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Reinvestigation of the A6Σ+-X6Σ+ transition of MnS: Analysis of the fine and hyperfine structures
JOURNAL OF MOLECULAR SPECTROSCOPY
129,47 l-482 (1988)
Reinvestigation of the A62’-X6Z+ Transition of MnS: Analysis of the Fine and Hyperfine Structures M. DOUAY, C. DUFOUR, AND B. PINCHEMEL Laboratoire de SpectroscopicMoltkuiaire, Unite’am&e au C.N.R.S. No. 779, Universitede Lilie Flandres Artois, UFR de Physique, BWnent PS, 59655 Villeneuved’Ascq Cedex, France TheA*Z’-x62+ (O-l) bandof MnShasbeenreinvestigated using SubDoppler laserspectroscopy. The 12 branches of the transition have been identified with the help of the pattern of the hyperhne structure. All the lines have been fitted simultaneously. It has been necessary to take into account the second-order spin-spin interaction (parameter 0) to explain the fine structure of the transition. The observation of a few extra lines in the perturbed region allowed a determination of the rotational constant of the perturbing state. The hyperhne constant b’ (k%+ state) has been ds ternlined. Q 1988 Academic PBS, Inc. 1. INTRODUCTION
In a recent paper (Z), we published a rotational analysis of three bands (O-O, O-l, and O-3) of the A’??+-X62+ transition of MnS. This analysis was based on spectra recorded using grating spectroscopy and Doppler-limited laser spectroscopy. The second technique allowed us to partially resolve the congested spectrum of the transition which exhibits six P branches and six R branches arising from the fine structure of the two electronic states. The manganese atom has a nuclear spin Z = $ which splits each of the electron spin sublevels of the two electronic states into six hyperhne levels. In a ‘% state belonging to a pure case (bar) coupling the six fine-structure sublevels of a given rotational level exhibit different hyperfme patterns which are in the ratios 1:3:5 (2, 3) (Fig. 1). It is well known that in a parallel transition such as a %-%, for which AN = AJ = A F = f 1, the lines adopt relative locations which are similar to the positions of the energy levels. This explains why in our previous analysis (I), only four branches (R3, P3, R4, P4) were intense enough to be easily observed in our spectra: their narrow hyperhne structures (HFS) give comparatively strong sharp lines at Doppler-limited resolution for the R3, P3, R4, and P4 lines. The hyper6ne structure in the other eight branches is spread out over a much larger space (up to 0.17 cm-i). Consequently it was difficult to identify these broad weak lines and moreover the overlaps induced spurious line-like regions of higher intensity with no obvious meaning In order to overcome the Doppler broadening we have recorded the O-l band over a range of 70 cm-’ by inter-modulated fluorescence (4). Under these conditions almost 500 lines (neglecting the HFS) belonging to the 12 branches have been identified and fitted simultaneously. The main feature of a high multiplicity electronic state is its fine structure which can be accounted for by two interactions, the spin-spin (parameter A)and the spin-rotation (parameter y). Generally these two parameters are sufficient to explain the fine structure (2) of a 62-62 transition but in the case of MnS we had 471
0022-2852/88 $3.00 Copyright0 1988 by Academic Press, Inc. All rights of reproduction
in any form m?swd.
472
DOUAY,
DUFOUR,
AND
PINCHEMEL
to take into account the higher order parameters: 0 (spin-spin) and ys (spin-rotation). To our knowledge it is the first time that the 0 parameter has been observed in a ‘Z?Z transition. In addition to this analysis we observed several local rotational perturbations. For one of them the presence of extra lines allowed us to estimate the B value of the perturbing state. From the hyperfine structure a value of the parameter b of the upper state has been calculated. 2. EXPERIMENTAL
DETAILS
In order to record the sub-Doppler spectrum of the A%??-X6C+ (0- 1) transition of MnS we used the well-known experimental method described by Sorem and Schawlow (4). The source, a Broida-type oven (5), has been already described in our previous paper (I). Great care was taken to reduce the scattered laser light and the emission of incandescent particles arising from the crucible. In order to increase the fluorescence signal, the oxidant gas (OCS) was injected directly into the crucible. We observed that the chemical reaction between the manganese atoms and OCS was enhanced when it occurred at high temperature (1300 K). In order to limit the linewidth, we reduced the amount of carrier gas (argon) to obtain a total pressure equal to 0.5 Torr; at a lower pressure the fluorescence signal was too weak to be recorded with a satisfactory signal-to-noise ratio. The dye laser (Coherent Inc., Model 699-29) running with rhodamine 110, delivered a total power of about 200 mW. A Glan-Thompson polarizer associated with a quarter wave retarder plate and a half-silvered mirror was used to obtain two laser beams of equal intensity and to avoid feedback of the beam into the laser cavity. The intermodulated signal was detected with a cooled Hamamatsu 928 photomultiplier tube and an associated lock-in amplifier. The signal was then recorded on a three pen chart recorder and simultaneously stored in the memory of the computer which controls the dye laser. The spectrum of I2 (6, 7) together with fringes from a 750-MHz confocal Fabry-Perot interferometer was used for the calibration. 3. ROTATIONAL
ANALYSIS
Up to now only a few high-multiplicity electronic transitions have been fully analyzed. During the last decade, A. J. Merer has performed pioneering work on such electronic states, involved in the spectra of the transition element oxides, to which this paper is largely indebted. It is not necessary here to describe extensively the fine and hyperfine energy level expressions because the frame of the present analysis is based on the theory sections of the papers devoted to the A6Z+-X6Z+ transition of MnO (3) and the C4Z--X4Z- transition of VO (8) by Merer d al. In these papers the Hamiltonians responsible for the fine and hyperfme structures are described and the corresponding matrix elements are derived. Therefore we will only develop here the parts of a ‘?Y state matrix corresponding to the second-order spin-spin and spinrotation interactions and their associated centrifugal distortions. Compared to the spectra of the two previously quoted transitions of MnO and VO, the spectrum of the MnS A6Z+-X6x+ (O-l) band is characterized by its regularity. Each pair of branches Pi and Ri (i = 1 to 6) can be fitted individually (when the few
A??+-X62+
(O-l)
BAND OF MnS
473
