- Email: [email protected]
The magnetic rotation spectrum of iodine monobromide
SPECTROSCOPY 70,270-278
JOURNALOFMOLECULAR
The Magnetic
Rotation
(1978)
Spectrum
of Iodine
W. H. EBERHARDT AND WAYNE
Monobromide
l
SULLIVAN~
School of Chemistry, Georgia Insti&Ae of Technology,
Atlanta, Georgia 30332
The MRS of IBr in the visible region of the spectrum has been studied at high resolution and a rotational and vibrational analysis is reported. The spectrum consists of short runs in J’ for several neighboring vibrational states of the mixed B, r&f, and B’, Of electronic states. These results imply that only a small number of closely related rotationalvibrational states of the combined system have sufficiently long lifetimes to provide the sharp lines required for the appearance of a MRS. The values observed extend to higher energies similar results reported by Selin for the absorption spectrum.
The existence previously transition
(1).
rotation
An extensive
spectrum
in the infrared
corresponding analysis
of a magnetic
to the 0+ +- ‘B transition
A laser-induced
the rotational
reported
tional levels of the electronic with reinstrumentation
vibrational rotational
ciated
in each
with transitions
that
report,
a precise
of the ground electronic by Weinstock
by Selin and Sijderberg
(5) confirms
and also extends
the vibra-
of these constants
much higher resolution
coupled has made
bands in the 0+ system. ground-state
levels in the excited states
constants recently
of two groups of bands partially
from several
“II, +- ‘Z
which, among other things, provides
of our system which permits
consists
prises transitions
study reported
Since
to the
bands were found
visible bands has been reported
ground state. The availability
possible an analysis of the MRS The MRS
(Z-4)
and rotational
fluorescence
constants
in the visible.
Sijderborg
values for the vibrational
in gaseous IBr was reported
corresponding
of badly structured
red and longer wavelength
by Lars Erik Selin and Berndt state.
(MRS)
was found
and a small number
of the infrared,
accurate
spectrum
electronic
vibrational
level.
to vibrational
superposed.
vibrational state Bands
Each
group com-
levels to a small number
of
and only a very small number
of
in the more
intense
levels near the dissociation
group
are asso-
limit, in the range
v’ = 27 to 31; bands in the weaker group correspond to v’ = 20 to 22, some of which (5). NO were analyzed by Selin and Siiderborg (3) and also observed by Weinstock other bands have been found in the MRS of the Of system. The existence of a MRS requires that the lines be sharp and also that some magnetic perturbation of either the energy or intensity of the Zeeman components of each line is possible
(6). The existence
of a magnetic
effect in this system is probably
1Supported by a Grant from the National Science Foundation. 2 Current address: Department of Mathematics,
University College, Belfield, Dublin, Ireland. 270
0022-2852/78/0702-0270$02.00/O Copyright 0 1978 by Academic Press. Inc. AU rights of reproduction in any form rewrved.
MRS
550
“‘1’
VI”2
““‘0 1
271
OF IBr
I
I
I
I
555
560
565
570
WAVELENGTH,
2
I
575
580
nm
FIG. 1. Low dispersion magnetic rotation spectrum of IBr. The band around 553 nm arises entirely from transitions from v” = 0 to v’ in the range 27-31; the band around 563 nm arises almost entirely from transitions from v” = 1 to the same set of excited states; the band around 570 nm arises primarily from 21” = 2 to the same set of excited states but also includes a number of weak lines associated with a” = 1 transitions to the set of states with ZI’in the range 20-23; the band around 580 nm arises almost entirely from transitions from v” = 2 to the same set of excited states around v’ = 20-23. The lines marked with Ne are neon emission lines superposed on the spectrum for orientation.
to be ascribed to some uncoupling phenomenon such as that suggested by Serber for the appearance of the many lines in the 12 spectrum (7). The importance of the present result lies in the detection of these lines by virtue of their sharpness. Selin and Siiderborg have pointed out that under high resolution lines in the red spectrum corresponding to transitions to states with absolute term values s 17,000 cm-’ are sharp but above this value most of the lines are diffuse. Throughout the remainder of the visible system analyzed by Selin, with z” ranging from 8 to 27, only small groups of sharp lines were located and analyzable. Thus, the phenomenon responsible for the MRS in the high U’ levels pervades much of the visible spectrum and is the principal source of interest in this study. The diffuse character of the lines has been explained as a predissociation caused by crossing of the bound 3II0+ state responsible for the red bands o’ = l-4 by a repulsive 0+ state as found in the corresponding spectrum of ICl by Brown and Gibson (S).3 The impressive part of the problem is not that the lines are diffuse, but rather that some, in limited sets of J values for particular vibrational levels, are sharp. The quantitative aspects of the problem were first addressed by 0. K. Rice (10) who treated the corresponding situation in ICI in terms of the crossing of two potential functions, each essentially linear functions of the internuclear distance in the aAlthough an extensive MRS has been reported for ICI corresponding to the 3ITr excited state (I), none has been found for the O+ state. This state is responsible for the sharp line spectrum studied by Brown and Gibson (8) and is also the source of fluorescence emission reported by Clyne and McDermid (9).
