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Line broadening by predissociation in the spectrum of IBr
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
85, 225-231 (1981)
Line Broadening by Predissociation H. KN~CKEL, Institut AftirExperimentalphysik,
E. TIEMANN,
AND
in the Spectrum of IBr D. ZOGLOWEK
Universitiit Hannover, AppelstrasseZ.
D-3000Hannover
I, Germany
Using laser excitation spectroscopy the linewidths of rotational transitions of the B’O’-X’Z+ system of IBr were measured for several vibrational bands. The change of the linewidth as a function of the rotational quantum number J could be attributed to predissociation of the B-state. It is demonstrated that the semiclassical description of the predissociation in the intermediate coupling case given by Child is in complete agreement with the experimental observations. INTRODUCTION
The appearance of fragmentary rotational fine structure in the vibrational bands of the transition B’O+-X1X+ of the IBr molecule (I, 2) is interpreted as predissociation of the B’O+ state which is developed by the interaction of the B311,,+state and a repulsive state with the same symmetry O+. A theoretical interpretation for the structure of the bands was given by Child (3). With a semiclassical treatment he showed that in the case of intermediate coupling of both electronic states the 3II0+and the repulsive Of bound rotational levels are formed if there exists a close coincidence between hypothetical rotational levels of both the diabatic potential curve 3II,,+and the new adiabatic potential curve B’O+ resulting from the avoided crossing. Using the spectroscopic data of Selin (2) and assuming that in the middle of each observed band fragment an exact coincidence of rotational levels with the same J-quantum number is given, Child was able to assign vibrational quantum numbers according to these potential curves and to deduce spectroscopic constants for the adiabatic state B’O+. In order to confirm this theoretical picture and the used coupling parameters Child suggested a study of the linewidth within the band fragments which could be compared with his predictions (3). Weinstock and Preston (4) started such a comparison in measuring relative intensities of the rotational transitions for one vibrational band in a laser excitation spectrum with fluorescence detection. These intensities are inversely proportional to the homogeneous linewidth of the transition. By such experiments they could demonstrate the functional dependence of the linewidth by the J-quantum number in agreement with Child’s model. But no absolute value of line broadening due to predissociation was deducible by this method, therefore the coupling parameters could not be proved. Additionally the authors neglected any influence by Doppler broadening and also by hyperfine splittings which give asymmetric lineprofiles in this case. In this paper we will report on direct linewidth observations scanning across the lineprofile. Three vibrational bands were measured, two of the isotope 12717gBr and 225
0022-2852/81/010225-07$02.00/O Copyright 0 1981 by Academic Press. Inc. All rights of reproduction
in any form reserved.
226 one of the isotope will be given.
KNdCKEL,
TIEMANN,
1271s1Br.A quantitative
EXPERIMENTAL
AND ZOGLOWEK
comparison
with Child’s prediction
DETAILS
In a first step an excitation spectrum of IBr was produced by piezoelectrically scanning a single mode dye laser (Spectra Physics 580) and observing the fluorescence. The excitation spectra of I2 and Br,, which are always present in an absorption cell of IBr, could be suppressed using a monochromator tuned to a specific fluorescence doublet of IBr. The absolute line positions were determined by comparison with the well-known absorption spectrum of IZ (5), which was observed in a separate optical path at the same time. In a second step the linewidths were measured by scanning the laser, now