rotationally perturbed lines are excluded from the fit), and the six resulting sets of rotational constants B and D are in good agreement with the values published in Ref. (1). In the formalism of Hund’s case (b) the fine structure, which splits each rotational energy level N into six components F, (J = N + $), Fi (J = N + $), F3 (J = N + $), F4 (J = N - f), F5 (J = N - $), and F6 (J = N - $), arisesmainly from spinorbit interactions of the states of interest with neighboring states according to the selection rules AA = 0, ?I, AS = 0, +l as discussed in Ref. (1). These interactions have the same form as the direct internal spin-spin (parameter X) and spin-rotation (parameter y) interactions (8,9). In this paper, for the sake of clarity, we will use these two symbols as is generally done in the literature. The selection rules AN = AJ = f 1 imply that each experimental line links two levels F$ and F;. For a given value of N we will observe 12 lines (6 R and 6 P). It is obvious that the relative positions of these lines must look like the spin fine structure of a hypothetical % state whose spin-spin and spin-rotation parameters would be X = X’- X”and y = y ’ - y”, respectively. In the absence of additional information such as extra lines (3,8), the individual values of Xand y in each state cannot be determined. As we have already explained in the Introduction the HFS allows us to identify the nature of the branches (3 or 4), (2 or 5), and (1 or 6) (Fig. 1). The relative effects of X and y are very easy to distinguish when the states are in pure case (b), which always occurs for the high values of N. Let us consider first the spin-spin interaction. For a given value of N the six sublevels form three close pairs almost regardless of the value of N. Figure 3 of Ref. (10) gives some examples of the spin-spin interaction. In a first approximation the diagonal elements of the matrix of a %Zstate in the case (b) basis also give a good idea of the influence of X on the fine structure (Ref. 3, Table 2). An interesting feature is the asymmetry in the positions of the three pairs: the distances between the pairs (3, 4), (2, 5), and (1, 6) are respectively in the ratio 1:2. A good example can be found in Fig. 1 of Ref. (3). Ricking for example the R (N = 22) lines in the 1-O band of MnO we observe that the splitting is about 1.42 cm-’ between the (3, 4) and (2, 5) groups and 2.65 cm-’ between the (2, 5) and (1, 6) groups. The ratio of these two values is close to 1:2. On the contrary the spin-rotation interaction is linear in N (dashed lines of Fig. 2 of Ref. (1)) and its influence induces a symmetrical evolution of the six levels. The very small value of y (2 X 10m4cm-‘) in MnO (3) does not allow the influence of the spin-rotation to be seen easily. The same experimental pattern can be expected in MnS. We can assume that the Ah value must be small because we observe only one bandhead; on the other hand the evolution of the splitting in each of the fine-structure pairs is characteristic of a Ay value larger than that of MnO. It is easy to subtract the influence of the spin-rotation interaction by calculating the mean of the frequencies of the lines of each group (l-6, 2-5, and 3-4). The location of the three resulting values should adopt the relative positions required by the spin-spin interaction. This is never actually observed in the spectrum of MnS for N values anywhere between 20 and 70: it is always found that the mean of the (1,6) pair lies between the means of the other pairs, which suggests that the spin-spin interaction is not completely described by the parameter X alone. We recall that in a Z-Z transition it is generally not possible to determine values of the fine-structure parameters separately for the two electronic states, meaning that
474
DOUAY, DUFOUR,
AND PINCHEMEL P,(41)
R,(41)
rTT
P3(41)
P, (41) r
V
T
I
4
18 327.000
cm-’
0.02 cm-1
P4(41)
1 0.02 cm-’
I8 326.300 cm-’
FIG. 1. Hyperfine structure of the six fine-structure rotational lines (N = 41) in the P branches of the A6Z+-XbE+ (O-l) band of MnS.
a small Ax value can be the difference between two large X’and X”constants. Baumann et al. (II) performed ESR experiments on MnS and suggested that the value of X” could be considerably larger than 1 cm-’ because of the large spin-orbit coupling constant of the sulfur atom. In a recent paper Femenias et al. (12) have observed in
A6Z+-X62+
(O-l)
BAND
OF MnS
475
the X4x- ground state of NbO a value of X equal to 15.6 cm-‘. Brown et al. (13) have published the expression of the effective Hamiltonian for the spin-orbit interaction including the high-order parameters: L&o. = AL&z
+ (2/3)X(3S$ - S2) + qLzS&
- (3s’ - 1)/5]
+ (1/12)8[35s4, - 30S2S$ + 25S$ - 6S2 + 3S4]. For a Z state, the first and the third terms vanish (A = 0), the second term is the wellknown expression for the spin-spin interaction, and the fourth term can be considered either fourth-order spin-orbit interaction or second-order spin-spin interaction. We will use this latter description. The fourth term (0) has been first discussed by Brown and Milton (14). Cheung et al. (15) introduced it in the matrix of the upper electronic state of the A%-X511 transition of CrO. The diagonal matrix elements in a case (b) basis can be derived most easily by matrix multiplication (A. J. Merer, private communication). The presence of three groups of lines gives an opportunity to estimate the values of AX and ABbecause two equations are available (describing the distances between the “centers” of each group of lines). We cannot expect good accuracy for such a calculation but it is an essential test to elucidate the spin-spin interaction before performing any fit to the experimental data, With values of AX = 0.023 cm-’ and Afl = 0.013 cm-’ it has been possible to reproduce the spin-spin splitting for different values of N between 20 and 60. The interpretation of the spin-rotation splitting is less puzzling: in a fashion similar to the spin-spin interaction we can use two parameters y and ys which correspond respectively to the first- and second-order spin-rotation interactions (8, 14). A full leastsquares analysis of the transition has been performed, each electronic state of the transition being represented by a matrix in the case (a) basis. In this basis, which does not seem a priori suitable to represent a Z state, the matrix consists of two 3 X 3 rotational submatrices, one for each sign of the parity (16), where the X- and &dependent terms are diagonal. On the contrary, in the case (b) basis the spin-spin Hamiltonian is not diagonal in N, and the algebraic forms of the matrix elements are much more awkward (3). Gordon and Merer (3) have published the matrices for a ‘% (a) state including terms in X and y. We have added the terms arising from the secondorder spin-spin (e) and spin-rotation (ys) interaction (Table I). Our data include values up to N = 75, so that we have had to consider the centrifugal distortion of each of the four fine-structure parameters. Table II gives the corresponding matrix elements deduced from the expressions published by Kov&zs (I 7) and Amiot (18). The HFS allows us to identify the exact spin subscript, (1 or 6), (2 or 5), and (3 or 4), in those pairs of branches which exhibit the same hyperhne widths. This can be done by observing the very first P lines, some of which are not completely blended with the intense R lines. All the values off and F must be positive (19). Because of the large values of S and 1, which are both equal to s in the two states of the transition, the appearance of the HFS of the lines for a given small value of N is strongly dependent on the labeling of the lines. Some lines are missing, and others have fewer than six hypertine components (20). For example, the observation of an N = 3 line for one member of the (PI, P6 pair) tells us that this line belongs to the PI branch (J = N + $) rather than to the P6 (J = N - $), for which there is no J level in the upper state.