272
EBERHARDT
AND SULLIVAN
MRS OF IBr
273
region of crossing, coupled by a perturbation independent of internuclear distance. This perturbation is effective over only a short range of internuclear distance centered around the crossing point because of the large difference in slopes of the two zero-order potential functions. More recently, Child and Bernstein have examined systematically the crossing of potential curves in the diatomic halogens (11). Bandrauk and Child (12) and Child (13) have applied JWKB techniques to the analysis of IBr in terms of “intercoupling between two Born-Oppenheimer states constructed from mediate strength” the bound B 3&+ and the B’ 0+ state resulting from the crossing of the B state by a repulsive 0+ state. Numerical application by Child (13) to data based in part on the studies reported here lead to the construction of potential functions for these states which appear to reproduce the experimental results. THE MAGNETIC ROTATION SPECTRUM The nature of the experiment has been described in detail (1). Essentially, radiation from a high pressure xenon arc is collimated, polarized by a Glan prism, passed through the sample in a longitudinal magnetic field variable to a maximum of 2.4 kg, through a second Glan analyzing prism and focussed on the slit of a modified JarrellAsh Mark IV Ebert spectrograph. Photographic measurements were made with Kodak 103a-F plates in the first and second orders of a 30,000 line per inch grating blazed at 13” and in the tenth order of a 7620 line per inch grating blazed at 59”. In addition, photometric measurements were obtained with an EMI 9558 photomultiplier cooied to dry-ice temperatures mounted in place of the plate holder. The plates were calibrated with iron and thorium emission lines. The sample was synthesized from the elements and purified by vacuum sublimation. An optical path of 60 cm in a single pass through the magnet was sufficient to develop good spectra with exposures ranging from 2 to 8 hr. Figure 1 provides a photometer trace of the spectrum at low dispersion indicating the observed bands. Figure 2 is a high-dispersion spectrum of the strongest band corresponding to v” = 1 and also indicates the analysis. The essential clue to the assignments was the intervals between successive bands in the z”’ progression which were identified precisely from Selin’s ground-state vibrational and rotational constants. Combination relations involving P and R branches with the same excited state J confirmed and extended this identification. The assignment of the observed levels is indicated in Table I4 and the term values observed in the MRS are shown as a function of J(J + 1) in Fig. 3. This figure contains all the lines reported sharp by Selin and also those found in this study; the strongest lines in the MRS are indicated by solid circles, those in absorption by open circles. Weinstock (5) observed fluorescence originating from four excited state levels: (u’, J’) = (20, 33), (20, 34), (21, .S8), and (22, 73) in IBr7$. Transitions from D’ 21 and 22 correspond within 0.1 cm-’ to lines we find strong in MRS. Transitions from v’ = 20 appear at sl ightly lower J values than those we find, but the lines are weak in our spectrum and our results would not preclude sharp lines with slightly lower values of J’. 4The vibrational numbering is a source of some confusion. We have followed the original assignments of W. G. Brown, although Child’s analysis demonstrates that these numbers have little reality.
39 40 41 42 43
38
37
36
92.21
95.26
03.80 01.16 98.25
06. a4
112.13 09.49
35
Ia
PiJ’)
=
0
ia
19.36 19.04 16.64 15.22
117.57 15.22 12.72 10.10 07.40 04. b4 01.84
NJ’)
12.13 10.42
13.65
20.60
14.71 13.14 11.52 09. a7 08.11
123.94
lb.17
la
NJ’)
21.77
J’
“1’
26
0
17.57
120.24
