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Rotational analysis of the a 3Σ+-X 1Σ+ transition of CuBr enhanced by transfer from laser-excited b 3Π1 state
ChemicalPhysics North-Holland
172 (1993) 147-152
Rotational analysis of the a 3E+-X ‘C+ transition of CuBr enhanced by transfer from laser-excited b 3111state I. H&met,
C.Dufour
and B. Pinchernell
Laboratoire de Dynamique h4okulaire et Photonique, Unite de Recherche AssociPe au CNRS No. 779, Universrtk des Sciences et Technologies de Lille, UFR de Physique, B&iment PS. 59655 Villeneuve d’Ascq Cedex, France
Received 6 November 1992
The new A’ (v’ =0)-X ‘Z+ (v” = 0) transition of CuBr, recently observed (P. Kowalczyk, I. Hikmet and N. Sadeghi, Chem. Phys. 160 (1992) 73) at 504.5 nm has been rotationally analysed. Different sequences of this transition are completely overlapped by the bands of the A %-X ‘Z+ transition. The intensity of the O-Oband of the A’-X transition has been enhanced by a selective laser excitation of the O-O band of the A-X transition followed by the collisional or/and radiative transfer to the A’ state. The analysis of the partially resolved O-Oband of the AI-X transition contirms the nature ?5+ of the A’ state as expected from the comparison with the spectrum of CuF and &Cl. The derived spectroscopic constants of this state are (in cm-‘) T,,= 19820.19, Bb =0.09415, Db =0.28x 10U7,&,= 1.0, y&=0.40. It turns out that, following theconventional notation, theA'% and the A ‘l-l states are now called a %+ and b ,lI respectively.
1. Introduction The spectrum of the molecule CuBr containing four electronic transitions A-X, B-X, C-X and D-X has been studied since about 70 years [ 1,2 1. The first rotational analysis of the C ‘x+-X ‘Z+ transition was done by Rao et al. [ 31 in 1967. Mishra et al. [4] studied the rotational structure of the A ‘n-X ‘C and B Ill-X ‘E+ transitions in 198 1. Recently, a new electronic state (A’ ) located about 660 cm-’ below the A state has been reported [ 5 1. The transition AI-X ‘E+ had never been identified before, obviously because of the superposition of vibrational sequences of the two electronic transitions A-X and AI-X. One should also take into account four isotopes of CuBr formed by 63Cu (70%), 65Cu (30%), 79Br (sOoh) and 8’Br (50%) which make the spectrum more complex. The Au= 0 sequence of the AI-X transition is mixed up with the Au= -2 sequence of the A 3111-X ‘C transition. This is shown clearly by Kowalczyk et al. [ 51 who made a vibrational analysis of these transitions and by comparing the experimental spectrum
with simulated ones estimated the rotational constants of the A’ state. For the nature of this new state, a comparison was made [ 5,6 ] with CuF [ 7 ] and CuCl [ 8 ] molecules where a 3Z+ state is located below the A ‘II state. To be able to make a correct analysis of the A’-X transition, it was necessary to enhance the population of the A’, v’ = 0 level relative to the A, v’ # 0 levels. For this purpose, the A= 488.0 nm line of an Ar+ laser was used to populate selectively the vibrational level v’ =O of the A 311 state. The A’ state is populated by either a rotational or/and a radiative transfer from a higher state excited by the laser line and we obtain a relatively high O-O band intensity in the AI-X transition. By this method, the populations of the v’ > 1 of the A ‘l-l state stay very low and, consequently, the O-O band of the AI-X transition is not overlapped by the l-3 and 2-4 bands of the A-X transition. In the following text, we shall call “a” the A’ state and “b” the A 311state as usually done when states of different multiplicity than the ground state are involved in the spectrum of a molecule [ 6,9 1.
’ To whom correspondence should be addressed. 0301-0104/93/$06.00
0 1993 Elsevier Science Publishers B.V. All rights reserved.
148
I. Hikmet et al. /Chemical Physics 172 (1993) 147-152
2. Experimental details and description of the band
488.35 nm [lo]. The laser line (6 W at 487.99 nm of a coherent CR-20 Ar+ laser, tix 8 x 10m3 nm) can only populate the U’= 0 vibrational level of the b 311 state. In a first step, the 470-530 nm spectral region was recorded at low resolution to observe the influence of the laser excitation on the intensities of the b-X and a-X transitions. As expected, the bands of the Au>0 vibrational sequences of the b-X transition are very weak because their upper v’ > 0 vibrational levels can only be populated by collisional transfers. On the other hand, the Au< 0 sequences exhibit intense O-v” bands (fig. 2). This is confirmed by the observation of a high resolution spectrum (M=0.5 nm) of the Au= -2 sequence of the b-X transition where four isotopic R heads of the O-2 bands are clearly observed, but no emission of the l3 and 2-4 bands overlaps the O-O band of the a-X transition. The laser line is broad enough to populate several rotational energy levels of the v’ =O level of the b state: we estimate that the laser line populated five of the very first rotational levels (Jx 10) through the congested Q branch and about two levels of the P branch (Jz 5 ) [ 4 1. In addition, collisional transfers occur between the rotational levels of the b 311, v’ = 0 state. This is observed in the induced fluorescence spectrum of the 0- 1 band of the b-X transition where a rotational structure is followed up to Jx 100, because of the relatively long lifetime of the b 311 state ( TZ 12 ps) [ 111. The O-O band of the a-X transition is displayed over a 40 cm-’ large spectral region with intense R and Q heads.
