Faraday Laser Magnetic Resonance Spectroscopy of Vibrationally Excited C2D

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

190, 112–124 (1998)

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Faraday Laser Magnetic Resonance Spectroscopy of Vibrationally Excited C2D Christian Schmidt,* Miljenko Peric´,† Petra Mu¨rtz,* Martin Wienkoop,* Martina Havenith,* and Wolfgang Urban* *Institut fu¨r Angewandte Physik, Universita¨t Bonn, Wegelerstrasse 8, D-53115 Bonn, Germany; and †Faculty of Physical Chemistry, University of Belgrade, P.O. Box 137, 11001 Belgrade, Yugoslavia Received December 31, 1997; in revised form February 23, 1998

We studied the gas phase spectrum of the deuterated ethynyl radical C 2D in the region between 3196 and 3243 cm01 using a Faraday LMR spectrometer in combination with a CO overtone laser. The C 2D radicals were generated in a dc glow discharge containing helium, deuterium, and acetylene. We observed a hot band between two vibronic 2 P states with an origin at 3225 cm01 . The lower level is assigned to the first excited bending level of the electronic X ground state. The upper level corresponds to the first excited electronic state A at 3513 cm01 , which was observed previously [ J. Mol. Struct. 190, 41 – 60 ( 1988 ) ] . This region is subject to strong vibronic interaction, caused by mixing of the electronic X ground state with the A state at 3513 cm01 . From the analysis of the spectra we could determine the orbital g factor of the upper level, which gave important information about the mixing ratios. In addition we were able to derive a precise term value for the first excited bending level of the electronic X ground state. The experimentally derived molecular parameters are compared with theoretically calculated values, obtained by ab initio calculations. q 1998 Academic Press 1. INTRODUCTION

Since its first observation in an argon matrix in 1964 (2) the deuterated ethynyl radical C2D has been investigated in several experimental and theoretical studies. In 1974 C2D was detected in the interstellar medium by Tucker et al. (3). A variety of techniques have been used to study the C2D spectrum, including millimeter-wave and sub-millimeter-wave spectroscopy (4, 5, 6), matrix isolation spectroscopy (7, 8), difference-frequency laser spectroscopy (9), photoelectron spectroscopy (10), and color center laser (11, 12) spectroscopy. Very recently, the spectra of C2H and C2D trapped in solid neon in the range from 700 to 12 000 cm01 have been observed and analyzed by Forney et al. (5). The linear three atomic C2D radical has an electronic X 2S / ground state and a low-lying first excited electronic A state at about 3500 cm01 (13, 14). The C2H/C2D radical is of special interest, because it serves as a prototype of unusual type of the Renner–Teller coupling involving three electronic species, X 2S / (1 2 A * ), A 2P (2 2 A * ), and A 2P (1 2 A * ). The spectrum of the electronic transition X 2S / r A 2P is very complicated due to vibronic interaction caused by mixing of the electronic X ground state and the electronic A state. Because of this coupling the wave functions of vibronic states of the electronic ground state gain a more or less large amount of the electronic P character. This mixing process causes uncertainties in the assignment of vibronic states below 5000 cm01 . The deuterated ethynyl radical was the object of several ab initio studies. In 1991 Peric et al. (14)

carried out extensive ab initio calculations and suggested an assignment for all vibronic levels below 7000 cm01 . In the present study we report the observation and analysis of a hot band, which arises from the vibronic X 2P (0, 1, 0) level. The molecular parameters of the lower level were known on the basis of millimeter wave (6) and color center laser measurements (12). However, the term value of the lower level was only roughly known. The only experimentally derived result of 270 { 20 cm01 was given by Ervin et al. (10). The upper level at 3513 cm01 corresponds to a mixture of the hypothetical pure A 2P (0, 0, 0) level and several vibrationally excited levels of the electronic X ground state with term values near 3500 cm01 . This level is tentatively assigned to the A 2P (0, 0, 0) level according to the conclusion in earlier studies (1). However, Jacox et al. (7) suggested the vibronic X 2P (0, 1, 2) level as an alternative assignment corresponding to the discussion in Ref. (14). This level at 3513 cm01 was observed previously in an infrared study by Stephens et al. (1). The results of both of the earlier studies facilitated the analysis of our LMR data. The focus of interest was the determination of the term value of the lower level X 2P (0, 1, 0) and the orbital g factor of the upper level. The orbital g factor provides important information about the mixing between the X and A states. The experimentally derived values are compared with theoretical results and are discussed in the final section. 2. EXPERIMENTAL DETAILS