frequency-locked to an external pressure tuned Fabry-Perot, over the line under study. A second stabilized Fabry-Perot provides frequency markers with a separation of 150 MHz. The typical bandwidth of the laser radiation is 5 MHz. The absorption cell was made out of glass, evacuated, filled with commercially available IBr and finally sealed. The cell could be cooled to reduce the vapor pressure and to avoid pressure broadening of the lines. The typical temperature used was 10°C. Three bands of the system B’O+-XV of IBr were selected for this investigation which fit best to the tuning range of the dye laser with Rhodamin 6G and which are very strong. These are V’ = 20 - U” = 1 for isotope lz71s1Br and 15 - 1, 20 - 1 for isotope 12717gBr.The latter was also studied by Weinstock and Preston (4). The observed line positions for the rotational transitions were compared with the wavenumbers given by Selin (2). This was the easiest way to obtain unambiguously the assignment of the rotational quantum numbers J’ - J”. Typically, one scan across a single line took about 10 min. To improve the S/N for weak lines in the case of strong predissociation of the upper electronic state a time constant of only 1 set was necessary in the current amplifier for the photomultiplier. Therefore any deformation of the line profile due to this time constant can be neglected. The S/N for the strongest lines was about 100 and that for the weakest about 5. All lines showed some very slight asymmetry caused by unresolved hyperflne splittings. The measured line positions and widths are shown in Table I. P- and R-lines were measured for comparison since in the case of the same rotational quantum number J’ in the upper state the observed linewidth should be equal within the experimental error. The agreement of the values obtained from the experiment is good. The experimental error of the line positions includes the accuracy of the iodine lines in Ref. (5) and our measurement error; that of the linewidth was estimated from the scatter of several observations and the obtained S/N of the line itself. ANALYSIS
OF THE LINE PROFILE
The linewidth is produced by different broadening effects and the observed line profile contains several unresolved hyperfine components due to the nuclear quad-
TABLE I Observed Line Position and Linewidth of Some Band Fragments of the B’O+-X12+ Transition of Both Molecular Isotopes”
ine psition
J’
"
line psiticm
Icm'l
"
lan'l
linewidth Av /ml
25
PC?61
7337.451(15)
17343.233(15)
1034(68)
26
PW)
35.945(15)
41.954(15)
806(16)
27
P (28)
34.382(15)
40.608(15)
735Cll)
28
P(29)
32.785(15)
39.214(15)
704(111
29
P(3O)
31.120(15)
37.78205)
679(5)
30
PC311
29.39au5)
36.275(15)
739(4)
31
P(32)
27.640(15)
34.735(15)
947(34)
32
P(331
25.77805)
33.150(15)
loa2(43)
1271
79=
"' = 20 - "'1
1.ine
J’
"
=
position
, line
linewidth
/44~1
lan'l
"
psition Ian'1
linewidth Au Iml
29
p(m)
135o(103P
R(28)
17582.510(15)
30
P(31)
73.958(15)
1024(89)
R(29)
aO.a62(15)
x364(41)
31
P(32)
72.030(15)
942(2o)
R(N)
79.169(15)
969(41)
32
P(33)
70.03au5)
84l(la)
R(31)
77.395(15)
a5l (lo)
33
P(34)
67.985(15)
78701)
R(321
75.55aci5)
778(7)
34
P(35)
65.885(15)
819(6)
R(33)
73.679(15)
836(33)
35
P(36)
63.714(15)
a7l(6)
R(34)
71.731(15)
891(24)
36
P(37)
61.49aCI5)
943(41)
R(35)
69.734(15)
37
p(3a)
59.20805)
lla7(55)
R(36)
67.682(15)
17575.al4u5)
1225EO)
96o(45) 1535t103)b)
I 127_ I
aI&
"' = 20 - ""
=
1 linewidth
J’
Au [ml 43
1135(15oJ
I 7538.585
44
P (45)
(15)
45
P(46)
35.871(15)
707(20)
697(8)
46
P(47)
33.110(15)
682(5)
687(a)
889
971(75jb)
(301
47
767(31)
48
1060(50)
49
1350(103)
a1 The vibrational
assignment of Selin (2) was used. In priciple
this can only be a numbering of the states not the usual quantum number following Childs argument
(2.).
b) Over.ap with IZ-line or other vibr. band of IBr.
Note: Last section of the table, third olumn, first line, last word should read principle.
should read line position
227
vlcm-‘1.