16 17 18 19 20 21 22 23 24 25
la
PU’)
=
J’
“I/
17
17
845.22 42.59 39.91 37. Lb 34.32 31.41 28.47 25.38 22.30
PIJ’)
IBr’9
44.45 42.74 41.2 39.15
46.14
47.76
849.23
P(J’)
lBr79
1
1
17
17
850.84 48.37 45.83 43.25 40.55 37.48 34.93
RU’)
“1
856.77 55.58 54.55 53.33 52.22 50. a7 49.57 48.12 46.62 45.22
NJ’)
17
67.08
75.50 72.66
78.18
588.17 85,75 83.31 80.79
NJ')
79.69
81.03
35.29
33.44
2% ab 31.63
28.13
26.45
ka 321.64 23.20 24. a0
75.98 76.97 78.01 79.11 80.25 al.43
85.75 84.28 82.71
271.73 72.48 73.28 74.13 75.03
la
T’
86.93
590.49 89.32 88.17
69.94
17
17
RCJ’)
57.30
2
2
I
WJ’I
17.44
52 53
77.44 72.96 68.30
58 59 60 61
al.51
57
77.44
81.91
86.28
90.71
94.87
99.07
07.05
111.00
03.19
18
86.2a
94.87
99.07
103.19
NJ’)
93.47
97.12
00.68
04.20
07.62
11.0
114.29
56
la
0
18
NJ’)
55
54
53
52
51
J’
y" i
P(J’)
81.51
51
54
89.19 85.41
50
92.97
49
103.60 00.12 96.65
18
0
17
17
06.55
11.03
15.48
24. 09 19. 81
28.29
32.54
36. bl
840.55
PW)
mr'9
14.93
la.84
22.62
26.30
29.95
837.16 33.57
P(J’)
lBr’9
Term Values of IBr
48
47
46
J'
“” z
of Lines of MRS and Absolute
60.38
b3.49
66.39
577.51 74.85 72.10 69. la
PtJ’)
74.00
76.01
585.27 83.78 82.21 80.79 79.34 77.51
P(P)
= 28
17
Yl = 27
Assignment
TABLE
I
i
17
17
NJ’)
19.70
24.20
32.63
41.86
46.34
50.74
55.11 28.47
59.40
563.49
32.54
17
PU’)
54.00
57.69
61.46
65.08
572.10 68.64
P(J’,
36.61
40.55
44.47
48.47
852.22
17
v' = 30
23.05
26.81
30.44
34.00
37.48
40.90
847.55 44.25
R(J’)
“8 = 29
17
17
L
2
55.27
59.78
63. bb
67.81
71.84
575.80
RW)
54.48
58.24
62.00
65.61
68.94
72.66
76.01
582.71 79.34
NJ’)
la
18
419.04
416.67
414.35
412.07
409.84
407.65
404.52
403. 42
401.48
399.38
397.42
T’
82.09
79.90
77.74
75.63
73.55
71.51
69.51
365.63 67.55
T'
0
18
095.50 90.90
18
810.16
WJ’)
1
66.65
65 66
NJ’)
837.95
95.85 97.65
45.24
11.03
47. a2
05.70
42 99.49
94.08
92.35
38. a6
08.28
01.83
75.68 72.96
70.26
40 41
88.99 90.65
87.37
285.78
50.33
ia
52. a45
59.78
562.00
T’
453.55
451.35
448.76
446.35
443.78
441.85
439.03
44.29 41.57
17
R(J’)
18
15.98 13.48
2
50.74
55.27
564.41
NJ’)
T’
57.69 55.27
551.97
WJ’I
36.38
40.98
45.73
17
2
49.50 46.93
17
WJ’l
550.33
Yl = 27
17
G-31
20.74 la.39
04.67
823.05
78.27
69.46
39
815.18
10.05 07.40
17
83.22 80.76
74. a4 72.20
37 38
087.95
WJ’)
NJ’)
10.42
94. a9
IBr81
15.12
19.70
00.26
05.30
12.64
77.44
36
18
WJ’I
al.50
86.28
24.54
85.61
79.92
082.39
34
35
PU’)
J’
La
71.64
64
“‘,
76.61
63
17
17
1
28.98
Oal.Ia
NJ’)
34.00
la
P(J’)
0
62
=
:
61
60
J’
“‘1
IBr’9
TABLE
03.22 99.11 95.72
85.92 81.
63.57 59.29
50
90.24
67.67
50.22
60
54.57
15.12 11.61 807.28
94.50
17
802.71
NJ’)
798.63
I
05.25 01.75
08.67
11.99
15.26
ala.39
59
17
WJ’)
IBr81
93.80 90.13
97.39
17
58
079.61
NJ’)
69.84 66.34
73.27
00.97
04.44
807.90
WJ’I
71.64
18
79.92 76.71
17
P(J’l
75.68
0
NJ’) 086.28
58.83
067.12
WJ’I
58.30 54.57
61.95
65.45
69.07
072.51
18
1
63.07
18
18
WJ’)
0
57
T
=
56
55
J’
y”
51 52
50
49
48
47
46
J’
“”
I-Continued
“’
17
= 29
17
WJ’)
23.10
27.52
531.72
WJ’I
30.90 27.25
34.53
38.06
41.57
44.91
548.39
2
2
17
17
85.25 87.
89.95
40.48 36.38 32.14
59
80.64
378.38 82.93
T’
45.22 47.45
43.05
40.93
38. a7
36. a7
334.92
48.39
I8
18
44.47
552.27
NJ’)
42.35 38.86
45.73
49.05
552.27
NJ’)
T’
.
!?
I+
%
0
CA
34.64
29.01
23.27
72
73
96.41
298.16
17
37
38
P(J’)
J’
“1, L 2
40. II
70
71
IBr79
45.51
050.76
68
69
NJ’)
J’
“‘I
18
33.13
67
E
38.19
66
68
43.19
057.83
65
18
PU’)
53.01 48.14
=
63 64
62
61
J’
“1’
0
18
18
0
R(J’)
“’
= 20
39.75
45.02
55.66
260.88
NJ’)
48.14
53.01
57.63
067.12 62.55
NJ’)
18
17
17
050.50
048.16
T’
59.35
64.99
70.61
75.96
81.46
786.73
P(J’)
1Br81
63.99
69.03
74.08
79.04
88.79 83.95
93.61
798.25
P(J’)
IBr8’
1
1
17
17
72.90
17
08.33
13.61
19.03
51
76.
59
283.4
P(J’)
58
60
P(J’)
06.53
11.47
16.50
524.22
80.25
17
= 2
Y’
T’
18
T’
15.92
413.64
82.79
86.24
89.73
93.08
296.41
R(J’) 18
= 21
NJ’)
21.35
26.22
30.90
148.