Our highly sensitive Faraday laser magnetic resonance (LMR) spectrometer was used for the measurements. In this

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spectroscopic method the transition frequency of gas phase radicals is tuned by an external magnetic field and probed with a fixed frequency laser. A more detailed description of the spectroscopic technique and the experimental setup is given elsewhere (15). In this study a liquid-nitrogen cooled CO overtone laser was used as light source (16). The laser frequency is stabilized on the gain maximum by a commercial stabilization system. A superconducting solenoid provides a maximum magnetic flux density of 3.2 T with a homogeneity of 0.1% on a length of 25 cm. The Zeeman tuning is modulated by a second magnetic field at 8.6 kHz with an amplitude of 0.01 Tpp (100 Gpp ), which allows phase sensitive detection with a lock-in amplifier. Therefore, the LMR signals appear as the first derivative of the diffraction lineshape. The spectra are detected by a liquid-nitrogen cooled InSb detector and recorded with a personal computer. We also are able to shift the laser frequency by 90 MHz using an acousto-optical modulator for sideband generation. This measurement yields additional information on the tuning rates of molecular transitions, which facilitates the assignment of the observed LMR signals. The systematic uncertainties can be estimated as 10 MHz for the laser frequency and 40 G for the magnetic field. The C2D radicals were generated in a normal dc glow discharge. We worked with a gas mixture of helium with deuterium and acetylene. The sample gas was pumped through the discharge cell by a rotary pump with a speed of approximately 6 m3 /h. Acetylene entered the discharge cell at the beginning of the homogenous region of the magnetic field. Two gas mixtures were optimized to produce the radicals. Initially, we used deuterated acetylene C2D2 as precursor with a stated purity of 99.8% for the observation of C2D signals. We obtained the best signal-to-noise ratio using a gas mixture of 1.5 Torr helium with 25 mTorr C2D2 and 125 mTorr deuterium. The optimum discharge current was 32 mA. After observing first LMR signals of the C2D radical we reproduced our signals using C2H2 as precursor. For this reason we increased the deuterium partial pressure in the discharge cell and reached nearly the same signal-to-noise ratio using a mixture of 1.4 Torr helium with 12 mTorr C2H2 and 200 mTorr deuterium. The optimum discharge current for this mixture was 45 mA. Unfortunately, hydrogen (or deuterium) was found to be efficient in relaxing hot C2H radicals initially prepared to the ground vibronic state ( 17). On the other hand, the use of deuterium in the discharge avoids the buildup of carbon coatings on the discharge cell walls and the electrodes. This effectively reduced the noise in the spectra caused by the discharge. Signals of the X 2P (0, 1, 0) r 2P (3513 cm01 ) vibronic transition of C2D could be detected on 10 laser lines in the frequency region between 3196 and 3242 cm01 . The 224 Zeeman components (including measurements on laser lines shifted in frequency using an acousto-optical modulator) originating from 21 rovibronical transitions of C2D could be

FIG. 1. LMR spectrum of C2D on the CO overtone laser line P(8)22 – 20 (3203.8291 cm01 ) transition X 2P (0, 1, 0) r 2P (3513 cm01 ), (N *, J *, P * R N 9, J 9, P 9 ) #, (7, 7.5, 01 R 8, 8.5, /1); ( / ):(7, 6.5, /1 R 8, 7.5, 01) ( ∗ ):(7, 6.5, 01 R 8, 7.5, /1).

assigned to the vibronic X 2P (0, 1, 0) r 2P (3513 cm01 ) hot band. Fig. 1 shows a typical LMR spectrum. Fig. 2 shows the corresponding Zeeman pattern. 3. ANALYSIS