A solid sample of CuBrz is heated to 600 K and carried out by a slow argon flow at a pressure of 2 torr in a microwave discharge, which induces a 20 cm long green post-discharge, characteristic of the excited CuBr emission. The speed of the gas flow is estimated as 5 m/s. The focused laser beam arrives vertically 20 cm downstream from the MW discharge and interacts at right angles to the gas flow (fig. 1). An intense fluorescence is obtained followed by a 1 cm long green triangular “tail” in the direction of the gas flow. The shape of the tail is due to the parabolic distribution of flow speeds of the molecules in the flow reaction. To increase the signal/noise ratio, the laser beam is reflected back by a mirror to interact twice with the molecules in the source region. The LIF signal is observed in the direction of the gas flow in order to collect the maximum fluorescence light. CuBr is produced in the off-axis arm of a Y-shaped glass tube to prevent the observation of the intense light emitted in the microwave discharge by the spectrometer. A concave mirror is set to focus the rear emitted light on the fluorescent beam. The fluorescent signal is focused on the 50 pm wide entrance slit of a double pass 1.5 m Jobin-Yvon spectrometer. It is then recorded by a PMT connected to a lock-in amplifier phased with the frequency of a mechanical chopper situated on the laser path to eliminate the back ground emission. The O-O and l- 1 red shaded bands of the b-X transition are respectively located at 487.93 and
20 cm
w
Vacuum c
*to
spectrometer
I
Vertical focused laser beam
Fig. 1. Scheme of the experimental reactor (horizontal section).
I. Hikmet et al. / Chemrcal Physics I72 (1993) 147-152
b3rl,-X’Z.+ (O-2)
149
Table 1 Matrix elements of the rotational Hamiltonian for a ‘C electronic state in case (a) coupling (x=J(J+ 1)). The 2x2 matrix with the upper sign ( + ) gives the F, and F, levels and the upper left term with the lower sign ( - ) gives the Fz level
a31+-x’II+ (0-O)
11) (11 T,+21/3-y + [B+21,/3-(2k -D(x+2&2)]x
0
_ii,
Onm
(0 1symmetric
5 1c)nm
Fig. 2. The 500-5 10 nm spectral region of CuBr (b-X: Au= - 2 sequence and a-X: Au=0 sequence). ( 1) Enhanced fluorescence. (2) Chemiluminescence emission (from ref. [ 5] ).
3. Rotational analysis The Hamiltonian of a 3X electronic state includes the rotational, the spin-spin and the spin-rotation terms and can be described by the expression [ 12,13 ]
+3n(3S2_S*)+Y(J--S)‘S.
(1)
Usually are also added the centrifugal distortion corrections on the spin-spin and spin-rotation interactions. The third order spin-spin and spin-rotation interactions [ 13 ] do not appear in the matrix of a )C state. The matrix of a 32 state is easy to write in the Hund’s case (a) basis set. The contributions of the centrifugal distortion corrections mentioned above (parameters AD and yb) are determined by a matrix multiplication as described by Amiot et al. [ 14 1. Table 1 summarizes the terms of a 3C matrix in the Hund’s case (a) coupling. The transition between a ‘C state and a ‘Z state depends on the symmetry of the states. If the two states are isosymmetric, four branches are observed [ 7 1. If the symmetries are different, five branches are present [ l&l6 ] and this does not depend on the relative
IO>
l)y,
Jx [ -2B+22,/3 +y+yb(x+4) +4D(x+l)] T,-4n/3-2y + (B-41,/3)(x+2) -4yu(x+l)-D(x2+8x+4)