Footnote
a
228
KNiiCKEL,
TIEMANN,
AND ZOGLOWEK
rupole interaction. But we are only interested in the part resulting from the predissociation. Each hyperfine component is broadened by natural radiation lifetime collision radiation power predissociation All these mechanisms will give a Lorentzian will also be a Lorentzian with a linewidth:
Ill Ic Ill r Pr lineshape,
therefore
the line profile
rL= r, + rc + rp+ rpr. Additionally each line is Doppler can be calculated.
broadened.
The width of the Gaussian
6v = 2(ln 2)112
(1) Sv
(2)
where T is the temperature of the absorption cell (T = 283 K) M the molecular mass, v,, the transition frequency and k, c the fundamental constants in their usual meanings. The Lorentzian and the Gaussian were convoluted to give the Voigt profile and finally such line profiles were summed over all hypertine components of the rotational transition under study. The value I’,_of the Lorentzian part was varied to fit the observed linewidth at half maximum. For this calculation the following hyperhne parameters of the B’-state were used: eqQ(‘“‘I) = -746 MHz,
eqQ(7gBr) = 229 MHz.
These values were estimated from known constants of comparable electronic states in similar molecules such as I2 (6) and ICI (7). The constants for the electronic ground state of IBr (v” = 1) are well known from mw-spectroscopy (8) eq,Q(r2’I) = -2752.9(3)
MHz,
eq,Q(7gBr) = 697.7(2) MHz.
Because of the great difference of these values for the ground and the excited states the influence of the exact value for the B’-state is not very large and it was proved by several calculations that the change of the derived Lorentzian linewidth IL was within the experimental error for reasonable ranges of the eqQ-parameters. The calculated linewidths IL were averaged for P- and R-transitions and the results are shown in Table II. The estimated error should represent a 90% confidence limit. For two transitions the observed linewidth could be described by Doppler broadening and overlapping hyperflne components alone. Therefore IL was set to zero. The column robs - Ical of Table II will be explained in the following section. INTERPRETATION OF THE LINEWIDTH
As mentioned in Eq. (1) IL contains several parts which are very different in magnitude. No direct measurements of the radiation lifetime of the W-state are
PREDISSOCIATION
229
OF IBr
TABLE II Lorentzian
Linewidth Calculated from the Observed Linewidth of Table I
rcbs-rcal
obs-rcal
880 (130)
-48
600 (1001
-38
86
34
-14
445
(60)
77
280
(30)
25
10
155
(20)
-22
-28
230
(50)
46
98
325
(60)
41
-101
455
(70)
-31
em
(90)
2
-
reported in the literature. We estimate from results on I2 (9), ICI (ZO), and IBr (11) on the B-state that I, 5 0.5 MHz. The vapor pressure in our absorption cell was of the order of 0.5 Torr. Using typical molecular pressure broadening parameters we assume I, to be not more than a few megahertz. Therefore both parts I,, and Ic can be neglected within our accuracy. The power broadening was checked by varying the laser power. No influence was observed and IP can be dropped for our experiment. We come to the conclusion that the observed value of IL represents the level broadening of the B’-state by predissociation. From the semiclassical interpretation of the predissociation Child (3) obtained the following formula for the width of the predissociating levels: IPr = yo- JG~,+(u~,J)
- E~~~+(u~,J)12,
(3)
where y. contains several molecular parameters like the coupling constant for the predissociation and the ratio of the vibrational frequencies for both potential curves. The bracket in Eq. (3) gives the energy difference of the diabatic and adiabatic
t
. 900
FIG. 1. Width of the predissociating
1100
1300
levels as a function ofJ(J
JlJ+lt
+ 1) in theB’O+-state u’ = 20 of 12’I’9Br.
230
KNOCKEL,
TIEMANN, AND ZOGLOWEK TABLE III
Predissociation
Parameters of IBr for the State B’O+
T
this
l-
mrk')
derived frm Child(3_) A
n-
YoAJf sign.2
2yoAT*AB
MHZ)
ww 1271
1211
1271
79&
15
79&
20
81g,
20
c)
-
9930.98
0.014098
f1020.
f0.0014
+2.4
-22.20
12939.68
0.09646
2993.
iO.m74
52191.29
0.011465
*54m.
f0.0012
_
-23.68
9860.