145.39
142.31
139.33
136.16
56
66.00
63.46
60.97
58.37
55.93
453.38
30.67
28.07
25.54
23.06
20.63
535.68
18
21.35 17
R(J’)
T’
18.25
2
2
26.22
30.90
535.63
IBr79
17
v’=31
17
P(J’)
57
56
J’
“”
75.96
81.46
86.73
91.88
797.06
RW)
84.02
88.88
93.61
02.87 98.25
07.40
811.99
R(J’)
Y’ = 30
TABLE
P(J’)
22.58 17.6
81
conventional
R(J’)
40.51
45.20
250.19
17
excited
an estimated
256.14
252.10
248.04
244.3
T’
061.9
059.04
056.69
054.34
052.1
T’
45.22
50. I9
54.92
259.74
P(J’)
IBr79
to the
wltb
17
18
17
= 2
= 22
R(J’)
v’
77.66
80.27
83.27
285.5
-1 in cm J’ xfers
17
17
75
74
73
72
71
J’
“”
Y’ = 20
tabulations.
Frequencies are quantum number
27.48
232.50
79
17
80
78
J’
“”
64.53
48
IB*81
67.08
70.18
46 47
72.90
45
= 2
P(J’) 275.99
44
17
z 2
IB*81
J’
y”
I--Contimed
17
= 2
17
F 2
state
T’
230.18
226.45
P(J’)
than
of
04.5
10.30
215.7
P(J’)
IBrBl
41.92
46.06
250.2
the
17
17
0.05
240.97
237.47
233.74
IBr81
18
rather
accuracy
90
89
88
a7
J’
“ll
67
66
65
J’
“”
67.08
71.52
75.99
280.27
R(J’)
Y’ = 22
-I cm , ground
24.42
29.98
35.57
241.01
R(J’)
v1 = 23
56.9
60.69
264.53
NJ’)
Y’ = 21
329.60
325.34
321.02
316.95
T’
163.46
160.01
156.65
T’
The rotational state as in
18
18
MRS
I
0
I
I
I
2000
277
OF IBr
I
4000 J(J+
I
6000
I
1
6000
1)
FIG. 3. Term values of excited states which give rise to sharp to the short runs in J' reported sharp by Selin and Siiderborg the most intense line of short runs of J’ found in MRS.
spectral lines. Open circles correspond in absorption; solid circles represent
DISCUSSION
A convincing interpretation of these data has been published by Child (13). In this interpretation, sharp lines are expected wherever there is accidental coincidence of term values with the same rotational quantum number J in the diabatic B state and the adiabatic B’ state formed from the crossing of a repulsive 0+ state with the B state. The width of spectral lines associated with rotational states near these states of exact coincidence increases as J differs from the value at coincidence. Detailed
278
EBERHARDT
AND SULLIVAN
expressions for the line width appear as a numerator which depends only slowly on energy and a denominator which depends on the difference in energy of the coupled states. The analysis leads to the construction of potential functions for the diabatic and adiabatic states which agree closely in the region of internuclear distance larger than the crossing point. The analysis also leads to apparent rotational constants determined by mixing between the two states which are, in effect, averages of the rotational constants of the two unmixed states. The vibrational numbering associated with any set of J’s is obscured since it is different in the two unmixed states and the paucity of data in the region between the crossing energy and that near dissociation does not permit a smooth continuation of the well established numbering of the low states of the B system. Although this interpretation is very convincing, it is possible to suggest an alternative conjecture which also rationalizes the existence of all of our data including isotopic shifts: lines appear sharp in this system for excited-state energies in which the vibrational wave function for the B %o+ state exhibits a node at the apparent crossing point of the bound B 3f10+ state and the repulsive B’ Of state. We were led to this conjecture by the qualitative argument that a matrix element coupling the two states would vanish at this crossing point if the perturbing term in the Hamiltonian varies rapidly with internuclear distance so that the electronic and vibrational factors cannot be separated. This conjecture suggests the correlation of observed states which is sketched, perhaps with some imagination for the lower energy states, by dashed lines in Fig. 3. It leads to the construction of a potential function for the B, 311g+state which differs only in detail from that of Child, but a very different function for the B’ state. Crossing of the two initial states appears at a similar internuclear separation and energy, but the effective potential function of the B state does not continue smoothly into the long distance part of the B’ state, but rather appears to intersect it at the minimum of the B’ potential function. Since we have not been able to devise a completely defensible argument for this conjecture, we do not at this time present the details of the analysis but simply state it as a possible alternative to Child’s analysis which does in fact also reproduce the experimental facts. RECEIVED:
October
13, 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
W. H. EBERHARDT, W. C. CHENG, AND H. RENNER, J. Mol. Spectrosc. 3, 664 (1959). L. E. SELIN, Ark. Fys. 21,479 (1962). L. E. SELIN AND B. SGDERBORG, Ask. Fys. 21, 515 (1962). L. E. SELIN, Ark. Fys. 21, 529 (1962). E. M. WEINSTOCK, J. Mol. Spectrosc. 61, 395 (1976). W. H. EBERHARDT AND H. RENNER, J. Mol. Spectrosc. 6, 483 (1961). R. SERBER, Phys. Rev. 41, 489 (1932). W. G. BROWN AND G. E. GIBSON, Phys. Rev. 40, 529 (1932). M. A. A. CLYNE AND I. S. MCDERMID, J. Chem. SOL, Faraday Trans. II, 2242 (1976). 0. K. RICE, J. Gem. Phys. 1, 37.5 (1933). M. S. CHILD AND R. B. BERNSTEIN, J. Chem. Phys. 59, 5916 (1973). A. D. BANDRAUK AND CHILD, Mol. Phys. 19,9.5 (1970). M. S. CHILD, Mol. Pkys. 32, 1495 (1976).
