing Hamiltonian matrices of dimension 3 x (25 + I) in a harmonic oscillatorsymmetric-top 1us, VI’,J,k) basis (actually factored into smaller submatrices of A, B, and E species symmetries). This allows us to include all the (Al,Ak) = (2,2)(q+), (2, -2)(q-), and (0,4)(&) interactions as off-diagonal elements as well as the U, = I t, ut = 1, 1, = k 1(R,,) Coriolis interaction term. The form of the resulting matrix is shown in Fig. 1. These matrices were set up and diagonalized for each quadrupole hyperfine component separately with both first- and second-order quadrupole energy contributions included in the diagonal terms. As in the case of BrF,, the centrifugal distortion constants DJ, D JK, and R, for both excited states
116
BALIKCI AND BRIER
FIG. 3. The calculated v,(E) = 1 spectrum for the J8 + 9 transition showing the two pairs of A,/A, and B,/B, doublings and splittings in the IF, spectrum. Note the discontinuities in the frequency scale above 48,500 MHz and below 49,100 MHz. This contraction of the spectrum omits the k/ = -2 transitions at 48,570 MHz and the kl = +2 transitions at 49,000 MHz.
were constrained to be zero.
at their ground-state
values and the constant r)tJ was constrained
RESULTS
The work of Truchetet et al. (2) on the ground-state spectrum of IF5 produced precise values for all the ground-state rotational parameters except for the quadrupole coupling constant esQ (due to the collapse of the hyperfine structure at the high J transitions studied by these authors). Therefore, before embarking on the study of the excited vibrational state spectrum, a series of absorption frequency measurements were made for the stronger and nonoverlapped hyperfine transitions of the ground-state spectrum from J3 + 4 through to 56 --, 7 on HP 8460A spectrometer in order to obtain an improved value for esQ. A least-squares refinement to a total of 88 data, constraining the centrifugal distortion constants DJ, DJK, and R6 to the values reported in Ref. (2), and including both first- and second-order contributions to the quadrupole splitting, gave the following results for B0 and esQ. B0 = 2727.4226 ‘_’0.0010 MHz (Ref. (2), 2727.4217 + 0.0010 MHz), and eqQ = 1069.07 ? 0.4 MHz (Ref. (2), 1067 5 10 MHz), all errors corresponding to one standard deviation. Frequency scans above and below the ground-state transitions revealed two groups of vibrational satellites. The group to the low-frequency side had a complex structure typical of an E-species excited state, while the group to the highfrequency side closely resembled the ground-state spectrum and corresponds therefore to a nondegenerate vibrational state. The large shifts of the excited state lines from the ground-state transitions in a 2:l ratio (6) indicate a Coriolis resonance interaction between the two vibrational states involved. In analogy with BrF, (6) and our previous discussion of the vibrational frequencies of IFS, we assign the two sets of satellites to the v,(E) = 1 and the 05(B1) = 1 states. Since
MICROWAVE
SPECTRUM TABLE
OF IF,
117
II
Refined Parameters for IF,
v5 - Y9
t546 380.
R5,9
3 134.1
B5*
(150.)
2 728.25 (0.9)
Cg + (Cc), - Bg* Cg - (Wg
(27 000.)
2 722.18 (1.8)
l
B9
- Bg*
_* Q9 Q; eqQ c5 - c9
III
II
I
t544 450.
+505 800.
3 122.8
2 900.
2 722.3
2 724.9
2 728.2
2 726.9
(1.8)
-1 132.8
-1 131.5
-470.58 (1.4)
-474.6
-480.8
-1 133.3
-4.91 (1.9) 2.26 1 067.0 3.0
(0.03) (1.5) (9.)
-5.04
-7.62
2.27
2.28
1 066.95
1 066.91
1.2
(FIXED)
-1.2
(FIXED)
(FIXED)
DERIVED QUANTITIES c9 Fy 9,9 v5
1 926.3
(0.8)
1 924.45
1 920.76
-0.17 (0.02) 207.2
(0.9)
REFINEMENT II
C5 - Cg CONSTRAINED TO 1.2 MHz AS ESTIMATED FROM 79/81 BrF5 DATA
REFINEMENT III
R5 g ADDITIONALLY CONSTRAINED TO 2900 MHz TO MAKE Bg* < Bo AS IN BrF5
All quantities in MHz except v5 (cm-') and r:,g (dimensionless). Quoted errors represent 2.5 standard deviations.
