Rotational Energy Transfer Rate Constants Research Articles

Rotational and vibrational energy transfer in vibrationally excited acetylene at energies near 6560 cm−1

Collisional energy transfer kinetics of vibrationally excited acetylene has been examined for states with internal energies near 6560 cm(-1). Total population removal rate constants were determined for selected rotational levels of the (1,0,1,0(0),0(0)) and (0,1,1,2(0),0(0)) states. Values in the range of (10-18) × 10(-10) cm(3) s(-1) were obtained. Measurements of state-to-state rotational energy transfer rate constants were also carried out for these states. The rotational energy transfer kinetics was found to be consistent with simple energy gap models for the transfer probabilities. Vibrational transfer out of the (0,1,1,2(0),0(0)) state accounted for no more than 16% of the total removal process. Transfer from (1,0,1,0(0),0(0)) to the u-symmetry (0,2,0,3(1),1(-1)), (0,1,1,2(0),0(0)), and (1,1,0,1(1),1(-1)) states was observed. Applying the principle of detailed balance to these data indicated that vibrational transfer to (1,0,1,0(0),0(0)) accounted for ~0.1% of the population loss from (0,2,0,3(1),1(-1)) or (0,1,1,2(0),0(0)), and 3% of the loss from (1,1,0,1(1),1(-1)). Relative rotational transfer probabilities were obtained for transfer to the g-symmetry (1,1,0,2(0),0(0))∕(0,0,2,0(0),0(0)) dyad. These results are related to recent studies of optically pumped acetylene lasers.

Erratum: “Direct determination of state-to-state rotational energy transfer rate constants via a Raman–Raman double resonance technique: ortho-acetylene in v2 = 1 at 155 K” [J. Chem. Phys. 132, 154303 (2010)

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Doublet rotational energy transfer of the SH (X 2Π, v′′ = 0) state by collisions with Ar

The rotational energy transfer (RET) by Ar collisions within the SH X (2)Π (v'' = 0, J'' = 0.5-10.5) state is characterized. The integral cross sections as a function of collision energy for each rotational transition are calculated using a quantum scattering method in which the constructed potential energy functions are based on a ground state potential energy surface (PES) reported previously. On the other hand, a laser-induced excitation fluorescence technique is employed to monitor the relaxation of the rotational population as a function of photolysis-probe delay time following the photodissociation of H(2)S at 248 nm. The rotational population evolution is comparable to its theoretical counterpart based on calculated Λ-resolved RET rate constants. The propensity in Λ-resolved RET transitions is found to approximately resemble the case of OH(X (2)Π, v'' = 0) + Ar. The Λ-averaged RET collisions are also analyzed and result in several propensity rules in the transitions. Most propensity rules are similar to those observed in the collisions of SH(A (2)Σ(+)) by Ar. However, the behavior of the conserving ratio, defined as rate constants for spin-orbit conserving transition divided by those for spin-orbit changing transition, shows distinct difference from those described by Hund's case (b).

Experimental and Theoretical Investigations of Rotational Energy Transfer in HBr + He Collisions

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 g(3)Σ(-)-X(1)Σ(+) (0-1) band. Collision-induced population evolution for transfer events with |ΔJ| ≤ 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) cm(3) 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 |ΔJ| ≥ 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.

Direct determination of state-to-state rotational energy transfer rate constants via a Raman-Raman double resonance technique: ortho-acetylene in v2=1 at 155 K

A new technique for the direct determination of state-to-state rotational energy transfer rate constants in the gas phase is presented. It is based on two sequential stimulated Raman processes: the first one prepares the sample in a single rotational state of an excited vibrational level, and the second one, using the high resolution quasi-continuous stimulated Raman-loss technique, monitors the transfer of population to other rotational states of the same vibrational level as a function of the delay between the pump and the probe stages. The technique is applied to the odd-J rotational states of v(2)=1 acetylene at 155 K. The experimental layout, data acquisition, retrieval procedures, and numerical treatment are described. The quantity and quality of the data are high enough to allow a direct determination of the state-to-state rate constant matrix from a fit of the experimental data, with the only conditions of detailed balance and of a closed number of states. The matrix obtained from this direct fit is also compared with those obtained using some common fitting and scaling laws.

