J. Phys. Chem. 1995, 99, 1666-1670
1666
Interference Effects in the (2 States of NO
+ 1) Photon Ionization Spectrum of the H and H’ Rydberg
A. Went2 N. Shafizadeh,” J. H. Fillion,” D. Gauyacq,*?*M. Horani,” and J. L. Lemairet Laboratoire de Photophysique MolCculaire du CNRS, Bat. 213, UniversitC de Paris-Sud, 91405 ORSAY Cedex, France, and DAMAP, URA 812, Observatoire de Meudon, 92195 Meudon, France Received: August 2, 1994; In Final Form: September 19, 1994@
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The (2 1) photon ionization spectrum of NO via the H22+, 3da and H’TI, 3dn (v = 0) Rydberg states has been recorded in the UV range between 317.7 and 320 nm. The rotational analysis and the line intensity calculation have been performed by using a propensity rule approach including the dominant contribution from the intermediate quasi-resonant C211 and D 2 F states (v = 0) to the two-photon transition moment. The line positions have been taken from the upper states and ground state rotational term values extracted from earlier absorption data. The calculations include 2-mixing between the d a and s a Rydberg states as well as 1-uncoupling between the close lying d o and dn components. In addition to the interference effects due to the mixing of the upper levels, a new type of interference occurs in the two-photon transition amplitude through the two different pathways via the C and D states. The mixing coefficients for the upper levels and the oscillator strengths for the C-X, D-X, H,H’-C, and H,H’-D transitions have been taken from the literature. Therefore, our calculation has been performed without any fitting of the molecular parameters. The resulting simulated two-photon spectrum agrees reasonably well with the observed one. This approach has been applied to reinvestigate a recently published analysis of the same system involving v = 1 in the upper states. We propose a completely revised analysis of this (1,O) two-photon band, showing a very good agreement between observed and calculated rotational profiles. This work demonstrates the ability of the propensity rule model for predictions of upper state rotational and parity relative populations in multiphoton excitation experiments. These predictions may be essential when these upper levels are used as intermediate levels for two-color experiments toward highly excited states or the ionization continuum.
1. Introduction The nd Rydberg series of NO converging to the X’Z+ ground state of NO have been observed by high-resolution absorption and emission spectroscopy.’ All these series show weak absorption, and only the n = 3 and 4 members of the nda and ndn series have been observed and a n a l y ~ e d . ~More - ~ recently, the nd series, v = 0, have been investigated by two-color REMPI, from the intermediate C2n,v = 0, state, with 6 5 n 5 8 and 25 5 n 5 40 and show evidence of predissociation for the ns u,n members with 6 5 n 5 25 and for the nd6 members with n 2 Finally the nd series, v = 1 (7 5 n 5 12), has also been investigated by one-color two-photon excitation and observed via vibrational autoionization between the NO+, XIZ+, v = 0, and v = 1 ionization thresholds by Pratt et alS6 Only the ndn- components, which are the less affected by predissociation, could be observed by this technique. The assignments were proposed on the basis of a multichannel quantum defect calculation of the s-d supercomplex structure and two-photon rotational line strength calculations. The rotational structure of the ndn-, v‘ = 1 X 2 n , v” = 0 transition shows only two branches, corresponding to the spin-unresolved doublets Ql1 PZIand 4 2 1 R11, in good agreement with rotational line strength calculations based on a simple propensity rule model. These calculations take into account only the strongest contributions of the nonresonant intermediate states. Thus, the C2nX211 two-photon spectrum recorded by Freedman’ was found to be dominated by Q branches, as a consequence of the major contribution of the A2Z+ state in the two-photon transition amplitude. Similar calculations derived for three-photon line
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* To whom correspondence +
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should be sent. Observatoire de Meudon. Universite de Paris-Sud. Abstract published in Advance ACS Absrructs, January 15, 1995
strengths in the case of the C21T-X2n three-photon spectrum showed a parity selectivity in the upper state arising from the influence of the nonresonant A2X+ intermediate state.* In the case of the nd X 2 n two-photon transition, Pratt et aL6 followed the same derivation as in ref 8 by assuming that the C 2 n and D2Z+ intermediate states dominate the two-photon transition amplitude. However, their calculations could not be compared with the complete nd complex experimental spectrum due to the absence of the predissociated nda and ndn+ components. These authors concluded that studies of the lowlying nd complexes (n = 3,4; v = 0-2) were needed in order to understand how the rotational band structure in the twophoton spectra evolves from low n to intermediate n. The aim of this work is to check the validity of this propensity rule model by comparing the two-photon line strength calculations with the experimental two-photon excitation spectrum of the lowest members of the nda,n+ Rydberg series of NO, i.e. H2X+, 3da and H’211, 3dn. Indeed none of the components of the 3d complex exhibit predissociation, so that a full comparison can be made between the observed rotational branches and the intensities predicted by the simple propensity rule calculation proposed by Pratt et a1.6