JOURNALOFMOLECULAR
The Magnetic
Rotation
(1978)
Spectrum
of Iodine
W. H. EBERHARDT AND WAYNE
Monobromide
l
SULLIVAN~
School of Chemistry, Georgia Insti&Ae of Technology,
Atlanta, Georgia 30332
The MRS of IBr in the visible region of the spectrum has been studied at high resolution and a rotational and vibrational analysis is reported. The spectrum consists of short runs in J’ for several neighboring vibrational states of the mixed B, r&f, and B’, Of electronic states. These results imply that only a small number of closely related rotationalvibrational states of the combined system have sufficiently long lifetimes to provide the sharp lines required for the appearance of a MRS. The values observed extend to higher energies similar results reported by Selin for the absorption spectrum.
The existence previously transition
(1).
rotation
An extensive
spectrum
in the infrared
corresponding analysis
of a magnetic
to the 0+ +- ‘B transition
A laser-induced
the rotational
reported
tional levels of the electronic with reinstrumentation
vibrational rotational
ciated
in each
with transitions
that
report,
a precise
of the ground electronic by Weinstock
by Selin and Sijderberg
(5) confirms
and also extends
the vibra-
of these constants
much higher resolution
coupled has made
bands in the 0+ system. ground-state
levels in the excited states
constants recently
of two groups of bands partially
from several
“II, +- ‘Z
which, among other things, provides
of our system which permits
consists
prises transitions
study reported
Since
to the
bands were found
visible bands has been reported
ground state. The availability
possible an analysis of the MRS The MRS
(Z-4)
and rotational
fluorescence
constants
in the visible.
Sijderborg
values for the vibrational
in gaseous IBr was reported
corresponding
of badly structured
red and longer wavelength
by Lars Erik Selin and Berndt state.
(MRS)
was found
and a small number
of the infrared,
accurate
spectrum
electronic
vibrational
level.
to vibrational
superposed.
vibrational state Bands
Each
group com-
levels to a small number
of
and only a very small number
of
in the more
intense
levels near the dissociation
group
are asso-
limit, in the range
v’ = 27 to 31; bands in the weaker group correspond to v’ = 20 to 22, some of which (5). NO were analyzed by Selin and Siiderborg (3) and also observed by Weinstock other bands have been found in the MRS of the Of system. The existence of a MRS requires that the lines be sharp and also that some magnetic perturbation of either the energy or intensity of the Zeeman components of each line is possible
(6). The existence
of a magnetic
effect in this system is probably
1Supported by a Grant from the National Science Foundation. 2 Current address: Department of Mathematics,
University College, Belfield, Dublin, Ireland. 270
0022-2852/78/0702-0270$02.00/O Copyright 0 1978 by Academic Press. Inc. AU rights of reproduction in any form rewrved.
MRS
550
“‘1’
VI”2
““‘0 1
271
OF IBr
I
I
I
I
555
560
565
570
WAVELENGTH,
2
I
575
580
nm
FIG. 1. Low dispersion magnetic rotation spectrum of IBr. The band around 553 nm arises entirely from transitions from v” = 0 to v’ in the range 27-31; the band around 563 nm arises almost entirely from transitions from v” = 1 to the same set of excited states; the band around 570 nm arises primarily from 21” = 2 to the same set of excited states but also includes a number of weak lines associated with a” = 1 transitions to the set of states with ZI’in the range 20-23; the band around 580 nm arises almost entirely from transitions from v” = 2 to the same set of excited states around v’ = 20-23. The lines marked with Ne are neon emission lines superposed on the spectrum for orientation.
to be ascribed to some uncoupling phenomenon such as that suggested by Serber for the appearance of the many lines in the 12 spectrum (7). The importance of the present result lies in the detection of these lines by virtue of their sharpness. Selin and Siiderborg have pointed out that under high resolution lines in the red spectrum corresponding to transitions to states with absolute term values s 17,000 cm-’ are sharp but above this value most of the lines are diffuse. Throughout the remainder of the visible system analyzed by Selin, with z” ranging from 8 to 27, only small groups of sharp lines were located and analyzable. Thus, the phenomenon responsible for the MRS in the high U’ levels pervades much of the visible spectrum and is the principal source of interest in this study. The diffuse character of the lines has been explained as a predissociation caused by crossing of the bound 3II0+ state responsible for the red bands o’ = l-4 by a repulsive 0+ state as found in the corresponding spectrum of ICl by Brown and Gibson (S).3 The impressive part of the problem is not that the lines are diffuse, but rather that some, in limited sets of J values for particular vibrational levels, are sharp. The quantitative aspects of the problem were first addressed by 0. K. Rice (10) who treated the corresponding situation in ICI in terms of the crossing of two potential functions, each essentially linear functions of the internuclear distance in the aAlthough an extensive MRS has been reported for ICI corresponding to the 3ITr excited state (I), none has been found for the O+ state. This state is responsible for the sharp line spectrum studied by Brown and Gibson (8) and is also the source of fluorescence emission reported by Clyne and McDermid (9).