State-to-state and total rotational energy transfer rate constants for CN(B 2Σ+,v=0,N)+H2, CN(X 2Σ+,v=2,N)+H2, D2, and CN(X 2Σ+,v=3,N)+NO

State-to-state and total rotational energy transfer (RET) rate constants were measured for collisions of CN(B 2Σ+,v=0,Ni=4,7,8,11) with H2, CN(X 2Σ+,v=2,Ni=4,11) with H2 and D2, and CN(X 2Σ+,v=3,Ni=4) with NO at room temperature and under single, or near-single, collision conditions. Rate constants were also measured for electronic quenching of CN(B 2Σ+,v=0,Ni=4,7,8,and 11) by H2. In general, state-to-state RET rate constants showed very small or no even–odd alternations as the final rotational state varied. Total rate constants for CN(X 2Σ+,v=2,N)/H2, D2 were found to decrease with increasing rotational quantum number, N. By contrast, total rate constants for CN(B 2Σ+,v=0,N)/H2 were found to be relatively independent of N. Exponential energy gap and angular momentum fitting functions were found to represent measured state-to-state RET rate constants very well and were substantially equally effective in this regard.

Rotational energy transfer in collisions of CH A2Δ, v = 0 with Ar, N2and CO2

Rotational energy transfer (RET) in collisions of CH A2Δ, v=0 with Ar, N2 and CO2 has been investigated experimentally. Laser excitation was used to prepare selected initial levels N=2,3,5 (all colliders), 8 (Ar and CO2) and 14 (Ar only). Additional fine-structure state selection was achieved for the lower levels, and Λ-doublet selection for the higher levels. Total and state-to-state RET rate constants were extracted from time-resolved dispersed fluorescence spectra. Partial fine-structure-state resolution was possible for N′⩽4, and Λ-doublet resolution for the highest levels. For Ar, good absolute agreement was found with previous state-selective experimental work and ab initio theoretical predictions. RET is substantially more efficient for N2 and CO2, for which the first reliable absolute rate constants are provided. A change of fine-structure state with ΔN=0 is the most probable single state-to-state channel at low N for all three partners. Partial conservation of the fine-structure label during ΔN≠0 collisions, previously observed for Ar, was found to extend to the other partners. The relative ΔN propensities are similar for all three partners. This is consistent with a simple impulsive model of the collision dynamics, in which energy constraints dominate because of the large rotational energy spacing characteristic of hydrides. This model does not, however, provide a straightforward explanation for the substantial differences in RET efficiency for Ar, N2 and CO2.

State-to-state and total rotational energy transfer rate constants for CN(B 2Σ+,v=0,N)+He and C2N2

Total rotational energy transfer (RET) rate constants, state-to-state RET rate constants, and radiative lifetimes have been measured for CN(B 2Σ+, v=0, Ni=0, 4, 6, 7, 8, 11 and 13). All experiments were conducted under single collision conditions in a static cell filled with previously prepared C2N2/He mixtures at various total pressures up to a maximum of 800 mTorr. The above initial states were prepared by pumping CN(X) with a pulsed dye laser tuned to appropriate frequencies in the P-branch of the CN-violet (0,0) band following the production of CN(X) by the excimer laser photolysis of C2N2 at 157 nm. Total RET rate constants and radiative lifetimes were determined from decay constants obtained with a transient digitizer over the above range of cell pressures. State-to-state RET rate constants were obtained from time-averaged fluorescence spectra in the R branch of the (0,0) band of the CN violet system at various cell pressures within the above range. A weak propensity for odd jumps in N was discernable in state-to-state RET rate constants in CN(B)/He collisions for N>4. Total RET rate constants varied only slightly with Ni for 0⩽Ni⩽19 with He as collision partner, but decreased monotonically with increasing Ni when C2N2 served as collision partner. No firm evidence for collisionally induced CN(B)↔CN(A) was apparent from our data.

Rotational energy transfer within CH A 2Δ(v=0) and B 2Σ−(v=0) states by collisions with He, Ar, N2, CO, N2O, and CHBr3 using a time-resolved Fourier transform spectrometer

By using a step-scan Fourier transform spectrometer, we have studied collisionally-induced rotational energy transfer (RET) of the CH A(2Δ) (N⩽16,v=0) and B(2Σ−) (N⩽16,v=0) states. The collision partners used for the B state are He, Ar, N2, CO, N2O, and CHBr3, while He and Ar are for the A state. The time-resolved spectra obtained in the nanosecond regime may yield the RET information straightforward under a single pressure of the collider. The resultant RET rate constants for both states range from 10−12 to 10−10 cm3 molecule−1 s−1, comparable to the gas kinetic. The trend follows the order of He∼Ar<N2∼CO<N2O<CHBr3 for the B state, and He<Ar for the A state. For the B state, the findings of multi-quantum changing collisions up to ΔN=±3 and markedly large rate constants imply that the RET collisions are dominated by long-range attractive force. The collision complexes possibly formed between the CH(B) and the colliders are long-lived enough to allow for effective removal of the rotational energy more than a quantum level in a single collision. In contrast, a single quantum change in the RET collision found in the A state suggests dominance of a repulsive interaction between the colliding species, which has been verified previously in the measurements of temperature dependence of the electronic quenching.

