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Analysis of the E-X and C-X band system isotopically enriched of Ag2
JOURNAL
27-32(1981)
OF MOLECULARSPECTROSCOPY!~~,
Analysis
of the E-X and C-X Band System Isotopically Enriched of Ag2 V.I.
SRDANOV
AND
D.S.
PEW
Physical Chemistry Laboratory, B. Kidri? Institute of Nuclear Science, 11001 Belgrade, P.O.B. 522, Yugoslavia The high-dispersion spectra of E-X and C-X systems of isotopic Ag, molecules were investigated in the region 247-271 nm. The vibrational numbering is determined by measuring the isotope displacements in the bandheads among ““Ag,, *07Ag109Ag,and losAg,. Molecular constants of the states involved are presented. INTRODUCTION
Electronic bands assigned to the Ag, molecule in the region 160-540 nm have been known for a long time (for previous references see Pearse and Gaydon (1) and Huber and Herzberg (2)). Employing different types of King furnaces absorption spectra of six band systems with red-degraded bands (H-X (169-173 nm), E-X (247-256 nm), D-X (256-261 nm), C-X (264-271 nm), and A-X (400-540 nm)) have been detected in the electronic spectrum of diatomic silver (I -4). A series of the bands around 250 and 265 nm were first reported by Ruamps (5) and Maheshwari (6), and they have been designated as the E-X and C-X transitions. Recently, bands were obtained under high resolution by Brown and Ginter (3). In the first two papers (5,6) main bands were identified and vibrational assignments were given. The reanalysis in Ref. (3) confirmed the bandhead measurements; they found no need to modify the vibrational numbering of the previous authors. These authors found that, even at a reciprocal dispersion of 1.2 A/mm, the isotopic assignments remained tentative. They assumed that the lower-state X is the common state for both systems, but rotational analysis was not possible for either transition. Unambiguous assignments of vibrational quantum numbers can be obtained by using the vibrational isotope effect. It seems worthwhile to perform the investigation with pure ‘O’Agisotope in order to confirm the analysis and to improve the accuracy of the vibrational constants. The results of this analysis are summarized in the present work. EXPERIMENTAL
DETAILS
Using a specture sample of metallic silver, natural and enriched lo7Ag, the absorption spectrum of Ag, was obtained in an evacuable King furnace. Natural silver is a mixture of two isotopes, lo7Ag and losAg, with relative abundances of 51.4 and 48.6%, respectively. The enriched silver was stated by the manufacturer (Techsnabexport, Moscow, USSR) to contain 90.2% lo7Ag. The graphite resistance 27
0022-2852/81/110027-Of5$02.00/0 Copyright 0 1981by Academic All rights
of reproduction
Press,
in any form
Inc. reserved.
28
SRDANOV
AND PESIC
heating element has a bore of 12 mm, and it is approximately 15 cm in length with a hot zone of 8 cm. A special profile of the tube in the hot zone minimized thermal gradients. It was observed that the temperature variations at 2100 K were normally less than 20 K throughout the hot zone. The strong bands were obtained at a temperature of 2100 K, and the weak bands at 2200 K. In order to lessen metal evaporation, an argon pressure of about 250 Torr was maintained within the cell. The absorption experiments were done with an optical arrangement which gave a parallel beam in the furnace, and after passing through the furnace, the image was focused onto the slit of the spectrograph. With a high-pressure xenon arc lamp (400 W) the exposure time from 2 to 3 min was found suitable for obtaining good spectrograms using Ilford N-30 and PH4 film. The spectra were photographed in the second order of a 6.4-m Ebert spectrograph (inverse dispersion of 0.6 A mm-‘). An iron arc comparison spectrum was used. The spectra were measured on an Abee comparator, and the data were reduced on a CDC-3600 computer. The measurement error for well-defined bands was 0.2 cm-l. RESULTS