272
EBERHARDT
AND SULLIVAN
MRS OF IBr
273
region of crossing, coupled by a perturbation independent of internuclear distance. This perturbation is effective over only a short range of internuclear distance centered around the crossing point because of the large difference in slopes of the two zero-order potential functions. More recently, Child and Bernstein have examined systematically the crossing of potential curves in the diatomic halogens (11). Bandrauk and Child (12) and Child (13) have applied JWKB techniques to the analysis of IBr in terms of “intercoupling between two Born-Oppenheimer states constructed from mediate strength” the bound B 3&+ and the B’ 0+ state resulting from the crossing of the B state by a repulsive 0+ state. Numerical application by Child (13) to data based in part on the studies reported here lead to the construction of potential functions for these states which appear to reproduce the experimental results. THE MAGNETIC ROTATION SPECTRUM The nature of the experiment has been described in detail (1). Essentially, radiation from a high pressure xenon arc is collimated, polarized by a Glan prism, passed through the sample in a longitudinal magnetic field variable to a maximum of 2.4 kg, through a second Glan analyzing prism and focussed on the slit of a modified JarrellAsh Mark IV Ebert spectrograph. Photographic measurements were made with Kodak 103a-F plates in the first and second orders of a 30,000 line per inch grating blazed at 13” and in the tenth order of a 7620 line per inch grating blazed at 59”. In addition, photometric measurements were obtained with an EMI 9558 photomultiplier cooied to dry-ice temperatures mounted in place of the plate holder. The plates were calibrated with iron and thorium emission lines. The sample was synthesized from the elements and purified by vacuum sublimation. An optical path of 60 cm in a single pass through the magnet was sufficient to develop good spectra with exposures ranging from 2 to 8 hr. Figure 1 provides a photometer trace of the spectrum at low dispersion indicating the observed bands. Figure 2 is a high-dispersion spectrum of the strongest band corresponding to v” = 1 and also indicates the analysis. The essential clue to the assignments was the intervals between successive bands in the z”’ progression which were identified precisely from Selin’s ground-state vibrational and rotational constants. Combination relations involving P and R branches with the same excited state J confirmed and extended this identification. The assignment of the observed levels is indicated in Table I4 and the term values observed in the MRS are shown as a function of J(J + 1) in Fig. 3. This figure contains all the lines reported sharp by Selin and also those found in this study; the strongest lines in the MRS are indicated by solid circles, those in absorption by open circles. Weinstock (5) observed fluorescence originating from four excited state levels: (u’, J’) = (20, 33), (20, 34), (21, .S8), and (22, 73) in IBr7$. Transitions from D’ 21 and 22 correspond within 0.1 cm-’ to lines we find strong in MRS. Transitions from v’ = 20 appear at sl ightly lower J values than those we find, but the lines are weak in our spectrum and our results would not preclude sharp lines with slightly lower values of J’. 4The vibrational numbering is a source of some confusion. We have followed the original assignments of W. G. Brown, although Child’s analysis demonstrates that these numbers have little reality.
39 40 41 42 43
38
37
36
92.21
95.26
03.80 01.16 98.25
06. a4
112.13 09.49
35
Ia
PiJ’)
=
0
ia
19.36 19.04 16.64 15.22
117.57 15.22 12.72 10.10 07.40 04. b4 01.84
NJ’)
12.13 10.42
13.65
20.60
14.71 13.14 11.52 09. a7 08.11
123.94
lb.17
la
NJ’)
21.77
J’
“1’
26
0
17.57
120.24
