Emission Spectroscopy of the Triplet System of the BH Radical

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

177, 90–105 (1996)

0121

Emission Spectroscopy of the Triplet System of the BH Radical C. R. Brazier Hughes STX, Phillips Lab./RKS, Edwards Air Force Base, California 93524-7680 Received November 20, 1995; in revised form February 15, 1996

The b3S0 –a3P system of BH has been extensively characterized by emission spectroscopy using a CESE source. Vibrational levels up to £ Å 8 in the b3S0 and £ Å 7 in the a3P state were observed, allowing construction of RKR potential curves covering almost 80% of the well depths. Dissociation energies were estimated from the observed vibrational levels using the near-dissociation extrapolation method. Comparison of the extrapolated curves with theoretical calculations resulted in the following best estimates for the dissociation energies: a3PDe Å 19 250 cm01, b3S0De Å 20 960 cm01. The BH singlet–triplet separation is estimated to be 10 410 cm01. The recently observed predissociation of the b3S0 state was too weak to be detected. q 1996 Academic Press, Inc.

are in reasonable agreement with recent theoretical work and current experimental data. During the course of this study, Yang et al. (25) used laser induced fluorescence to determine the lifetime of several rotational and vibrational levels of the b3S0 state. In this work, the triplet system of BH was originally recorded as part of a study of boron species that focused primarily on B2 (26–28), with the overall goal of studying species that could be stored in solid hydrogen for use as high energy density rocket fuels (29). Extremely strong spectra of BH were observed; since only the 0–0 band of the triplet system had previously been recorded (1, 3), and then only with low precision, the D£ Å 0 sequence was measured at high resolution using the Fourier transform spectrometer at Kitt Peak National Observatory. To permit full determination of the energy levels in both states, the weaker off-diagonal bands were subsequently recorded using a 1.3 m monochromator and OMA. We present here a detailed analysis of the observed bands, which extend up to 80% of the dissociation limit in the a3P state and 75% in the b3S0 state. The potential curves derived from these observations are compared with the most recent theoretical results (23). The intensities of the observed lines were carefully examined, and the results are compared with the theoretical predictions of predissociation by the (1)3S/ state (24, 25).

INTRODUCTION

The BH molecule has been the subject of numerous spectroscopic (1–9) and theoretical (10–16) studies. Most of these have tended to concentrate on the singlet systems, especially the A1P –X1S/ system (6, 7, 13). The presence of a shallow well and a barrier to dissociation in the A1P state has made possible an accurate determination of the dissociation energy for BH (17–20). The lowest limit of BH {B(2P) / H(2S)} also gives rise to the a3P state. The b3S0 – a3P transition near 27 000 cm01 is the only known triplet system of the BH radical. This system was first observed by Lochte-Holtgreven and van der Vleugel in 1931 (1) and more extensively analyzed and assigned as 3S – 3P by Almy and Horsfall in 1937 (3). They analyzed the 0–0 band and obtained rotational constants and the 3P state spin–orbit splitting graphically. Recently, Yang and Dagdigian (9) observed chemilumenescent emission in the b3S0 –a3P system from the reaction of 4p 2P boron with hydrogen. There had been no further rotationally resolved observations of the BH triplet system until the present work. Interest in the triplet system of BH has increased recently due to the development of a possible chemical laser based on the A1P –X1S/ system of BH (21, 22). The BH molecules were excited from the ground X1S/ state to the A1P state in two steps via the a3P state by near-resonant energy transfer from excited NF. Accurate characterization of the triplet states of BH is important for understanding the excitation process and for performing reliable diagnostic measurements (22). Theoretical calculations of the radiative decay rate of the a3P state (23) and the radiative and nonradiative decay rates of the b3S0 state (24) have been performed by Pederson et al. to assist in the characterization of the BH excitation scheme. These calculations have also proved useful for comparison with the present experimental observations. Most of the other theoretical calculations that have included the triplet states of BH (10, 11) are quite old, although the results

EXPERIMENTAL

The BH radicals were produced in a corona excited supersonic expansion (CESE) (30) of dilute diborane (B2H6) in 3 atm helium. The seeded gas is expanded through a glass nozzle into a vacuum chamber evacuated by a Roots pump. A tungsten wire extends almost to the tip of the nozzle, and when a high voltage is applied a corona discharge is generated in the throat of the expansion. Detailed experimental information can be found in the earlier work on B2 (26). 90