E-X
AND DISCUSSION
System
The most intense sequences of the E-X electronic transition of Ag, molecule appear throughout the region 247-262 nm. The system consists of single-headed, red-degraded bands with very dense rotational structure. In the region close to the bandheads the profiles of the bands of ordinary Ag, are modified due to partly resolved isotope splitting which causes difficulties in the position measurements. Thus the present vibrational analysis is based on the pure lo7Ag2 isotope. The measurements of the identified bandheads for three isotopic species and the vibrational quantum numbers of all classified bands are given in Table I. The positions of lo7AglogAg bands agree quite well with those given by Brown and Ginter (3) and by Ruamps (5). The spectrum of pure lo7Ag2 and the observed vibrational isotope shifts in the spectra of ordinary silver provided the basis for vibrational quantum numbering for all measured bands. The bandheads identified in the different sequences of the lo7Ag2 spectrum can be represented with an average difference of 0.3 cm-’ by the vibrational constants given in Table II. Bands due to lo7AglogAg molecule are well represented by the corresponding constants: o: = 146.8, o& = 1.56, wz = 193.3, and o$g = 0.61 cm-l, calculated by the isotope relations. These constants are very similar to those obtained by Brown and Ginter for the same molecule with a slight change in the value of the wz constant. In the spectra of ordinary silver it was possible to detect heads of lo7Ag,, lo7Ag10sAg,and logAg, species (Table I). A portion of the Ag, absorption spectrogram in the region 250.1-252.3 nm is reproduced in Fig. 1. As can be seen from the Table I, the bands starting from Au = -1 sequences exhibit well resolved vibrational shifts. The observed isotope separations of the bandheads between molecules lo7Ag2 and lo7AglosAg and between ro7Ag2, and logAg, agree very well (within +0.15 cm-‘) with those calculated from the standard formula
ANALYSIS
29
OF Ag, SPECTRA TABLE I
Bandheads Data of E-X System v’
107
,v”
107*
109
logA
*g2
*g2 i
"
2,o
v
Avi talc. obs.
u
&L obs,
talc.
39946.0
1.0
0.9
39900.5 39850.9
1.2 1.3
1.1 1.4
39711.1
1.9
2.1
39614.7
2.4
2.5
39430.4 39380.7
3.5 3.4
39247.3
4.1 4.3 4.6 5.2
40419.5 40364.6 40308.7
3,1 4.2
40279.6
1;o 2,l 3.2
40228.3 40175.6 40136.7 40088.8 40039.9 39945.0 39899.2 39849.6 39799.7 39709.2 39661.7 39612.3 39561.1 39475.0
0;o 1,1 2.2 0.1 1,2 2.3 3;4 1,3 2,4 3,5 4,6 2.5 3;6 4,7 5,8
39426.9 39377.3
39325.1 39271.1 39243.2 39194.4 39143.7 39090.6 39035.8
6,9 3.7 4;tl 5.9 6;lO 7.11
Au = (p - 1) 1o;(v’
39198.7 39148.3 39095.8
39946.9 39901.6
1.9 2.4
1.8 2.2
39713.4
4.2
4.2
3.3 3.6
39433.6 39384.2
6.7 6.9
6.6 7.2
4.2 4.4 4.6 4.9
39203.2 39153.0 39100.7
8.8 9.3 10.1
8.8 9.2 9.8
+ l/2) - of(u” + l/2) 1 - (p” x Iw;x;(v’
1)
+ l/2)” - w;x;(v” + l/2)” 1.
(1)
The vibrational constants given in Table II were used for these calculations. The values of (p - 1) calculated for the pairs lo7Ag2- 107Ag10gAgand lo7Ag2- logAg are 0.00462 and 0.00922, respectively. TABLE II Vibrational Constants of ‘O’Ag, (cm-‘)
Te
we
WeXe
E
40159.4+0.4=
146.2kO.3
1.5520.05
X
0
192.4to.2
0.60f0.02
'Uncertainties
reoresent
the standard
deviations.
30
SRDANOV AND PESIC Fe 269.07
Fe 269.91 “m
I
I
Fe 250.56 I
Fe 250 11 I
O,l
192
Fe 252.213nm
Fe 25176 I
1.3
I
2.4
FIG. 1. The C-X bands of natural silver (a) and lU7Ag2(b). The E-X bands of ‘07Ag2(c) and natural silver (d).
