Cross sections and rate constants for the vibrational relaxation of D2 (υ = 1,j = 0) in collisions with 4He

Fully converged quantum cross sections for ⁴He—D² (υ = 1,j = 0) vibrational relaxation were determined using the coupled-states method and a modified version of the Gordon—Secrest surface. First-order forbidden rotational transitions play a significant role, comparable to that observed previously for the He—H₂ system. At 60 K the υ = 1,j = 0 level of D₂ is predicted to relax ≈4 times slower than the corresponding level of H₂. This difference decreases with increasing temperature.     

Vibrational relaxation of HF(υ = 3,4)

The vibrational relaxation of pure HF(υ = 3 and υ = 4) has been studied by pumping HF directly from υ = 0 to υ = 4. The relaxation rates of υ = 3 and υ = 4 were determined to be k³_T = (2.8 ± 0.4) × 10^?11 cm³ molecule^?1 s^?1 and k⁴_T = (7.2. ± 0.5) × 10^?11 cm³ molecule^?1 s^?1 at 293 K. It is shown that sigle quantum energy transfer can account for all the vibrational relaxation.     

Vibrational relaxation of N2(A3Σu+,υ = 1, 2,3) by CH4 and CF4

N₂(A, υ = 0-3) produced by the Ar(³P_0,2) + N₂ reaction and detected by laser-induced fluorescence undergoes rapid, stepwise vibrational relaxation but slow electronic quenching with added CH₄ or CF₄. Rate constants, k_Q^υ, of 1.5, 3.1, and 5.0 × 10^?12 cm³ s^?1 are measured for Q = CH₄, υ = 1-3, and 0.47, 1.8, and 5.5 × 10^?12 cm³ s^?1 for Q = CF₄, υ = 1-3, with ≈±20% accuracy (1σ). Information is also obtained for the unrelaxed, relative υ populations.     

Rotation-vibration-translation energy transfer in laser excited Li2 (B1Πu)

Using the method of laser fluorescence, inelastic collisions with rare gas atoms of electronically excited ⁷Li₂ molecules in the υ = 2 and 4 levels were studied. Vibrational transitions ranging from Δ = +2 to ?4 were observed. The simultaneous rotational transitions were completely resolved, and detailed rate constants k_{Δυ, ΔJ} for specific collision- induced quantum jumps Δυ, ΔJ were determined. The effect of secondary rotational relaxation was eliminated by an extrapolation to zero pressure. By integration over ΔJ, rate constants k_Δυ, were found. They are, within the error limits, independent of the collision partner and on the initial υ (2 or 4) and depend rather weakly on Δυ. These findings are compared with theoretical results from various methods, generally based on a collinear collision model. The apparent disagreement in all respects suggests strongly the importance of rotational degrees of freedom in the collision. Experimental evidence for this is the large amount of V — R transfer observed, which about equals the V — T transfer. The mean cross sections σ(Δυ) for specific vibrational transitions Δυ range between 6 and 15 A², among the largest ever observed.     

State-selected molecular-beam reaction dynamics of K with HF (υ = 1, j = 5, 6 and 7)

The crossed-molecular-beam method has been used to measure relative integral cross sections σ_r (υ = 1, j; E) of the endothermic (0.75 eV) reaction K + HF (υ = 1, j) → KF + H as a function of both the rotational quantum number j (j = 5, 6 and 7) and the translational energy E (0.55 ? E ? 1.32 eV) of the reagents. The vibrational-rotational (υ, j) states of HF were populated by infrared pumping with the radiation of a properly tuned pulsed chemical HF laser. In addition, relative cross sections with υ = 0 but averaged with respect to the initial rotational-state distribution of the HF molecules were also determined. The results exhibit three remarkable features: (a) σ_r (υ = 1, j; E) rises with increasing j, (b) the steepness of the ascent roughly decreases with increasing E, (c) at E = 0.98 eV reagent vibrational energy is about a factor of 200 more efficient in promoting the reaction than reagent translational energy. An intuitive dynamical model suggests that observations (a) and (b) are to be expected for a reaction governed by a potential-energy surface with a late barrier. This is consistent with the well-known interpretation of large vibrational effects as indicated by result (c).     

