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The A1Π-X1Σ band system of CD+
IOURNAL
OF MOLECULAR
SPECTROSCOPY
75,197-204
The AllYI-X12 Spectroscopic
(1979)
Band System of CD+ Constants
A. ANTIC-J•
and Isotope
VANOVIC AND
Shifts
V. BOJOVIC
Institute of Physical Chemistry, Faculty of Science, University of Belgrade, Belgrade, Yugoslavia
D. s. PESIC B. Kidric Institute
of Nuclear
Sciences,
POB 522, Belgrade.
Yugoslavia
AND S. WENIGER Observatoire
de Paris,
Laboratoire
de Spectroscopic.
Meudon,
France
Six bands of the A’II-X12 system of CD+ in the region 3800-4800 A have been recorded in emission using an aluminum hollow-cathode discharge in the He-C,H, mixture. From the vibrational and rotational analysis of the observed bands, the following constants (cm-‘) are obtained:
A’H X’S
23 747.5 0
1367.3 2035
60.6
(2101.6)
(33.3)
0.75
6.428 7.650
5.7 4.1
0.388
0.190
AGli2; (w,), (q-xx,) are calculated from isotope relation. The electronic isotope shift Av: = T,(CH+) - T,(CD+) = -13 cm-r has been derived according to the theoretical expression given by Bunker. A somewhat smaller value was obtained from the pure electronic energy difference using “experimental” values of the zero point energies. 1. INTRODUCTION
The red-degraded bands of the A ‘II-X’Z$ system of CH+ were first obtained by Douglas and Herzberg (1, 2) using a high frequency electrodeless discharge through helium mixed with a trace of benzene. These authors observed, and made rotational and vibrational analysis, of the O-O, I-O, 2-0, and O-l bands; they also discussed the nature of the band emitter. Douglas and Morton (3) have performed the analysis of the 0- 1, l- 1, 2- 1, 3- 1, and 4- 1 bands. Carre (4) recorded two new bands (3-O and 4-O near 3580 and 3450 A, respectively) by studying the emission spectra of CH, and C2H, excited by proton impact. 197
0022-2852/79/050197-08$02.00/O Copyright
0 1979 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
ANTIC-JOVANOVI6
198
ET AL.
However, for the isotopic CD+ ion only fragmentary data concerning the z+,and VHvalues of four bands have been given by Cisak and Rytel(5). Since this simple system of CH+ is of special astrophysical interest, we have undertaken a new investigation of the spectrum of CD+. The study of the observed isotope displacements revealed the existence of a rather large electronic isotope shift which is a direct consequence of partial breakdown of the BomOppenheimer approximation used in solving the rovibronic wave equation, and which was observed already in the case of several diatomic hydrides (6-9). 2. EXPERIMENTAL
METHOD
For the excitation of the emission CD+ spectrum a water cooled hollowcathode discharge tube, described by Vujisic (IO), was employed. An aluminum cup was used as a cathode. The tube was filled with a mixture of He + CzD2 (10: 1) at about 3 mm Hg and the cathode glow was obtained by using a dc of 250350 mA and 600 V between electrodes. The bands situated in the 3800-4800-A region were photographed in the first order of a 3-m Eagle spectrograph (dispersion 2.6 &mm) using Word HP4 film and an exposure time of 30-60 min. An iron arc gave the reference spectrum. The films were measured on a Zeiss Abbe comparator and the spectra were reduced on a CDC-3600 computer. The absolute accuracy of the wavenumbers for unblended rotational lines is estimated to be to.05 cm-‘. 3. BAND ANALYSIS
Six bands (O-l, O-O, l-0, 2-1, 2-0, and 3-l) were observed in the investigated region. Their vibrational assignment, supported by observed isotope shifts, presented no difficulty. Table I represents the Deslandres table of the origins and bandheads of these bands. It should be mentioned here that our data for the O-O, TABLE
I
Deslandres Table (uO,hH)of the CD+ Bands v” v’ 0 0
23747.5 wO3.52
1
24996.0 3995.30
2
26130.0 3822.96
3
1 21712.5 4595.85
24094.5 4145.45 25118.5 3977.27
V, - position of zero line (cm-l) A, - position of B head (8)
THE
AT-X'S BAND SYSTEM OF CD+
199