position of the states in the transition (‘C-‘C or ‘C-3X). Both experimental [ 71 and theoretical analyses [ 17 ] on CuF suggest that the ‘Z and the ‘X states are of the same positive symmetry. A characteristic of a C state of odd multiplicity equal to or larger than three is that one of the fine-structure levels is not affected by a spin-rotation interaction with the other levels. This is illustrated in fig. 6 of ref. [ 13 ] for the A ?E state of CrO and fig. 5 of ref. [ 71 for the a 3C+ state of CuF. For this reason, it is possible to disconnect completely the F2 (a= 1) level from the two others in a ‘C state, as it was done by Fink et al. [ 161, and to analyse the ‘X ( F2)-‘C transition as a ‘L’C transition. When the rotational constants B” and D” of the ground state are known, it is very easy to identify the R2 and P2 branches arising from the F2 level even if, as observed here, the R2 branch is not resolved and to deduce the values of the rotational constants of the 3C state. Whatever the fine structure parameters 1 and y are, the F3 level is always close to the F2 level and gives rise to a single unheaded Q3 branch with the ground state (B’
150
I. Hikmet et al. /Chemical Physics I72 (1993) 147-1.52
Table 2 Assigned rotational lines of the a ‘x+-X ‘Z+ (0, 0) band of 63Cu79Brin cm-’ (numbers in parentheses are the observed-calculated differences)
J
P2
6 7 8 9 10
19818.98(-4) 19818.79(5) 19818.47(5) 19818.12(2) 19817.73(-3) 19817.45(4) 19817.06(2) 19816.70(5) 19816.27(2) 19815.84(O) 19815.37( -3) 19814.94( -2) 19814.50(O) 19813.99( -2) 19813.48( -4) 19812.97(-5) 19812.50(O) 19811.91(-5) 19811.36(-5) 19810.78( -6) 19810.27( - 1) 19809.60( -6) 19809.01(-6) 19808.42( -2) 19807.83(2) 19807.20(5) 19806.54(5)
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
19796.38( -4) 19795.52( -3) 19794.61(-4) 19793.79(3) 19792.89(5) 19791.91(O) 19791.01(5) 19790.03(4) 19789.05(3) 19788.03(l) 19787.05(3) 19785.99(O) 19784.90( -5) 19783.92(l) 19782.86(l) 19781.69(-6) 19780.67(O)
43
Rz
QI
19821.02(O) (head) 19821.81(6) (head)
19799.17(-5) 19798.34( -7) 19797.56(-2) 19796.77( 1) 19795.91(l) 19795.13(6) 19794.15(O) 19793.25(O) 19792.31(-2) 19791.48(6) 19790.50(2) 19789.52(O) 19788.55(O) 19787.64(6) 19786.51(-5) 19785.45(-6) 19784.55(3) 19783.46( - 1)
I. Hikmet et al. /Chemical Physics I72 (1993) 147-152
branch are identified for the 63Cu7gBr molecule (table 2). They cannot be confused with lines of the P branch arising from the 63Cu81Br molecule, because the wavenumbers of the lines of this branch calculated with the isotopic constants [ 9 ] do not coincide with the experimental values. The determination of the A and y tine structure parameters requires two equations using the wavenumbers of the rotational lines of the two branches Q, and Q3. The value of A is strongly sensitive to the location of the Qi band which is unfortunately unresolved. The only available information is the position of its head which cannot be determined precisely. Moreover, the spin-rotation parameter y is heavily correlated to A in the fitting procedure. In a first step, we built a table to estimate the values of 1 and y reproducing the experimental location of the Q, head. Then, we introduced the wavenumber of the Q, head in the fit allowing the five parameters (T,, B, D, A and y) of the upper 3Z+ state to be adjusted. The constants of the a ‘Z+ state of 63Cu7gBr are summarized in table 3. To take into account the non-determination of the location of the Q, band-head, the uncertainties on A and y are taken equal to 30~.
4. Discussion The interest of this work was to confirm the ‘Z+ nature of the CuBr(a) state reported previously by Kowalczyk et al. [ 5 ] through the identification of the four expected branches for a ‘Z+-‘E+ transition. If we consider the energy diagram of the electronic states already known of CuF, CuCl and CuBr [ 19,201, the energy of a given state increases with the atomic weight of the halogen associated to Cu. This is also true for the ‘Z+ state of CuF ( 14580 cm- ’ ) and CuBr ( 19820 cm-’ ) but not for CuCl where the transition analysed by Balfour and Ram [ 8 1, lies at 13 500 cm- ‘. We remark that the Qi branch of this transition has not been observed yet.