the latter are to the high-frequency side of the ground-state spectrum then, for IF 5, Q(B~) > v,(E). An approximate value for the quantity 2R$,/A - 35 (where A = ug - vg) could immediately be obtained from the gross shifts (6) and combined with a theoretical estimate of 1R,,, 1 - 3010 2 100 MHz (using a force constant calculation of 1i& 1 - 0.78) gives A = vg - ug - + 17 cm-l. The accidental vibrational degeneracy of v5 and vg in IF, is therefore much less close than in BrF, (A - -6.8 cm-‘). The observed transitions in both excited state spectra were readily assigned from theoretical predictions of the spectrum using initial estimates of the rovibrational parameters involved in the energy matrix of Fig. 1. Figure 2 shows part of the measured v,(E) = 1 spectrum for the 56 + 7 transition together with the calculated spectrum. Table I lists all the observed frequencies and their assignments. In-Fig. 3 we show the two pairs of AI/A, and B,/B, doublings and splittings observable in the v,(E) = 1 spectrum of IF, for the 58 + 9 transition at 48.8 GHz (calculated spectrum). The CJ+doubling of the kl = + 1 transitions is the wellknown consequence of the (Ak,Al) = (2,2) interaction linking the originally
118
BALIKCI
AND BRIER
degenerate pair of states 9: (kf = + 1). The q- doubling of the I/$ (kl = - 1) transitions is similarly due to the nonzero (2, -2) interaction, but enhanced into a case of giant l-doubling by the further (Coriolis) interaction between the $7 (kl = - 1) and $I~(k = 0) states (6). In addition to the above, there is an AJA, splitting of the kl = -3 transitions caused by the Coriolis interaction linking the I/$ (kl = -3) levels with the I-doubled (q+) I,!$ (kl = + 1) levels via the intermediate I,!J~’ (kl = 2) st a t es. (The (2, -2)qinteraction which links these levels directly has a much smaller effect). Finally, there is a B,/B, splitting of the kf = +3 transitions caused by the (2,2)q+ coupling between the IJF (kl = +3) and the giant I-doubled JIT (kl = -1) levels. The major interaction here is between the Coriolis perturbed +; (kl = - 1) states with the $J; (kl = 1-3) states due to an accidental near degeneracy and avoided crossing of these states estimated to be in the region Jl I- 13. This causes a further shift of the +; (kl = - 1) transitions in addition to the kl = +3 splittings. At J8 + 9 the calculated kl = -3 splittings are 3.5 MHz approximately and the kf = +3 splittings 2.3 MHz. DISCUSSION
A least-squares refinement of the rovibrational parameters involved in the vg-vg Coriolis resonance gave the results listed in the first column of Table II. The refinement proved stable but the least-squares minimum is not deep and well defined. The probable errors are therefore conservatively quoted as 2.5 standard deviations. These errors are comparable to those reported for BrF, (8, 9) when allowance is made for the stronger Coriolis resonance in the latter case. Not shown in Table II are the results of refining separate values for eqQ@) and eqQct) which gave 1066.3 (1.5) and 1067.6 (2.0) MHz, respectively, with negligible changes in any of the other parameter values. For BrF, it was found that 2a$ + I$ = 6.85 MHz whereas for IF, we find 3.54 MHz, i.e., approximately one-half the BrF, value. In view of the large error associated with C, - C,,, we therefore carried out a second refinement (see Table II) constraining this quantity to one-half the BrF, result. This produced changes in the values of the other parameters which are typically less than one-quarter of the corresponding standard deviations of the original calculation (except for C, + (C& - B; and C, - (C& - B,* which changed by approximately one and three standard deviations, respectively). These changes are not significant. A further feature of the original refinement is that it gives a value of Bg*greater than the ground-state constant B. (a$ - -0.8 + 0.4 MHz) whereas the reverse was the case for both isotopes of BrF, (CX~- + 1.1 2 0.3 MHz) (12). The vibrational frequencies of BrF, and IF, are such that, at least for the nonresonant, hnmonic contributions to (Yeand ag (both (Yeand cyB),one would not expect such a reversal of sign. It is, of course, difficult to make any predictions concerning the differences expected between the anharmonic contributions to the a-constants. We did make a final refinement for IFS, therefore, constraining R5,9 to a value (2900 MHz) which gives a result for (wg* approximately half the BrF, result (Table II). In terms of the original theoretical estimate for R,,g (3010 ? 