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2. Experimental Section
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The NO (2 1) photon ionization spectrum was recorded in a conventional ionization cell. The setup was initially designed for V W experiments, and the NO cell was usually used for V W power monitoring. The output of a commercial NdlYAG pumped dye laser (Quantel TDLSO) was frequency doubled to provide fundamental W radiation around 320 nm with pulse energies around 16 mJ and with a band width of about 0.1 cm-’ in the W range. This W beam was focused with a 10 cm focal length lens in a first cell for third harmonic generation in
0022-3654/95/2099-1666$09.00/0 0 1995 American Chemical Society
H and H Rydberg States of NO
J. Phys. Chem., Vol. 99, No. 6, 1995 1667
P
S
d I-uncoupling observed states
{
in the present work
// // //
3d6
-.“---A
hv
/
I
F 2A
1
3do s-d mixing 4so 7 \ \ \ \ \
hv
Ot
(3d + 4s) complex
\ \
1
x 2ll
Figure 1. Energy level diagram for the lowest Rydberg states of NO. The two-photon transition to the H,H’ states (solid arrows) and the two dominant quasi-resonant pathways through the C and D states (dashed arrows) are indicated. Inset: the structure of the (4s 3d) complex resulting from the s-d mixing and I-uncoupling interactions (from ref 9).
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xenon. The produced W and V W beams were refocused through a LiF lens, which also serves as a window, into the main cell and, then, through a MgF2 window, into the ionization cell. At the center of this cell, the UV beam only is collimated while the V W beam is diverging. The ( 2 1) REMPI spectrum of NO presented in the next section was recorded with these focusing conditions and with no gas in the V W conversion cell. Pure NO was introduced in the cell at a pressure of 0.8 Torr. The MPI signal was recorded by using a set of two parallel plates (separated by 2 cm) on which a 300 V voltage was applied, and fed into a conventional boxcar detection system. Absolute laser wavelength calibration was made by adding a small amount of H2 in the VUV conversion cell (a few hundredths of a torr) and by detecting simultaneously a few rotational lines of the H2, B-X (3-0) absorption system in the VUV range and the NO spectrum in the W range. An accuracy better than 0.1 cm-’ was obtained for the two-photon line positions and allowed us to unambiguously assign the observed transitions by comparison with calculated line positions (section 3 below shows the procedure used for obtaining these line positions). In these experiments, the UV laser beam was linearly polarized.
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3. Two-Photon Line Strength Calculations 3.1. H,H X(0,O) Two-Photon Band. An energy diagram of the lowest Rydberg states of NO is presented in Figure 1. Among the low-lying possible intermediate states, A2X+,C2n, and D2X+ are the closest to the one-photon energy. As previously discussed by Pratt et al.,6 the C and D states are the most important quasi-resonant states in the two-photon transition amplitude, due to their atomic 3p character, while the A state, with its dominant 3s character, does not contribute significantly to the two-photon transition moment of the 3d complex. Therefore, only two interfering pathways, Le. H2E+, H’211 C211 X211and H2C+,H’2rI D2C+ X2n, were considered +
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in the present calculation, as shown in Figure 1. The inset of Figure 1 shows in more detail the structure of the 4s 3d complex, which has been earlier described by J ~ n g e n .The ~ strong s-d mixing between the 4so and 3da components is mostly responsible for the energy pattem within the 3d complex, resulting in two close-lying components, i.e. 3do and 3&, and a lower component, 3dd. As a consequence, the upper components H2Z+ and H’211+ of the 3d complex are strongly mixed by rotational interaction, the so-called I-uncoupling, while the H’211- and the P A (3dd) components are essentially unaffected. In order to calculate correctly the rotational intensities of the two-photon spectrum, it is therefore necessary to include both s-d mixing and I-uncoupling in the upper state wave functions, since they give rise to interference effects in any spectrum involving these states9 The s-d mixing has been introduced following ref 5 as shown below:
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I3”d”o) = cos 8 13do)
+ sin 8 14~0)
14”s”~)= -sin 8 13do)
+ cos 8 14~0)
(1)
where the mixing angle 8 has been taken to be -38” as in ref 5 , reflecting a 1-mixing of almost 50%. More important in the present case, in which we observed only the H and H’ components of the 3d complex, is the I-uncoupling between the H22+ and H’211+ components, since this interaction leads to interference effects directly observable in the present two-photon spectrum. We have included this I-uncoupling interaction by writing the upper state wave functions as follows:
where the N-dependent mixing coefficients a and are positive
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TABLE 1: Oscillator Strengths between the Czn and D2X+ States and the X2n, H W ,and H2nStates C2l-I D*Z+ a
X2l-I
H2Z+
H’Zl-I+
H’2l-I -
25 10-40 25 x 10-4 a
0.25b 0.16b
0.25b 0.16b
0.27b O.2gb
From ref 10. From ref 11.