Semiclassical calculation of cross sections and rate constants for vibrational deactivation of HD (v = 1) colliding with 4He

A semiclassical collision model has been used to calculate the rate constant for vibrational relaxation in HD (v = 1, j = 0) colliding with ⁴He. The He + HD potential surface was obtained from an analytical He + H₂ surface previously used for similar calculations on He + H₂ and He + D₂. The theoretically calculated rate constant is about 50% below that experimentally determined in the temperature range 80–300 K.     

Experimental and theoretical study of the rovibrational relaxation of CH4 and CD4 by Ar

Experimental results are reported for the vibrational relaxation of the lowest bending modes of CH₄ and CD₄ br Ar in the temperature range of 140–376 K. Theoretical calculations are carried out in the framework of the semiclassical coupled-states approximation using asymptotic expressions of (3j) symbols and a first-order perturbation treatment. The confrontation of experimental and theoretical rate constants confirms the crucial role of rotational energy transfer upon the vibrational relaxation transfer.     

Fully converged sudden rotation total integral cross sections for 4He + H2 (ν = 0, j = 0) → 4He + H2 (ν′ = 1, j′)

Total integral cross sections for ⁴He + H₂ (ν = 0, j = 0) → ⁴He + H₂ (ν′ = 1, j′ = 0, 2) have been calculated in the total energy range 1.2 to 5.5 eV, according to a quantal sudden approximation for the H₂ rotational degrees of freedom and a close coupling expansion of the vibrational degree of freedom. Convergence of the above cross sections is investigated by employing four vibration basis sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 and 5.5 eV calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is found that at least four vibrational basis functions are needed to converge (to within 5–10%) these cross sections in the above energy range. Comparison of breathing sphere calculations and summed sudden rotation results shows good agreement for the (weakly anisotropic) Mies-Krauss potential. However, as expected the former results underestimate the vibrational 0 → 1 total integral cross sections.     

Mode-to-mode vibrational energy flow in S1 benzene

Resolved fluorescence spectra from low pressures of benzene with nine added gases have been used to follow mode-to-mode vibrational relaxation in the S₁ state of benzene under “single-collision” conditions. Cw pumping of the S₁ fundamental 6¹ (ν″₆ = 522 cm^?1) allows study of collisional vibrational energy flow into each of four channels. Two channels consist of flow into single levels, and the others represent flow into unresolved pairs of levels. The mode-to-mode cross sections are much larger than those usually observed in ground electronic states, being near gas kinetic even for partners transferring energy by VT, R processes alone. The mode-to-mode transfer has highly specific patterns, with roughly seventy percent of the transfer going into the four channels in spite of many other nearby levels. The largest cross sections are always to a level 237 cm^?1 above the initial level rather than to a level nearly resonant (ΔE = 7 cm^?1) with the initia l level. A common pattern of flow occurs for the four gases transferring energy by VT, R processes alone, and another common pattern is established for the five gases which can also use VV transfers. With the exception of one channel, VV resonances with vibrationally complex partners increase cross sections by less than a factor of two over that provided by the VT, R path. VV transfers have a similarly small effect on the overall vibrational relaxation rate out of the initial level 6¹. Both the flow patterns and the VV versus VT, R competitions are accounted for with an extremely simple and general set of propensity rules taken directly from SSH calculations made by others for vibrational relaxation in ground electronic states. The rules are based on the degeneracies of the final levels, the number of vibrational quantum changes, and the amount of energy exchanged between vibrational and translational/rotational degrees of freedom. The rules seem general to relaxation in both ground and excited electronic states, whereas large cross sections seem a special property of the excited state. The cross sections for collision partners SF₆ and perfluorohexane are small relative to those for other partners with similar vibrational complexity and mass.     

Energy disposal in the photodissociation HCN(Ã1A″) → H + CN(X 2Σ) at 193 nm

Rotational energy disposal has been measured in CN(X ²Σ, υ″ = 0, 1, 2) following 193 nm dissociation of HCN vapor at 295 K. The fractional populations for the three vibrational states are 0.56 ± 0.08, 0.33 ± 0.13, and 0.11 ± 0.03 for υ″ = 0, 1 and 2 respectively. This distribution is fit well by a Poisson distribution with an average vibrational quantum number of 0.55 corresponding to the average vibrational energy of 1128 ± 294 cm⁻¹. This energy represents (10 ± 3)% of the available energy. The rotational distributions in all three vibrational states can be represented by a single surprisal which depends linearly on N″/N″_max where N″_max is the maximum value of the rotational quantum number permitted by energy conservation and the prior distribution is similarly constrained. The average energy in rotation is 1055 ± 373 cm⁻¹ which represents (9 ± 3)% of that available for disposal. Time-dependence measurements indicate that product CN(X ²Σ, υ = 0) is formed in both a fast (τ < 80 ns) and a slow process. No evidence is found for the production of CN(A ²Π, υ ≈ 0).     