l-0, and 2- 1 bands agree with those given by Cisak and Rytel (5) within experimental errors, but the agreement between data concerning the 0- 1 band is somewhat less satisfying. From the u0 values of the O-O, l-0, and 2-O bands we derived the vibrational constants o:, w:x:, and w:yk listed in Table IV in which all the molecular constants of CD+ are collected. Due to the small number of bands in the 2)” progression the equilibrium constants of the lower electronic state could not be verified. However, assuming that the levels involved are unperturbed and that the vibrational energy can be represented with a quadratic expression, it was possible to estimate the approximate values of these constants from the following relations for two isotopes AG’I,,(CH+) = w; - 2o%xk’, AG’;,2(CD+) = po; - 2p%&;. With AG’;,,(CH+) = 2739.7 cm-’ (3), AG’&,(CD+) = 2035.0 cm-l, and p = 0.73397, we obtained ws = 2863.3 cm-’ and w$z = 61.8 cm-’ for CH+, and 2101.6 and 33.3 cm-’ for CD+, respectively. These values agree very well with those obtained very recently by Gerard et al. (II) by studying the emission produced by the reaction of He+ ions with &Hz and C,D, in near-thermal charge exchange. The vibrational equation y0 = 24 121.0 + [1367.3(v’ + 1%) - 60.6(v’ + ‘/)” + 0.75(0’ + ‘/)“I - [2101.6(~” + y2) - 33.3(~” + %)2], calculated by the method of the least squares, represents bands in Table I with the error of -eO.6 cm-l. The rotational analysis of the bands, which have an open structure like the CH+ bands, was easily performed using computed spectra and the second combination differences. Approximate values of the rotational constants were obtained from the isotopic relation and the constants of CH+ (3). These synthetic spectra were used for picking out P, Q, and R branches and rotational quantum number assignments. The wavenumbers of all identified band lines are listed in Table II. Rotational structure of the O-O and 1-O bands is shown in Fig. 1. Good agreement was found between the second combination differences of the corresponding bands. On the other hand, the A,&“(J) values of each band calculated from R(J)-Q(J) differed from those determined from Q(J + 1) - P(J + l), and the combination defect was observed. Due to this fact, the rotational constants of the upper state were evaluated independently from Q lines (B$) and from P and R lines (B:R). The lower state constants B:’ and 0; as well as Bt,“l values were determined from the average A,F”(J) and A,F’(J), respectively, by a least-squares fit of the relations A$(J)
= 4B(J + 1/) - 8D(J + X2>“,
while the B$ and D$ were obtained by finding B’-B” and D’-D” Q(J) versus J(J + 1). The final results are given in Table III.
from the plot
200
ET AL.
ANTIkJOVANOVIc TABLE Wavenumbers
of the Rotational
II
Lines of the A’II-X2
C-O
Band System
of CD+
O-l
1-o
J R(J) 0
Q(J)
P(J)
R(J)
Q(J)
P(J)
R(J)
21724.85
23760.03
Q(J)
P(J)
25007.72
735.15 21710.10
1
769.63
2
776.93
739.46 23714.63
742.91
705.45 21680.80
020.83
985.73 24962.57
3
781.35
731.40
694.20
740.44
698.58
661.62
022.33
975.44
940.46
4
763.00
720.62
671.10
751.60
689.36
639.86
020.24
961.71
915.20
5
782.02
707.10
645.35
752.68
677.85
616.20
014.60
944.47
8e6.49
6
777.90
690.86
616.94
750.92
663.91
590.00
005.42
923.77
854.35
7
771.10
671.66
585.96
746.64
647.67
561.80 24992.62
899.57
818.72
552.25
740.46
628.95
976.26
871.73
731.27
w.e4
956.08
840.25
932.30
805.12
23774.9
8
761.53
650.05
9
748.90
625.40
10
733.31
597.88
11
714.65
567.38
015.86 24992.62
558.10
TABLE
II-Continued 2-l
2-o
3-1
J R(J)
Q(J)
R(J)
P(J)
R(J)
Q(J)
P(J)
24105.67
26143.78
0
P(J)
P(J)
112.90 24691.05
1
147.74 26125.82
2
150.33
117.22
116.01
003.28
3
148.70
104.84 26072.33
115.a
on.90
4
142.81
0+.0;,
044.66
111.49
056.70
5
132.76
067.11
012.50
6
118.29
7
099.39
25134.44 25114.00 135.76
164.64
24039.15
132.15
691.27
013.15
124.14
073.11
103.30
037.65 23983.24
111.43
OY.49
041.87 25977.02
091.05
014.69
949.84
093.95
012.47
075.02 23987.85
912.44
957.16
871.31
936.98
022.80 24990.91 954.22
8
076.03 25978.50
9
048.51
940.32
922.42
912.72
10
016.30
897.67
883.75
866.45
054.90
840.82
11
From
A’II
the differences
state:
satisfactorily plotting
BcR-B$
we
obtained
[R(J)
with -
those
Q(J)]
-
found [Q(J
from +
1) -
the P(J
4. ISOTOPE As It was
the A-doubling
q,, = 0.018, q1 = 0.013, and q2 = 0.012 cm-‘.