151
When a C state is far from any other state the spinrotation parameter y is small and can be considered as characteristic of the true spin-rotation interaction. This is usually observed when a ‘Z state is the ground state of a diatomic molecule, for example in PBr, Colin [ 151 found y= - 0.007 1 cm-’ for the X ‘I; state. On the other hand, when a C state is close to other electronic states, “it is well known [ 12,2 1 ] that the parameter y is the sum of the true spin-rotation interaction and a second-order spin-orbit term involving II states of the same multiplicity: yS.o=-2(CIAL_
Il-I)(lIlBL+
IX)”
(2)
(quoted from ref. [ 13 ] ) . The large experimental value of y is certainly related to the proximity of the b 311state (A&.x = 700 cm-’ ). If we compare with CuF, for which a study of the structure of the electronic states has been performed [ 171, the b 311 and the close lying 3Z+ states are assigned to a single structure Cu+ ( 3dg4s)F- ( 2p6) and differ by molecular orbitals localised on the 3d shell of the copper atom. The model of the pure procession discussed by Mulliken and Christy [ 2 1] for ‘II or ‘II states can be used to interpret the contribution to the effective value of the line structure parameters y of a C state induced by the interaction of a close-lying electronic II state. Brown and Merer [22] suggest that the methods developped by Mulliken and Christy can be extended to states of higher multiplicity. If we use the well known expression [21] (3)
En-&
with the estimated spin-orbit constant A = 400 cm- ’ which is roughly half of the spin-orbit parameter of the copper atom <3d=813 cm-’ [ 171, B=O.l cm-‘, 1~2 (for the 3d atomic orbital) and En-E,=700 cm-‘, we obtain ~~50.6 cm-‘. This value is of the order of magnitude with the experimental value (~~0.40 cm-‘). The difference could be explained
Table 3 Molecular constants (in cm-‘) for the %+ state of 63Cu79Br(uncertainties are 3a for To, B0 and Do; see text for 1, and p,) TO
Bo
D,, (x10’)
10
Yo
19820.19(l)
0.09415(5)
0.28(4)
1.0(2)
0.40( 1)
152
I. Hikmet et al. /Chemical Physics 172 (1993) 147-152
by the contribution of the 4p6 atomic shell of Br inducing an effective value of 1smaller than 2. The value of A is small compared to those observed in CuF for which A=43 cm-’ [ 71. The theoretical literature is poor in information about the origin of this parameter which leads ?Z states to obey to the Hund’s coupling case (a) rather than the expected case (b) for Z states. No correlation can be made with the value of y; for example, in Se0 [ 161, for the ground 31Zstate, the fine structure parameters are y= -0.00656 cm-’ and ;I= 84.11 cm-‘. For this molecule it is easy to interpret the small value of y by the absence of any close-lying interacting 31Tstate from the ground state. The value of 1 seems not to be sensitive to the presence of close-lying states.
5. Conclusion The rotational analysis of the a 3C state of CuBr has been made possible by a very simple experiment, in which the population of the U> 0 levels of the b state were kept low to reduce dramatically the contamination of the a-X transition by the b-X lines. The rather low resolution would be overcome if the experiment could be done in a molecular beam. The low rotational temperature could then allow to observe the very first lines of the unresolved Rz and Q, branches and simultaneously reduce the Doppler broadening. Nevertheless, there is now no doubt that the a state of CuBr is a 3C+ state as suggested by the comparison with CuF and CuCl [ 6 1. The value of the effective spin-rotation parameter y of the a3C+ state is compatible with the pure procession model characteristic of an interaction with the b 3TI state.
Acknowledgement We thank Dr. Nader Sadeghi for his interest in this work and helpful comments on the manuscript.
References [ 11 R. Ritschl, Z. Physik 42 ( 1927) 172. [ 2 ] P.R. Rao and K.V.S.R. Apparao, Proc. Indian Acad. Sci. A 60 (1964) 57. [3] P.R. Rao and K.V.S.R. Apparao, Can. J. Phys. 45 (1967) 2805. [4] G.P. Mishra, R. Tripathi, S.B. Rai, K.N. Upadhya and D.K. Rai, J. Mol. Spectry. 85 ( 198 1) 245. [ 5 1P. Kowalczyk, I. Hikmet and N. Sadeghi, Chem. Phys. 160 (1992) 73. [6] N. Sadeght, I. Hikmet, I. Colomb and D.W. Setser, Chem. Phys., in press. [7] F. Ahmed, R.F. Barrow, A.H. Chojnicki, C. Dufour and J. Schamps, J. Phys. B 15 (1982) 3801. [8] W.J. Balfour and R.S. Ram, J. Phys. B 17 (1984) L19. [ 91 G. Herzberg, Spectra of diatomic molecules, 2nd Ed. (Van Nostrand, Princeton, 1950). [ 10] B. Rosen, Spectroscopic data relative to diatomic molecules (Pergamon Press, Oxford, 1970). [ 111 I. Hikmet, P. Kowalczyk and N. Sadeghi, Chem. Phys. Letters 188 (1992) 287. [ 121 J.H. Van Vleck, Rev. Mod. Phys. 23 (1951) 213. [ 131 A.S.C. Cheung, W. Zymicki and A.J. Merer, J. Mol. Spectry. 104 (1984) 315. [ 141 C. Amiot, J.P. Maillard and J. Chauville, J. Mol. Spectry. 87 (1981) 196. [ 151 R. Colin, Can. J. Phys. 57 (1979) 1051. [ 16 ] E.H. Fink, K.D. Setzer, D.A. Ramsay and M. Vervloet, J. Mol. Spectry. 125 (1987) 66. [ 171 C. Dufour, J. Schamps and R.F. Barrow, J. Phys. B 15 (1982) 3819. 1’8 E.L. Manson, F.C. de Lucia and W. Gordy, J. Chem. Phys. 63 (1975) 2724. 1’9 1 C. Dufour, Thesis, University of Lille I, France ( 1987). Constants of diatomic [20 K.P. Huber and G. Herzberg, molecules (Van Nostrand Reinhold, New York, 1979). [21 R.S. Mulliken and A. Christy, Phys. Rev. 38 ( 1931) 87. [22 1J.M. Brown and A.J. Merer, J. Mol. Spectry. 74 (1979) 488.