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The only significant difference for this study was that the BH signal was optimized at slightly lower diborane concentrations, typically 100 ppm. When the discharge was operating correctly, a bright purple glow from the strong A1P – X1S/ system of BH was visible in the supersonic flow. This glow continued past the shock fronts into the background gas all the way to the electrical ground. The A1P –X1S/ system of BH was so intense that even the extremely weak (calculated Franck–Condon factor 0.001 for 0–2 (6)) 0–2, 1–3, and 2–4 bands were observed. The light from the region just beyond the tip of the nozzle was focused onto the entrance window of the 1 m Fourier transform spectrometer at Kitt Peak National Observatory. The use of diborane in a CESE source leads to significant production of solid polymer, which tends to clog the nozzle. Consequently a series of short accumulations of data were made, for a total of 10 scans in 20 min. The observed linewidth was 0.14 cm01, comprising an instrumental width of 0.07 cm01 and a Doppler spread of 0.12 cm01. The fairly large Doppler spread is due to the use of a moderately wide slot nozzle (31, 32) to minimize clogging. The small aspect ratio of the slot (300 mm 1 1500 mm) results in a significant spread of molecules toward and away from the spectrometer. The resolution was still sufficient to resolve the spin structure throughout the spectrum. The strongest transitions in the BH spectrum have a signal-to-noise ratio of 150:1 and as the FWHM is 0.14 cm01, it is possible to determine the relative positions of these lines to about 0.001 cm01. The measurement precision for the other bands drops with the decreasing signal-to-noise ratio but is typically on the order of 0.01 cm01. The accuracy of the measurements is limited by the absolute calibration of the FTS. Slight misalignments of the source with respect to the FTS or directing of the jet towards or away from the spectrometer could lead to shifts of 0.01 cm01 or more. The only available calibration line in the current spectrum ˚ . The 33P–23S line is the 33P–23S helium line at 3888.65 A appears in the current spectrum as a partially resolved doublet with one component eight times as strong as the other. The strong line comprises the unresolved 3P2 – 3S and 3P1 – 3 S components and the weak line the 3P0 – 3S component. The term energies of all the components are given to high accuracy by Martin (33). The relevant data are also listed in the NIST Database for Atomic Spectroscopy (34). The 3 P2 – 3S and 3P1 – 3S lines are at 25 708.5875(10) cm01 and 25 708.6095(10) cm01, respectively. The intensity weighted average position for the two overlapped components is 25 708.6007(10) cm01. Measurement of the position of the 33P–23S He line in the BH spectra is complicated by an apparent splitting of both the strong and weak components. The size of the splitting and relative intensities of the two components is different for each of the three scans, as can be seen in Fig. 1. This suggests that the structure of the line is a result of the source. The position of the 33P–23S He line was determined by

FIG. 1. The 3P– 3S helium line, as it appears in the three data scans. The 3P2 – 3S and 3P1 – 3S components are unresolved at this resolution. The line shows different structure in each of the three scans. The position of the emission line shifts in each scan due to changes in alignment of the jet. The splitting of the lines is from absorption by the background gas in the chamber, which does not change between scans. The sinusoidal structure is ringing, an instrumental artifact.

fitting two peaks to the split line and averaging the positions, weighted by the areas of the two components. The 33P–23S He line was found to be red shifted by 0.0440 and 0.0602 cm01 for the second and third data sets relative to the first. Comparable shifts were also seen in the BH spectra; for example, the 0–0 P1(2) line exhibits shifts of 0.0443 cm01 and 0.0599 cm01 between the three data sets. As for the BH line position measurements, the actual calibration was performed using the sum of the three spectra resulting in a weighted average line position of 25 708.5782 cm01. This is a shift of 0.0225 cm01 compared to the known position, which corresponds to a fractional shift of 8.752 1 1007. The frequencies of all of the BH lines were adjusted by this factor. The absolute accuracy of the BH line position measurements is limited to about {0.005 cm01 by the difficulty of estimating the effects of the structure on the calibration line. The relative precision of the measurements remains high, up to 0.001 cm01 for strong unblended lines. The origin of the structure of the helium line is most likely self absorption in the background gas between the jet and the window of the vacuum system. The 23S state of He is metastable with a very long gas phase lifetime in the absence of collisions. The fact that the position of the absorption peak remains fixed, while the emission peak shifts as the alignment of the jet is changed, supports this supposition. The amount of absorption is somewhat different in each scan, but if an average absorption of 40% is assumed then this equates to a population density of metastable He 23S of about 3 1 1006 Torr over the approximate 10 cm path length. The intent when recording the FT data was to measure only the strong 0–0 and possibly the 1–1 and 2–2 bands. Consequently the region of observation was restricted to the

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FIG. 2. The origin region of the 0–0 band of the b3S0 –a3P system of BH. Each line is split into three due to the spin structure in the a3P state. In addition, each transition has a weak satellite due to the 10BH isotope.

25 600–28 600 cm01 range by appropriate filters (Corning 7-60 UV-transmitting black glass and Schott WG-360 red pass). While this improved the signal-to-noise ratio by blocking out the strong BH A1P –X1S/ and B1S/ –A1P systems, it also blocked any off-diagonal triplet bands. To provide information on the vibrational frequencies in the a3P and b3S0 states, additional BH emission spectra were recorded using a 1.3 m monochromator and OMA. The resolution was lower, about 0.85 cm01, but the sensitivity was much higher. The D£ Å /1 sequence was observed out to the 8–7 band and some bands in the D£ Å /2 and D£ Å 01 sequences were also observed. The higher sensitivity also allowed extension of the D£ Å 0 observations up to the 7–7 band and to higher rotational levels for the previously observed bands. The OMA spectra were calibrated by recording the spectrum of a thorium/neon hollow cathode lamp placed behind the cell, with the emission imaged at the tip of the jet so as to minimize alignment errors. The observed thorium and neon lines were compared with those listed in the atlas of Palmer and Engleman (35) and a calibration function was generated for the region of interest. RESULTS