C-X
System
A number of double-headed, red-degraded bands were recorded in the region between 264 and 271 nm. It was noted (3,6) that in all bands double heads should be assigned as R and Q heads assuming this to be a II-X transition or transition with AR 2 1 according to Hund’s case (c). Vibrational assignments for measured bands, including a well developed Au = -2 sequence, have been supported by the isotope shifts (Av’ (107Ag2-107Ag10gAg)and Av’ (107Ag,-10gAgJ) (4). With the assumption that double heads represent R and Q heads, the data could be fitted by the formulas L# = 37 631.3 + 171.4(u’ + l/2) - 0.91(u’ + 1/2)2 - 192.2(~” + l/2) + 0.61(v” + l/2)’ - O.O2(v’ + 1/2)(u” + l/2),
(2)
vh”= 37 642.2 + 165.2(v’ + l/2) + O.l2(v’ + l/2)’ - 188.l(v” + l/2) + 0.91(u” + l/2)2 - 1.33(u’ + 1/2)(u” + l/2).
(3)
It is found that a correction term 13(v’+ 1/2)(v” + l/2) which indicates the headorigin separation, has to be applied in order to obtain accurate vibrational equations. The difference between 0 values in the correction term indicates that corresponding heads are differently separated from the band origins. These 8 values in
31
ANALYSIS OF Ag, SPECTRA TABLE III The (v,, - q,) Separations in the C-X System of *07Ag2
v’
‘o -
v’,
obs.
1,O 2,1 3,2 4,3 5.4 6.5 7.6 o,o 1,l 2,2 3.3
-5.6. -4.9 -3.1 -3.4 -2.9 -2.5 -2.0 -9.1 -7.4 -5.8 -5.0
'h talc.
-5.2 -4.4 -3.9 -3.4 -3.0 -2.7 -2.5 -9.5 -7.2 -5.8 -4.9
v' v"
(-3.8jb (-3.3) (-2.9) (-2.61 (-2.3) (-2.1) (-1.9) (-6.8) (-5.3) (-4.3) (-3.7)
4.4 5,5 6,6 7.7 2;4 3,5 4,6 5.1 6;8 7,9 9,ll
aWavenumbers of the bandheads given in the paler (4) b("o
- vh) separations
Brown
and Ginter
'0 - 'h obs. talc. -5.0 -3.4 -3.2 -2.9 -14.7 -11.2 -8.8 -5.7 -4.4 -2.0 -1.4
-4.2 -7.6 -3.2 -2.9 -15.2 -10.1 -1.5 -5.9 -4.9 -4.9 -3.1
of C-X System
are calculated
from
(-3.2) (-2.8) (-2.5) (-2.2) (-1470) (-8.9) (-6.5) (-5.1) (-4.2) (-3.5) (-2.7)
of Ag2 are
the data of
(3)
Eqs. (2) and (3) support the expectation that Q heads are very near to the band origin, while the R heads are remote from them. Figure lb shows the Av = -2 sequence and clearly illustrates typical R-Q head separations. The vibrational constants for the X state, obtained from the Q heads, is the same as the mean value (we = 192.4 cm-‘) given by previous authors (3-6). The measurements of the well-developed vR-v# distances (Fig. 1 and Table III) in the sequences Au = + 1, 0, and -2 of lo7Ag2, together with the assumption that the position of Q heads is very near to the origin of the bands (ue - vo) provide an opportunity to re-evaluate the rotational constants for the C and X states given by Brown and Ginter (3). The observed data (Table III) for all bands were fitted by a nonlinear least-squares procedure (8) and used to derive B:, cwi, and Or::constants in the equation
v, - Uh =
IB; - (Y’(U)+ l/2) + B; - a"(~" + l/2) I2 41B; - (Y’(v’ + l/2) - B; + a"(~" + l/2)1 ’
(4)
In this fitting procedure, the value of Bz constant, obtained by semiempirical relations (7), was fixed at 0.05121 cm-‘. The resulting constants are presented in Table IV. The value of 0.05088 cm-l given by Brown and Ginter for the B: constants is smaller than the experimental value reported in Table IV. This disagreement can be explained as due to the different procedures used in the calculation. A comparison of observed and calculated differences (Y, - vi,) derived from these constants is shown in Table III. For most vibrational levels the agreement is within 0.5 cm-‘. Figure 1 demonstrates that the (8, 10) band has a single head,
32
SRDANOV AND PESIC TABLE IV Molecular Constants of lorAg, (cm-‘)
C
0.05098+0.00002a
2.220.13
X
0.05121
1.36tO.13
=see
footnote
(a), Table
II.