quantities resulting from the diagonalization of the 1-uncoupling Hamiltonian matrix, which involves the interacting components 3”d”uf and 3d&, and the off-diagonal matrix element, which amounts to 5.43[N(N 1)]1’2cm-1.2 In the present work, we have neglected the weak I-uncoupling responsible for the mixing between the Hf211- and F A - components, so that pure A = 1 orbital angular momentum is assumed for the H f 2 I T state. On the basis of the propensity rule model, the two-photon transition amplitude from the ground state to the unperturbed 3“d“u+, 3&+, and 3d.7~-states (which actually are not the observed H and H’ states but rather the right-hand-side wave functions of eq 2 above) can be derived following the procedure proposed by Pratt et al. (eq 3 of ref 6). In the case of linearly polarized light, the transition amplitude between pure A states is given by
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NJ 3% 2%
Fl F2
2% 1 Y2
F1 F2
- e 2n312
Figure 2. Allowed two-photon pathways via the C and D states for
J’ k=03
1
J”
(2k+1){1
J 1 1 k J’ k } ( O 0 O)(-M’
k0 J”’,) (3) M
where all the double-primed symbols refer to the ground state X2n,the primed symbols to the upper states A‘ = 0 and A‘ = 1, and the unprimed symbols to the intermediate C and D states. A is the intermediate state angular momentum, Le., A = 0 for the D2Z+ state and A = 1 for-the C211 state. The parameters pi’ contain the product of the radial and angular factors for the two single-photon transitions involving pure A states, as well as the energy denominator, which takes into account the energy mismatch between the one-photon energy and the C and D state energies (21 845 and 20 926 cm-’, respectively). The two-photon transition amplitude to the parity levels of the real states, H2Z+, Hf211+, and Hf211-, is given by
11 + 17cf/~-1)N+J”+l/2 ][1
+ 1717’(-1)N+“+’]
(4)
where 6’’ labels the e or f spin-rovibronic symmetry of the case (a) ground state wave functions and q and q’ label the symmetry of the case (b) intermediate and upper level wave functions, Le., q(q’) = +1 for the Z+and II+ levels and q(q’) = -1 for the l T level. The c$ coefficients are given in eq 2, Le., for q’ = +1, they are given by the 1-uncoupling coefficients a and /3 and, for q’ = -1, c i , = 1. The relative magnitudes of the electronic (radial angular) one-photon transition moments have been taken proportional to the oscillator strengths given in ref 10 for the ground to intermediate state transitions and given by Gallusser and Dressler” for the intermediate to upper state transitions. These values are summarized in Table 1. Finally the relative phases of the wave functions and transition
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the &(3 I/*) line, following the propensity rule model; solid arrows indicate strongly allowed pathways, and dashed arrows indicate forbidden or weakly allowed pathways. Interference effects between the allowed pathways, i.e. via the C2n+and D 2 F quasi-resonant states, are not indicated in this figure.