The b3S0 –a3P system of BH is a typical Hund’s case b to case b 3S – 3P transition with strong P and Q branches and weaker R branches, and with each rotational transition split into three components due to the electron spin. This can be seen clearly in Fig. 2, which shows the origin region of the 0–0 band. The first lines are clearly visible, and as the F1 component is the strongest, assignment of the branches is straightforward. For low J values there are also a limited number of weak satellite branch lines (DJ x DN), which are useful for simultaneously determining the spin structure

in both the S and P states. Boron has two naturally occurring isotopes, 10B and 11B, present in the ratio 1:4. This results in weak 10BH satellite lines on the side away from the origin for the 0–0 band lines, as can be seen in Fig. 2. Even though the BH molecules were produced in a supersonic expansion the spectrum shows little sign of rotational cooling. The strongest part of the spectrum, near the origin, has a rotational temperature near 300 K, and there is also a weaker high temperature tail extending out to J of about 40, which corresponds to a ‘‘temperature’’ of approximately 4000 K. The positions of the BH D£ Å 0 b3S0 –a3P band lines were determined from the FT spectrum using DECOMP, a spectral deconvolution program developed at the National Solar Observatory. A list of the line positions and the estimated errors from the least squares analysis is given in Table 1. The 0–0 band rotational lines are generally free from overlap, except for the R branch, which reaches a bandhead at N Å 17, a crossing of the F2 and F3 components in the Q branch, and a crossing of the isotopic satellite lines through the main transitions. A least-squares fit of the calibrated BH 0–0 band lines to standard 3P and 3S0 Hamiltonians was performed. The Hamiltonian and principal matrix elements are given by Brown et al. (36), while explicit matrix elements to high order in centrifugal distortion are given by Brazier et al. (37). The 0–0 band data extend up to N Å 40, which has 17 800 cm01 of rotational energy. Hence it was necessary to include the terms B, D, H, and L for the rotational expansion. As the transition quickly becomes case b in character, the only other term requiring a large centrifugal distortion expansion was the lambda doubling parameter q, since the high N levels split into two groups with effective rotational constants differing by q. The 0–0 band line positions were fitted to their estimated measurement accuracy. The parameters determined from the fit of the 0–0 band data are given in Table 2. Subsequently, the other D£ Å 0 bands, 1–1, 2–2, 3–3, 4–4, and 5–5, were identified and fitted. The vast majority of the lines observed were in the main DN Å DJ branches, but a small number of low J satellite lines were observed, 22 in the 0– 0 band and fewer in the other bands. The line positions and errors from the least-squares fit are given in Table 1. The high resolution FTS data for the D£ Å 0 bands were supplemented by data recorded at 0.85 cm01 resolution using a monochromator and OMA detector for the off-diagonal bands. The b3S0 and a3P potential curves of BH are very similar, so the off-diagonal bands are expected to be weak. A search was made in both the D£ Å /1 and D£ Å 01 regions based on theoretical estimates of the vibrational frequencies (23). The search was complicated by overlapping BH singlet bands in both regions. The 1–0 band was eventually found, under the main D£ Å 0 sequence of the B1S/ – A1P system. The higher bands in the D£ Å /1 sequence of the b3S0 –a3P system were then traced out all the way from 1–0 through 8–7. Line positions and errors from the least-

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TABLE 1 Observed Transitions in the b3S0 –a3P System of BH (in cm01)

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TABLE 1—Continued

squares analysis are given in Table 1. The intensities of the bands change very little until the 6–5 band, which is weaker than the earlier bands by a factor of 4. All of the higher bands are relatively weak. With the observation of the 1–0 band, the location of the 0–1 band could be predicted exactly. The 0–1 band was found to be extremely weak, and in addition it was overlapped by the 2–1 band of the A1P – X1S/ system. No further bands in the D£ Å 01 sequence were sufficiently strong to be measured. The significantly higher signal-to-noise ratio of the monochromator/OMA data, combined with coverage of the regions blocked by the spectral filters in the FTS data, made possible the extension of the D£ Å 0 data set to higher rotational levels. In addition the 6–6 and 7–7 bands were found. The D£ Å /1 bands were each analyzed separately. The

bands could be fitted while the rotational constants were constrained to values determined from the D£ Å 0 bands. Most of the bands were well behaved and the data could be fitted using a small number of parameters that varied in a predictable way from band to band. The 6–5 and 6–6 bands, however, were very difficult to reproduce adequately, and the parameters determined were different from those expected based on analysis of the other bands. This is clear evidence of a perturbation in £ Å 6 of the b3S0 state. While the b3S0 lines were clearly shifted, there was no evidence of extra lines from the perturbing state. In order to perform a complete analysis of all the bands, a modified fitting program was developed in which all of the parameters in both states could be expanded in Dunham type series in the vibrational quantum number. Since