mentioned examined
in Section in detail
3, the isotope
as described
slope +
l)]
constants These
of the straight against
(J
+
line
values
for
the
agree
obtained
by
1)‘.
EFFECT shift has been
below.
detected
in all bands.
2
FIG. 1. Rotational structure of the O-O and 1-O bands of CD+.
R
4735.6
P
x
202
ANTIC-JOVANOVIC
TABLE
ET AL.
III
Rotational Constants of the Various Vibrational Levels of CD+ (cm-l)
lrl
v BQ v
11 Baver v
gR -?
0
6.225
6.243
6.234
1
5.640
5.653
5.646
2
5.461
5.473
5.467
Daver.104 5.7
Bv
$.104
7.555
4.1
7.365
The isotope splitting at J = 0 should be the vibrational isotope effect A& It has been calculated by known third degree expression using Douglas and Morton’s values for w:, wkx:, and wdyk, and our above calculated values for WE and wzxl. Obtained results are given in column 3 of Table V. The rotational isotope effect for the lines at the bandhead was derived by following Eq. (12) Au; = (1 - $)[B:J’(J’
+ 1) - B;J”(J”
- crS(v” + ,),“(J”
+ l)] - (1 - p3)[cy:(v’ + l/;)J’(J’
+ l)] - (1 - pJ)[D’J’2(J’
+ 1)’ - W.P(J”
+ 1) + 1)2].
From the known rotational constants (3) and the corresponding J values for the lines at the head of each band we obtained results summarized in column 4 of Table V. It was found that the observed isotope shifts of the CD+ heads show rather large discrepancies from those calculated as the sum of the Auk and Au: contributions. The reason for this discrepancy is the electronic isotope effect which also must be taken into account in determining the total isotope displacement. The former represents the difference between the pure electronic TABLE
IV
Molecular Constants of the CD+ (cm-‘)
Be
a,
lrl
11
6.426
7.650
0.36s
0.190
5.7
4.1
De.104
1367.3
W, W-l?
60.6
W,
(2101.6)
(33.3)
0.75
T 00
23747.5
%
24121.0
*
2035.0”
~Gl,2iw,,~&~
values in parentheses am
calculated from isotope relatiOns.
THE A%-X’S
203
BAND SYSTEM OF CD+ V
Isotope
in the
Bands
0,1
-843.5
+34.3
-822.2
-820.2
0.0
-138.7
+27.5
-124.2
-123.5
Cl.7
1.0
+255.8
+15.6
+258.4
+259,1
-0.7
+2.0
-13 2.0
+557.8
+10.3
+555.1
+553.8
+1.3
291
-146.9
+12.1
-147.8
-148.6
-0.6
391
+ 72.2
+ 5.2
+ 64.4
+ 64.6
-0,2
AVi - electronicisotope shift AVi - vibrationalisotope shift
Avf -
rotationalisotope ehift
term values T, of both isotope molecules, expression
which we have calculated
using the
T, = T,, - E;, + E;.