while (7,9) and (9,ll) bands in the same sequences have well defined double heads. The position of this band (37 075.2 cm-‘) deviates from both, calculated by Eqs. (2) and (3) for R head-37 070.5 cm-‘, and that for Q head-37 069.8 cm-‘. It appears from this that the position of this band is affected by the perturbation effect, supporting the Brown and Ginter interpretation about the perturbation of V’ = 8 in this system. CONCLUSION
In the present work, the study of isotope effect was used to confirm the emitter and improve the vibrational analysis of bands belonging to the systems E-X and C-X. The Q- and R-head separations in C-X system has led to the determination of the R:, ai and a%constants for the upper C state. The study of this separation, which was based on Brown and Ginter’s and our data, has shown the usefulness of this procedure for obtaining the molecular constants from unresolved electronic spectra. The good agreement obtained using the analysis the BE constant, calculated by semiempirical relations, corroborates the correctness of this X-state rotational constant. ACKNOWLEDGMENTS The authors would like to thank Drs. B. Vujisic and A. Antic-Jovanovic for helpful discussions. This work was supported by the Serbian Research Fund. RECEIVED:
March 26, 1981 REFERENCES
1. R. W. B. PEARSEAND A. G. GAYDON, “The Identification of Molecular Spectra,” 4th ed., Chapman & Hall, London, 1976. 2. K. P. HUBERAND G. HERZBERG,“Constants of Diatomic Molecules,” Van Nostrand-Reinhold, New York, 1979. 3. C. M. BROWNAND M. L. GINTER,J. Mol. Spectrosc. 69, 25-36 (1978). 4. V. 1. SRDANOVAND D. S. P&C, Bull. Sot. Chim. Beograd 44, 281-289 (1979). 5. J. RUAMPS,Ann. Phys. Paris 4, 1111-1129 (1959). 6. R. C. MAHESHWARI, Indian J. Phys. 37, 368-374 (1963). 7. G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 1950. 8. M. H. LIETZKE(unpublished).
27-32(1981)
OF MOLECULARSPECTROSCOPY!~~,
Analysis
of the E-X and C-X Band System Isotopically Enriched of Ag2 V.I.
SRDANOV
AND
D.S.
PEW
Physical Chemistry Laboratory, B. Kidri? Institute of Nuclear Science, 11001 Belgrade, P.O.B. 522, Yugoslavia The high-dispersion spectra of E-X and C-X systems of isotopic Ag, molecules were investigated in the region 247-271 nm. The vibrational numbering is determined by measuring the isotope displacements in the bandheads among ““Ag,, *07Ag109Ag,and losAg,. Molecular constants of the states involved are presented. INTRODUCTION
Electronic bands assigned to the Ag, molecule in the region 160-540 nm have been known for a long time (for previous references see Pearse and Gaydon (1) and Huber and Herzberg (2)). Employing different types of King furnaces absorption spectra of six band systems with red-degraded bands (H-X (169-173 nm), E-X (247-256 nm), D-X (256-261 nm), C-X (264-271 nm), and A-X (400-540 nm)) have been detected in the electronic spectrum of diatomic silver (I -4). A series of the bands around 250 and 265 nm were first reported by Ruamps (5) and Maheshwari (6), and they have been designated as the E-X and C-X transitions. Recently, bands were obtained under high resolution by Brown and Ginter (3). In the first two papers (5,6) main bands were identified and vibrational assignments were given. The reanalysis in Ref. (3) confirmed the bandhead measurements; they found no need to modify the vibrational numbering of the previous authors. These authors found that, even at a reciprocal dispersion of 1.2 A/mm, the isotopic assignments remained tentative. They assumed that the lower-state X is the common state for both systems, but rotational analysis was not possible for either transition. Unambiguous assignments of vibrational quantum numbers can be obtained by using the vibrational isotope effect. It seems worthwhile to perform the investigation with pure ‘O’Agisotope in order to confirm the analysis and to improve the accuracy of the vibrational constants. The results of this analysis are summarized in the present work. EXPERIMENTAL
DETAILS
Using a specture sample of metallic silver, natural and enriched lo7Ag, the absorption spectrum of Ag, was obtained in an evacuable King furnace. Natural silver is a mixture of two isotopes, lo7Ag and losAg, with relative abundances of 51.4 and 48.6%, respectively. The enriched silver was stated by the manufacturer (Techsnabexport, Moscow, USSR) to contain 90.2% lo7Ag. The graphite resistance 27
0022-2852/81/110027-Of5$02.00/0 Copyright 0 1981by Academic All rights
of reproduction
Press,
in any form
Inc. reserved.