16 17 18 19 20 21 22 23 24 25
la
PU’)
=
J’
“I/
17
17
845.22 42.59 39.91 37. Lb 34.32 31.41 28.47 25.38 22.30
PIJ’)
IBr’9
44.45 42.74 41.2 39.15
46.14
47.76
849.23
P(J’)
lBr79
1
1
17
17
850.84 48.37 45.83 43.25 40.55 37.48 34.93
RU’)
“1
856.77 55.58 54.55 53.33 52.22 50. a7 49.57 48.12 46.62 45.22
NJ’)
17
67.08
75.50 72.66
78.18
588.17 85,75 83.31 80.79
NJ')
79.69
81.03
35.29
33.44
2% ab 31.63
28.13
26.45
ka 321.64 23.20 24. a0
75.98 76.97 78.01 79.11 80.25 al.43
85.75 84.28 82.71
271.73 72.48 73.28 74.13 75.03
la
T’
86.93
590.49 89.32 88.17
69.94
17
17
RCJ’)
57.30
2
2
I
WJ’I
17.44
52 53
77.44 72.96 68.30
58 59 60 61
al.51
57
77.44
81.91
86.28
90.71
94.87
99.07
07.05
111.00
03.19
18
86.2a
94.87
99.07
103.19
NJ’)
93.47
97.12
00.68
04.20
07.62
11.0
114.29
56
la
0
18
NJ’)
55
54
53
52
51
J’
y" i
P(J’)
81.51
51
54
89.19 85.41
50
92.97
49
103.60 00.12 96.65
18
0
17
17
06.55
11.03
15.48
24. 09 19. 81
28.29
32.54
36. bl
840.55
PW)
mr'9
14.93
la.84
22.62
26.30
29.95
837.16 33.57
P(J’)
lBr’9
Term Values of IBr
48
47
46
J'
“” z
of Lines of MRS and Absolute
60.38
b3.49
66.39
577.51 74.85 72.10 69. la
PtJ’)
74.00
76.01
585.27 83.78 82.21 80.79 79.34 77.51
P(P)
= 28
17
Yl = 27
Assignment
TABLE
I
i
17
17
NJ’)
19.70
24.20
32.63
41.86
46.34
50.74
55.11 28.47
59.40
563.49
32.54
17
PU’)
54.00
57.69
61.46
65.08
572.10 68.64
P(J’,
36.61
40.55
44.47
48.47
852.22
17
v' = 30
23.05
26.81
30.44
34.00
37.48
40.90
847.55 44.25
R(J’)
“8 = 29
17
17
L
2
55.27
59.78
63. bb
67.81
71.84
575.80
RW)
54.48
58.24
62.00
65.61
68.94
72.66
76.01
582.71 79.34
NJ’)
la
18
419.04
416.67
414.35
412.07
409.84
407.65
404.52
403. 42
401.48
399.38
397.42
T’
82.09
79.90
77.74
75.63
73.55
71.51
69.51
365.63 67.55
T'
0
18
095.50 90.90
18
810.16
WJ’)
1
66.65
65 66
NJ’)
837.95
95.85 97.65
45.24
11.03
47. a2
05.70
42 99.49
94.08
92.35
38. a6
08.28
01.83
75.68 72.96
70.26
40 41
88.99 90.65
87.37
285.78
50.33
ia
52. a45
59.78
562.00
T’
453.55
451.35
448.76
446.35
443.78
441.85
439.03
44.29 41.57
17
R(J’)
18
15.98 13.48
2
50.74
55.27
564.41
NJ’)
T’
57.69 55.27
551.97
WJ’I
36.38
40.98
45.73
17
2
49.50 46.93
17
WJ’l
550.33
Yl = 27
17
G-31
20.74 la.39
04.67
823.05
78.27
69.46
39
815.18
10.05 07.40
17
83.22 80.76
74. a4 72.20
37 38
087.95
WJ’)
NJ’)
10.42
94. a9
IBr81
15.12
19.70
00.26
05.30
12.64
77.44
36
18
WJ’I
al.50
86.28
24.54
85.61
79.92
082.39
34
35
PU’)
J’
La
71.64
64
“‘,
76.61
63
17
17
1
28.98
Oal.Ia
NJ’)
34.00
la
P(J’)
0
62
=
:
61
60
J’
“‘1
IBr’9
TABLE
03.22 99.11 95.72
85.92 81.
63.57 59.29
50
90.24
67.67
50.22
60
54.57
15.12 11.61 807.28
94.50
17
802.71
NJ’)
798.63
I
05.25 01.75
08.67
11.99
15.26
ala.39
59
17
WJ’)
IBr81
93.80 90.13
97.39
17
58
079.61
NJ’)
69.84 66.34
73.27
00.97
04.44
807.90
WJ’I
71.64
18
79.92 76.71
17
P(J’l
75.68
0
NJ’) 086.28
58.83
067.12
WJ’I
58.30 54.57
61.95
65.45
69.07
072.51
18
1
63.07
18
18
WJ’)
0
57
T
=
56
55
J’
y”
51 52
50
49
48
47
46
J’
“”
I-Continued
“’
17
= 29
17
WJ’)
23.10
27.52
531.72
WJ’I
30.90 27.25
34.53
38.06
41.57
44.91
548.39
2
2
17
17
85.25 87.
89.95
40.48 36.38 32.14
59
80.64
378.38 82.93
T’
45.22 47.45
43.05
40.93
38. a7
36. a7
334.92
48.39
I8
18
44.47
552.27
NJ’)
42.35 38.86
45.73
49.05
552.27
NJ’)
T’
.
!?
I+
%
0
CA
34.64
29.01
23.27
72
73
96.41
298.16
17
37
38
P(J’)
J’
“1, L 2
40. II
70
71
IBr79
45.51
050.76
68
69
NJ’)
J’
“‘I
18
33.13
67
E
38.19
66
68
43.19
057.83
65
18
PU’)
53.01 48.14
=
63 64
62
61
J’
“1’
0
18
18
0
R(J’)
“’
= 20
39.75
45.02
55.66
260.88
NJ’)
48.14
53.01
57.63
067.12 62.55
NJ’)
18
17
17
050.50
048.16
T’
59.35
64.99
70.61
75.96
81.46
786.73
P(J’)
1Br81
63.99
69.03
74.08
79.04
88.79 83.95
93.61
798.25
P(J’)
IBr8’
1
1
17
17
72.90
17
08.33
13.61
19.03
51
76.
59
283.4
P(J’)
58
60
P(J’)
06.53
11.47
16.50
524.22
80.25
17
= 2
Y’
T’
18
T’
15.92
413.64
82.79
86.24
89.73
93.08
296.41
R(J’) 18
= 21
NJ’)
21.35
26.22
30.90
148.