The zero point energies Eb and B’i for the A’II and PC states, respectively, were obtained according to the expression given by Dunham (13): E. = G(0) + Yoo
where G(0) represents
the energy of the ZI= 0 level and
the Dunham zero-order coefficient. The latter expression is approximate and involves a rather large uncertainty in the AT: determination, as pointed out by Bunker (I#), except if the difference Yh, - Y& is very small. The T, values of both CH+ and CD+, derived using constants from Table IV and those given in (3), are: T,(CH+) = 24 111.3 cm-l and T,(CD+) = 24 121.0 cm-‘, giving for electronic isotope shift Avh = ATi = T,(CH+) - T,(CD+) = 9.7 cm-l. Using this value we obtained total isotope displacements for CD+ bandheads which differed for 1S-4.6 cm-l from those directly measured from the spectrum. This fact indicated that the electronic isotope shift was somewhat larger than it was calculated. Improvement was made by using Bunker’s theoretical expression for the electronic isotope displacement (14). According to his Eq. (55), we can write:
204
ANTIC-JOVANOVIC ET AL.
T; = T,(CH+) - T,(CD+) = [B,(CH+) - B,(CD+)]A[(i2)
- A2 + S(S + 1) - Z2 - f-PIA
- [B,(CH+) - B,(CD+)][(i2)
- A2 + S(S + 1) - S2 - @lx.
This expression requires the knowledge of the (L2) value for the corresponding molecule. However, the equation also gives good results when separated atom values L(L + 1) are used for (i2). In the present case, both states ATI and XiZ correlate with separated atom states C+(2P) + H(*S) and, therefore, (iz)A = (i”)” is estimated to be [l(l + 1) + O(0 + l)] = 2. Further, we have: for the A state
A2 = R2 = 1; S(S + 1) = 22 = 0;
for the X state
A2 = S(S + 1) = Y = W = 0.
and Thus one obtains T,(CH+)A - T,(CD+)” = -[B,(CH+) = -[14.18
- B,(CD+)]X.2
- 7.653.2
= -13 cm-‘. This value of ATi(Avb) is in much better agreement with experimental observation than that previously determined by the “experimental” method; one can expect that its accuracy is of the order of 0.5-l cm-‘. The differences between calculated and measured isotope shifts of observed bandheads are now 0.2-2 cm-’ (column 7 in Table V), which can be considered satisfactory. ACKNOWLEDGMENTS The authors are indebted to Dr. P. R. Bunker for helpful discussion and valuable comments. This work is supported by the fund for financing Scientific Activities of Serbia. RECEIVED:
June 2, 1978 REFERENCES
I. A. E. DOUGLASAND G. HERZBERG, Astrophys. J. 94, 381 (1941). 2. A. E. DOUGLASAND G. HERZBERG,Canad. .I. Res. 20, 71-82 (1942). 3. A. E. DOUGLASAND J. R. MORTON,Astrophys. J. 131, l-7 (1960). 4. M. CARRE,Physica 41, 63-66 (1969). 5. H. CISAKAND M. RYTEL,Acta Phys. Pot. A 39, 627-628 (1971). 6. S. H. BAUER, G. HERZBERG,AND J. W. C. JOHNS,J. Mol. Spectrosc. 13, 256-280 (1964). 7. J. W. C. JONS, F. A. GREEM,AND R. F. PORTER,J. Mol. Spectrosc. 22, 435-451 (1967). 8. B. A. MORROW, Canad. J. Phys. 44, 2447-2459 (1966). 9. D. DE GREEFAND R. COLIN,J. Mol. Spectrosc. 53, 455-465 (19’74). 10. B. VUJISIC,Thesis for doctorate. University of Belgrade, Belgrade (1977). 11. M. GERARD, T. R. GOVERS,AND R. MARIX, Chem. Phys. 30, 75-83 (1978). 12. G. HERZBERG, “Molecular Spectra and Molecular Structure I,” p. 145, Van Nostrand, New York, 1966. 13. J. L. DUNHAM,Phys. Rev. 41, 721-731 (1932). 14. P. R. BUNKER,J. Mol. Spectrosc. 28, 422-443 (1968).