0.01:
0.011
t1.7
0.011
-48.93 +-5.0
-
The three parameters c,r,q were varied independently to allow for the minimum of r to be not zero. pr
Note. For definitions of these parameters
levels involved. The rotational dependence
see text.
of these energies can be written as
E 83rlo+(2)rJ)= Tn(%) + B,;J(J Eeto+(vo,J) = T,,(Q) + B,;J(J
+ 1) + * * *, + 1) + * . *.
(4)
T includes the electronic and vibrational energy of the specific state and B is the appropriate rotational constant. The centrifugal correction will be neglected. Including Eq. (4) in Eq. (3) we derive IPr = y,,(AT + AB*J(J + 1))’
(5)
with AT = Tn(on) - TO(Q), AB = B,,, - B,,. From Eq. (5) one expects a parabola for IPr vs J(J + l), which is shown in Fig. 1 for one vibrational band. The observations are in complete agreement with this behavior. If AT and AB have different signs there exists according to Eq. (5) a positive J-value for which Ipr has a minimum and this minimum is zero. But for the example of Fig. 1 this is not the case. We believe that this small discrepancy is the first hint that centrifugal corrections are not completely negligible. Therefore the three measured vibrational bands of Table II were fitted to a quadratic function of J(J + 1). The quality of the fit is demonstrated in Table II by column robs - Ical. From such calculations one derives the parameters yo.AT2 and yo.AB2 and the relative signs of the parameters AT and AB. The results are presented in Table III. Each value in Table III shows more figures than would be
PREDISSOCIATION
OF IBr
231
significant by the experimental error. But these figures are necessary to reproduce the deviations robs - Ical of Table II. Taking the results of Child (3) which he obtained solely from the line positions and the assumption about the narrowest line in each vibrational band which should have an exact coincidence, one can calculate the same parameters for predissociation as we used to describe our observation. These values are given in Table III for comparison. The overall agreement is very good although significant errors cannot be given for the values derived from Child’s calculation. There are only weak deviations for the vibrational state ZI’= 20 for both isotopes. Just in these cases Child made a wrong guess at the narrowest rotational transition by 3 units. This can easily explain the small discrepancy. Therefore we demonstrated in a completely independent way that the semiclassical description of predissociation in the intermediate coupling case is adequate for the experimental accuracy available up to now. Furthermore, from our results one can derive more directly the separation of nearly coinciding levels with the same J-quantum number of the hypothetical potential curves of B3110+ and B’O+ which are calculable only in an iteration procedure with data of the type used by Child. ACKNOWLEDGMENT We thank the “Deutsche RECEIVED:
Forschungsgemeinschaft”
for financial support.
March 7, 1980 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. IO. II.
W. G. BROWN, Phys. Rev. 42, 355-363 (1932). L.-E. SELIN, Ark. Fys. 21, 529-541 (1%2). M. S. CHILD, Mol. Phys. 32, 1495-1510 (1976). E. M. WEINSTOCK AND A. PRESTON, J. Mol. Spectrosc. 70, 188-I% (1978). S. GERSTENKORNAND P. Luc, Atlas du spectre d’absorption de la molecule d’lode, Laboratoire Aim&Cotton CNRS, Orsay, France, 1977. B. M. LANDSBERG, Chem. Phys. Lett. 43, 102-104 (1976). H. KN~CKEL AND E. TIEMANN, Chem. Phys. Lett. 64, 593-595 (1979). E. TIEMANN AND TH. MILLER, 2. Natudorsch. A 30, 986-991 (1975). M. BROYER, J. VIGUB, AND J. C. LEHMANN, J. Chem. Phys. 63, 5428-5431 (1975). M. A. A. CLYNE AND I. S. MCDERMID, J. Chem. Sot. Faraday II 73, 1094- 1106 (1977). J. J. WRIGHT AND M. D. HAVEY, J. Chem. Phys. 68, 864-865 (1978).