Measurements of ground-state OH rotational energy-transfer rates

We have studied rotational energy transfer (RET) in collisions of OH with the bath gases Ar, N2, O2, and H2O at 293 K. Rotationally hot OH(X 2Π3/2, v″=0, N″=1–12) was generated by photolysis of H2O2 at 266 nm, and collisional relaxation of the nascent rotational distribution was monitored by laser-induced fluorescence. The data are remarkably well described by an exponential-gap model for the matrix of state-to-state RET rate constants. For Ar, N2, and O2, RET rates are significantly faster at low N″ than high N″; for H2O, RET is approximately an order of magnitude faster than for the other bath gases, and the rate is not as strongly dependent on N″. The rates of rotationally inelastic energy transfer are similar in the X and A states, but the X-state depopulation rate constants (including nearly elastic, Λ-doublet-changing collisions) are faster than the A-state values. By comparing the depopulation rates derived from the present experiment with previous linewidth measurements, we conclude that RET is the dominant source of pressure broadening for OH microwave transitions and makes a significant contribution for ultraviolet A–X transitions. While generally good agreement is found between the present results and previous OH RET studies for both the ground and excited electronic states, some significant discrepancies are noted.

Picosecond laser-induced fluorescence measurement of rotational energy transfer of OH A^2Σ^+ (v′ = 2) in atmospheric pressure flames

Rate constants for total and state-specific rotational energy transfer (RET) of OH A(2) ?(+) (v? = 2) have been measured directly in atmospheric methane-air and methane-oxygen flames for the first time to our knowledge. We used a picosecond Raman-excimer laser (tau(l) = 300 ps, lambda = 268 nm) to excite the P(11) (12.5) and Q(11) (16.5) A -X transitions in the (2, 0) band of OH molecules. We analyzed the resultant fluorescence with a high-resolution spectrometer in combination with a fast-gated, intensified CCD camera (tau(g) = 400 ps). We recorded the temporal evolution of the emission spectrum by shifting the detection time with respect to the laser pulse. Measured emission spectra were inverted to yield the time-dependent population of rotational levels in the excited state. We calculated rate constants for RET from the results of the fit. The total RET in v? = 2 is similar to v? = 0, 1. The state-specific rates are represented well by a simple energy-gap law.

Rotational energy transfer in vibrationally excited acetylene X̃ 1Σg(ν2″=1,J″):ΔJ propensities

A complete set of state-to-state rotational energy transfer rate constants has been measured for acetylene–acetylene collisions at room temperature under single collision conditions. Initial rotational states (Ji=5,7,...,25) were prepared and final states (Jf=1,...,25) interrogated. The measurements were carried out in a typical gas phase pump and probe arrangement. The initial vibrationally excited state was prepared by stimulated Raman pumping using strong Q-branch transitions. State preparation via this branch produces an isotropic spatial distribution of the excited state which is important for data analysis. Narrow bandwidth lasers ensure single rotational state selectivity. The rotational distribution after collisions is monitored by time-delayed laser-induced fluorescence via the à 1Au(ν3′ = 1)←X̃ 1Σg(ν2″ = 1) transition. In general, the rate constants decrease exponentially with the transferred rotational energy. The complete rate constant matrix can consistently be described by a simple parameter set within the dynamical infinite order sudden power approximation. In addition to this general behavior a significant ΔJ propensity of the rate constants is observed. Using the energy corrected sudden approximation with a power law basis an excellent match, reproducing the ΔJ propensities, to the rate constant matrix is obtained, again with a single set of parameters.

Determination of temperature from N2 and O2 cars spectra at very high pressure

Using least-squares routines, temperatures have been obtained from fitting computer-generated spectral shapes of collapsed N2 and O2 Q-branch coherent anti-Stokes Raman scattering (CARS) spectra to experimental data at high densities between 120 and 725 amagat (1 amagat=2.67×1019 cm−3) in the temperature range from 300–850 K. Experimental data were obtained from high-pressure gases enclosed in a temperature-controlled vessel that is equipped with sapphire windows for optical access. In the fitting codes, for each temperature interation step, densities have been readjusted by calculating pVT data from equations of state. Inelastic rotational energy transfer rate constants, necessary for spectral modeling, were calculated from known energy gap scaling laws. Alternatively, temperature-fitting results from the modeling of unresolved Q-branch band shapes using a quasi-classical description of rotational relaxation are presented. Within the pressure range investigated, for nitrogen at 300 K, best agreement is obtained for the polynominal energy gap (PEG) law, whereas the classical model is reasonably good at 700 K. For oxygen at 300 K, the modified exponential gap (MEG) model and, at higher temperatures, the quasi-classical model are preferred.