476
DOUAY, DUFOUR,
AND PINCHEMEL
TABLE I Matrix Elements of the First-Order (h and y) and Second-Order (8 and 7s) Spin-Spin and Spin-Rotation Hamiltonians in Case a Coupling for a ??I+State I$,? >
?A
12 -e >
I;,? >
2'
+ 58 - ;Y
(;Y + 6YJ[ 50
- 311"2
-q,-l,e-~Y
Note
:
the
upper
(Fz.
F4>
signs F6).
correspond 2 =
(.I + $)(J
to -
the
(Y - 3Y,)(2ZP2
e
levels
(F,,
F3,
F5),
the
lower
ones
to
the
r
levels
$.
So far we have not performed a simultaneous fit of the fine and hypertine structures, and must therefore assign a single frequency to represent each fine-structure line. In the branches labeled 1, 2, 5, and 6, the HFS follows the regular IandC pattern (2) except when N is smaller than 15 where the variation of F, for a given J value, induces a slow evolution of the distance between the six HFS components. The off-diagonal terms in the matrix of the magnetic hyperfme Hamiltonian in case bsJ coupling (3) are of the form (N, J( HHFs 1N, J f 1). The absence of perturbations in the HFS of the lines of the branches 1, 2, 5, and 6 shows that the distances between the three groups of two lines (1,6), (2,5), and (3,4) are large enough to prevent any interaction
TABLE II Matrix Elements of the Centrifugal Corrections to the Spin-Spin and Spin-Rotation Case a Coupling for a 9+ State
Hamiltonians in
477
A6Z+-X62+ (O-l) BAND OF MnS
between the fine-structure levels i and i + 1, except for the levels 3 and 4 which will be discussed later. This regular structure is a confirmation of the assumption that the spin-spin parameters are large in both the upper and the lower electronic states. Consequently the splitting of the six hyperfme components is symmetric and we have assigned the wavenumber of the middle of the hyperline pattern as the rotational frequency for these four branches. We estimate the absolute calibration to be good to 0.005 cm-‘. The assignment of a frequency to the lines of the branches 3 and 4 is less easy. These lines link respectively the close-lying FX (J = N + 4) and F4 (J = N - 4) levels of the two electronic states, and the off-diagonal matrix elements of the hyperfine Hamiltonian (A./ = sf:1) are of importance. This interaction produces a nonsymmetrical splitting of the hyperfme components which is responsible for the irregular HFS of these lines which is not clearly resolved (Fig. 2). The Land6 pattern is more or less reached when iV is larger than 60, so that we can assume that the F3 and F4 energy levels have been split enough by the spin-rotation interaction that the influence of the off-diagonal terms is canceled. For these lines we chose the rotational frequency to be the average of the third and fourth hyperfine components because a few tests performed for different values of X showed that the hyperfme levels are centered about this position. For these lines the uncertainty on the wavenumbers is estimated to be 0.02 cm-‘. The values listed in Table III have been corrected as suggested in Ref. (7). The rotational lines of the (0- 1) band were fitted using a weighted, nonlinear, leastsquares approach (21). The original fitting routines used were written by Stem et al. (22) and revised by Kotlar and co-workers (23) In its general form, the matrix of each
P3(21) WT-
P3(31)
P6(21) P5(21)
< V
I
tiii
V
18 354.088 cm-’
J!k 18 341.962 cm-’
0.02 cm-’
P3(41)
“TV-
18 326.566
cm-’
18 307.892 cm-’
V
<
I
18 327.671 cm-’
FIG. 2. Evolution with N of the hypertine perturbation, induced by the off-diagonal term (J k 1) HHFs)J) of the case (b) matrix, in the lines of the branches Ps and R3.
TABLE III Rotational Lines of the (0,O) Band of the A6Z+-X62+ Transition of MnS (in cm-‘) N
N
P
p1
p2
p3
p4
p5
‘6
Rl
R2
R3
R4
R5
R6
:
perturbed
lines. 478
479
A%‘+-X62+ (O-l) BAND OF MnS
‘?Z state includes eight parameters responsible for the fine structure, X, 19,y, and ys, and their centrifugal distortion corrections, hD, on, yn and ysn. These parameters were arbitrarily fixed to zero in the ground state because only the differences ACY= (Y’ - LX”(a = any of X, 19,y, and ys) and AQ (LY D = any of AD, dD, ?D, and TsD) can be determined in a parallel transition of this type. Because of the flexibility allowed in the calculation there is no doubt that the fit performed with the eight ha and ACYD parameters free to vary should correspond to the smallest variance and should be considered to be the ‘best” one. This point of view is too optimistic for two major reasons: first, we observe that the correlations between the ACXand Aan parameters are large and that the presence or absence of the ACXD parameters induces an unexpected variation in the values of the ACYparameters (a factor of 2 on AX and A@; second, we have no way to check the physical significance of the derived values which are merely small differences between two unknown parameters, so that no comparison can be made with another experimental work as, for example, ESR experiments. The experimental values of the parameters listed in Table IV have been calculated by the following method. In a first step the three larger parameters AX, Ay, and A8 were included and then we added successively each of the five other parameters expected to be smaller than 10P3 cm-‘. A significant improvement of the variance was obtained only when the fit included Ays. This is satisfying because the two interactions responsible for the electron fine structure, namely the spin-spin and spin-rotation, then require the same number of parameters to be accounted for properly. In a second step, we fixed the ha parameters at the values obtained previously and we floated the four ACXD parameters. The variance of the fit was not significantly improved and moreover the uncertainties on these parameters are very large, so that these values must be considered just as an order of magnitude estimate. 4. ROTATIONAL
PERTURBATIONS
The high resolution of the recorded spectra allowed the observation of three small rotational perturbations. In all cases, the perturbed state is the A%+ state because the perturbations at R(N) and P(N + 2) are equal. TABLE IV Parameters of the MnS A%‘-X62’ ” .46x+
0
X"Tf
L
al
T0
B
18369.06(4) 0.17794(6) 0
0.194,0(6)
IO'D
1.70) 1.4(Z)
lO'A.4
10'60
(O-l) Transition (in cm-‘) IO'Ay
10=Ays
:
10'AyDa
106AySDa
-1.92(7) -,.66(b) 0.115(3) o.ooe(,) -z.z(~) -,.2(z) -o.o08(9) o.oi~(z) -
These parameters have been determined with the values of y:-yi fixed to the values which appear in the table (see
Note
lOLAADa 106ABDa
Numbers in parentheses are 10 uncertainties. Aa = .‘-a” with a any of the fine-structure and y SD’
parameters
?,‘-,I”, e’-e”, the text).