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95

TABLE 1—Continued

the £ Å 6 level was known to be perturbed, the parameters for this level were allowed to float separately from the Dunham parameters. The individual vibrational bands were added one at a time to the fit, and the number of

parameters slowly increased. All of the levels observed, £ Å 0 through £ Å 7 in the a3P state and £ Å 0 through £ Å 8 in the b 3S0 state (except £ Å 6), could be adequately reproduced using a single set of Dunham parameters for

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TABLE 1—Continued

each state. The levels above £ Å 6 in the b3S0 state show some effects of possible perturbation. In the final fit the parameters for £ Å 8 were allowed to float separately. This level could be fitted simultaneously with the others, but only by including extra terms in the vibrational and rotational parameter expansions, which then led to significantly different values for the other terms in each expansion. For the final fit a total of 69 parameters were required

to reproduce the 1336 lines observed. The equilibrium parameters and their one standard deviation error estimates from the least-squares fit are listed in Table 3. The higher order corrections to the parameters, which do not have common designations, are named by the parameter and the correction order in parentheses. The set of parameters consisted of 34 for the a3P state, 24 for the b3S0 state, and 11 for the £ Å 6 and £ Å 8 levels of b3S0 (listed in Table 4), which were allowed to float separately. The

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TABLE 1—Continued

vibrational levels observed extend from the bottom of the potential wells most of the way to dissociation; hence, a large number of constants were required to reproduce the observed line positions to within experimental error. One

TABLE 2 Spectroscopic Constants for the 0–0 Band of the b3S0 –a3P System of BH (in cm01)

less parameter than the number of vibrational intervals observed was required to reproduce the vibrational energy levels for both the a3P and the b3S0 states. Similarly six rotational constants were required for the seven b3S0 levels, although only five were needed for the eight a3P levels. The larger number of rotational constants required for the b3S0 state is probably due to the perturbation that has its strongest effect at £ Å 6. The electronic character of the two states clearly varies little with £, and hence with r, as only a single spin – spin parameter was required for each electronic state and the spin – orbit interaction in the a3P state required only two terms. As was the case for NH (37), the spin – rotation interaction, g, and the centrifugal correction to the spin-orbit interaction, AD, could not be simultaneously determined. The parameter AD was constrained to the value calculated from the formula due to Veseth (38), but modified for equilibrium values, AD Å 2AJ Å 2aADe/(ae / 6Be2/ve), where aA is the vibrational correction to the spin – orbit parameter A. The 10BH isotopomer lines could be identified for all of the strong bands, but only for the 0 – 0 band were the line positions measured and fitted. A list of the line positions is given in Table 5, and the molecular parameters are in Table 6. Except for the origin, the constants for the 0 – 0 band of 10BH are all within 3 s of the values estimated from the 11BH parameters by scaling appropriately for the

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TABLE 3 Equilibrium Constants for the b3S0 –a3P System of BH (in cm01)

tion energy is extremely close, while the equilibrium separations are slightly shorter than predicted. The vibrational frequencies are also slightly higher than predicted for both electronic states, indicating that the binding in the theoretical potential curves is not quite tight enough near equilibrium. Values of the De, He, and ae rotational constants for both electronic states can be readily evaluated from standard formulae (39). A comparison with the observed values is shown in Table 8. The values for De and ae match extremely well, indicating that the bottom of each potential well is well described by a Morse oscillator, for which the formulae are exact. A slightly larger deviation is observed for He, which is determined by more highly excited rotational levels that sample higher regions of the potential. Approximate values for the fine structure parameters for diatomic hydrides may be obtained from the atomic fine structure parameters by following the methods of LefebvreBrion and Field (40). For the a3P state (1s22s23s11p1) the spin–orbit splitting, A, is equal to z/2, where z is the atomic spin–orbit parameter for boron (z Å 10.7 cm01). This gives A Å 5.4 cm01 compared to the observed value of 4.39 cm01. While ab initio calculations of A have not been performed, the off-diagonal »3P1ÉHSOÉ1P1… term was calculated to be 4.45 cm01 at the equilibrium separation (23). If the vibrational overlap between the 3P and 1P states is close to a delta function, a good approximation for these potentials near equilibrium, then the off-diagonal term is equal to the diagonal one (40). The match between the calculated offdiagonal spin–orbit interaction and the measured diagonal spin–orbit interaction is extremely good. The spin–spin splitting in the b3S0 state can arise either from the direct first-order spin–spin interaction, or via second-order spin–orbit effects. The second-order effect arises mainly from the interaction with the 1S/ state that comes from the same 1s22s21p2 configuration as the b3S0 state (40). Bauer et al. (4) showed that this is the C1S/ state, with B1S/ being the 3s Rydberg state. Using the singlet–triplet separation from this work (see later), the b3S0 –C1S/ separa-

TABLE 4 Spectroscopic Constants for the Perturbed £ Å 6 and 8 levels of the b3S0 State of BH (in cm01)

reduced mass. The 10BH bands show an overall electronic isotope shift of /0.214 cm01 relative to the 11BH bands. DISCUSSION

Molecular Constants The equilibrium constants for the triplet states of BH have been determined for the first time. For the 0–0 band, which had been observed previously (1, 3), the constants are consistent, but much more precise. The equilibrium constants are compared with ab initio predictions (23) in Table 7. The transiCopyright q 1996 by Academic Press, Inc.