Energy transfer rate constants for highly excited rovibrational levels of I2(X)

Rate constants for collisional transfer between highly excited levels of I2(X) have been measured. A single vibration–rotation state (v″=42, J″=17) was populated by stimulated emission pumping. The prepared level, and collisionally populated levels, were detected by laser excitation of the D–X system. Relaxation kinetics were determined by variation of the delay between the dump and probe laser pulses. Collisions with He, Ar, I2, and O2 were investigated. Rotational energy transfer rate constants were measured for all collision partners. Vibrational energy transfer (Δv=−1) was observed for He, and O2, but this process was immeasurably slow for Ar and I2.

State-to-state rotational energy transfer and reaction with ketene of highly vibrationally excited b̃ 1B1 CH2 by time-resolved Fourier transform emission spectroscopy

Dispersed fluorescence spectra from the CH2 b̃ 1B1→ã 1A1 band were recorded with time-resolution by Fourier transform emission spectroscopy after pulsed excitation of a single rotational level of the b̃ 1B1 (0,160,0) state. Fluorescence observed from the initially excited level and from levels populated by rotational energy changing collisions with the bath gas (ketene) was used to deduce the state-to-state rate constants for rotational energy transfer and the state-resolved rate constants for total collisional removal of b̃ 1B1 CH2. The observed propensity rules for rotational energy transfer—ΔJ=±2, ΔKa=0, and ΔKc=±2—are consistent with a quadrupole–dipole interaction between b̃ 1B1 (0,160,0) CH2 and ketene. The existence of a quadrupole in the intermolecular interaction suggests that the structure of CH2 in the b̃ 1B1 (0,160,0) state, averaged over the time of a collision, must be linear. The state-to-state rotational energy transfer rate constants range from approximately equal to the hard sphere gas kinetic rate to four times the gas kinetic rate, with the largest rate constants between rotational levels with the smallest energy gaps. Examination of fluorescence spectra recorded with polarization analysis shows that rotationally elastic (ΔJ=0)M changing collisions are negligible. State-resolved rate constants for reactive collisions between b̃ 1B1 CH2 and ketene were obtained by subtracting the rotational energy transfer contribution from the total rate constants for collisional removal of b̃ 1B1 CH2 (obtained from a Stern–Volmer analysis). These rate constants vary from one to five times the hard sphere gas kinetic rate, and increase with rotational energy for the levels studied. Their magnitudes show that CH2 is about two times as reactive in its b̃ 1B1 state than its ã 1A1 state.

State-to-state spin–orbit and rotational energy transfer of very highly vibrationally excited nitric oxide

PUMP–DUMP–PROBE experiments were performed on nitric oxide (NO) in order to study the rotational and spin–orbit energy transfer in a highly vibrationally excited diatomic. Total depopulation as well as state-to-state rotational and spin–orbit energy transfer rate constants were measured for v=8 and 19 of the ground electronic state. By comparing this new set of results with previously measured results for v=2 [Aa. Sudbo and M. M. T. Loy, J. Chem. Phys. 76, 3646 (1982)] the vibrational influence on the rotational and spin–orbit energy transfer dynamics could be evaluated. Total depopulation rate constants for individual rovibrational states were found to be very similar for v=2, 8, and 19. State-to-state rotational energy transfer rate constants could be compared for v=8 and 19, and again only small differences were found. It appears that vibrational energy does not have a significant impact on the rotational and spin–orbit energy transfer dynamics for NO–NO collisions.

Rotational energy transfer in HF(v=2): Double resonance measurements and fitting law analysis

Data from overtone vibration-laser double resonance experiments show extremely rapid rotational relaxation in HF (v=2) for rotational states up to J=6 and serve to test energy based fitting laws for rotational energy transfer rate constants. The observed rotational states equilibrate in less than a gas kinetic collision with some individual rates being more than twice the hard sphere collision rate. Energy based fitting laws reproduce the observed evolution of the state populations to within 30% but fail systematically for higher (J=5 and 6) rotational levels. Fitting laws formulated for collisions between an atom and a molecule are virtually as successful as those for collisions between two molecules. The extracted rate constants show that multiple rotational quantum energy transfer is an important aspect of relaxation dynamics.