moments have been chosen in agreement with ref 5 eqs 14 and 15 and ref 12 eqs 5-8. Figure 2 illustrates how the propensity rules, as expressed by eqs 3 and 4, apply in the example of the 012(3 l/2) twophoton line: the Of‘, branches are related to the H2Z+ X211 and Hf211+ X211 transitions, while the branch is related to the Hf2H- X211 transition. From the diagram of Figure 2, it can be seen that only the C2n+ and the D2Zf intermediate states contribute to the Of‘, rotational line strength while only the C211- intermediate state contributes to the Of2 rotational line strength. These different pathways give rise to unequal intensities between the parity doublets not only in the case of 0-type transitions but also for all other branches. Consequently, the rotational intensity distribution of the two-photon band is significantly affected. Finally destructive interferences between the C and D pathways also occur, leading to complete extinction of some branches. Finally the line positions were calculated from the term values of the H and H’ upper states derived from absorption data2 and from those of the ground state.I3 Rotational and parity selection rules as well as propensity rules are automatically applied by using eq 2. The resulting simulated spectra are shown in Figure 3 and compared to the observed spectrum. A Boltzmann distribution at 300 K was assumed for the ground state, and the line widths were convoluted with a Gaussian profile of 0.5 cm-’, close to the experimental resolution. With the energy scale displayed in this figure, it is not possible to label all the allowed 60 branches. In fact, among these allowed branches, some are very weak or absent because of destructive interferences, so it was possible to resolve most of the spectrum and to make a one-by-one comparison between observed and
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H and H Rydberg States of NO
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a) Experimental
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Figure 3. Comparison between the simulated spectra and the experimental spectrum: (a) simulated spectrum calculated by using the H,H' D2Z+ X pathway only; (b) simulated spectrum calculated by using the H,H' C211 X pathway only; (c) simulated spectrum calculated by using the two interfering D and C pathways; (d) observed spectrum. s-d mixing and l-uncouplin are taken into account in the calculations for parts a-c (see the text for details).
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calculated lines. Parts a and b of Figure 3 show the calculated spectra when only one quasi-intermediate state is considered, either the D or C state, respectively. Figure 3c shows the calculated spectrum when both interfering pathways are considered. In this case, some branches loose intensity, as can be noticed on the red side of the band, in the region of 0-branches. This spectrum is dominated by Q-branch structure, which was not obvious from only intuitive arguments. Indeed, both Z and ll symmetries are involved in this two-photon transition, both in the upper and intermediate states. Then, one would rather expect any branch (0,P, Q, R, and S ) to have a significant intensity. Figure 4 shows part of the experimental and calculated spectra in the blue side of the two-photon band, in an enlarged scale with respect to the overall spectra of Figure 3. This figure shows that the rotational structure is indeed dominated by Q lines. It also shows in detail the degree of agreement between our simulations and the observed spectrum in a region free from any possible experimental saturation effect. One can see that weak rotational lines predicted by the propensity rule model are even weaker in the observed spectrum, due to even more destructive interference effects. Given the fact that we did not try to adjust any molecular parameter, we consider that the agreement between observed and calculated spectra is excellent. 3.2. H,H' X(1,O) Two-Photon Band. Recently, the twophoton excitation spectra of the (l,O), (2,0), and (3,O)bands of the same system as well as of the (0,O) and (1,O) bands of the 0,0'(4da,x)-X system have been observed by S. Y. Zhao et al., by using laser-induced fluorescence dete~ti0n.I~These authors assigned the transitions observed in the region around
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ENERGY (em-')
Figure 4. Part of the two-photon spectrum in an enlarged scale showing the Q-line dominant structure: (a)experimental spectrum; (b) calculated
spectrum.
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65 000 cm-' to the H'211X211 two-photon transition, involving 12 branches with unresolved spin-splitting, namely, S21, S I I+ R21, Rii + Q21, Q I I + P21, Pi1 + 021, 0 1 1 , S22, Si2 + R22, RIZ + Q22, 4 1 2 + P22, P12 + 0 2 2 , and 0 1 2 . From the observed band of the H'-X system they proposed a new set of molecular constants for the upper state, differing from the molecular constants derived from the analysis of the absorption and emission spectra by Huber and Miescher2 and Huber.I2 In fact they did not discuss the discrepancies, since they did not even refer to these earlier data (the Te values for the H'211 state differ by more than 45 cm-I, after correcting a misprint in their paper; Le., T, = 62 537.5 cm-' instead of 61 537.5 cm-'). We propose here a different interpretation of their spectra, which at first sight shows the same rotational profile as the (0,O) two-photon transition discussed in the above section. Indeed, since no predissociation occurs in the v = 1 level of the H,H' states as in the v = 0 level, the propensity rule model should apply with exactly the same degree of accuracy. The only change in the calculations comes from the slight variation of the molecular parameters and interaction parameters with the vibrational quantum number. The quasi-intermediate states of interest are in this case the C(v = 1) and D(v = 1) levels instead of the v = 0 levels. The term values of the upper levels have been taken from ref 12 for the lowest N value (N5 20) and extrapolated to higher N values by using the Hamiltonian matrix and the molecular parameters given in ref 15. The term values for the ground state are taken again from ref 13. The 2-uncoupling parameter responsible for the mixing between the upper H 2 P and H'%+ levels has been taken to be equal to 5.36[N(N 1)I1l2 cm-I, according to ref 2. The rest of the calculation of the (1,O) band follows exactly the same procedure as in section 3.1 above. The resulting simulated spectrum is shown in comparison with the observed spectrum of ref 14 in Figure 5 . In order to compare
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Figure 5. Two-photon H,H’-X(l,O) excitation spectra: (a) calculated spectrum following the method used for the (0,O)band (see text for details). The lines have been convoluted with a Gaussian width of 3 cm-I. (b) Observed spectrum as shown in Figure 3 of ref 14. The energy scale has been shifted by - 15 cm-I with respect to the figure of ref 14, in order to fit with the correct spectral positions.