172 (1993) 147-152
Rotational analysis of the a 3E+-X ‘C+ transition of CuBr enhanced by transfer from laser-excited b 3111state I. H&met,
C.Dufour
and B. Pinchernell
Laboratoire de Dynamique h4okulaire et Photonique, Unite de Recherche AssociPe au CNRS No. 779, Universrtk des Sciences et Technologies de Lille, UFR de Physique, B&iment PS. 59655 Villeneuve d’Ascq Cedex, France
Received 6 November 1992
The new A’ (v’ =0)-X ‘Z+ (v” = 0) transition of CuBr, recently observed (P. Kowalczyk, I. Hikmet and N. Sadeghi, Chem. Phys. 160 (1992) 73) at 504.5 nm has been rotationally analysed. Different sequences of this transition are completely overlapped by the bands of the A %-X ‘Z+ transition. The intensity of the O-Oband of the A’-X transition has been enhanced by a selective laser excitation of the O-O band of the A-X transition followed by the collisional or/and radiative transfer to the A’ state. The analysis of the partially resolved O-Oband of the AI-X transition contirms the nature ?5+ of the A’ state as expected from the comparison with the spectrum of CuF and &Cl. The derived spectroscopic constants of this state are (in cm-‘) T,,= 19820.19, Bb =0.09415, Db =0.28x 10U7,&,= 1.0, y&=0.40. It turns out that, following theconventional notation, theA'% and the A ‘l-l states are now called a %+ and b ,lI respectively.
1. Introduction The spectrum of the molecule CuBr containing four electronic transitions A-X, B-X, C-X and D-X has been studied since about 70 years [ 1,2 1. The first rotational analysis of the C ‘x+-X ‘Z+ transition was done by Rao et al. [ 31 in 1967. Mishra et al. [4] studied the rotational structure of the A ‘n-X ‘C and B Ill-X ‘E+ transitions in 198 1. Recently, a new electronic state (A’ ) located about 660 cm-’ below the A state has been reported [ 5 1. The transition AI-X ‘E+ had never been identified before, obviously because of the superposition of vibrational sequences of the two electronic transitions A-X and AI-X. One should also take into account four isotopes of CuBr formed by 63Cu (70%), 65Cu (30%), 79Br (sOoh) and 8’Br (50%) which make the spectrum more complex. The Au= 0 sequence of the AI-X transition is mixed up with the Au= -2 sequence of the A 3111-X ‘C transition. This is shown clearly by Kowalczyk et al. [ 51 who made a vibrational analysis of these transitions and by comparing the experimental spectrum
with simulated ones estimated the rotational constants of the A’ state. For the nature of this new state, a comparison was made [ 5,6 ] with CuF [ 7 ] and CuCl [ 8 ] molecules where a 3Z+ state is located below the A ‘II state. To be able to make a correct analysis of the A’-X transition, it was necessary to enhance the population of the A’, v’ = 0 level relative to the A, v’ # 0 levels. For this purpose, the A= 488.0 nm line of an Ar+ laser was used to populate selectively the vibrational level v’ =O of the A 311 state. The A’ state is populated by either a rotational or/and a radiative transfer from a higher state excited by the laser line and we obtain a relatively high O-O band intensity in the AI-X transition. By this method, the populations of the v’ > 1 of the A ‘l-l state stay very low and, consequently, the O-O band of the AI-X transition is not overlapped by the l-3 and 2-4 bands of the A-X transition. In the following text, we shall call “a” the A’ state and “b” the A 311state as usually done when states of different multiplicity than the ground state are involved in the spectrum of a molecule [ 6,9 1.
’ To whom correspondence should be addressed. 0301-0104/93/$06.00
0 1993 Elsevier Science Publishers B.V. All rights reserved.
148
I. Hikmet et al. /Chemical Physics 172 (1993) 147-152
2. Experimental details and description of the band
488.35 nm [lo]. The laser line (6 W at 487.99 nm of a coherent CR-20 Ar+ laser, tix 8 x 10m3 nm) can only populate the U’= 0 vibrational level of the b 311 state. In a first step, the 470-530 nm spectral region was recorded at low resolution to observe the influence of the laser excitation on the intensities of the b-X and a-X transitions. As expected, the bands of the Au>0 vibrational sequences of the b-X transition are very weak because their upper v’ > 0 vibrational levels can only be populated by collisional transfers. On the other hand, the Au< 0 sequences exhibit intense O-v” bands (fig. 2). This is confirmed by the observation of a high resolution spectrum (M=0.5 nm) of the Au= -2 sequence of the b-X transition where four isotopic R heads of the O-2 bands are clearly observed, but no emission of the l3 and 2-4 bands overlaps the O-O band of the a-X transition. The laser line is broad enough to populate several rotational energy levels of the v’ =O level of the b state: we estimate that the laser line populated five of the very first rotational levels (Jx 10) through the congested Q branch and about two levels of the P branch (Jz 5 ) [ 4 1. In addition, collisional transfers occur between the rotational levels of the b 311, v’ = 0 state. This is observed in the induced fluorescence spectrum of the 0- 1 band of the b-X transition where a rotational structure is followed up to Jx 100, because of the relatively long lifetime of the b 311 state ( TZ 12 ps) [ 111. The O-O band of the a-X transition is displayed over a 40 cm-’ large spectral region with intense R and Q heads.