OF MOLECULAR
SPECTROSCOPY
75,197-204
The AllYI-X12 Spectroscopic
(1979)
Band System of CD+ Constants
A. ANTIC-J•
and Isotope
VANOVIC AND
Shifts
V. BOJOVIC
Institute of Physical Chemistry, Faculty of Science, University of Belgrade, Belgrade, Yugoslavia
D. s. PESIC B. Kidric Institute
of Nuclear
Sciences,
POB 522, Belgrade.
Yugoslavia
AND S. WENIGER Observatoire
de Paris,
Laboratoire
de Spectroscopic.
Meudon,
France
Six bands of the A’II-X12 system of CD+ in the region 3800-4800 A have been recorded in emission using an aluminum hollow-cathode discharge in the He-C,H, mixture. From the vibrational and rotational analysis of the observed bands, the following constants (cm-‘) are obtained:
A’H X’S
23 747.5 0
1367.3 2035
60.6
(2101.6)
(33.3)
0.75
6.428 7.650
5.7 4.1
0.388
0.190
AGli2; (w,), (q-xx,) are calculated from isotope relation. The electronic isotope shift Av: = T,(CH+) - T,(CD+) = -13 cm-r has been derived according to the theoretical expression given by Bunker. A somewhat smaller value was obtained from the pure electronic energy difference using “experimental” values of the zero point energies. 1. INTRODUCTION
The red-degraded bands of the A ‘II-X’Z$ system of CH+ were first obtained by Douglas and Herzberg (1, 2) using a high frequency electrodeless discharge through helium mixed with a trace of benzene. These authors observed, and made rotational and vibrational analysis, of the O-O, I-O, 2-0, and O-l bands; they also discussed the nature of the band emitter. Douglas and Morton (3) have performed the analysis of the 0- 1, l- 1, 2- 1, 3- 1, and 4- 1 bands. Carre (4) recorded two new bands (3-O and 4-O near 3580 and 3450 A, respectively) by studying the emission spectra of CH, and C2H, excited by proton impact. 197
0022-2852/79/050197-08$02.00/O Copyright
0 1979 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
ANTIC-JOVANOVI6
198
ET AL.
However, for the isotopic CD+ ion only fragmentary data concerning the z+,and VHvalues of four bands have been given by Cisak and Rytel(5). Since this simple system of CH+ is of special astrophysical interest, we have undertaken a new investigation of the spectrum of CD+. The study of the observed isotope displacements revealed the existence of a rather large electronic isotope shift which is a direct consequence of partial breakdown of the BomOppenheimer approximation used in solving the rovibronic wave equation, and which was observed already in the case of several diatomic hydrides (6-9). 2. EXPERIMENTAL
METHOD
For the excitation of the emission CD+ spectrum a water cooled hollowcathode discharge tube, described by Vujisic (IO), was employed. An aluminum cup was used as a cathode. The tube was filled with a mixture of He + CzD2 (10: 1) at about 3 mm Hg and the cathode glow was obtained by using a dc of 250350 mA and 600 V between electrodes. The bands situated in the 3800-4800-A region were photographed in the first order of a 3-m Eagle spectrograph (dispersion 2.6 &mm) using Word HP4 film and an exposure time of 30-60 min. An iron arc gave the reference spectrum. The films were measured on a Zeiss Abbe comparator and the spectra were reduced on a CDC-3600 computer. The absolute accuracy of the wavenumbers for unblended rotational lines is estimated to be to.05 cm-‘. 3. BAND ANALYSIS
Six bands (O-l, O-O, l-0, 2-1, 2-0, and 3-l) were observed in the investigated region. Their vibrational assignment, supported by observed isotope shifts, presented no difficulty. Table I represents the Deslandres table of the origins and bandheads of these bands. It should be mentioned here that our data for the O-O, TABLE
I
Deslandres Table (uO,hH)of the CD+ Bands v” v’ 0 0
23747.5 wO3.52
1
24996.0 3995.30
2
26130.0 3822.96
3
1 21712.5 4595.85
24094.5 4145.45 25118.5 3977.27
V, - position of zero line (cm-l) A, - position of B head (8)
THE
AT-X'S BAND SYSTEM OF CD+
199