1. Hamiltonian The analysis of the spectra is carried out with a vibronic P effective Hamiltonian in the N 2 formulation as described by Brown, Colburn, Watson, and Wayne (18). From previous studies (19) it is known, that the X 2P (0, 1, 0) level as well as the upper level 2P (3513 cm01 ) can be described in a Hund’s case (b) basis set. The K-type doubling of the levels was treated as L doubling. The same Hamiltonian was used in a study of the X 2P (0, 1, 0) r A 2P (0, 0, 0) transition of the C2H radical by Pfelzer et al. (19). 2

Heff Å Hrot / Hsr / Hso / Hld / Hzeem

[1]

Hrot Å BN 2 0 DN 4

[1a]

Hsr Å gNrS

[1b]

with

Hso Å ALrS 2

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H1d Å 1/4[p / pd N , L S0 N0 / L S/ N/ ]/ 0 1/2(q / qd N 2 )( L 2/ N 20 / L 20 N 2/ )

[1d]

Hzeem Å gLmB LrB / gSmB SrB / gl mB (Sx Bx / Sy By ),

[1e]

with gS being the electron spin factor, gL the electron orbital g factor, and gl an anisotropic correction to the electron spin

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FIG. 2. Simulated Zeeman pattern of the three rovibrational transitions of C2D in the LMR spectrum of Fig. 1. For an assignment see marks on the frequency scale. Transition X 2P(0, 1, 0) r 2P (3513 cm01 ), (N *, J *, P * R N 9, J 9, P 9 ) #, (7, 7.5, 01 R 8, 8.5, /1); ( / ):(7, 6.5, /1 R 8, 7.5, 01); ( ∗ ):(7, 6.5, 01 R 8, 7.5, /1).

g factor. A more detailed description is given by Brown et al. (20). 2. Fit of the Observed Data We fitted our data set in a least-squares fit with a Hund’s case (b) basis set truncated at DN Å {2. Seven molecular parameters including g factors could be determined. Parameters not included in the fitting procedure were fixed to their values determined in earlier studies. The values for the vibronic levels X 2P (0, 1, 0) and 2P (3513 cm01 ) obtained in the best fit are listed in Tables 1 and 2, respectively. The observed and calculated Zeeman resonances are given in Table 3. The signs for the doubling parameters had to be changed with respect to the convention in Ref. (20), because they were given in l-type doubling sign convention. The frequencies of the CO overtone laser lines used in the fitting procedure were calculated using the Dunham coefficients given by George et al. (21). The molecular parameters of the ground state were restricted to the values as obtained in Ref. (12). For the upper state the parameters can be compared with the previous IR data of Ref. (1). The parameters describing higher rotational distortion were fixed to the previous values, because our LMR data include only low J levels. The standard deviation of 3.3r10 03 cm01 is in the same order of magnitude as the experimental accuracy 3r10 03 cm01 .

4. RESULTS AND DISCUSSION

From our measurements the origin of the vibronic X 2P (0, 1, 0) r A 2P (0, 0, 0) transition is determined to be at 3225.2664(8) cm01 . The term value of the upper level has been given in Ref. (1) as 3513.477(1) cm01 . Therefore, we can deduce for the first time an exact value for the X 2P (0, 1, 0) state. The result is 288.210(1) cm01 , which is in good agreement with the earlier result by Ervin et al. (10), who determined a value of 270 { 20 cm01 using photoelectron spectroscopy. The fitted parameter gL can be interpreted as the product of the orbital g factor of an electron, which is equal to one (neglecting relativistic effects), multiplicated with the z component of the orbital angular momentum » LZ … . Hence, geff Å gLr» LZ … . In pure electronic S and P states gL should be equal to zero and one, respectively. For the upper level gL is determined to be 0.209(6). This value gives direct evidence of vibronic interaction between the X and A electronic states and can be compared with results of theoretical studies. The measured orbital g factors and the spin–orbit constants enabled us to estimate the spin–orbit constant A* of the unperturbed A 2P state using the equation A* Å A/ » Lz … É A/gL .