X, 8, y.
ys,
y’-y”
and
XD, BD, yD
480
DOUAY,
DUFOUR,
AND PINCHEMEL
In one instance we observed four weak extra lines arising from the perturbing levels. Attempts were made to characterize the perturbing state, and its rotational constant B was found to be about 0.169 cm-‘. In their analysis of the equivalent transition of MnO, Gordon and Merer (3) suggested that the v’ = 0 level of the A%+ state is strongly perturbed by the v” = 25 level of the ground X6Z+ state. If we follow the same hypothesis for MnS, the vibrational level of the ground state lying close to the u’ = 0 level is the t?’ = 46 + 1 level. This value is too large for us to have confidence in the value of & (=O. 15 1 cm-‘) extrapolated from the equilibrium constants (I). The perturbing state cannot be a close-lying ‘%Z+or % state because such states are not expected in the neighborhood of the A6Z+ state (24) and in any case should give radiative transitions to the ground state. We cannot eliminate the hypothesis of a perturbation induced by a quartet state since the selection rule AS = 0 does not hold strictly (18) but theoretical calculations (24) have shown that the quartet states should lie several thousands of centimeter-’ above the A%+ state. 5. HYPERFINE
STRUCTURE
The hyperfme structure has been a useful guide throughout our analysis of the fine structure. The experimental setup was not accurate enough to study the HFS from the absolute wavenumbers of the hyperline line as was done on VO by Cheung et al. (8). Our analysis is based on the relative distances between the hyperfine components of rotational lines (25). In Ref. (If) Baumann et al. give the values b” = 0.0047 cm-’ and c” = -0.0045 cm-’ for the hyperline constants of the ground state. We know also the exact label (1 to 6) of each rotational line; consequently it is easy to derive the magnetic hyperfine constants b’ and possibly c’ of the upper A??? state. For N < 15 the hyperfme components in the P, , Pz, Ps, and P6 lines are not equidistant because the variation of the quantum number F is noticeable for given values of N and J. As we know the ground b” constant, a fit performed on the HFS of six well-resolved lines lying between N = 5 and 10 gives b’ = -0.0085(3) cm-’ but a meaningless value of -0.0003(9) cm-’ for c’. An attempt was made to calculate simultaneously b’ and b”; however, the correlation between these two parameters is very large and we cannot expect an accurate result. The derived values are b’ = -0.007( 1) cm-’ and b” = +0.006( 1) cm -I. It is satisfying to observe that the sign and the order of magnitude of b” are in agreement with the value (0.0047 cm-‘) given by Baumann et al. (II). The negative value of b’ is characteristic of a contribution of the 4s(Mn) orbital to the open-shell c orbitals (2) which is weaker than that suggested in Ref (24). A confirmation of the value of b’ can be generally obtained from the observation of the relative intensities of the hyperfine components of the rotational lines. The intensity must increase with the quantum number F. This is clearly observed in the figures displayed by Cheung et al. in their paper on VO (8). In the case of MnS, the evolution of the intensities of the hypertine components is very weak in the branches labeled 1, 2, 5, and 6 and is very often hidden by numerous overlaps (Fig. 1). Consequently the assignment of F values to the hypertine components based on the intensity cannot be seriously considered.
A’%+-X6X+ (O-l) BAND OF MnS
481
On the contrary the relative intensities of the hyperflne components of the rotational lines labeled 3 and 4 seem quite dependent on the quantum number F. But the splittings of the hyperfine components as well as their intensities are perturbed by the interaction between the energy levels 3 and 4. No conclusion can be derived from these lines until the interaction has vanished (N > 60). We can observe in Fig. 2 that the intensities of the hyperhne components are then almost independent with F. 6. CONCLUSION
The present work has been devoted mainly to the analysis of the fine structure of the A6Z+-X6X+ (0- 1) band of MnS, though the observation of the HFS has been the key to the interpretation. The almost perfect regularity of the spectrum allowed us to perform a fit including all 12 branches of the transition. An important feature of the analysis is that the spin-spin interaction required two parameters X and 0. The presence of the higher order interaction is a confirmation of the expected large value of x” in the ground state as calculated by Baumann et al. (11). The next step in the analysis of the A6X’-X6Zi transition of MnS will be to focus our attention on the region close to the origin. In this region we can expect to be close to a case (a) coupling where the strict AN = AJ = AF = & 1 selection rules do not hold perfectly. Observation of Q lines should allow a direct calculation of the individual values of the fine-structure parameters. There is no doubt that these lines will be very weak. The Broida-type oven does not appear to be a suitable source because of the fairly high argon pressure and the difficulty to eliminate completely the noise arising from the chemiluminescence. A quieter source, of the model successfully used by Merer et al. for MnO (3), VO (8), and NbO (12), could be more convenient for this purpose. ACKNOWLEDGMENTS We thank Dr. J. M. Brown for communicating a copy of Ref. (13) prior to publication. We are also indebted to Professor A. J. Merer for his encouragement and numerous comments on the high-multiplicity electronic transitions. RECEIVED:
October 26, 1987 REFERENCES
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AND PINCHEMEL
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66 (1973). 22. R. C. STERN, R. H. GAMMON, M. E. LESK, R. S. FREUND,AND W. A. KLEMPERER,J. Chem. Phys. 52, 3467-3482 (1970). 23. A. J. KOTLAR, PH.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (1978); A. J. Kotlar, R. W. Field, J. I. Steinfeld, and J. Coxon, J. Mol. Spectrosc. 80, 86-108 (1980). 24. B. PINCHEMELAND J. SCHAMPS,Chem. Phys. 18,481-489 (1976). 25. P. F. BERNATH,B. PINCHEMEL,AND R. W. FIELD,J. Chem. Phys. 74,5508-55 15 (1981).