A solid sample of CuBrz is heated to 600 K and carried out by a slow argon flow at a pressure of 2 torr in a microwave discharge, which induces a 20 cm long green post-discharge, characteristic of the excited CuBr emission. The speed of the gas flow is estimated as 5 m/s. The focused laser beam arrives vertically 20 cm downstream from the MW discharge and interacts at right angles to the gas flow (fig. 1). An intense fluorescence is obtained followed by a 1 cm long green triangular “tail” in the direction of the gas flow. The shape of the tail is due to the parabolic distribution of flow speeds of the molecules in the flow reaction. To increase the signal/noise ratio, the laser beam is reflected back by a mirror to interact twice with the molecules in the source region. The LIF signal is observed in the direction of the gas flow in order to collect the maximum fluorescence light. CuBr is produced in the off-axis arm of a Y-shaped glass tube to prevent the observation of the intense light emitted in the microwave discharge by the spectrometer. A concave mirror is set to focus the rear emitted light on the fluorescent beam. The fluorescent signal is focused on the 50 pm wide entrance slit of a double pass 1.5 m Jobin-Yvon spectrometer. It is then recorded by a PMT connected to a lock-in amplifier phased with the frequency of a mechanical chopper situated on the laser path to eliminate the back ground emission. The O-O and l- 1 red shaded bands of the b-X transition are respectively located at 487.93 and
20 cm
w
Vacuum c
*to
spectrometer
I
Vertical focused laser beam
Fig. 1. Scheme of the experimental reactor (horizontal section).
I. Hikmet et al. / Chemrcal Physics I72 (1993) 147-152
b3rl,-X’Z.+ (O-2)
149
Table 1 Matrix elements of the rotational Hamiltonian for a ‘C electronic state in case (a) coupling (x=J(J+ 1)). The 2x2 matrix with the upper sign ( + ) gives the F, and F, levels and the upper left term with the lower sign ( - ) gives the Fz level
a31+-x’II+ (0-O)
11) (11 T,+21/3-y + [B+21,/3-(2k -D(x+2&2)]x
0
_ii,
Onm
(0 1symmetric
5 1c)nm
Fig. 2. The 500-5 10 nm spectral region of CuBr (b-X: Au= - 2 sequence and a-X: Au=0 sequence). ( 1) Enhanced fluorescence. (2) Chemiluminescence emission (from ref. [ 5] ).
3. Rotational analysis The Hamiltonian of a 3X electronic state includes the rotational, the spin-spin and the spin-rotation terms and can be described by the expression [ 12,13 ]
+3n(3S2_S*)+Y(J--S)‘S.
(1)
Usually are also added the centrifugal distortion corrections on the spin-spin and spin-rotation interactions. The third order spin-spin and spin-rotation interactions [ 13 ] do not appear in the matrix of a )C state. The matrix of a 32 state is easy to write in the Hund’s case (a) basis set. The contributions of the centrifugal distortion corrections mentioned above (parameters AD and yb) are determined by a matrix multiplication as described by Amiot et al. [ 14 1. Table 1 summarizes the terms of a 3C matrix in the Hund’s case (a) coupling. The transition between a ‘C state and a ‘Z state depends on the symmetry of the states. If the two states are isosymmetric, four branches are observed [ 7 1. If the symmetries are different, five branches are present [ l&l6 ] and this does not depend on the relative
IO>
l)y,
Jx [ -2B+22,/3 +y+yb(x+4) +4D(x+l)] T,-4n/3-2y + (B-41,/3)(x+2) -4yu(x+l)-D(x2+8x+4)