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TABLE 5 Observed Transitions in the 0–0 Band of the b3S0 –a3P System of 10BH (in cm01)

tion is calculated to be 18 180 cm01. The spin–orbit contribution to l is 2A(3P) Å 0.0021 cm01, E( S/)–E(3S0) 1

which is less than 1% of the observed value. The direct contribution can be calculated approximately for a hydride

TABLE 6 Spectroscopic Constants for the 0–0 Band of the b3S0 –a3P System of 10BH (in cm01)

as six times the atomic spin–spin interaction of the heavy atom. The value for the spin–spin interaction for boron is not known very precisely, but is consistent with the observed spin–spin splitting. There are three lambda-doubling terms in the a3P state, o, p, and q. The o term has contributions from direct firstorder spin – spin effects as well as second order spin – orbit effects (40). As for the spin – spin interaction in the b3S0 state, the second order effects are found to contribute less than 1% of the interaction. Using the interaction terms of Horani et al. (41) and scaling for the boron spin – spin interaction, the first order contribution to o is estimated to be 0.4 cm01, fortuitously close to the observed value of 0.403 cm01. The primary contribution to the other lambda doubling terms p and q is from the interaction with the b3S0 state. The simple pure-precession formulae should hold fairly well

TABLE 7 Comparison with ab initio Predictions

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TABLE 8 Comparison of Molecular Constants (in cm01)

in this case as the orbitals involved are close to boron 2p in character and the Franck–Condon factors for D£ Å 0 between the b3S0 and a3P states are close to unity near the bottom of the wells. The values determined, pÅ

04AB Å 0.00832 cm01 and E( P) 0 E(3S0)

qÅ

04B2 Å 0.0245 cm01, E(3P) 0 E(3S0)

3

are fairly similar to the observed p Å 0.0052 cm01 and q Å 0.0201 cm01. The discrepancy most probably arises from neglect of interactions with other higher lying 3S states, in particular the repulsive (1)3S/ state. This state has a shelf in the region of the a3P minimum (24) due to an avoided crossing between the repulsive 3S/ state coming from the lowest asymptote, which has a 1s22s23s14s1 configuration, and the lowest 3S/ Rydberg state (3s), which has a 1s22s23s15s1R configuration. The interaction with the shelf part of the repulsive potential is expected to produce significant contributions to the lambda doubling parameters.

The two curves lie almost exactly above each other, with ˚ more tightly bound. As a result the a3P state being 0.03 A the transition is highly diagonal in nature, at least for the lower lying levels. Figure 4 shows the two potential curves shifted so that their minima are both at zero energy. The relative experimental intensities are in agreement with this observation, as can be seen in Table 10. The values in Table 10 reflect both the Franck–Condon factors for the transitions and the populations of the vibrational levels in the b3S0 state. The values for 0–0 through 5–5 are taken from the Fourier transform data and hence are fairly reliable. The remaining data is from the series of spectra taken using an OMA detector, scaled to match the FTS data. Due to variations in source conditions, wavelength dependence of the instrument response, and changes in sensitivity across the width of the array detector, the precision of the data is fairly low. It should only be used as an approximate guide to relative intensities. For the higher vibrational levels we would expect to see other sequence bands becoming strong. Experimentally the D£ Å /1 sequence is observed to gain rapidly in intensity; in addition, the D£ Å 01 and D£ Å /2 were also observed although they were much weaker than the D£ Å 0 and D£ Å /1 sequences. A simple Franck–Condon factor calculation based on the experimental RKR curves was performed, but the results did not match the experimental observations. In particular the D£ Å 01 sequence was predicted to become strong for the higher vibrational levels, but experimentally this sequence was observed to be weak and die out at higher £. The tendency toward the D£ Å 01 sequence, or red part TABLE 9 RKR Parameters

RKR Potential Curves A large number of vibrational levels have been observed and characterized for both the a3P and b3S0 states of BH. Comparison with the theoretically calculated dissociation limits (23) suggested that the experimentally observed levels covered more than 80% of the potential energy surfaces for both states. The RKR method was used to generate experimental potential curves from the vibrational energies and rotational constants. For the perturbed £ Å 6 level in the b3S0 state the calculated energy and rotational constants from the fit to the other experimental levels were used rather than the observed values. The RKR turning points, together with the vibrational energies and rotational constants, are listed in Table 9. The experimental curves extend well into the anharmonic region of the potential as can be seen in Fig. 3. Copyright q 1996 by Academic Press, Inc.