The phase modulated semiclassical sudden approximation. Study of the transitions υ = 1, j → υ = 0 j′ in the pH2 + He4 system

A modified version of the semiclassical sudden approximation is presented. The expressions retain the attractive simplicity of the original sudden theory approximations but they take into account, due to a phase modulation, the adiabaticity modifications which are produced by the transitions between the rotational states. The comparison between the calculated total ro-vibrational and the close coupling cross sections for the couple pH₂ + He ⁴ gives satisfactory agreement. The influence of the non rigidity of the rotator and the role of the intramolecular anharmonicity are studied. The strong influenced of the υ = 2 state on the one quantum transitions (υ = 1, j) → (υ = 0, j′) can also be seen.     

The relaxation of HCl(ν = 1) and DCl(ν = 1) by O atoms between 196 and 400 K

The rates of relaxation of HCl(ν = 1) and DCl(ν = 1) by atomic oxygen have been determined between 196 and 400 K using the laser induced vibrational fluorescence method. The values of the rate constants, κ_1,H and κ_1,D, can be matched quite well by Arrhenius expressions: κ_1,H = 6.2 × 10^?12 exp (?1.0₅ kcal mole^?1/RT) cm³ molecule^?1 s^?1 and κ_1,D = 2.9 × 10^?12 exp (?0.5 kcal mole^?1/RT) cm³ molecule^?1 s^?1. The most likely explanation of the absolute and relative magnitudes of these rate constants appears to be that relaxation occurs as a result of non-adiabatic vibronic transitions during collisions.     

Semiclassical calculation of energy transfer in polyatomic molecules. XI. Cross sections and rate constants for Ar + CO2

Data from electron gas calculation on the short-range potential and theoretical van der Waals coefficients C_n (n = 6, 8) have been used to construct a potential surface for the Ar+CO₂ system. The surface has been used to calculate: second virial coefficient, viscosity and diffusion coefficient, rotational relaxation rates, rate constants for vibrational transitions in CO₂ and high-enery/small-angle differential cross sections.     

Dynamically based fitting law for thermal rate coefficients in rotational relaxation

An earlier analytical, approximative result for the semi-classical, sudden limit of energy dependent j_o → j cross sections of rotational relaxation of homonuclear, diatomic molecules perturbed by an atom has been integrated to obtain dynamical fitting of temperature dependent rate coefficients. The result can be written by using two parameters, k_jjo = [(2j + 1)/(2j_o + 1)] ^1/2a (lj - 1]^?1 ? b), where the parameters a and b are given from the assumed intermolecular potential, The reduced mass for the collisions and the temperature. A comparison with several experimental results proves the validity of the above expression and gives some statements about the intermolecular potentials for the systems considered.     

Comparison of quantum mechanical and semiclassical cross sections and rate constants for vibrational relaxation of N2 and CO colliding with 4He

Semiclassical cross sections and rate constants for vibrational/rotational relaxation of CO and N₂ colliding with ⁴He are compared with quantum coupled-states calculations. If the same analytical potential energy surface is used good agreement is obtained. It is also shown that the small cross sections are very sensitive to the representation of the surface.     

Measurement of state-to-state rotational transfer rates in collision of I2*(B 0u+, υ = 15, j) with 3He, 4He,Ne, Ar,H2, D2 and I2