l-0, and 2- 1 bands agree with those given by Cisak and Rytel (5) within experimental errors, but the agreement between data concerning the 0- 1 band is somewhat less satisfying. From the u0 values of the O-O, l-0, and 2-O bands we derived the vibrational constants o:, w:x:, and w:yk listed in Table IV in which all the molecular constants of CD+ are collected. Due to the small number of bands in the 2)” progression the equilibrium constants of the lower electronic state could not be verified. However, assuming that the levels involved are unperturbed and that the vibrational energy can be represented with a quadratic expression, it was possible to estimate the approximate values of these constants from the following relations for two isotopes AG’I,,(CH+) = w; - 2o%xk’, AG’;,2(CD+) = po; - 2p%&;. With AG’;,,(CH+) = 2739.7 cm-’ (3), AG’&,(CD+) = 2035.0 cm-l, and p = 0.73397, we obtained ws = 2863.3 cm-’ and w$z = 61.8 cm-’ for CH+, and 2101.6 and 33.3 cm-’ for CD+, respectively. These values agree very well with those obtained very recently by Gerard et al. (II) by studying the emission produced by the reaction of He+ ions with &Hz and C,D, in near-thermal charge exchange. The vibrational equation y0 = 24 121.0 + [1367.3(v’ + 1%) - 60.6(v’ + ‘/)” + 0.75(0’ + ‘/)“I - [2101.6(~” + y2) - 33.3(~” + %)2], calculated by the method of the least squares, represents bands in Table I with the error of -eO.6 cm-l. The rotational analysis of the bands, which have an open structure like the CH+ bands, was easily performed using computed spectra and the second combination differences. Approximate values of the rotational constants were obtained from the isotopic relation and the constants of CH+ (3). These synthetic spectra were used for picking out P, Q, and R branches and rotational quantum number assignments. The wavenumbers of all identified band lines are listed in Table II. Rotational structure of the O-O and 1-O bands is shown in Fig. 1. Good agreement was found between the second combination differences of the corresponding bands. On the other hand, the A,&“(J) values of each band calculated from R(J)-Q(J) differed from those determined from Q(J + 1) - P(J + l), and the combination defect was observed. Due to this fact, the rotational constants of the upper state were evaluated independently from Q lines (B$) and from P and R lines (B:R). The lower state constants B:’ and 0; as well as Bt,“l values were determined from the average A,F”(J) and A,F’(J), respectively, by a least-squares fit of the relations A$(J)
= 4B(J + 1/) - 8D(J + X2>“,
while the B$ and D$ were obtained by finding B’-B” and D’-D” Q(J) versus J(J + 1). The final results are given in Table III.
from the plot
200
ET AL.
ANTIkJOVANOVIc TABLE Wavenumbers
of the Rotational
II
Lines of the A’II-X2
C-O
Band System
of CD+
O-l
1-o
J R(J) 0
Q(J)
P(J)
R(J)
Q(J)
P(J)
R(J)
21724.85
23760.03
Q(J)
P(J)
25007.72
735.15 21710.10
1
769.63
2
776.93
739.46 23714.63
742.91
705.45 21680.80
020.83
985.73 24962.57
3
781.35
731.40
694.20
740.44
698.58
661.62
022.33
975.44
940.46
4
763.00
720.62
671.10
751.60
689.36
639.86
020.24
961.71
915.20
5
782.02
707.10
645.35
752.68
677.85
616.20
014.60
944.47
8e6.49
6
777.90
690.86
616.94
750.92
663.91
590.00
005.42
923.77
854.35
7
771.10
671.66
585.96
746.64
647.67
561.80 24992.62
899.57
818.72
552.25
740.46
628.95
976.26
871.73
731.27
w.e4
956.08
840.25
932.30
805.12
23774.9
8
761.53
650.05
9
748.90
625.40
10
733.31
597.88
11
714.65
567.38
015.86 24992.62
558.10
TABLE
II-Continued 2-l
2-o
3-1
J R(J)
Q(J)
R(J)
P(J)
R(J)
Q(J)
P(J)
24105.67
26143.78
0
P(J)
P(J)
112.90 24691.05
1
147.74 26125.82
2
150.33
117.22
116.01
003.28
3
148.70
104.84 26072.33
115.a
on.90
4
142.81
0+.0;,
044.66
111.49
056.70
5
132.76
067.11
012.50
6
118.29
7
099.39
25134.44 25114.00 135.76
164.64
24039.15
132.15
691.27
013.15
124.14
073.11
103.30
037.65 23983.24
111.43
OY.49
041.87 25977.02
091.05
014.69
949.84
093.95
012.47
075.02 23987.85
912.44
957.16
871.31
936.98
022.80 24990.91 954.22
8
076.03 25978.50
9
048.51
940.32
922.42
912.72
10
016.30
897.67
883.75
866.45
054.90
840.82
11
From
A’II
the differences
state:
satisfactorily plotting
BcR-B$
we
obtained
[R(J)
with -
those
Q(J)]
-
found [Q(J
from +
1) -
the P(J
4. ISOTOPE As It was
the A-doubling
q,, = 0.018, q1 = 0.013, and q2 = 0.012 cm-‘.