OF
MOLECULAR
SPECTROSCOPY
85, 225-231 (1981)
Line Broadening by Predissociation H. KN~CKEL, Institut AftirExperimentalphysik,
E. TIEMANN,
AND
in the Spectrum of IBr D. ZOGLOWEK
Universitiit Hannover, AppelstrasseZ.
D-3000Hannover
I, Germany
Using laser excitation spectroscopy the linewidths of rotational transitions of the B’O’-X’Z+ system of IBr were measured for several vibrational bands. The change of the linewidth as a function of the rotational quantum number J could be attributed to predissociation of the B-state. It is demonstrated that the semiclassical description of the predissociation in the intermediate coupling case given by Child is in complete agreement with the experimental observations. INTRODUCTION
The appearance of fragmentary rotational fine structure in the vibrational bands of the transition B’O+-X1X+ of the IBr molecule (I, 2) is interpreted as predissociation of the B’O+ state which is developed by the interaction of the B311,,+state and a repulsive state with the same symmetry O+. A theoretical interpretation for the structure of the bands was given by Child (3). With a semiclassical treatment he showed that in the case of intermediate coupling of both electronic states the 3II0+and the repulsive Of bound rotational levels are formed if there exists a close coincidence between hypothetical rotational levels of both the diabatic potential curve 3II,,+and the new adiabatic potential curve B’O+ resulting from the avoided crossing. Using the spectroscopic data of Selin (2) and assuming that in the middle of each observed band fragment an exact coincidence of rotational levels with the same J-quantum number is given, Child was able to assign vibrational quantum numbers according to these potential curves and to deduce spectroscopic constants for the adiabatic state B’O+. In order to confirm this theoretical picture and the used coupling parameters Child suggested a study of the linewidth within the band fragments which could be compared with his predictions (3). Weinstock and Preston (4) started such a comparison in measuring relative intensities of the rotational transitions for one vibrational band in a laser excitation spectrum with fluorescence detection. These intensities are inversely proportional to the homogeneous linewidth of the transition. By such experiments they could demonstrate the functional dependence of the linewidth by the J-quantum number in agreement with Child’s model. But no absolute value of line broadening due to predissociation was deducible by this method, therefore the coupling parameters could not be proved. Additionally the authors neglected any influence by Doppler broadening and also by hyperfine splittings which give asymmetric lineprofiles in this case. In this paper we will report on direct linewidth observations scanning across the lineprofile. Three vibrational bands were measured, two of the isotope 12717gBr and 225
0022-2852/81/010225-07$02.00/O Copyright 0 1981 by Academic Press. Inc. All rights of reproduction
in any form reserved.
226 one of the isotope will be given.
KNdCKEL,
TIEMANN,
1271s1Br.A quantitative
EXPERIMENTAL
AND ZOGLOWEK
comparison
with Child’s prediction
DETAILS
In a first step an excitation spectrum of IBr was produced by piezoelectrically scanning a single mode dye laser (Spectra Physics 580) and observing the fluorescence. The excitation spectra of I2 and Br,, which are always present in an absorption cell of IBr, could be suppressed using a monochromator tuned to a specific fluorescence doublet of IBr. The absolute line positions were determined by comparison with the well-known absorption spectrum of IZ (5), which was observed in a separate optical path at the same time. In a second step the linewidths were measured by scanning the laser, now frequency-locked to an external pressure tuned Fabry-Perot, over the line