position of the states in the transition (‘C-‘C or ‘C-3X). Both experimental [ 71 and theoretical analyses [ 17 ] on CuF suggest that the ‘Z and the ‘X states are of the same positive symmetry. A characteristic of a C state of odd multiplicity equal to or larger than three is that one of the fine-structure levels is not affected by a spin-rotation interaction with the other levels. This is illustrated in fig. 6 of ref. [ 13 ] for the A ?E state of CrO and fig. 5 of ref. [ 71 for the a 3C+ state of CuF. For this reason, it is possible to disconnect completely the F2 (a= 1) level from the two others in a ‘C state, as it was done by Fink et al. [ 161, and to analyse the ‘X ( F2)-‘C transition as a ‘L’C transition. When the rotational constants B” and D” of the ground state are known, it is very easy to identify the R2 and P2 branches arising from the F2 level even if, as observed here, the R2 branch is not resolved and to deduce the values of the rotational constants of the 3C state. Whatever the fine structure parameters 1 and y are, the F3 level is always close to the F2 level and gives rise to a single unheaded Q3 branch with the ground state (B’
150
I. Hikmet et al. /Chemical Physics I72 (1993) 147-1.52
Table 2 Assigned rotational lines of the a ‘x+-X ‘Z+ (0, 0) band of 63Cu79Brin cm-’ (numbers in parentheses are the observed-calculated differences)
J
P2
6 7 8 9 10
19818.98(-4) 19818.79(5) 19818.47(5) 19818.12(2) 19817.73(-3) 19817.45(4) 19817.06(2) 19816.70(5) 19816.27(2) 19815.84(O) 19815.37( -3) 19814.94( -2) 19814.50(O) 19813.99( -2) 19813.48( -4) 19812.97(-5) 19812.50(O) 19811.91(-5) 19811.36(-5) 19810.78( -6) 19810.27( - 1) 19809.60( -6) 19809.01(-6) 19808.42( -2) 19807.83(2) 19807.20(5) 19806.54(5)
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
19796.38( -4) 19795.52( -3) 19794.61(-4) 19793.79(3) 19792.89(5) 19791.91(O) 19791.01(5) 19790.03(4) 19789.05(3) 19788.03(l) 19787.05(3) 19785.99(O) 19784.90( -5) 19783.92(l) 19782.86(l) 19781.69(-6) 19780.67(O)
43
Rz
QI
19821.02(O) (head) 19821.81(6) (head)
19799.17(-5) 19798.34( -7) 19797.56(-2) 19796.77( 1) 19795.91(l) 19795.13(6) 19794.15(O) 19793.25(O) 19792.31(-2) 19791.48(6) 19790.50(2) 19789.52(O) 19788.55(O) 19787.64(6) 19786.51(-5) 19785.45(-6) 19784.55(3) 19783.46( - 1)
I. Hikmet et al. /Chemical Physics I72 (1993) 147-152
branch are identified for the 63Cu7gBr molecule (table 2). They cannot be confused with lines of the P branch arising from the 63Cu81Br molecule, because the wavenumbers of the lines of this branch calculated with the isotopic constants [ 9 ] do not coincide with the experimental values. The determination of the A and y tine structure parameters requires two equations using the wavenumbers of the rotational lines of the two branches Q, and Q3. The value of A is strongly sensitive to the location of the Qi band which is unfortunately unresolved. The only available information is the position of its head which cannot be determined precisely. Moreover, the spin-rotation parameter y is heavily correlated to A in the fitting procedure. In a first step, we built a table to estimate the values of 1 and y reproducing the experimental location of the Q, head. Then, we introduced the wavenumber of the Q, head in the fit allowing the five parameters (T,, B, D, A and y) of the upper 3Z+ state to be adjusted. The constants of the a ‘Z+ state of 63Cu7gBr are summarized in table 3. To take into account the non-determination of the location of the Q, band-head, the uncertainties on A and y are taken equal to 30~.
4. Discussion The interest of this work was to confirm the ‘Z+ nature of the CuBr(a) state reported previously by Kowalczyk et al. [ 5 ] through the identification of the four expected branches for a ‘Z+-‘E+ transition. If we consider the energy diagram of the electronic states already known of CuF, CuCl and CuBr [ 19,201, the energy of a given state increases with the atomic weight of the halogen associated to Cu. This is also true for the ‘Z+ state of CuF ( 14580 cm- ’ ) and CuBr ( 19820 cm-’ ) but not for CuCl where the transition analysed by Balfour and Ram [ 8 1, lies at 13 500 cm- ‘. We remark that the Qi branch of this transition has not been observed yet.