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TABLE 10 Approximate Relative Intensities of the Observed Bands

FIG. 3. RKR potential curves and vibrational energy levels for the a3P and b3S0 states of BH. The observed levels extend well into the anharmonic region of the potential in both cases.

of the Franck–Condon parabola, for high £ arises from the slight shift of the two potentials that results in preferential overlap for this sequence for the outer lobes of the vibrational

wavefunctions. The lack of intensity for this part of the Franck–Condon parabola implies that although the molecules are spending the majority of the time in the outer part of the potential they are not fluorescing while in this region of the potential. This observation is consistent with the theoretical transition dipole moment function of Pederson et al. (23), which, as can be seen in Fig. 4, is strongly peaked toward short internuclear distances. When the transition dipole moment function is included in the Franck–Condon factor calculation, the calculated values match the experimental observations much more closely. If the slope of the transition dipole moment function is adjusted slightly to ˚ rather than the calculated 2.5 A ˚, bring it to zero near 2 A then the match is exact, considering the accuracy of the experimental intensity measurements. The strong peaking of the transition moment to shorter internuclear separations results in emission from the higher vibrational levels occurring when the molecules are near the inner wall of the molecular potential. As the b3S0 state has a slightly longer bond length than the a3P state, this favors the blue part of the Franck–Condon parabola and particularly the D£ Å /1 sequence. Dissociation Energies

FIG. 4. The RKR potential curves shifted so that both equilibrium points are at zero energy. The a3P state is slightly more tightly bound, which would usually favor D£ Å 01 bands for the higher vibrational levels due to more favorable overlap of the outer parts of the vibrational wavefunctions. The theoretical transition dipole moment function is strongly peaked toward short internuclear distances. This leads to emission from high vibrational levels occurring at the inner turning point, favoring D£ Å /1 bands.

The observed vibrational levels in both the a3P and b3S0 states cover a substantial fraction of the bound part of the potential, such that it should be possible to obtain reasonable estimates of the dissociation energy for both states. The Birge–Sponer (42) extrapolation gives rather poor results, unless the potential is fairly well approximated by a Morse function. The Leroy–Bernstein (43) method improves on this by forcing the extrapolation to have the correct functional form at long range. Recently this method has been much improved by Leroy (44) by including direct fitting of the observed vibrational intervals to many functional forms that all extrapolate correctly to long range. For Leroy’s long range expansion technique to work, an estimate is needed of the leading long-range attraction term. As both dissociation limits involve the 2S state of

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TABLE 11 Long Range Attraction Parameters

hydrogen, this is the C6/r6 term (45). The C6 terms were estimated from the long-range part of the theoretical potential curves (23) for the a3P and b3S0 states. The 15 a0 ˚ ) points were taken as the separated atom limits and (7.9 A ˚ ) points as representative of the long range the 5 a0 (2.6 A region where the C6/r6 term is dominant. The values determined are listed in Table 11. Following the formula from Leroy (44), for the case n Å 6 (the leading long range term) and t Å 1 (next term is C8/ r 8) the vibrational energies are given by G(£) Å D 0 X0(6)(£D 0 £)3

1

1 / p2(£D 0 £)2 / p3(£D 0 £)3 / rrr / p1/L(£D 0 £)1/L 2 1 / q2(£D 0 £) / q3(£D 0 £)3 / rrr / q1/M(£D 0 £)1/M

s

,

[1]

where D is the dissociation energy, £D is the effective (noninteger) vibrational level at dissociation, and the parameters pi and qi are effective fitting constants. The exponent s can be either 1 or 3. The term X0(6) is readily evaluated from C6 (46) and is listed in Table 11 for both states. The eight observed a3P and nine observed b3S0 vibrational energy levels were initially fitted separately to Eq. [1] using different groups of parameters with s Å 1 or 3. The dissociation energy and £D were allowed to vary while X0(6) was held fixed. Typically three additional parameters (L / M Å 3) were required to reproduce the a3P energies, while four were needed for the b3S0 state. The true precision of the vibrational energy level measurements is much less than the error estimates obtained from fitting the experimental data, as it is limited by the accuracy with which the OMA detector could be calibrated. At best the detector was calibrated to half of one pixel, which equates to 0.15 cm01. As a conservative estimate, any parameter set that reproduced the data to within 0.45 cm01 was considered acceptable. Once it had been determined that the two sets of energy levels could be fitted adequately, they were combined together. The difference of the a3P and b3S0 dissociation limits can be evaluated from the equilibrium transition energy and the separation of the boron 2P and 4P limits (34). The degeneracy weighted average of the spin–orbit components was used to obtain the separation of the two boron limits, 28 867.1 cm01. Subtracting the transition energy gives a difference in the dissociation limits of 1714.4 cm01, with