129,47 l-482 (1988)
Reinvestigation of the A62’-X6Z+ Transition of MnS: Analysis of the Fine and Hyperfine Structures M. DOUAY, C. DUFOUR, AND B. PINCHEMEL Laboratoire de SpectroscopicMoltkuiaire, Unite’am&e au C.N.R.S. No. 779, Universitede Lilie Flandres Artois, UFR de Physique, BWnent PS, 59655 Villeneuved’Ascq Cedex, France TheA*Z’-x62+ (O-l) bandof MnShasbeenreinvestigated using SubDoppler laserspectroscopy. The 12 branches of the transition have been identified with the help of the pattern of the hyperhne structure. All the lines have been fitted simultaneously. It has been necessary to take into account the second-order spin-spin interaction (parameter 0) to explain the fine structure of the transition. The observation of a few extra lines in the perturbed region allowed a determination of the rotational constant of the perturbing state. The hyperhne constant b’ (k%+ state) has been ds ternlined. Q 1988 Academic PBS, Inc. 1. INTRODUCTION
In a recent paper (Z), we published a rotational analysis of three bands (O-O, O-l, and O-3) of the A’??+-X62+ transition of MnS. This analysis was based on spectra recorded using grating spectroscopy and Doppler-limited laser spectroscopy. The second technique allowed us to partially resolve the congested spectrum of the transition which exhibits six P branches and six R branches arising from the fine structure of the two electronic states. The manganese atom has a nuclear spin Z = $ which splits each of the electron spin sublevels of the two electronic states into six hyperhne levels. In a ‘% state belonging to a pure case (bar) coupling the six fine-structure sublevels of a given rotational level exhibit different hyperfme patterns which are in the ratios 1:3:5 (2, 3) (Fig. 1). It is well known that in a parallel transition such as a %-%, for which AN = AJ = A F = f 1, the lines adopt relative locations which are similar to the positions of the energy levels. This explains why in our previous analysis (I), only four branches (R3, P3, R4, P4) were intense enough to be easily observed in our spectra: their narrow hyperhne structures (HFS) give comparatively strong sharp lines at Doppler-limited resolution for the R3, P3, R4, and P4 lines. The hyper6ne structure in the other eight branches is spread out over a much larger space (up to 0.17 cm-i). Consequently it was difficult to identify these broad weak lines and moreover the overlaps induced spurious line-like regions of higher intensity with no obvious meaning In order to overcome the Doppler broadening we have recorded the O-l band over a range of 70 cm-’ by inter-modulated fluorescence (4). Under these conditions almost 500 lines (neglecting the HFS) belonging to the 12 branches have been identified and fitted simultaneously. The main feature of a high multiplicity electronic state is its fine structure which can be accounted for by two interactions, the spin-spin (parameter A)and the spin-rotation (parameter y). Generally these two parameters are sufficient to explain the fine structure (2) of a 62-62 transition but in the case of MnS we had 471
0022-2852/88 $3.00 Copyright0 1988 by Academic Press, Inc. All rights of reproduction
in any form m?swd.
472
DOUAY,
DUFOUR,
AND
PINCHEMEL
to take into account the higher order parameters: 0 (spin-spin) and ys (spin-rotation). To our knowledge it is the first time that the 0 parameter has been observed in a ‘Z?Z transition. In addition to this analysis we observed several local rotational perturbations. For one of them the presence of extra lines allowed us to estimate the B value of the perturbing state. From the hyperfine structure a value of the parameter b of the upper state has been calculated. 2. EXPERIMENTAL
DETAILS
In order to record the sub-Doppler spectrum of the A%??-X6C+ (0- 1) transition of MnS we used the well-known experimental method described by Sorem and Schawlow (4). The source, a Broida-type oven (5), has been already described in our previous paper (I). Great care was taken to reduce the scattered laser light and the emission of incandescent particles arising from the crucible. In order to increase the fluorescence signal, the oxidant gas (OCS) was injected directly into the crucible. We observed that the chemical reaction between the manganese atoms and OCS was enhanced when it occurred at high temperature (1300 K). In order to limit the linewidth, we reduced the amount of carrier gas (argon) to obtain a total pressure equal to 0.5 Torr; at a lower pressure the fluorescence signal was too weak to be recorded with a satisfactory signal-to-noise ratio. The dye laser (Coherent Inc., Model 699-29) running with rhodamine 110, delivered a total power of about 200 mW. A Glan-Thompson polarizer associated with a quarter wave retarder plate and a half-silvered mirror was used to obtain two laser beams of equal intensity and to avoid feedback of the beam into the laser cavity. The intermodulated signal was detected with a cooled Hamamatsu 928 photomultiplier tube and an associated lock-in amplifier. The signal was then recorded on a three pen chart recorder and simultaneously stored in the memory of the computer which controls the dye laser. The spectrum of I2 (6, 7) together with fringes from a 750-MHz confocal Fabry-Perot interferometer was used for the calibration. 3. ROTATIONAL
ANALYSIS
Up to now only a few high-multiplicity electronic transitions have been fully analyzed. During the last decade, A. J. Merer has performed pioneering work on such electronic states, involved in the spectra of the transition element oxides, to which this paper is largely indebted. It is not necessary here to describe extensively the fine and hyperfine energy level expressions because the frame of the present analysis is based on the theory sections of the papers devoted to the A6Z+-X6Z+ transition of MnO (3) and the C4Z--X4Z- transition of VO (8) by Merer d al. In these papers the Hamiltonians responsible for the fine and hyperfme structures are described and the corresponding matrix elements are derived. Therefore we will only develop here the parts of a ‘?Y state matrix corresponding to the second-order spin-spin and spinrotation interactions and their associated centrifugal distortions. Compared to the spectra of the two previously quoted transitions of MnO and VO, the spectrum of the MnS A6Z+-X6x+ (O-l) band is characterized by its regularity. Each pair of branches Pi and Ri (i = 1 to 6) can be fitted individually (when the few
A??+-X62+
(O-l)
BAND OF MnS
473