Taking the experimentally derived values for A and gL , one

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TABLE 1 Molecular Parameters for the X 2P (0, 1, 0) r 2P (3513 cm01 ) Hot Band of C2D: X 2P (0, 1, 0)

a

Parameters constrained to the value from Ref. ( 12). Parameter constrained to this value. c From Curl’s relationship (30). b

obtains a value for A* of 030(1) cm01 , which is close to the theoretically obtained value for A* of 025 cm01 (22). To facilitate the interpretation of experimental results ab initio computations of the spin–orbit splittings and the values of the rotational constant B in K Å 1 vibronic levels of C2D are carried out. In these calculations the potential surfaces and the approach for handling this three-state electronic problem are taken from previous calculations by Peric´ et al. (14, 22–29) and the experimentally derived value of the spin–orbit constant A* ( Å 030(1) cm01 ) of the unperturbed A 2P state was employed. The results of the calculated vibronic energies, ‘‘P character’’ of the vibronic states in question and the spin–orbit splittings of these levels in the region 0–4500 cm01 are presented in the left-hand part of Table 4. The vibronic levels are assigned by the quantum numbers £2 , £3 corresponding to the bending and C–C stretching, respectively. The results for the levels involving the excited D–C mode, (1, 1, 0), (1, 3, 0), and (1, 5, 0) are not given because the present theoretical treatment, in which the D–C stretching is assumed to be separable from other rovibrational modes, does not enable a proper description of the interaction of these states with the neighboring £1 Å 0 species. Let us stress that the assignment of the vibronic levels in Table 4 is in several cases tentative [as discussed in detail elsewhere (14, 24, 28, 29)] because of strong mixing of different basis functions in the corresponding vibronic wavefunctions. This concerns particularly the levels (0 0 , 0) (the lowest-lying vibronic level assigned to belong predominantly to the P electronic state) and (1, 2). A reliable description of the vibronic energy splitting due to the spin–orbit interaction is one of the most difficult tasks in the molecular ab initio calculations (22, 28, 29). In the usual two-state Renner–Teller case with both of the potential surfaces having the common minimum at the linear molecu-

lar geometry most of the effect of the spin–orbit coupling is concentrated in the ‘‘unique level,’’ the lowest-lying K x 0 vibronic level. The spin–orbit splitting of this level is comparable in magnitude with the value of the spin–orbit constant A. In other vibronic states the splitting is quenched effectively. In the present three-state problem the situation is even more complicated. The strength of the interaction between the neighboring levels belonging predominantly to the different potential surfaces is strongly dependent on the relative positions of these levels; on the other hand the accuracy with which the vibrational term values, corresponding to the potential energy surfaces calculated in the framework of the Born–Oppenheimer approximation (or their diabatic counterparts), are computed is limited by the uncertainty of the points determining the latter. There are strong indications (14, 24–29) that the energy difference between the minima of the A 2P and the X 2S / electronic states of C2D, DTe , is underestimated by 200–400 cm01 in the present ab initio calculations. It is clear that this error is too large to ensure a quantitatively reliable reproduction of the mentioned ‘‘local’’ effects and this must be kept in mind in interpretation and prediction of the experimental observations. The above-mentioned difficulties are reflected in Table 4 where the results of the present ab initio calculations are compared with previous experimental results. The spin–orbit splitting of 00.24 cm01 for the lowest-lying K Å 1 vibronic level is in a very reasonable agreement with the corresponding experimental result of 00.217(3) cm01 (12). Let us stress that the appearance of the spin–orbit splitting in this vibronic species, assigned to the S / electronic state,

TABLE 2 Molecular Parameters for the X 2P (0, 1, 0) r 2P (3513 cm01 ) Hot Band of C2D: 2P (3513 cm01 )

a The numbers in parentheses correspond to one standard derivation of the least-squares fit in units of the last quoted decimal place. b Parameters constrained to the value from Ref. ( 1). c From Curl’s relationship (30).

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TABLE 3 LMR Data of the Vibronic X 2II (0, 1, 0) r 2II (3513 cm01) Transition of C2D Included in the Least-Squares Fit

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TABLE 3 —Continued

can be explained only by vibronic coupling of the S / with the P electronic state. The agreement between the computed and the experimentally derived value for the B rotational constant [1.196 and 1.2035(1) cm01 , respectively] is, as

expected, very satisfactory because this quantity is determined predominantly by the equilibrium geometry of the S / electronic state. However, the agreement between the theoretical and experimental results is much worse for the