mentioned examined
in Section in detail
3, the isotope
as described
slope +
l)]
constants These
of the straight against
(J
+
line
values
for
the
agree
obtained
by
1)‘.
EFFECT shift has been
below.
detected
in all bands.
2
FIG. 1. Rotational structure of the O-O and 1-O bands of CD+.
R
4735.6
P
x
202
ANTIC-JOVANOVIC
TABLE
ET AL.
III
Rotational Constants of the Various Vibrational Levels of CD+ (cm-l)
lrl
v BQ v
11 Baver v
gR -?
0
6.225
6.243
6.234
1
5.640
5.653
5.646
2
5.461
5.473
5.467
Daver.104 5.7
Bv
$.104
7.555
4.1
7.365
The isotope splitting at J = 0 should be the vibrational isotope effect A& It has been calculated by known third degree expression using Douglas and Morton’s values for w:, wkx:, and wdyk, and our above calculated values for WE and wzxl. Obtained results are given in column 3 of Table V. The rotational isotope effect for the lines at the bandhead was derived by following Eq. (12) Au; = (1 - $)[B:J’(J’
+ 1) - B;J”(J”
- crS(v” + ,),“(J”
+ l)] - (1 - p3)[cy:(v’ + l/;)J’(J’
+ l)] - (1 - pJ)[D’J’2(J’
+ 1)’ - W.P(J”
+ 1) + 1)2].
From the known rotational constants (3) and the corresponding J values for the lines at the head of each band we obtained results summarized in column 4 of Table V. It was found that the observed isotope shifts of the CD+ heads show rather large discrepancies from those calculated as the sum of the Auk and Au: contributions. The reason for this discrepancy is the electronic isotope effect which also must be taken into account in determining the total isotope displacement. The former represents the difference between the pure electronic TABLE
IV
Molecular Constants of the CD+ (cm-‘)
Be
a,
lrl
11
6.426
7.650
0.36s
0.190
5.7
4.1
De.104
1367.3
W, W-l?
60.6
W,
(2101.6)
(33.3)
0.75
T 00
23747.5
%
24121.0
*
2035.0”
~Gl,2iw,,~&~
values in parentheses am
calculated from isotope relatiOns.
THE A%-X’S
203
BAND SYSTEM OF CD+ V
Isotope
in the
Bands
0,1
-843.5
+34.3
-822.2
-820.2
0.0
-138.7
+27.5
-124.2
-123.5
Cl.7
1.0
+255.8
+15.6
+258.4
+259,1
-0.7
+2.0
-13 2.0
+557.8
+10.3
+555.1
+553.8
+1.3
291
-146.9
+12.1
-147.8
-148.6
-0.6
391
+ 72.2
+ 5.2
+ 64.4
+ 64.6
-0,2
AVi - electronicisotope shift AVi - vibrationalisotope shift
Avf -
rotationalisotope ehift
term values T, of both isotope molecules, expression
which we have calculated
using the
T, = T,, - E;, + E;.
