J. Phys. Chem. A 2010, 114, 11109–11116
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Experimental and Theoretical Investigations of Rotational Energy Transfer in HBr + He Collisions† Md. Humayun Kabir, Ivan O. Antonov, Jeremy M. Merritt, and Michael C. Heaven* Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: March 15, 2010; ReVised Manuscript ReceiVed: May 5, 2010
Rotational relaxation rates for HBr(V ) 1) colliding with helium atoms at room temperature have been measured using a time-resolved optical-optical double resonance technique. Rotational state selective excitation of V ) 1 for rotational levels in the range J ) 1-9 was achieved by stimulated Raman pumping. The population decay in the prepared states and the transfer of population to nearby rotational states was monitored via 2 + 1 resonance-enhanced multiphoton ionization (REMPI) spectroscopy using the g3Σ--X1Σ+ (0-1) band. Collision-induced population evolution for transfer events with |∆J| e 8 was observed at pressures near 0.7 Torr. The experimental data were analyzed using fitting and scaling functions to generate state-to-state rotational energy transfer rate constant matrices. Total depopulation rate constants were found to be in the range (1.3 to 2.0) × 10-10 cm3 s-1. As a test of current computational methods, state-to-state rotational energy transfer rate constants were calculated using ab initio theory. The total removal rate constants were in good agreement with the measured values, but the transfer probabilities for events with |∆J| g 3 were underestimated. Inspection of the anisotropic characteristics of the potential energy surface did not yield an obvious explanation for the discrepancies, but it is most likely that the problem stems from inaccuracies in the potential surface. 1. Introduction Knowledge of state-to-state rotational energy transfer (RET) rate constants is needed for a variety of applications, such as the prediction of heat transport, thermalization rates, and the analysis of systems that are operating under nonequilibrium conditions (e.g., chemically or optically pumped lasers). Measurement of these rate constants poses a challenge in terms of the number of observations that are needed to characterize even simple systems.1,2 For example, for a diatomic molecule where rotational levels J ) 0-9 have significant populations at thermal equilibrium, a 10 × 10 rate constant matrix is needed to describe RET (provided that the internal states of the collision partner are ignored). The number of observations required to construct this matrix is reduced by application of the principle of detailed balance, but measurement of the 45 remaining independent rate constants is still a laborious task. Clearly, the ability to obtain such a rate constant matrix from first principles theory is highly desirable. Although the techniques required for these calculations are well-established, there have been relatively few investigations of the reliability of thermal rate constant matrices that were predicted using stateof-the-art methods. Studies of collisions between hydrogen halides (HX) and rare gas atoms (Rg) can provide valuable benchmark data. The distribution of states populated by such events are determined by the intermolecular potential energy surface (PES). For several HX-Rg pairs, these surfaces have been derived from cross-beam scattering data, spectroscopic studies of van der Waals dimers, and ab initio theoretical calculations.3-14 Once the PES has been determined, state-tostate energy transfer probabilities and rate constants may be obtained from quantum scattering calculations. (See, for example, refs 15 and 16.) †
Part of the “Klaus Mu¨ller-Dethlefs Festschrift”. * Corresponding author. E-mail:
[email protected].
In the present study, we have investigated HBr + He RET using both experimental measurements and theoretical calculations. There was some practical motivation for the choice of halide, as optically pumped HBr lasers are currently being developed for high power applications.17-19 A pulsed laser pump-probe technique was used to excite individual rotational levels of HBr(V ) 1, J) and follow the transfer of this population to nearby rotational levels induced by collisions with He. A complete set of state-to-state rate constants was compiled by fitting parametric rate constant models1,2,20 to the measured values. Electronic structure calculations were used to compute a PES for HBr + He. Subsequently, full close coupled scattering calculations were applied to generate transfer cross sections and thermal rate constants from the PES. Comparison of the measured and calculated rate constants shows that the latter successfully reproduced the total energy transfer rate constants (state-to-field) but significantly underestimated the probabilities for transfer events with |∆J| g 3. These discrepancies are explored here but not resolved. 2. Experimental Details The pulsed laser pump-probe technique used in these experiments was the same as that of our previous study of HBr + HBr energy transfer.21 Therefore, just the essential features of the experiment are summarized here. Individual rotational levels of HBr V ) 1 were populated by stimulated Raman excitation of the Q-branch lines. The populations in the initially excited level and nearby levels that were populated by collisional energy transfer were probed using resonantly enhanced multiphoton ionization (REMPI). The g3Σ--X1Σ+ (0-1) band was used as the resonant step in the ionization sequence.22 The state preparation and detection lasers both operated with nominal pulse durations of 10 ns. The time between the laser pulses was controlled using a precision delay generator (SRS DG535). A mixture of HBr in He (1:6 ratio) was prepared using a gas manifold and stored in a 2 L glass bulb for later use. Prior to
10.1021/jp102334t 2010 American Chemical Society Published on Web 06/02/2010
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J. Phys. Chem. A, Vol. 114, No. 42, 2010
Kabir et al.
preparation of the mixture, HBr (Matheson Co., purity 99.8%) was purified from H2 and Br2 by freeze-thaw cycles at liquid nitrogen temperature and trap-to-trap (dry ice-ethanol bath) distillation. The ionization cell was evacuated by a rotary pump, and measurements were carried out with a slow gas flow to avoid the build up of products from photodecomposition. The gas flow rate was adjusted to maintain a total pressure in the ionization cell of ∼0.7 Torr. The pressure was measured using a capacitance manometer (MKS Baratron). As described in ref 21, monitoring of the CARS signal from an HBr reference cell was used to ensure that the excitation laser was tuned to the V, J line of interest. The reference spectrum showed clear resolution of the H79Br and H81Br isotopomers for Q branch lines with J > 0. (See Figure 3 of ref 21.) However, the isotope splitting was not resolved in the REMPI spectra used to probe the energy transfer kinetics. Consequently, the results presented here are averaged over the two isotopomers. Note also that the Q(0) and Q(1) lines of the CARS spectrum were partially overlapped, such that data for exclusive excitation of J ) 0 could not be obtained. 3. Results and Data Analysis Two measurement strategies were used to characterize HBr + He RET. In one series of experiments, the lasers were set to excite and detect specific rotational levels (J and J′). The intensity of the detected signal was then characterized as a function of the delay between the laser pulses. The kinetics for the removal of population from the initially excited level was observed when J′ ) J. In the second set of measurements, the delay between the excitation and probe laser pulses was fixed, and the REMPI spectrum showing all populated levels was recorded. Data of this kind were taken for a number of delay times to build up an overall picture of the population evolution. The loss of HBr(V ) 1, J) due to vibrational relaxation was negligible for the pressures and delay times used for the RET measurements. The rate constants for vibrational relaxation induced by HBr and He are 1.8 × 10-14 and