rotationally perturbed lines are excluded from the fit), and the six resulting sets of rotational constants B and D are in good agreement with the values published in Ref. (1). In the formalism of Hund’s case (b) the fine structure, which splits each rotational energy level N into six components F, (J = N + $), Fi (J = N + $), F3 (J = N + $), F4 (J = N - f), F5 (J = N - $), and F6 (J = N - $), arisesmainly from spinorbit interactions of the states of interest with neighboring states according to the selection rules AA = 0, ?I, AS = 0, +l as discussed in Ref. (1). These interactions have the same form as the direct internal spin-spin (parameter X) and spin-rotation (parameter y) interactions (8,9). In this paper, for the sake of clarity, we will use these two symbols as is generally done in the literature. The selection rules AN = AJ = f 1 imply that each experimental line links two levels F$ and F;. For a given value of N we will observe 12 lines (6 R and 6 P). It is obvious that the relative positions of these lines must look like the spin fine structure of a hypothetical % state whose spin-spin and spin-rotation parameters would be X = X’- X”and y = y ’ - y”, respectively. In the absence of additional information such as extra lines (3,8), the individual values of Xand y in each state cannot be determined. As we have already explained in the Introduction the HFS allows us to identify the nature of the branches (3 or 4), (2 or 5), and (1 or 6) (Fig. 1). The relative effects of X and y are very easy to distinguish when the states are in pure case (b), which always occurs for the high values of N. Let us consider first the spin-spin interaction. For a given value of N the six sublevels form three close pairs almost regardless of the value of N. Figure 3 of Ref. (10) gives some examples of the spin-spin interaction. In a first approximation the diagonal elements of the matrix of a %Zstate in the case (b) basis also give a good idea of the influence of X on the fine structure (Ref. 3, Table 2). An interesting feature is the asymmetry in the positions of the three pairs: the distances between the pairs (3, 4), (2, 5), and (1, 6) are respectively in the ratio 1:2. A good example can be found in Fig. 1 of Ref. (3). Ricking for example the R (N = 22) lines in the 1-O band of MnO we observe that the splitting is about 1.42 cm-’ between the (3, 4) and (2, 5) groups and 2.65 cm-’ between the (2, 5) and (1, 6) groups. The ratio of these two values is close to 1:2. On the contrary the spin-rotation interaction is linear in N (dashed lines of Fig. 2 of Ref. (1)) and its influence induces a symmetrical evolution of the six levels. The very small value of y (2 X 10m4cm-‘) in MnO (3) does not allow the influence of the spin-rotation to be seen easily. The same experimental pattern can be expected in MnS. We can assume that the Ah value must be small because we observe only one bandhead; on the other hand the evolution of the splitting in each of the fine-structure pairs is characteristic of a Ay value larger than that of MnO. It is easy to subtract the influence of the spin-rotation interaction by calculating the mean of the frequencies of the lines of each group (l-6, 2-5, and 3-4). The location of the three resulting values should adopt the relative positions required by the spin-spin interaction. This is never actually observed in the spectrum of MnS for N values anywhere between 20 and 70: it is always found that the mean of the (1,6) pair lies between the means of the other pairs, which suggests that the spin-spin interaction is not completely described by the parameter X alone. We recall that in a Z-Z transition it is generally not possible to determine values of the fine-structure parameters separately for the two electronic states, meaning that
474
DOUAY, DUFOUR,
AND PINCHEMEL P,(41)
R,(41)
rTT
P3(41)
P, (41) r
V
T
I
4
18 327.000
cm-’
0.02 cm-1
P4(41)
1 0.02 cm-’
I8 326.300 cm-’
FIG. 1. Hyperfine structure of the six fine-structure rotational lines (N = 41) in the P branches of the A6Z+-XbE+ (O-l) band of MnS.
a small Ax value can be the difference between two large X’and X”constants. Baumann et al. (II) performed ESR experiments on MnS and suggested that the value of X” could be considerably larger than 1 cm-’ because of the large spin-orbit coupling constant of the sulfur atom. In a recent paper Femenias et al. (12) have observed in
A6Z+-X62+
(O-l)
BAND
OF MnS
475
the X4x- ground state of NbO a value of X equal to 15.6 cm-‘. Brown et al. (13) have published the expression of the effective Hamiltonian for the spin-orbit interaction including the high-order parameters: L&o. = AL&z
+ (2/3)X(3S$ - S2) + qLzS&
- (3s’ - 1)/5]
+ (1/12)8[35s4, - 30S2S$ + 25S$ - 6S2 + 3S4]. For a Z state, the first and the third terms vanish (A = 0), the second term is the wellknown expression for the spin-spin interaction, and the fourth term can be considered either fourth-order spin-orbit interaction or second-order spin-spin interaction. We will use this latter description. The fourth term (0) has been first discussed by Brown and Milton (14). Cheung et al. (15) introduced it in the matrix of the upper electronic state of the A%-X511 transition of CrO. The diagonal matrix elements in a case (b) basis can be derived most easily by matrix multiplication (A. J. Merer, private communication). The presence of three groups of lines gives an opportunity to estimate the values of AX and ABbecause two equations are available (describing the distances between the “centers” of each group of lines). We cannot expect good accuracy for such a calculation but it is an essential test to elucidate the spin-spin interaction before performing any fit to the experimental data, With values of AX = 0.023 cm-’ and Afl = 0.013 cm-’ it has been possible to reproduce the spin-spin splitting for different values of N between 20 and 60. The interpretation of the spin-rotation splitting is less puzzling: in a fashion similar to the spin-spin interaction we can use two parameters y and ys which correspond respectively to the first- and second-order spin-rotation interactions (8, 14). A full leastsquares analysis of the transition has been performed, each electronic state of the transition being represented by a matrix in the case (a) basis. In this basis, which does not seem a priori suitable to represent a Z state, the matrix consists of two 3 X 3 rotational submatrices, one for each sign of the parity (16), where the X- and &dependent terms are diagonal. On the contrary, in the case (b) basis the spin-spin Hamiltonian is not diagonal in N, and the algebraic forms of the matrix elements are much more awkward (3). Gordon and Merer (3) have published the matrices for a ‘% (a) state including terms in X and y. We have added the terms arising from the secondorder spin-spin (e) and spin-rotation (ys) interaction (Table I). Our data include values up to N = 75, so that we have had to consider the centrifugal distortion of each of the four fine-structure parameters. Table II gives the corresponding matrix elements deduced from the expressions published by Kov&zs (I 7) and Amiot (18). The HFS allows us to identify the exact spin subscript, (1 or 6), (2 or 5), and (3 or 4), in those pairs of branches which exhibit the same hyperhne widths. This can be done by observing the very first P lines, some of which are not completely blended with the intense R lines. All the values off and F must be positive (19). Because of the large values of S and 1, which are both equal to s in the two states of the transition, the appearance of the HFS of the lines for a given small value of N is strongly dependent on the labeling of the lines. Some lines are missing, and others have fewer than six hypertine components (20). For example, the observation of an N = 3 line for one member of the (PI, P6 pair) tells us that this line belongs to the PI branch (J = N + $) rather than to the P6 (J = N - $), for which there is no J level in the upper state.