28
SRDANOV
AND PESIC
heating element has a bore of 12 mm, and it is approximately 15 cm in length with a hot zone of 8 cm. A special profile of the tube in the hot zone minimized thermal gradients. It was observed that the temperature variations at 2100 K were normally less than 20 K throughout the hot zone. The strong bands were obtained at a temperature of 2100 K, and the weak bands at 2200 K. In order to lessen metal evaporation, an argon pressure of about 250 Torr was maintained within the cell. The absorption experiments were done with an optical arrangement which gave a parallel beam in the furnace, and after passing through the furnace, the image was focused onto the slit of the spectrograph. With a high-pressure xenon arc lamp (400 W) the exposure time from 2 to 3 min was found suitable for obtaining good spectrograms using Ilford N-30 and PH4 film. The spectra were photographed in the second order of a 6.4-m Ebert spectrograph (inverse dispersion of 0.6 A mm-‘). An iron arc comparison spectrum was used. The spectra were measured on an Abee comparator, and the data were reduced on a CDC-3600 computer. The measurement error for well-defined bands was 0.2 cm-l. RESULTS
E-X
AND DISCUSSION
System
The most intense sequences of the E-X electronic transition of Ag, molecule appear throughout the region 247-262 nm. The system consists of single-headed, red-degraded bands with very dense rotational structure. In the region close to the bandheads the profiles of the bands of ordinary Ag, are modified due to partly resolved isotope splitting which causes difficulties in the position measurements. Thus the present vibrational analysis is based on the pure lo7Ag2 isotope. The measurements of the identified bandheads for three isotopic species and the vibrational quantum numbers of all classified bands are given in Table I. The positions of lo7AglogAg bands agree quite well with those given by Brown and Ginter (3) and by Ruamps (5). The spectrum of pure lo7Ag2 and the observed vibrational isotope shifts in the spectra of ordinary silver provided the basis for vibrational quantum numbering for all measured bands. The bandheads identified in the different sequences of the lo7Ag2 spectrum can be represented with an average difference of 0.3 cm-’ by the vibrational constants given in Table II. Bands due to lo7AglogAg molecule are well represented by the corresponding constants: o: = 146.8, o& = 1.56, wz = 193.3, and o$g = 0.61 cm-l, calculated by the isotope relations. These constants are very similar to those obtained by Brown and Ginter for the same molecule with a slight change in the value of the wz constant. In the spectra of ordinary silver it was possible to detect heads of lo7Ag,, lo7Ag10sAg,and logAg, species (Table I). A portion of the Ag, absorption spectrogram in the region 250.1-252.3 nm is reproduced in Fig. 1. As can be seen from the Table I, the bands starting from Au = -1 sequences exhibit well resolved vibrational shifts. The observed isotope separations of the bandheads between molecules lo7Ag2 and lo7AglosAg and between ro7Ag2, and logAg, agree very well (within +0.15 cm-‘) with those calculated from the standard formula
ANALYSIS
29
OF Ag, SPECTRA TABLE I
Bandheads Data of E-X System v’
107
,v”
107*
109
logA
*g2
*g2 i
"
2,o
v
Avi talc. obs.
u
&L obs,
talc.