151
When a C state is far from any other state the spinrotation parameter y is small and can be considered as characteristic of the true spin-rotation interaction. This is usually observed when a ‘Z state is the ground state of a diatomic molecule, for example in PBr, Colin [ 151 found y= - 0.007 1 cm-’ for the X ‘I; state. On the other hand, when a C state is close to other electronic states, “it is well known [ 12,2 1 ] that the parameter y is the sum of the true spin-rotation interaction and a second-order spin-orbit term involving II states of the same multiplicity: yS.o=-2(CIAL_
Il-I)(lIlBL+
IX)”
(2)
(quoted from ref. [ 13 ] ) . The large experimental value of y is certainly related to the proximity of the b 311state (A&.x = 700 cm-’ ). If we compare with CuF, for which a study of the structure of the electronic states has been performed [ 171, the b 311 and the close lying 3Z+ states are assigned to a single structure Cu+ ( 3dg4s)F- ( 2p6) and differ by molecular orbitals localised on the 3d shell of the copper atom. The model of the pure procession discussed by Mulliken and Christy [ 2 1] for ‘II or ‘II states can be used to interpret the contribution to the effective value of the line structure parameters y of a C state induced by the interaction of a close-lying electronic II state. Brown and Merer [22] suggest that the methods developped by Mulliken and Christy can be extended to states of higher multiplicity. If we use the well known expression [21] (3)
En-&
with the estimated spin-orbit constant A = 400 cm- ’ which is roughly half of the spin-orbit parameter of the copper atom <3d=813 cm-’ [ 171, B=O.l cm-‘, 1~2 (for the 3d atomic orbital) and En-E,=700 cm-‘, we obtain ~~50.6 cm-‘. This value is of the order of magnitude with the experimental value (~~0.40 cm-‘). The difference could be explained
Table 3 Molecular constants (in cm-‘) for the %+ state of 63Cu79Br(uncertainties are 3a for To, B0 and Do; see text for 1, and p,) TO
Bo
D,, (x10’)
10
Yo
19820.19(l)
0.09415(5)
0.28(4)
1.0(2)
0.40( 1)
152
I. Hikmet et al. /Chemical Physics 172 (1993) 147-152
by the contribution of the 4p6 atomic shell of Br inducing an effective value of 1smaller than 2. The value of A is small compared to those observed in CuF for which A=43 cm-’ [ 71. The theoretical literature is poor in information about the origin of this parameter which leads ?Z states to obey to the Hund’s coupling case (a) rather than the expected case (b) for Z states. No correlation can be made with the value of y; for example, in Se0 [ 161, for the ground 31Zstate, the fine structure parameters are y= -0.00656 cm-’ and ;I= 84.11 cm-‘. For this molecule it is easy to interpret the small value of y by the absence of any close-lying interacting 31Tstate from the ground state. The value of 1 seems not to be sensitive to the presence of close-lying states.
5. Conclusion The rotational analysis of the a 3C state of CuBr has been made possible by a very simple experiment, in which the population of the U> 0 levels of the b state were kept low to reduce dramatically the contamination of the a-X transition by the b-X lines. The rather low resolution would be overcome if the experiment could be done in a molecular beam. The low rotational temperature could then allow to observe the very first lines of the unresolved Rz and Q, branches and simultaneously reduce the Doppler broadening. Nevertheless, there is now no doubt that the a state of CuBr is a 3C+ state as suggested by the comparison with CuF and CuCl [ 6 1. The value of the effective spin-rotation parameter y of the a3C+ state is compatible with the pure procession model characteristic of an interaction with the b 3TI state.
Acknowledgement We thank Dr. Nader Sadeghi for his interest in this work and helpful comments on the manuscript.
References [ 11 R. Ritschl, Z. Physik 42 ( 1927) 172. [ 2 ] P.R. Rao and K.V.S.R. Apparao, Proc. Indian Acad. Sci. A 60 (1964) 57. [3] P.R. Rao and K.V.S.R. Apparao, Can. J. Phys. 45 (1967) 2805. [4] G.P. Mishra, R. Tripathi, S.B. Rai, K.N. Upadhya and D.K. Rai, J. Mol. Spectry. 85 ( 198 1) 245. [ 5 1P. Kowalczyk, I. Hikmet and N. Sadeghi, Chem. Phys. 160 (1992) 73. [6] N. Sadeght, I. Hikmet, I. Colomb and D.W. Setser, Chem. Phys., in press. [7] F. Ahmed, R.F. Barrow, A.H. Chojnicki, C. Dufour and J. Schamps, J. Phys. B 15 (1982) 3801. [8] W.J. Balfour and R.S. Ram, J. Phys. B 17 (1984) L19. [ 91 G. Herzberg, Spectra of diatomic molecules, 2nd Ed. (Van Nostrand, Princeton, 1950). [ 10] B. Rosen, Spectroscopic data relative to diatomic molecules (Pergamon Press, Oxford, 1970). [ 111 I. Hikmet, P. Kowalczyk and N. Sadeghi, Chem. Phys. Letters 188 (1992) 287. [ 121 J.H. Van Vleck, Rev. Mod. Phys. 23 (1951) 213. [ 131 A.S.C. Cheung, W. Zymicki and A.J. Merer, J. Mol. Spectry. 104 (1984) 315. [ 141 C. Amiot, J.P. Maillard and J. Chauville, J. Mol. Spectry. 87 (1981) 196. [ 151 R. Colin, Can. J. Phys. 57 (1979) 1051. [ 16 ] E.H. Fink, K.D. Setzer, D.A. Ramsay and M. Vervloet, J. Mol. Spectry. 125 (1987) 66. [ 171 C. Dufour, J. Schamps and R.F. Barrow, J. Phys. B 15 (1982) 3819. 1’8 E.L. Manson, F.C. de Lucia and W. Gordy, J. Chem. Phys. 63 (1975) 2724. 1’9 1 C. Dufour, Thesis, University of Lille I, France ( 1987). Constants of diatomic [20 K.P. Huber and G. Herzberg, molecules (Van Nostrand Reinhold, New York, 1979). [21 R.S. Mulliken and A. Christy, Phys. Rev. 38 ( 1931) 87. [22 1J.M. Brown and A.J. Merer, J. Mol. Spectry. 74 (1979) 488.