the b3S0 state more deeply bound. The same set of fitting parameters pi and qi were used for both states, but with one extra term in the longer series for the b3S0 state. This was a total of 10 variable parameters to fit the 17 observed energy levels. This compares with 13 parameters to fit the observed energy levels using standard polynomial expansions of harmonic frequencies and anharmonic corrections. The results of the five fits that adequately reproduced the data are listed in Table 12. The five values for De for the a3P state were simply averaged together, without weighting the answers by the quality of the fit, as the more precise fits seemed to reproduce the data to better than their estimated precision. The mean dissociation energy of the a3P state was found to be 19 710 cm01 with a standard deviation of 50 cm01. The De for the b3S0 state is then 21 420 cm01. The effect of varying the C6 long range attraction term was investigated by repeating the fit that had best reproduced the data with either one or both of the C6 terms either increased or decreased by 30%. The maximum change in dissociation energy in this series of fits was 210 cm01. As this represents the estimated error due to the value for C6, the precision of the dissociation energy calculation is estimated to be 1s Å 200 cm01. If the values of X0(6) were allowed to vary in the least-squares fit, then the X0(6) values determined changed only slightly from the calculated values. The change in dissociation energy was also less than the estimated error limit for all parameter combinations tried with X0(6) varying. The £ Å 6 level of the b3S0 state is clearly perturbed and it is possible that the £ Å 7 and 8 levels are also somewhat affected. To ensure that the perturbed levels were not leading to incorrect values for the dissociation limit, sample fits were performed without the £ Å 6, 7, and 8 levels of the b3S0 state. The change in the dissociation energy from these fits was much less than the estimated error, indicating no undue influence on the fit. The experimental dissociation energies are significantly larger than the most recent theoretical calculations (23) (a3P De Å 18 600 cm01, b3S0 De Å 20 190 cm01). The experimental data extend closer to the dissociation limit for the a3P state, so some sample fits of the a3P data were performed with the dissociation energy constrained to lower values. Using De Å 18 600 cm01 for the a3P state it was impossible

TABLE 12 Satisfactory Fits to the Near Dissociation Expansion

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THE TRIPLET SYSTEM OF BH

to fit the experimental data even if X0(6) was allowed to vary. However, as De was allowed to increase, the quality of fit improved rapidly. With De fixed at 19 250 cm01, it was possible to reproduce the data adequately when X0(6) was allowed to float. The value obtained for X0(6) was 41.52 cm01, which corresponds to a 45% reduction from the estimated value of C6 for the a3P state. Considering the approximation used in obtaining a value for C6 this change is not unreasonable. The lowest value for the a3P dissociation limit compatible with the current data is then De Å 19 250 cm01, which is slightly more than 2s from the best estimate. To obtain an idea of which value for the a3P dissociation limit is most reasonable, extrapolated potential curves were generated from the near-dissociation fits and compared with the theoretical potential curves. Two extrapolations were used, one from the best fit set which yielded an a3P dissociation limit of 19 571 cm01 and one with De Å 19 250 cm01, the lowest value compatible with the experimental data. The predicted vibrational energy levels from the near-dissociation fits were combined with estimated rotational constants and the experimental data for the observed levels to obtain RKR potential curves extending close to the dissociation limit. The inner walls of the extended curves were corrected by fitting the inner turning points for the four highest observed levels to an inverse r function. The result obtained ˚ ngstroms. The outer was E Å 5833 1 r08.14 cm01 with r in A turning points for the extrapolated data were adjusted by the same amount as the inner turning points. The two experimental curves were plotted and compared with the theoretical curve (23). Careful examination of the extrapolated long range part of the best fit experimental curve indicates that it is too attractive at large r. This is most likely a result of the long-range fitting process which presumes that the character of the curve does not change between the observed region and dissociation (44). When the extrapolated part of the curve obtained with the dissociation limit fixed at 19 250 cm01 is compared with theory the match at long range is very close. This implies that, while the experimental energies are not reproduced quite as well by this curve, it is probably a more accurate representation of the bound part of the potential. When this curve is plotted along with the theoretical curve such that the dissociation limits match, the difference between them increases steadily as the internuclear distance drops. This indicates that the attractive binding interaction in the theoretical calculations is not quite strong enough. When the theoretical curve was scaled to give a dissociation energy of 19 250 cm01 the match with the experimental curve was essentially perfect. As the difference between the 19 250 cm01 estimate for the dissociation limit and the best fit experimental and theoretical ones is large, the error on the dissociation limit is conservatively estimated to be 1s Å 300 cm01. The b3S0 dissociation limit is then estimated to be 20 960 { 300 cm01. Since the a3P and X1S/ states both dissociate to the same limit, the a3P dissociation limit can be combined with the