39946.0
1.0
0.9
39900.5 39850.9
1.2 1.3
1.1 1.4
39711.1
1.9
2.1
39614.7
2.4
2.5
39430.4 39380.7
3.5 3.4
39247.3
4.1 4.3 4.6 5.2
40419.5 40364.6 40308.7
3,1 4.2
40279.6
1;o 2,l 3.2
40228.3 40175.6 40136.7 40088.8 40039.9 39945.0 39899.2 39849.6 39799.7 39709.2 39661.7 39612.3 39561.1 39475.0
0;o 1,1 2.2 0.1 1,2 2.3 3;4 1,3 2,4 3,5 4,6 2.5 3;6 4,7 5,8
39426.9 39377.3
39325.1 39271.1 39243.2 39194.4 39143.7 39090.6 39035.8
6,9 3.7 4;tl 5.9 6;lO 7.11
Au = (p - 1) 1o;(v’
39198.7 39148.3 39095.8
39946.9 39901.6
1.9 2.4
1.8 2.2
39713.4
4.2
4.2
3.3 3.6
39433.6 39384.2
6.7 6.9
6.6 7.2
4.2 4.4 4.6 4.9
39203.2 39153.0 39100.7
8.8 9.3 10.1
8.8 9.2 9.8
+ l/2) - of(u” + l/2) 1 - (p” x Iw;x;(v’
1)
+ l/2)” - w;x;(v” + l/2)” 1.
(1)
The vibrational constants given in Table II were used for these calculations. The values of (p - 1) calculated for the pairs lo7Ag2- 107Ag10gAgand lo7Ag2- logAg are 0.00462 and 0.00922, respectively. TABLE II Vibrational Constants of ‘O’Ag, (cm-‘)
Te
we
WeXe
E
40159.4+0.4=
146.2kO.3
1.5520.05
X
0
192.4to.2
0.60f0.02
'Uncertainties
reoresent
the standard
deviations.
30
SRDANOV AND PESIC Fe 269.07
Fe 269.91 “m
I
I
Fe 250.56 I
Fe 250 11 I
O,l
192
Fe 252.213nm
Fe 25176 I
1.3
I
2.4
FIG. 1. The C-X bands of natural silver (a) and lU7Ag2(b). The E-X bands of ‘07Ag2(c) and natural silver (d).
C-X
System
A number of double-headed, red-degraded bands were recorded in the region between 264 and 271 nm. It was noted (3,6) that in all bands double heads should be assigned as R and Q heads assuming this to be a II-X transition or transition with AR 2 1 according to Hund’s case (c). Vibrational assignments for measured bands, including a well developed Au = -2 sequence, have been supported by the isotope shifts (Av’ (107Ag2-107Ag10gAg)and Av’ (107Ag,-10gAgJ) (4). With the assumption that double heads represent R and Q heads, the data could be fitted by the formulas L# = 37 631.3 + 171.4(u’ + l/2) - 0.91(u’ + 1/2)2 - 192.2(~” + l/2) + 0.61(v” + l/2)’ - O.O2(v’ + 1/2)(u” + l/2),
(2)
vh”= 37 642.2 + 165.2(v’ + l/2) + O.l2(v’ + l/2)’ - 188.l(v” + l/2) + 0.91(u” + l/2)2 - 1.33(u’ + 1/2)(u” + l/2).
(3)
It is found that a correction term 13(v’+ 1/2)(v” + l/2) which indicates the headorigin separation, has to be applied in order to obtain accurate vibrational equations. The difference between 0 values in the correction term indicates that corresponding heads are differently separated from the band origins. These 8 values in
31
ANALYSIS OF Ag, SPECTRA TABLE III The (v,, - q,) Separations in the C-X System of *07Ag2
v’
‘o -
v’,
obs.
1,O 2,1 3,2 4,3 5.4 6.5 7.6 o,o 1,l 2,2 3.3
-5.6. -4.9 -3.1 -3.4 -2.9 -2.5 -2.0 -9.1 -7.4 -5.8 -5.0
'h talc.