The selective laser excitation and induced fluorescence observation technique has been used to study rotationally inelastic collisions of I₂^*(B 0_u⁺, υ = 15,j) with I₂, ³He, ⁴He, Ne, Ar, H₂ and D₂. For each collision partner, several initial rotational levels ranging from j_i = 12 up to j_i = 146 have been excited. For purely rotational transfer within the υ = 15 level, our data are perfectly consistent with energy sudden (eventually corrected) scaling laws. Thus, any thermally averaged rate constant, k(j_i → j_f), can be expressed as a function of the basis rate constants k(l → 0). Furthermore, these k(l → 0) are found to follow simple empirical fitting laws. Consequently any k(j_i → j_f) can be predicted given a set of two or three fitting parameters. Collisions with relatively heavy particles (I₂, Ar and Ne) are well described by using the inverse power fitting law k(l → 0) = b[l(l+1)]^?γ, where b = 1.7, 1.2 and 1.2×10^?10 cm³ s^?1 and γ = 1.08, 1.02 and 1.17 for I₂^*-Ne, I₂^*-Ar and I₂^*-I₂ collisions respectively. For collisions with light particles (³He, ⁴He, H₂ and D₂), k(l → 0) shows a sharp decrease with l which can be accounted for by a hybrid power-exponential fitting law k(l → 0) = b[l(l+1)]^?γ exp[-l(l+1)/l^* (l^*+1)], where b = 0.84, 0.71, 2.77 and 2.78×10^?10 cm³ s^?1l⁺ = 20.6, 23.1, 18.8 and 31.4, and γ = 0.66, 0.66, 0.78 and 0.91 for I₂^*-³He, I₂^*-He, I₂^*-H₂ and I₂^*-D₂ collisions, respectively. We confirm that the rotational transfer dynamics in heavy molecules is mainly governed by angular momentum exchange.     

The QCT calculation of the rate constants for the N(4S)+O2(X3Σ g ? ) →NO(X2Π)+O(3P) reaction

A quasi-classical trajectory (QCT) calculation with the fourth-order explicit symplectic algorithm for the N(⁴S) + O₂(X³Σ_g⁻) → NO(X²Π) + O(³P) reaction has been performed by employing the ground and first-excited potential energy surfaces (PESs). Since the translational temperature considered is up to 5000 K, the larger relative translational energy and the higher vibrational and rotational level of O₂ molecule have been taken into account. The affect of the relative translational energy, the vibrational and rotational level of O₂ molecule in the reaction cross-sections of the ground and first-excited PESs has been discussed in a extensive range. And we exhibit the dependence of microscopic rate constants on the vibrational and rotational level of O₂ molecule at T = 4000 K. The thermal rate constants at the translational temperature betweem 300 and 5000 K have been evaluated and the corresponding Arrhenius curve has been fitted for reaction (1). It is found by comparison that the thermal rate constants determined in this work have a better agreement with the experimental data and provide a more valid theoretical reference.     

Sensitization of the OH(A 2Σ+ → X 2Πi) emission by Hg(6 3P0) metastables

The electronic energy transfer process Hg(6 ³P₀) + OH(X²Π_i, υ = 0,K) → Hg(6 ¹S₀) + OH(A ²Σ⁺, υ,K) has been studied by the sensitized fluorescence method. A rather broad spectrum of rotational population, N_υ′K′, was obtained under conditions of minimum relaxation, which illustrates the non-resonant and non-optical nature of this energy transfer process. The fractions of the exoergicity, above electronic excitation of OH(A ²Σ⁺, υ = 0, K = 0), going into vibrational, rotational and translational excitation are 0.11, 0.31, and 0.58, respectively. A statistical mode of energy partitioning, such as would result from long-lived complex formation, seems to account well for these observations.     

Analytical ab initio potential-energy surfaces for the ground and the first singlet excited states of HeH2

Analytical potential-energy surfaces have been constructed for the ground and the first excited states of HeH₂. The functions fit ab initio MRD CI calculations with standard deviations of 0.05 and 0.13 eV for the ground and the excited surface respectively. Classical trajectory calculations for collisions of ⁴Hc with HD(B ¹Σ_u⁺, υ = 3, J = 2) at the temperature T = 297 K yields the electronic quenching cross section σ_Q = 6.5 A² and the vibrational cross section σ_3→2 = 3.8 A². The results are in qualitative agreement with the experimental values of Fink, Akins and Moore.     

Ab initio computation of vibrational relaxation rate coefficients for the collisions of CO2 with helium and neon atoms

Ab initio calculations of rate coefficients are reported for the vibrational relaxation of CO₂ molecules in collision with helium and neon atoms. Self consistent-field computations have been performed to parameterise simple three-dimensional potential energy functions which have been used in vibrational close-coupling, rotational infinite-order-sudden calculations of rate coefficients. Excellent agreement is obtained between the calculated and experimental rate coefficients for the deactivation of the (01₁0) vibrational level in the He + CO₂ system at temperatures of 300 K and above. The ab initio predictions of rate coefficients for relaxation of CO₂ vibrational levels such as (10⁰0) and (02⁰0) should be useful in computer simulations of CO₂ lasers.