476
DOUAY, DUFOUR,
AND PINCHEMEL
TABLE I Matrix Elements of the First-Order (h and y) and Second-Order (8 and 7s) Spin-Spin and Spin-Rotation Hamiltonians in Case a Coupling for a ??I+State I$,? >
?A
12 -e >
I;,? >
2'
+ 58 - ;Y
(;Y + 6YJ[ 50
- 311"2
-q,-l,e-~Y
Note
:
the
upper
(Fz.
F4>
signs F6).
correspond 2 =
(.I + $)(J
to -
the
(Y - 3Y,)(2ZP2
e
levels
(F,,
F3,
F5),
the
lower
ones
to
the
r
levels
$.
So far we have not performed a simultaneous fit of the fine and hypertine structures, and must therefore assign a single frequency to represent each fine-structure line. In the branches labeled 1, 2, 5, and 6, the HFS follows the regular IandC pattern (2) except when N is smaller than 15 where the variation of F, for a given J value, induces a slow evolution of the distance between the six HFS components. The off-diagonal terms in the matrix of the magnetic hyperfme Hamiltonian in case bsJ coupling (3) are of the form (N, J( HHFs 1N, J f 1). The absence of perturbations in the HFS of the lines of the branches 1, 2, 5, and 6 shows that the distances between the three groups of two lines (1,6), (2,5), and (3,4) are large enough to prevent any interaction
TABLE II Matrix Elements of the Centrifugal Corrections to the Spin-Spin and Spin-Rotation Case a Coupling for a 9+ State
Hamiltonians in
477
A6Z+-X62+ (O-l) BAND OF MnS
between the fine-structure levels i and i + 1, except for the levels 3 and 4 which will be discussed later. This regular structure is a confirmation of the assumption that the spin-spin parameters are large in both the upper and the lower electronic states. Consequently the splitting of the six hyperfme components is symmetric and we have assigned the wavenumber of the middle of the hyperline pattern as the rotational frequency for these four branches. We estimate the absolute calibration to be good to 0.005 cm-‘. The assignment of a frequency to the lines of the branches 3 and 4 is less easy. These lines link respectively the close-lying FX (J = N + 4) and F4 (J = N - 4) levels of the two electronic states, and the off-diagonal matrix elements of the hyperfine Hamiltonian (A./ = sf:1) are of importance. This interaction produces a nonsymmetrical splitting of the hyperfme components which is responsible for the irregular HFS of these lines which is not clearly resolved (Fig. 2). The Land6 pattern is more or less reached when iV is larger than 60, so that we can assume that the F3 and F4 energy levels have been split enough by the spin-rotation interaction that the influence of the off-diagonal terms is canceled. For these lines we chose the rotational frequency to be the average of the third and fourth hyperfine components because a few tests performed for different values of X showed that the hyperfme levels are centered about this position. For these lines the uncertainty on the wavenumbers is estimated to be 0.02 cm-‘. The values listed in Table III have been corrected as suggested in Ref. (7). The rotational lines of the (0- 1) band were fitted using a weighted, nonlinear, leastsquares approach (21). The original fitting routines used were written by Stem et al. (22) and revised by Kotlar and co-workers (23) In its general form, the matrix of each
P3(21) WT-
P3(31)
P6(21) P5(21)
< V
I
tiii
V
18 354.088 cm-’
J!k 18 341.962 cm-’
0.02 cm-’
P3(41)
“TV-
18 326.566
cm-’
18 307.892 cm-’
V
<
I
18 327.671 cm-’
FIG. 2. Evolution with N of the hypertine perturbation, induced by the off-diagonal term (J k 1) HHFs)J) of the case (b) matrix, in the lines of the branches Ps and R3.
TABLE III Rotational Lines of the (0,O) Band of the A6Z+-X62+ Transition of MnS (in cm-‘) N
N
P
p1
p2
p3
p4
p5
‘6
Rl
R2
R3
R4
R5
R6
:
perturbed
lines. 478
479
A%‘+-X62+ (O-l) BAND OF MnS
‘?Z state includes eight parameters responsible for the fine structure, X, 19,y, and ys, and their centrifugal distortion corrections, hD, on, yn and ysn. These parameters were arbitrarily fixed to zero in the ground state because only the differences ACY= (Y’ - LX”(a = any of X, 19,y, and ys) and AQ (LY D = any of AD, dD, ?D, and TsD) can be determined in a parallel transition of this type. Because of the flexibility allowed in the calculation there is no doubt that the fit performed with the eight ha and ACYD parameters free to vary should correspond to the smallest variance and should be considered to be the ‘best” one. This point of view is too optimistic for two major reasons: first, we observe that the correlations between the ACXand Aan parameters are large and that the presence or absence of the ACXD parameters induces an unexpected variation in the values of the ACYparameters (a factor of 2 on AX and A@; second, we have no way to check the physical significance of the derived values which are merely small differences between two unknown parameters, so that no comparison can be made with another experimental work as, for example, ESR experiments. The experimental values of the parameters listed in Table IV have been calculated by the following method. In a first step the three larger parameters AX, Ay, and A8 were included and then we added successively each of the five other parameters expected to be smaller than 10P3 cm-‘. A significant improvement of the variance was obtained only when the fit included Ays. This is satisfying because the two interactions responsible for the electron fine structure, namely the spin-spin and spin-rotation, then require the same number of parameters to be accounted for properly. In a second step, we fixed the ha parameters at the values obtained previously and we floated the four ACXD parameters. The variance of the fit was not significantly improved and moreover the uncertainties on these parameters are very large, so that these values must be considered just as an order of magnitude estimate. 4. ROTATIONAL
PERTURBATIONS
The high resolution of the recorded spectra allowed the observation of three small rotational perturbations. In all cases, the perturbed state is the A%+ state because the perturbations at R(N) and P(N + 2) are equal. TABLE IV Parameters of the MnS A%‘-X62’ ” .46x+
0
X"Tf
L
al
T0
B
18369.06(4) 0.17794(6) 0
0.194,0(6)
IO'D
1.70) 1.4(Z)
lO'A.4
10'60
(O-l) Transition (in cm-‘) IO'Ay
10=Ays
:
10'AyDa
106AySDa
-1.92(7) -,.66(b) 0.115(3) o.ooe(,) -z.z(~) -,.2(z) -o.o08(9) o.oi~(z) -
These parameters have been determined with the values of y:-yi fixed to the values which appear in the table (see
Note
lOLAADa 106ABDa
Numbers in parentheses are 10 uncertainties. Aa = .‘-a” with a any of the fine-structure and y SD’
parameters
?,‘-,I”, e’-e”, the text).