the two spectra, we have first allowed for a global shift of 15 cm-’ on the energy scale (probably due to a calibration error in ref 14), and we have convoluted the calculated rotational line with a width of 3 cm-’, close to the experimental one. As discussed above, the spectrum is dominated by the Q-branches and does involve the three upper level components, Le., H W , H’211+, and H’TII-, and not only the H’211- component, as proposed in ref 14. The agreement between the observed and calculated spectra is excellent, taking into consideration that we did not allow ourselves to fit any parameter known from previous studies, in contrast with the work of ref 14.
4. Concluding Remarks As said before, the simulated spectra of Figure 3c and Figure 5a were obtained with all molecular and transition moment parameters fixed at the values previously determined in the literature. This calculation first demonstrates the good quality of the absorption and emission data on NO, since they can be used without any further adjustment in order to interpret new data arising from a completely different kind of experiment. It also demonstrates the validity of the simple model used by F’ratt et aL6 for the higher members of the nd series, even if an evolution of t h e rotational band structure is expected from low n to intermediate n. Finally this propensity rule model can be used very efficiently for quantitative predictions about the relative populations of the upper rotational and pari@ levels through two- or three-photon excitation. This information may
be essential when these upper levels are used as intermediate levels for two-color experiments toward the ionization continuum, as has been pointed out recently.16
Acknowledgment. We would like to thank Dr. F. Rostas (Meudon) for helpful and stimulating discussions and 0. Benoit d’Azy for providing a scanner output of the spectrum of ref 14. References and Notes (1) Miescher, E.; Huber, K. P. Znt. Rev. Sci. Phys. Chem. 1976, Ser. 2, 3, 37 and references therein. (2) Huber, K. P.; Miescher, E. Helv. Phys. Acra 1963, 36, 257. (3) Miescher, E. Can. J . Phys. 1971, 49, 2350. (4) Suter, R. Can. J. Phys. 1969, 47, 881. (5) Fredin, S., Gauyacq, D.; Horani, M.; Jungen, Ch.; Leevre, G.; Masnou-Seews, F. Mol. Phys. 1987, 60, 825. (6) Pratt, S. T.; Jungen, Ch.; Miescher, E. J. Chem. Phys. 1989, 90, 5971. (7) Freedman, P. A. Can. J. Phys. 1977, 55, 1387. (8) Gauyacq, D.; Fredin, S.; Jungen, Ch. Chem. Phys. 1987,117,457. (9) Jungen, Ch. J. Chem. Phys. 1970, 90, 5971. (10) Bethke, G. W. J. Chem. Phys. 1959, 31, 662. (11) Gallusser, R.; Dressler, K. Z. Angew. Math. Phys. 1971, 22, 792. (12) Huber, M. Helv. Phys. Acta 1964, 37, 329. (13) Amiot, C.; Back, R.; Guelachvili, G. Can.J. Phys. 1978, 56, 251. (14) Zhao, S.;Zhang, S. M.; Zhong, M. C.; Zhang, P. L. J. Quanr. Spectrosc. Rudiat. Transfer 1993, 50, 319. (15) Bernard, A.; Effantin, C.; d’Incan, J.; Fabre, G.; Stringat, R.; Barrow, R. Mol. Phys. 1989, 67, 1. Bernard, A.; Effantin, C.; d’Incan, J.; Amiot, C.; VergBs, J. Mol. Phys. 1991, 73, 221. (16) Rudolph, H.; Mc Koy, V. J. Chem. Phys. 1990, 93, 7054. JP941992W