under study. A second stabilized Fabry-Perot provides frequency markers with a separation of 150 MHz. The typical bandwidth of the laser radiation is 5 MHz. The absorption cell was made out of glass, evacuated, filled with commercially available IBr and finally sealed. The cell could be cooled to reduce the vapor pressure and to avoid pressure broadening of the lines. The typical temperature used was 10°C. Three bands of the system B’O+-XV of IBr were selected for this investigation which fit best to the tuning range of the dye laser with Rhodamin 6G and which are very strong. These are V’ = 20 - U” = 1 for isotope lz71s1Br and 15 - 1, 20 - 1 for isotope 12717gBr.The latter was also studied by Weinstock and Preston (4). The observed line positions for the rotational transitions were compared with the wavenumbers given by Selin (2). This was the easiest way to obtain unambiguously the assignment of the rotational quantum numbers J’ - J”. Typically, one scan across a single line took about 10 min. To improve the S/N for weak lines in the case of strong predissociation of the upper electronic state a time constant of only 1 set was necessary in the current amplifier for the photomultiplier. Therefore any deformation of the line profile due to this time constant can be neglected. The S/N for the strongest lines was about 100 and that for the weakest about 5. All lines showed some very slight asymmetry caused by unresolved hyperflne splittings. The measured line positions and widths are shown in Table I. P- and R-lines were measured for comparison since in the case of the same rotational quantum number J’ in the upper state the observed linewidth should be equal within the experimental error. The agreement of the values obtained from the experiment is good. The experimental error of the line positions includes the accuracy of the iodine lines in Ref. (5) and our measurement error; that of the linewidth was estimated from the scatter of several observations and the obtained S/N of the line itself. ANALYSIS
OF THE LINE PROFILE
The linewidth is produced by different broadening effects and the observed line profile contains several unresolved hyperfine components due to the nuclear quad-
TABLE I Observed Line Position and Linewidth of Some Band Fragments of the B’O+-X12+ Transition of Both Molecular Isotopes”
ine psition
J’
"
line psiticm
Icm'l
"
lan'l
linewidth Av /ml
25
PC?61
7337.451(15)
17343.233(15)
1034(68)
26
PW)
35.945(15)
41.954(15)
806(16)
27
P (28)
34.382(15)
40.608(15)
735Cll)
28
P(29)
32.785(15)
39.214(15)
704(111
29
P(3O)
31.120(15)
37.78205)
679(5)
30
PC311
29.39au5)
36.275(15)
739(4)
31
P(32)
27.640(15)
34.735(15)
947(34)
32
P(331
25.77805)
33.150(15)
loa2(43)
1271
79=
"' = 20 - "'1
1.ine
J’
"
=
position
, line
linewidth
/44~1
lan'l
"
psition Ian'1
linewidth Au Iml
29
p(m)
135o(103P
R(28)
17582.510(15)
30
P(31)
73.958(15)
1024(89)
R(29)
aO.a62(15)
x364(41)
31
P(32)
72.030(15)
942(2o)
R(N)
79.169(15)
969(41)
32
P(33)
70.03au5)
84l(la)
R(31)
77.395(15)
a5l (lo)
33
P(34)
67.985(15)
78701)
R(321
75.55aci5)
778(7)
34
P(35)
65.885(15)
819(6)
R(33)
73.679(15)
836(33)
35
P(36)
63.714(15)
a7l(6)
R(34)
71.731(15)
891(24)
36
P(37)
61.49aCI5)
943(41)
R(35)
69.734(15)
37
p(3a)
59.20805)
lla7(55)
R(36)
67.682(15)
17575.al4u5)
1225EO)
96o(45) 1535t103)b)
I 127_ I
aI&
"' = 20 - ""
=
1 linewidth
J’
Au [ml 43
1135(15oJ
I 7538.585
44
P (45)
(15)
45
P(46)
35.871(15)
707(20)
697(8)
46
P(47)
33.110(15)
682(5)
687(a)
889
971(75jb)
(301
47
767(31)
48
1060(50)
49
1350(103)
a1 The vibrational
assignment of Selin (2) was used. In priciple
this can only be a numbering of the states not the usual quantum number following Childs argument
(2.).
b) Over.ap with IZ-line or other vibr. band of IBr.
Note: Last section of the table, third olumn, first line, last word should read principle.
should read line position
227
vlcm-‘1.