145.39
142.31
139.33
136.16
56
66.00
63.46
60.97
58.37
55.93
453.38
30.67
28.07
25.54
23.06
20.63
535.68
18
21.35 17
R(J’)
T’
18.25
2
2
26.22
30.90
535.63
IBr79
17
v’=31
17
P(J’)
57
56
J’
“”
75.96
81.46
86.73
91.88
797.06
RW)
84.02
88.88
93.61
02.87 98.25
07.40
811.99
R(J’)
Y’ = 30
TABLE
P(J’)
22.58 17.6
81
conventional
R(J’)
40.51
45.20
250.19
17
excited
an estimated
256.14
252.10
248.04
244.3
T’
061.9
059.04
056.69
054.34
052.1
T’
45.22
50. I9
54.92
259.74
P(J’)
IBr79
to the
wltb
17
18
17
= 2
= 22
R(J’)
v’
77.66
80.27
83.27
285.5
-1 in cm J’ xfers
17
17
75
74
73
72
71
J’
“”
Y’ = 20
tabulations.
Frequencies are quantum number
27.48
232.50
79
17
80
78
J’
“”
64.53
48
IB*81
67.08
70.18
46 47
72.90
45
= 2
P(J’) 275.99
44
17
z 2
IB*81
J’
y”
I--Contimed
17
= 2
17
F 2
state
T’
230.18
226.45
P(J’)
than
of
04.5
10.30
215.7
P(J’)
IBrBl
41.92
46.06
250.2
the
17
17
0.05
240.97
237.47
233.74
IBr81
18
rather
accuracy
90
89
88
a7
J’
“ll
67
66
65
J’
“”
67.08
71.52
75.99
280.27
R(J’)
Y’ = 22
-I cm , ground
24.42
29.98
35.57
241.01
R(J’)
v1 = 23
56.9
60.69
264.53
NJ’)
Y’ = 21
329.60
325.34
321.02
316.95
T’
163.46
160.01
156.65
T’
The rotational state as in
18
18
MRS
I
0
I
I
I
2000
277
OF IBr
I
4000 J(J+
I
6000
I
1
6000
1)
FIG. 3. Term values of excited states which give rise to sharp to the short runs in J' reported sharp by Selin and Siiderborg the most intense line of short runs of J’ found in MRS.
spectral lines. Open circles correspond in absorption; solid circles represent
DISCUSSION
A convincing interpretation of these data has been published by Child (13). In this interpretation, sharp lines are expected wherever there is accidental coincidence of term values with the same rotational quantum number J in the diabatic B state and the adiabatic B’ state formed from the crossing of a repulsive 0+ state with the B state. The width of spectral lines associated with rotational states near these states of exact coincidence increases as J differs from the value at coincidence. Detailed
278
EBERHARDT
AND SULLIVAN
expressions for the line width appear as a numerator which depends only slowly on energy and a denominator which depends on the difference in energy of the coupled states. The analysis leads to the construction of potential functions for the diabatic and adiabatic states which agree closely in the region of internuclear distance larger than the crossing point. The analysis also leads to apparent rotational constants determined by mixing between the two states which are, in effect, averages of the rotational constants of the two unmixed states. The vibrational numbering associated with any set of J’s is obscured since it is different in the two unmixed states and the paucity of data in the region between the crossing energy and that near dissociation does not permit a smooth continuation of the well established numbering of the low states of the B system. Although this interpretation is very convincing, it is possible to suggest an alternative conjecture which also rationalizes the existence of all of our data including isotopic shifts: lines appear sharp in this system for excited-state energies in which the vibrational wave function for the B %o+ state exhibits a node at the apparent crossing point of the bound B 3f10+ state and the repulsive B’ Of state. We were led to this conjecture by the qualitative argument that a matrix element coupling the two states would vanish at this crossing point if the perturbing term in the Hamiltonian varies rapidly with internuclear distance so that the electronic and vibrational factors cannot be separated. This conjecture suggests the correlation of observed states which is sketched, perhaps with some imagination for the lower energy states, by dashed lines in Fig. 3. It leads to the construction of a potential function for the B, 311g+state which differs only in detail from that of Child, but a very different function for the B’ state. Crossing of the two initial states appears at a similar internuclear separation and energy, but the effective potential function of the B state does not continue smoothly into the long distance part of the B’ state, but rather appears to intersect it at the minimum of the B’ potential function. Since we have not been able to devise a completely defensible argument for this conjecture, we do not at this time present the details of the analysis but simply state it as a possible alternative to Child’s analysis which does in fact also reproduce the experimental facts. RECEIVED:
October
13, 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
W. H. EBERHARDT, W. C. CHENG, AND H. RENNER, J. Mol. Spectrosc. 3, 664 (1959). L. E. SELIN, Ark. Fys. 21,479 (1962). L. E. SELIN AND B. SGDERBORG, Ask. Fys. 21, 515 (1962). L. E. SELIN, Ark. Fys. 21, 529 (1962). E. M. WEINSTOCK, J. Mol. Spectrosc. 61, 395 (1976). W. H. EBERHARDT AND H. RENNER, J. Mol. Spectrosc. 6, 483 (1961). R. SERBER, Phys. Rev. 41, 489 (1932). W. G. BROWN AND G. E. GIBSON, Phys. Rev. 40, 529 (1932). M. A. A. CLYNE AND I. S. MCDERMID, J. Chem. SOL, Faraday Trans. II, 2242 (1976). 0. K. RICE, J. Gem. Phys. 1, 37.5 (1933). M. S. CHILD AND R. B. BERNSTEIN, J. Chem. Phys. 59, 5916 (1973). A. D. BANDRAUK AND CHILD, Mol. Phys. 19,9.5 (1970). M. S. CHILD, Mol. Pkys. 32, 1495 (1976).