100 MHz) there is nothing to choose between this value and the refinement result (3134 2 60 MHz). However, the parameter values from this refinement differ from the original refinement results
119
MICROWAVE SPECTRUM OF IF,
by four standard deviations typically and are therefore of marginal credibility. For all three sets of rovibrational parameters in Table II, we deduce a value for the rotational constant C, in the region 1920- 1925 MHz which differs significantly from the preferred prediction of Heenan and Robiette (4) (C, - C, = 1945 +- 10 MHz) from a combined refinement of electron diffraction data and the microwave measurement of BO, even allowing for the probable differences between Cg and Co/C,. We make no further comments on the present refinements or the detailed molecular structure of IF,. It is hoped that rovibrational parameters of considerably improved precision may be obtained with the aid of additional experimental data for the Jll --;, 12 and/or 512 + 13 transitions at 65 and 70 GHz, respectively. Absorption frequencies of the kl = - 1 and kl = +3 lines for these transitions are expected to show splittings and shifts of several hundred megahertz due to the near accidental degeneracy and avoided crossing of the I,!J;(kl = - 1) and I/J; (kl = +3) levels presently predicted to occur at almost exactly J = 12. Absorption frequency measurements for transitions involving these states should provide data particularly sensitive to the magnitudes of the rovibrational parameters of the Coriolis resonance. This effect is entirely analogous to the situation reported for BrF, (9) at J = 8 except, in that case, the negative value of A = vg - vg leads to an avoided crossing of the I/I: (kf = - 1) and I,!J[(kl = +3) levels. A klystron source for the region 65-75 GHz will be available to us in the near future and it is hoped to report these important measurements at a later date. ACKNOWLEDGMENTS It is a pleasure to thank Professor I. M. Mills, Reading University for the use of the HP 8460A spectrometer and Dr. J. G. Baker, Schuster Laboratory, Manchester University for the use of the millimeter wave equipment. We should also like to thank Dr. J. G. Smith, Newcastle University for his help and encouragement in attempts to measure the IF, spectrum at 70 GHz using a source modulation spectrometer and harmonic generation. One of us (B.B.) would like to thank the Government of Turkey, Ministry of Education for financial support during the period of this research. RECEIVED:
February
28, 1980 REFERENCES
1. R. H. BRADLEY,P. N. BRIER, AND M. J. WHITTLE, C/rem. Phys. Lert. 11, 192-193 (1971). 2. F. TRUCHETET,R. JUREK, AND J. CHANUSSOT,Canad. J. Phys. 56, 601-609 (1978). 3. A. G. ROBIETTE, R. H. BRADLEY, AND P. N. BRIER, f. C&m. Sot. D 1567-1568 (1971). 4. R. K. HEENAN AND
A. G. ROBIETTE,J. Mol. Struct. 55, 191-197 (1979).
5. D. W. OSBORNE,F. SCHREINER,AND H. SELIG, .I. Chem. Phys. 54, 3790-3798 (1971). 6. P. N. BRIER, S. R. JONES, AND J. G. BAKER, J. Mol. Spectrosc. 60, 18-30 (1976). 7. G. M. BEGUN, W. H. FLETCHER, AND D. F. SMITH. J. Chem. Phys. 42, 2236-2242 (1965). 8. P. N. BRIER, S. R. JONES. J. G. BAKER, AND C. GHEORGHIOU,J. Mol. Spectrosc. 64, 415-428 (1977). 9. C. GHEORGHIOU,P. N. BRIER, J. G. BAKER, AND S. R. JONES, J. Mol. Spectrosc. (1978). IO. C. DI LAURO AND I. M. MILLS, J. Mol. Spectrosc. 21, 386-413 (1966). II. G. J. CARTWRIGHTAND I. M. MILLS, J. Mol. Spectrosc. 34, 415-439 (1970). 12. P. N. BRIER. Unpublished improved refinements of the BrF, data.
13. G. AMAT, H. H. NIELSEN, AND G. TARRAGO,in “Rotation-Vibration cules.” Chap. VI, Dekker, New York, 1971.
72, 282-292
of Polyatomic
Mole-