Footnote
a
228
KNiiCKEL,
TIEMANN,
AND ZOGLOWEK
rupole interaction. But we are only interested in the part resulting from the predissociation. Each hyperfine component is broadened by natural radiation lifetime collision radiation power predissociation All these mechanisms will give a Lorentzian will also be a Lorentzian with a linewidth:
Ill Ic Ill r Pr lineshape,
therefore
the line profile
rL= r, + rc + rp+ rpr. Additionally each line is Doppler can be calculated.
broadened.
The width of the Gaussian
6v = 2(ln 2)112
(1) Sv
(2)
where T is the temperature of the absorption cell (T = 283 K) M the molecular mass, v,, the transition frequency and k, c the fundamental constants in their usual meanings. The Lorentzian and the Gaussian were convoluted to give the Voigt profile and finally such line profiles were summed over all hypertine components of the rotational transition under study. The value I’,_of the Lorentzian part was varied to fit the observed linewidth at half maximum. For this calculation the following hyperhne parameters of the B’-state were used: eqQ(‘“‘I) = -746 MHz,
eqQ(7gBr) = 229 MHz.
These values were estimated from known constants of comparable electronic states in similar molecules such as I2 (6) and ICI (7). The constants for the electronic ground state of IBr (v” = 1) are well known from mw-spectroscopy (8) eq,Q(r2’I) = -2752.9(3)
MHz,
eq,Q(7gBr) = 697.7(2) MHz.
Because of the great difference of these values for the ground and the excited states the influence of the exact value for the B’-state is not very large and it was proved by several calculations that the change of the derived Lorentzian linewidth IL was within the experimental error for reasonable ranges of the eqQ-parameters. The calculated linewidths IL were averaged for P- and R-transitions and the results are shown in Table II. The estimated error should represent a 90% confidence limit. For two transitions the observed linewidth could be described by Doppler broadening and overlapping hyperflne components alone. Therefore IL was set to zero. The column robs - Ical of Table II will be explained in the following section. INTERPRETATION OF THE LINEWIDTH
As mentioned in Eq. (1) IL contains several parts which are very different in magnitude. No direct measurements of the radiation lifetime of the W-state are
PREDISSOCIATION
229
OF IBr
TABLE II Lorentzian
Linewidth Calculated from the Observed Linewidth of Table I
rcbs-rcal
obs-rcal
880 (130)
-48
600 (1001
-38
86
34
-14
445
(60)
77
280
(30)
25
10
155
(20)
-22
-28
230
(50)
46
98
325
(60)
41
-101
455
(70)
-31
em
(90)
2
-
reported in the literature. We estimate from results on I2 (9), ICI (ZO), and IBr (11) on the B-state that I, 5 0.5 MHz. The vapor pressure in our absorption cell was of the order of 0.5 Torr. Using typical molecular pressure broadening parameters we assume I, to be not more than a few megahertz. Therefore both parts I,, and Ic can be neglected within our accuracy. The power broadening was checked by varying the laser power. No influence was observed and IP can be dropped for our experiment. We come to the conclusion that the observed value of IL represents the level broadening of the B’-state by predissociation. From the semiclassical interpretation of the predissociation Child (3) obtained the following formula for the width of the predissociating levels: IPr = yo- JG~,+(u~,J)
- E~~~+(u~,J)12,
(3)
where y. contains several molecular parameters like the coupling constant for the predissociation and the ratio of the vibrational frequencies for both potential curves. The bracket in Eq. (3) gives the energy difference of the diabatic and adiabatic
t
. 900
FIG. 1. Width of the predissociating
1100
1300
levels as a function ofJ(J
JlJ+lt
+ 1) in theB’O+-state u’ = 20 of 12’I’9Br.
230
KNOCKEL,
TIEMANN, AND ZOGLOWEK TABLE III
Predissociation
Parameters of IBr for the State B’O+
T
this
l-
mrk')
derived frm Child(3_) A
n-
YoAJf sign.2
2yoAT*AB
MHZ)
ww 1271
1211
1271
79&
15
79&
20
81g,
20
c)
-
9930.98
0.014098
f1020.
f0.0014
+2.4
-22.20
12939.68
0.09646
2993.
iO.m74
52191.29
0.011465
*54m.
f0.0012
_
-23.68
9860.