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TABLE 3 —Continued

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TABLE 3 —Continued

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TABLE 3 —Continued

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TABLE 3 —Continued

cases where strong mixing of all three electronic species takes place. Particularly, the spin–orbit splitting computed for the level assigned to (07, 0) (at 3477 cm01 ) of 011.93 cm01 overestimates by almost a factor of two the previous experimental value of 06.363(2) cm01 (1), as well as the result of present measurements (value constrained to 06.363 cm01 ). An appreciable difference also is noted for the value of the B rotational constant (computed: 1.142 cm01 , previous experiment: 1.16245(1) cm01 (11), present experiment: 1.16240(1) cm01 ). As has been found in our previous studies (19, 22, 25–29), the main reason for discrepancies between the results of the ab initio calculations and the corre-

sponding experimental data seems to be the error in computation of the energy separation of the minima of the P and S / potential surfaces. To analyze the effect of this error on the computed spin–orbit splittings and the B rotational constant, we carried out a series of calculations increasing the value for DTe up to 400 cm01 with respect to the originally computed energy difference of 3468 cm01 . Figure 3 presents the spin–orbit splittings computed for three levels calculated to lie in the energy region between 3400 and 4100 cm01 . They are plotted as functions of the increment of the energy separation DTe between the P and S / electronic states with respect to the original ab initio value. At DTe Å

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TABLE 4 Spin–Orbit Splitting AE, Vibronic Energies E, and P Character of the K Å 1 Vibronic Levels in C2D

Note. All vibronic states correspond to £1 (D–C) Å 0. E Å vibronic energy [with respect to the lowest-lying vibronic level (0, 0, 0), K Å 0]; AE Å spin–orbit splitting; P Char. Å P character defined as sum of squared coefficients over the vibrational basis functions corresponding to both components of the pure P electronic state.

3468 cm01 these vibronic species are assigned to (0, 0 0 , 0), (0, 1, 2), and (0, 7, 1) (14). The term values and P character of the levels in question also are indicated. Two of the vibronic states considered, assigned at DTe Å 3468 cm01 to (0, 11, 0) and (1, 3, 0), are characterized with small values for the spin–orbit splitting, not changing appreciably by varying the energy difference between the P and S / electronic states. On the other hand the vibronic species assigned tentatively as (0, 0 0 , 0), (0, 1, 2), and (0, 7, 1), according to the form of the corresponding wavefunc-

tions and some additional criteria that first excited bending level of the electronic X ground state (14), undergo dramatic changes in energy and particularly in P character during the process of shifting of the P potential surface upward. The energy of the first and second of these three states in the increasing energy order (denoted in Fig. 3 by 1 and 2, respectively) increases by 180 cm01 , that for the highest-lying species (curve 3 in Fig. 3) by almost 200 cm01 on increasing the P – S / separation from 3468 to 3868 cm01 . The P character, as well as the magnitude of the spin–orbit splitting

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FIG. 3. Ab initio computed spin–orbit splittings A SO of some K Å 1 vibronic levels of C2D lying in the energy region between 3400 cm01 and 4100 cm01 as functions of the energy separation between the P and S electronic states employed in the calculations. The experimentally derived value for A* Å 30 cm01 is employed. Tentative assignments ( n1 , n2 , n3 ) on the right-hand side of the curves is made according to the compositions of the vibronic wavefunctions computed at DTe Å 3468 cm01 . At several points the term value and the P character (in parentheses) of the vibronic level in question are given. Horizontal dashed line indicates the magnitude of the experimentally observed spin–orbit splitting in the vibronic level considered in the present study.

of the lowest-energy species [(0, 0 0 , 0) according to the assignment resulting from calculations in which the originally computed P – S / separation is employed] decreases continuously by enlarging the P – S / separation; the situation is just opposite with the highest-energy species 3. A consequence of such behavior is that the character of these two states is interchanged at the P – S / separation of /385 cm01 close to the previously estimated proper value of approximately 3468 / 270 cm01 (19). The P character of the level 2 [assigned to (0, 1, 2) at the original P – S / separation] is nearly unchanged for a small increase of the P – S / separation ( DTe Å 0–100 cm01 ) and decreases continuously at further enlargement of this quantity. The experimentally observed spin–orbit splitting of the vibronic level is 06.363(2) cm01 (1). The horizontal line in Fig. 3 corresponds to this experimentally determined spin–orbit splitting. Species 1 in Fig. 3 at the value of DTe of approximately 3468 / 385 cm01 indicates that the original ab initio result underestimates the actual energy difference between the P and the S / electronic states by this amount, in reasonable accordance with the conclusion of our study on C2H (19). The corresponding term value of the vibronic level in question is É3620 cm01 , which is in reasonable agreement with the experimental result of 3513 cm01 . The P character of this species is computed to be É0.33. On the other hand, the value for the spin–orbit splitting of the level