-5.2 -4.4 -3.9 -3.4 -3.0 -2.7 -2.5 -9.5 -7.2 -5.8 -4.9
v' v"
(-3.8jb (-3.3) (-2.9) (-2.61 (-2.3) (-2.1) (-1.9) (-6.8) (-5.3) (-4.3) (-3.7)
4.4 5,5 6,6 7.7 2;4 3,5 4,6 5.1 6;8 7,9 9,ll
aWavenumbers of the bandheads given in the paler (4) b("o
- vh) separations
Brown
and Ginter
'0 - 'h obs. talc. -5.0 -3.4 -3.2 -2.9 -14.7 -11.2 -8.8 -5.7 -4.4 -2.0 -1.4
-4.2 -7.6 -3.2 -2.9 -15.2 -10.1 -1.5 -5.9 -4.9 -4.9 -3.1
of C-X System
are calculated
from
(-3.2) (-2.8) (-2.5) (-2.2) (-1470) (-8.9) (-6.5) (-5.1) (-4.2) (-3.5) (-2.7)
of Ag2 are
the data of
(3)
Eqs. (2) and (3) support the expectation that Q heads are very near to the band origin, while the R heads are remote from them. Figure lb shows the Av = -2 sequence and clearly illustrates typical R-Q head separations. The vibrational constants for the X state, obtained from the Q heads, is the same as the mean value (we = 192.4 cm-‘) given by previous authors (3-6). The measurements of the well-developed vR-v# distances (Fig. 1 and Table III) in the sequences Au = + 1, 0, and -2 of lo7Ag2, together with the assumption that the position of Q heads is very near to the origin of the bands (ue - vo) provide an opportunity to re-evaluate the rotational constants for the C and X states given by Brown and Ginter (3). The observed data (Table III) for all bands were fitted by a nonlinear least-squares procedure (8) and used to derive B:, cwi, and Or::constants in the equation
v, - Uh =
IB; - (Y’(U)+ l/2) + B; - a"(~" + l/2) I2 41B; - (Y’(v’ + l/2) - B; + a"(~" + l/2)1 ’
(4)
In this fitting procedure, the value of Bz constant, obtained by semiempirical relations (7), was fixed at 0.05121 cm-‘. The resulting constants are presented in Table IV. The value of 0.05088 cm-l given by Brown and Ginter for the B: constants is smaller than the experimental value reported in Table IV. This disagreement can be explained as due to the different procedures used in the calculation. A comparison of observed and calculated differences (Y, - vi,) derived from these constants is shown in Table III. For most vibrational levels the agreement is within 0.5 cm-‘. Figure 1 demonstrates that the (8, 10) band has a single head,
32
SRDANOV AND PESIC TABLE IV Molecular Constants of lorAg, (cm-‘)
C
0.05098+0.00002a
2.220.13
X
0.05121
1.36tO.13
=see
footnote
(a), Table
II.
while (7,9) and (9,ll) bands in the same sequences have well defined double heads. The position of this band (37 075.2 cm-‘) deviates from both, calculated by Eqs. (2) and (3) for R head-37 070.5 cm-‘, and that for Q head-37 069.8 cm-‘. It appears from this that the position of this band is affected by the perturbation effect, supporting the Brown and Ginter interpretation about the perturbation of V’ = 8 in this system. CONCLUSION
In the present work, the study of isotope effect was used to confirm the emitter and improve the vibrational analysis of bands belonging to the systems E-X and C-X. The Q- and R-head separations in C-X system has led to the determination of the R:, ai and a%constants for the upper C state. The study of this separation, which was based on Brown and Ginter’s and our data, has shown the usefulness of this procedure for obtaining the molecular constants from unresolved electronic spectra. The good agreement obtained using the analysis the BE constant, calculated by semiempirical relations, corroborates the correctness of this X-state rotational constant. ACKNOWLEDGMENTS The authors would like to thank Drs. B. Vujisic and A. Antic-Jovanovic for helpful discussions. This work was supported by the Serbian Research Fund. RECEIVED:
March 26, 1981 REFERENCES
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