0.01:
0.011
t1.7
0.011
-48.93 +-5.0
-
The three parameters c,r,q were varied independently to allow for the minimum of r to be not zero. pr
Note. For definitions of these parameters
levels involved. The rotational dependence
see text.
of these energies can be written as
E 83rlo+(2)rJ)= Tn(%) + B,;J(J Eeto+(vo,J) = T,,(Q) + B,;J(J
+ 1) + * * *, + 1) + * . *.
(4)
T includes the electronic and vibrational energy of the specific state and B is the appropriate rotational constant. The centrifugal correction will be neglected. Including Eq. (4) in Eq. (3) we derive IPr = y,,(AT + AB*J(J + 1))’
(5)
with AT = Tn(on) - TO(Q), AB = B,,, - B,,. From Eq. (5) one expects a parabola for IPr vs J(J + l), which is shown in Fig. 1 for one vibrational band. The observations are in complete agreement with this behavior. If AT and AB have different signs there exists according to Eq. (5) a positive J-value for which Ipr has a minimum and this minimum is zero. But for the example of Fig. 1 this is not the case. We believe that this small discrepancy is the first hint that centrifugal corrections are not completely negligible. Therefore the three measured vibrational bands of Table II were fitted to a quadratic function of J(J + 1). The quality of the fit is demonstrated in Table II by column robs - Ical. From such calculations one derives the parameters yo.AT2 and yo.AB2 and the relative signs of the parameters AT and AB. The results are presented in Table III. Each value in Table III shows more figures than would be
PREDISSOCIATION
OF IBr
231
significant by the experimental error. But these figures are necessary to reproduce the deviations robs - Ical of Table II. Taking the results of Child (3) which he obtained solely from the line positions and the assumption about the narrowest line in each vibrational band which should have an exact coincidence, one can calculate the same parameters for predissociation as we used to describe our observation. These values are given in Table III for comparison. The overall agreement is very good although significant errors cannot be given for the values derived from Child’s calculation. There are only weak deviations for the vibrational state ZI’= 20 for both isotopes. Just in these cases Child made a wrong guess at the narrowest rotational transition by 3 units. This can easily explain the small discrepancy. Therefore we demonstrated in a completely independent way that the semiclassical description of predissociation in the intermediate coupling case is adequate for the experimental accuracy available up to now. Furthermore, from our results one can derive more directly the separation of nearly coinciding levels with the same J-quantum number of the hypothetical potential curves of B3110+ and B’O+ which are calculable only in an iteration procedure with data of the type used by Child. ACKNOWLEDGMENT We thank the “Deutsche RECEIVED:
Forschungsgemeinschaft”
for financial support.
March 7, 1980 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. IO. II.
W. G. BROWN, Phys. Rev. 42, 355-363 (1932). L.-E. SELIN, Ark. Fys. 21, 529-541 (1%2). M. S. CHILD, Mol. Phys. 32, 1495-1510 (1976). E. M. WEINSTOCK AND A. PRESTON, J. Mol. Spectrosc. 70, 188-I% (1978). S. GERSTENKORNAND P. Luc, Atlas du spectre d’absorption de la molecule d’lode, Laboratoire Aim&Cotton CNRS, Orsay, France, 1977. B. M. LANDSBERG, Chem. Phys. Lett. 43, 102-104 (1976). H. KN~CKEL AND E. TIEMANN, Chem. Phys. Lett. 64, 593-595 (1979). E. TIEMANN AND TH. MILLER, 2. Natudorsch. A 30, 986-991 (1975). M. BROYER, J. VIGUB, AND J. C. LEHMANN, J. Chem. Phys. 63, 5428-5431 (1975). M. A. A. CLYNE AND I. S. MCDERMID, J. Chem. Sot. Faraday II 73, 1094- 1106 (1977). J. J. WRIGHT AND M. D. HAVEY, J. Chem. Phys. 68, 864-865 (1978).