3 computed employing the same P – S / separation is approximately 011.41 cm01 , its term value is 4017 cm01 and its P character is 0.73. This level should correspond to the observed 3856-cm01 feature. These results support the conclusion by Forney et al. (7) that ‘‘. . . A Ç (0, 0, 0) is the minor component and X Ç (0, 1, 2) is the major component of the band near 3500 cm01 and . . . the reverse is true for the 3856 cm01 band.’’ In favor of this assignment also the values for the B rotational constants are computed for these states, 1.163 cm01 for the level corresponding to the experimentally observed 3513-cm01 feature [experimental derived value 1.1625(1) cm01 (1)] and 1.135 cm01 for the counterpart of the 3856-cm01 band [experimental value 1.13160(2) cm01 (12)]. Let us note that the interchange of the character of the vibronic states assigned to (0, 0, 0) and (0, 1, 2) on correcting the P – S / separation was anticipated in our previous work (14). The vibronic term values, P character, and the spin–orbit splitting for the K Å 1 vibronic levels of C2D, computed employing the P – S / separation enlarged by 385 cm01 are presented on the right-hand side of Table 4. The splitting for the lowest K Å 1 level calculated in this way is 00.24 cm01 , in excellent agreement with the experimental result of 00.217(3) cm01 (12). These ab initio calculations [employing the corrected P – S / separation and the experimentally derived value for A* Å 030(1) cm01 ] reproduce cor-

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rectly the experimental finding that the largest spin–orbit splitting in the energy region considered corresponds to the level observed at 3856 cm01 . Even the magnitude of this splitting computed 011.41 cm01 is in excellent agreement with the experimentally derived counterpart 011.167(2) cm01 (1) (the spin–orbit splitting would be 09.51 cm01 only employing the enlarged P – S / separation, but the ab initio determined spin–orbit constant A* of 025 cm01 ). This indicates that for a better agreement the energy difference between the minima of the potential surfaces for the P – S / electronic species had to be corrected. The same conclusion was derived by Forney et al. (7), as well as in our previous study on C2H (19). So, for example, the level denoted by 2 in Fig. 3 is computed to lie rather close ( É140 cm01 ) to the level 3 (corresponding to the observed 3856-cm01 feature) when the original P – S / separation of the potential surfaces is enlarged by 385 cm01 —the spin–orbit splitting of the former species is computed to be approximately 1.3 cm01 , which can be explained by the P character borrowing from the vibronic state 3. The fact that the ab initio computed potential surface for the P electronic state had to be shifted by somewhat different amounts in the case of C2D than for C2H (19) indicates that not only the energy difference between the minimums of the two electronic states in question, but also the form of the corresponding potential surfaces should be modified slightly in order to achieve better reproduction of the experimental results. This has already been stated by Forney et al. (7). A consequence of the modifications of the form of the potential surfaces, particularly for the S / electronic state, would be a significant change in the positions of the vibronic levels corresponding higher £2 quantum numbers; the term values for the levels (0, 0, 0) and (0, 1, 2) would be much less influenced. 5. SUMMARY

In this publication we reported the measurement of a hot band of the X 2S / r A 2P electronic transition by Faraday LMR spectroscopy. The analysis of the data allowed us to determine the term value of the first excited bending mode X 2P (0, 1, 0). The mixing between the electronic X and A states could be deduced using the orbital g factor of the upper level. The comparison of the experimentally derived values with theoretical calculations allowed a sensitive test of the theoretical model. The energy difference between the potential surfaces of the X and A states had to be shifted upward É385 cm01 to get good agreement with the experimental results. These corrections yielded a new interpretation and assignment of the energy levels of this radical. ACKNOWLEDGMENTS The authors are grateful to Dr. H. Ko¨rsgen for experimental advice and helpfull discussions. This work has been supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 334.

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