X, 8, y.
ys,
y’-y”
and
XD, BD, yD
480
DOUAY,
DUFOUR,
AND PINCHEMEL
In one instance we observed four weak extra lines arising from the perturbing levels. Attempts were made to characterize the perturbing state, and its rotational constant B was found to be about 0.169 cm-‘. In their analysis of the equivalent transition of MnO, Gordon and Merer (3) suggested that the v’ = 0 level of the A%+ state is strongly perturbed by the v” = 25 level of the ground X6Z+ state. If we follow the same hypothesis for MnS, the vibrational level of the ground state lying close to the u’ = 0 level is the t?’ = 46 + 1 level. This value is too large for us to have confidence in the value of & (=O. 15 1 cm-‘) extrapolated from the equilibrium constants (I). The perturbing state cannot be a close-lying ‘%Z+or % state because such states are not expected in the neighborhood of the A6Z+ state (24) and in any case should give radiative transitions to the ground state. We cannot eliminate the hypothesis of a perturbation induced by a quartet state since the selection rule AS = 0 does not hold strictly (18) but theoretical calculations (24) have shown that the quartet states should lie several thousands of centimeter-’ above the A%+ state. 5. HYPERFINE
STRUCTURE
The hyperfme structure has been a useful guide throughout our analysis of the fine structure. The experimental setup was not accurate enough to study the HFS from the absolute wavenumbers of the hyperline line as was done on VO by Cheung et al. (8). Our analysis is based on the relative distances between the hyperfine components of rotational lines (25). In Ref. (If) Baumann et al. give the values b” = 0.0047 cm-’ and c” = -0.0045 cm-’ for the hyperline constants of the ground state. We know also the exact label (1 to 6) of each rotational line; consequently it is easy to derive the magnetic hyperfine constants b’ and possibly c’ of the upper A??? state. For N < 15 the hyperfme components in the P, , Pz, Ps, and P6 lines are not equidistant because the variation of the quantum number F is noticeable for given values of N and J. As we know the ground b” constant, a fit performed on the HFS of six well-resolved lines lying between N = 5 and 10 gives b’ = -0.0085(3) cm-’ but a meaningless value of -0.0003(9) cm-’ for c’. An attempt was made to calculate simultaneously b’ and b”; however, the correlation between these two parameters is very large and we cannot expect an accurate result. The derived values are b’ = -0.007( 1) cm-’ and b” = +0.006( 1) cm -I. It is satisfying to observe that the sign and the order of magnitude of b” are in agreement with the value (0.0047 cm-‘) given by Baumann et al. (II). The negative value of b’ is characteristic of a contribution of the 4s(Mn) orbital to the open-shell c orbitals (2) which is weaker than that suggested in Ref (24). A confirmation of the value of b’ can be generally obtained from the observation of the relative intensities of the hyperfine components of the rotational lines. The intensity must increase with the quantum number F. This is clearly observed in the figures displayed by Cheung et al. in their paper on VO (8). In the case of MnS, the evolution of the intensities of the hypertine components is very weak in the branches labeled 1, 2, 5, and 6 and is very often hidden by numerous overlaps (Fig. 1). Consequently the assignment of F values to the hypertine components based on the intensity cannot be seriously considered.
A’%+-X6X+ (O-l) BAND OF MnS
481
On the contrary the relative intensities of the hyperflne components of the rotational lines labeled 3 and 4 seem quite dependent on the quantum number F. But the splittings of the hyperfine components as well as their intensities are perturbed by the interaction between the energy levels 3 and 4. No conclusion can be derived from these lines until the interaction has vanished (N > 60). We can observe in Fig. 2 that the intensities of the hyperhne components are then almost independent with F. 6. CONCLUSION
The present work has been devoted mainly to the analysis of the fine structure of the A6Z+-X6X+ (0- 1) band of MnS, though the observation of the HFS has been the key to the interpretation. The almost perfect regularity of the spectrum allowed us to perform a fit including all 12 branches of the transition. An important feature of the analysis is that the spin-spin interaction required two parameters X and 0. The presence of the higher order interaction is a confirmation of the expected large value of x” in the ground state as calculated by Baumann et al. (11). The next step in the analysis of the A6X’-X6Zi transition of MnS will be to focus our attention on the region close to the origin. In this region we can expect to be close to a case (a) coupling where the strict AN = AJ = AF = & 1 selection rules do not hold perfectly. Observation of Q lines should allow a direct calculation of the individual values of the fine-structure parameters. There is no doubt that these lines will be very weak. The Broida-type oven does not appear to be a suitable source because of the fairly high argon pressure and the difficulty to eliminate completely the noise arising from the chemiluminescence. A quieter source, of the model successfully used by Merer et al. for MnO (3), VO (8), and NbO (12), could be more convenient for this purpose. ACKNOWLEDGMENTS We thank Dr. J. M. Brown for communicating a copy of Ref. (13) prior to publication. We are also indebted to Professor A. J. Merer for his encouragement and numerous comments on the high-multiplicity electronic transitions. RECEIVED:
October 26, 1987 REFERENCES
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DOUAY, DUFOUR,
AND PINCHEMEL
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