The zero point energies Eb and B’i for the A’II and PC states, respectively, were obtained according to the expression given by Dunham (13): E. = G(0) + Yoo
where G(0) represents
the energy of the ZI= 0 level and
the Dunham zero-order coefficient. The latter expression is approximate and involves a rather large uncertainty in the AT: determination, as pointed out by Bunker (I#), except if the difference Yh, - Y& is very small. The T, values of both CH+ and CD+, derived using constants from Table IV and those given in (3), are: T,(CH+) = 24 111.3 cm-l and T,(CD+) = 24 121.0 cm-‘, giving for electronic isotope shift Avh = ATi = T,(CH+) - T,(CD+) = 9.7 cm-l. Using this value we obtained total isotope displacements for CD+ bandheads which differed for 1S-4.6 cm-l from those directly measured from the spectrum. This fact indicated that the electronic isotope shift was somewhat larger than it was calculated. Improvement was made by using Bunker’s theoretical expression for the electronic isotope displacement (14). According to his Eq. (55), we can write:
204
ANTIC-JOVANOVIC ET AL.
T; = T,(CH+) - T,(CD+) = [B,(CH+) - B,(CD+)]A[(i2)
- A2 + S(S + 1) - Z2 - f-PIA
- [B,(CH+) - B,(CD+)][(i2)
- A2 + S(S + 1) - S2 - @lx.
This expression requires the knowledge of the (L2) value for the corresponding molecule. However, the equation also gives good results when separated atom values L(L + 1) are used for (i2). In the present case, both states ATI and XiZ correlate with separated atom states C+(2P) + H(*S) and, therefore, (iz)A = (i”)” is estimated to be [l(l + 1) + O(0 + l)] = 2. Further, we have: for the A state
A2 = R2 = 1; S(S + 1) = 22 = 0;
for the X state
A2 = S(S + 1) = Y = W = 0.
and Thus one obtains T,(CH+)A - T,(CD+)” = -[B,(CH+) = -[14.18
- B,(CD+)]X.2
- 7.653.2
= -13 cm-‘. This value of ATi(Avb) is in much better agreement with experimental observation than that previously determined by the “experimental” method; one can expect that its accuracy is of the order of 0.5-l cm-‘. The differences between calculated and measured isotope shifts of observed bandheads are now 0.2-2 cm-’ (column 7 in Table V), which can be considered satisfactory. ACKNOWLEDGMENTS The authors are indebted to Dr. P. R. Bunker for helpful discussion and valuable comments. This work is supported by the fund for financing Scientific Activities of Serbia. RECEIVED:
June 2, 1978 REFERENCES
I. A. E. DOUGLASAND G. HERZBERG, Astrophys. J. 94, 381 (1941). 2. A. E. DOUGLASAND G. HERZBERG,Canad. .I. Res. 20, 71-82 (1942). 3. A. E. DOUGLASAND J. R. MORTON,Astrophys. J. 131, l-7 (1960). 4. M. CARRE,Physica 41, 63-66 (1969). 5. H. CISAKAND M. RYTEL,Acta Phys. Pot. A 39, 627-628 (1971). 6. S. H. BAUER, G. HERZBERG,AND J. W. C. JOHNS,J. Mol. Spectrosc. 13, 256-280 (1964). 7. J. W. C. JONS, F. A. GREEM,AND R. F. PORTER,J. Mol. Spectrosc. 22, 435-451 (1967). 8. B. A. MORROW, Canad. J. Phys. 44, 2447-2459 (1966). 9. D. DE GREEFAND R. COLIN,J. Mol. Spectrosc. 53, 455-465 (19’74). 10. B. VUJISIC,Thesis for doctorate. University of Belgrade, Belgrade (1977). 11. M. GERARD, T. R. GOVERS,AND R. MARIX, Chem. Phys. 30, 75-83 (1978). 12. G. HERZBERG, “Molecular Spectra and Molecular Structure I,” p. 145, Van Nostrand, New York, 1966. 13. J. L. DUNHAM,Phys. Rev. 41, 721-731 (1932). 14. P. R. BUNKER,J. Mol. Spectrosc. 28, 422-443 (1968).