best available ground state dissociation limit (19) (X1S/ De Å 29 660 { 170 cm01) to yield the singlet–triplet energy separation. The value obtained, Te –Se Å 10 410 { 300 cm01, is somewhat less than the ab initio estimates, 10 847 cm01 (14) and 10 643 cm01 (23), due to the larger experimental value for the dissociation energy of the a3P state. Predissociation of the b3S0 State Recently Pederson and Yarkony (24) predicted that the £ Å 3 and higher levels of the b3S0 state should be significantly predissociated by a crossing with the repulsive (1)3S/ state that correlates to the lowest 2P / 2S limit. The predicted drop in fluorescence intensity was fairly small, about 30% for £ Å 3. Such a change in intensity is hard to detect in the present spectra, as the excited state vibrational populations do not necessarily vary in a regular way. The population distribution can also change over time due to variations in source conditions. However, as the predissociation is between a 3S0 state and a 3S/ state, the F2 spin level is predissociated at about twice the rate of the other two spin components. This is because the F2 level can couple to two of the 3 / S spin components, while the F1 and F3 levels can only couple to one. The result of this is a predicted change in the relative intensities of the three spin components for each rotational line. The change in relative intensity between the three spin components should have been large enough to detect in the present spectra, but careful examination of several low J lines in the 3–3 and 4–4 bands indicated no significant changes in intensity. During the course of this investigation, Yang et al. (25) made pulsed laser induced fluorescence measurements of the fluorescent lifetimes of the low rotational levels in £ Å 0 through £ Å 4 of the b3S0 state of BH. They found that the fluorescent lifetime was substantially shorter than that predicted by Pederson et al. (24), about 100 nsec compared with about 200 nsec. A degeneracy factor was found to have been omitted in the theoretical calculations, resulting in a factor of 2 error in the calculated fluorescent lifetimes. The corrected theoretical lifetimes are given by Yang et al. (25). The LIF lifetimes clearly showed evidence of predissociation of the b3S0 state above £ Å 3, in good agreement with the revised theoretical predictions. Using the revised lifetimes, the predicted effect on the relative intensities in the emission spectra is a factor of 2 smaller than before. This is at the limit of detectability, considering the low signal-to-noise of the high £ lines and the many overlapping transitions. Hence the lack of any significant change in the intensities in the current spectra does not disagree with the latest lifetime estimates (25). Perturbation of the b3S0 State While no signs of interaction between the b3S0 and (1)3S/ states were observed, there is clear evidence of a perturbation of the £ Å 6 level for the b3S0 state. This level could not

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104

C. R. BRAZIER

be fitted simultaneously with the other b3S0 levels. There was also a sharp drop off in emission intensity (see Table 10) from the levels £ Å 6 and above, presumably due to loss of population from the b3S0 state into the perturbing state. The origin of the £ Å 6 level is shifted up by 0.25 cm01 compared to its predicted position. The rotational constant is also significantly higher than would be expected (9.266 cm01 compared to 9.194 cm01). The spin–rotation interaction is more than an order of magnitude larger than for the other vibrational levels. The shifts in the origin and rotational constant are consistent with an interaction with a lower lying level for which the crossing occurs below N Å 0. The N Å 0 level itself has only one spin component, F1, J Å 1, and was observed only in the 6–5 P1(2) line. This transition could not be fitted with the other lines from the band, and had a residual deviation of 0.3 cm01. A calculation of the 6–5 band using the constants that fitted all of the other vibrational levels (Table 2) showed that the P1(2) line was exactly where it should be if there was no perturbation. The lack of any interaction for N Å 0 and the fact that the remaining lines could be fitted with an effective Hamiltonian, although with significantly different constants from the other levels, is consistent with the perturbation being due to a 3P level. A full deperturbation of the interaction has not yet been completed and will be published elsewhere. If the perturbation of the b3S0 state is due to a 3P state then it is presumably the first excited 3P state that correlates to the same 4P / 2S limit as the b3S0 state. The dominant configuration for the a3P state near equilibrium is 1s22s23s11p1, where the 2s orbital is primarily s-bonding and 3s is primarily nonbonding. The first excited 3P configuration is then 1s22s13s21p1, which is likely to be at least weakly bound. The minimum binding energy required for the perturbing state (presuming that the interaction occurs with £ Å 0) is about 9000 cm01. The 4P / 2S limit gives rise to two other states 5S0 and 5P. The 5S0 state with a 1s22s13s11p2 configuration is likely to be fairly well bound and could be responsible for the b3S0 perturbation, while the 5P state with a 1s22s13s14s11p1 configuration is expected to be highly repulsive. There have not been any ab initio calculations of the higher lying triplet or quintet states of BH, and these would be very useful in understanding the perturbations that have been observed. CONCLUSION

The b3S0 –a3P system of BH has been extensively analyzed. Equilibrium molecular constants for both states were determined. The observation of high lying vibrational levels and off-diagonal bands has made possible the determination of potential curves for both states extending almost 80% of the way to dissociation. The dissociation energies were found to be somewhat larger than predicted by ab initio theory. From the dissociation energies the separation of the singlet and triplet manifolds was determined; this separation

was consequently smaller than had been predicted. Careful examination of the relative intensities showed that the predissociation in the b3S0 state is too weak to be detected in emission. The £ Å 6 level of the b3S0 state was found to be perturbed by a level of an unidentified state, possibly the second 3P state. ACKNOWLEDGMENTS I appreciate the expert technical assistance of J. Wagner, P. Hartman, and G. Ladd of Kitt Peak National Observatory in obtaining the Fourier transform spectra. I thank P. Carrick for assistance in obtaining the spectra and many helpful discussions. I am thankful to L. Pederson and D. Yarkony for communicating their results prior to publication and for providing additional unpublished data. I thank X. Yang and P. Dagdigian for informing me about their very recent fluorescent lifetime measurements. I appreciate the assistance of J. Selco in reviewing the manuscript.

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