B. S. Rabinovitch

Accurate evaluation of internal energy level sums and densities including anharmonic oscillators and hindered rotors

The calculation of molecular energy level sums and densities is necessary for the treatment of many physical and chemical problems including reaction rates. An extension of Beyer and Swineharts algorithm for directly computing harmonic oscillator eigenstate sums and densities is described. With this new algorithm it is possible to compute exact or near‐exact energy level sums and densities for degrees of freedom such as free and hindered rotors and anharmonic oscillators so long as the energy levels for each degree of freedom can be specified. Computer calculation by this technique is practical even for large molecules up to all chemically interesting energies and error is confined to small rounding errors. Results by this algorithm are compared to values of energy level sums that have been given in the literature by various alternative approximate treatments and permit more rigorous testing of the latter and assessment of the approximations involved.

Kinetics of the Thermal Cis‐Trans Isomerization of Dideuteroethylene

The thermal cis‐trans isomerization of trans‐ethylene, d2 has been studied from 450° to 550°C over a pressure range of 0.9 cm to 31 cm Hg in two quartz reactors. The rate is pressure dependent over the entire pressure range. It is concluded that at 0.9 cm the reaction is a homogeneous, unimolecular reaction. A high pressure activation energy of 65 kcal and frequency factor of 1013 sec—1 are deduced. At higher pressures the reaction is sensitized by processes attendant on polymerization, which occurs as a side reaction with propylene as the principal product. The relation of this study to other work on substituted ethylenes is discussed briefly, as well as a few other topics pertinent to the results obtained.

Collisional Energy Transfer. Thermal Unimolecular Systems in the Low‐Pressure Region

Collisional activation—deactivation efficiencies, β, for thermal unimolecular reactions in the second‐order region were computed on a stochastic model by use of an iterative procedure. Four assumed collisional transition probability models were used: stepladder, Gaussian, Poisson, and exponential; detailed balance and completeness were observed. The collisional efficiencies increase with increase of average energy removed per collision, 〈ΔE〉, and with decrease in the average excess energy of the molecules, 〈E+〉, above the critical energy for reaction. Efficiency is defined as a product, β=γNγP, and varies with inert gas dilution.Calculations were made for the nitrous oxide, nitryl chloride, methyl isocyanide, cyclopropane, and 1,2‐dimethylcyclopropane systems over a range of temperatures. This provides a large variation in the internal vibrational‐energy densities and critical energies in question. For a particular transition probability model, β may be expressed as a quasiuniversal function of the reduce...

On the use of exact state counting methods in RRKM rate calculations

Abstract The use of direct counts of molecular energy level degeneracies, P(E) , t internal energy, E , RRKM unimolecular reaction rate calculations is clarified. Highly accurate densities of states for use in practical rate calculations can be obtained by utilizing an energy level “grain” size of 1–5 cm −1 and by suitable averaging of P(E) over small energy intervals. An easily programmed algorithm for rounding energy levels to multiples of this “grain” size is given and applied to sum and density calculations.

Unimolecular Decomposition of Chemically Activated sec‐Butyl Radicals from H Atoms plus cis‐Butene‐2

Chemically activated sec‐deuterobutyl radicals were produced at 25°C by the reaction of D atoms with cis‐butene‐2. These vibrationally excited species contain an increment of energy above that of the corresponding light radicals as formed from H plus cis‐butene‐2 in a previous study [B. S. Rabinovitch and R. W. Diesen, J. Chem. Phys. 30, 735 (1959)]. Apparent rate constants for the unimolecular decomposition to propylene of the deuterobutyl radicals were obtained as a function of pressure, relative to the collision induced stabilization process. Theoretical values for the rate constants at the limits of high and low pressures were calculated using a direct count for the density of vibrational energy levels. The calculated and experimental results are compared with one another, and with the results of the previous study of the sec‐butyl radical decomposition. The expected energy effect is observed; the deuterobutyl radicals appear slightly more monoenergetic than the equivalent nondeuterated species.

COLLISIONAL TRANSITION PROBABILITIES FOR VIBRATIONAL DEACTIVATION OF CHEMICALLY ACTIVATED sec-BUTYL RADICALS. THE RARE GASES

Vibrationally excited sec‐butyl radicals, having a narrow range of energies above 40 kcal mole−1, were produced in a heat bath of cis‐butene‐2‐rare‐gas mixtures by H addition to cis‐butene‐2. He, Ne, Ar, and Kr were used. Two competing reactions of the chemically activated radicals, decomposition by C–C rupture with critical energy of 33 kcal mole−1 and collisional stabilization, were studied as a function of pressure. Apparent rate constants for decomposition ka were obtained at three temperatures over a range of bath pressures by analysis of the decomposition and stabilization products. Strong and weak multistep collisional deactivation processes, corresponding to transfer of all or only part of the initial excess vibration energy (≥7 kcal mole−1) of the radicals, were considered. Multistep models of various step sizes (ΔE) give a family of calculated curves of ka as a function of p, each of which turns up from a quasi‐constant value at higher pressures to higher values at low pressures. Comparison with...

Collisional Deactivation of Highly Vibrationally Excited Cyclopropane

Vibrationally excited cyclopropane molecules were produced by chemical activation at ≈100 kcal mole—1 above the ground level; methylene radicals were formed by photolysis of ketene at 3200 A and were added to ethylene. Collisional deactivation has been studied at 298° and 423°K, with ethylene as the inert deactivator, and at 298° with He, Ar, and N2 as deactivators.The average amount of energy removed by ethylene per collision was calculated on a stepladder model and found to be in excess of 10 kcal mole—1, and not higher than 14 kcal, from the present data. Nitrogen and argon appear to have lesser efficiency than ethylene. Helium is the most inefficient gas; it removes ≈ 6 kcal mole—1 per effective collision, with some evidence that an important fraction of collisions (≈ 0.67) are elastic, i.e., result in only a little or no energy transfer. This suggests that a bimodal distribution of collisional transition probabilities, or other distribution skewed toward smaller step sizes, may be more appropriate fo...

COLLISIONAL TRANSITION PROBABILITIES FOR VIBRATIONAL DEACTIVATION OF CHEMICALLY ACTIVATED SEC-BUTYL RADICALS. DIATOMIC AND POLYATOMIC MOLECULES

The study of collisional transitional probabilities for the de‐excitation by inert gases of chemically activated sec‐butyl radicals, excited to internal energies in excess of 40 kcal mole−1, has been extended to H2, D2, N2, CO2, CH4, CD3F, CH3Cl, and SF6. The diatomic gases display behavior similar to the rare gases, and on a preferred exponential model of collisional transition probabilities the average amount of energy transferred per collision is 〈ΔE〉expon≃1.3 kcal mole−1. On a stepladder model the corresponding amount is ΔE≃2.5 kcal mole−1. From higher‐pressure data, the efficiency for CD3F, CH3Cl, and SF6 is deduced to be comparable with that for butene and, on a preferred stepladder model, ΔE>9 kcal. For CO2 and CH4 the behavior is intermediate. The possible importance of the role of internal rotation of butyl in facilitating energy transfer is noted; some uncertainty concerning the role of over‐all rotations and vibrational modes of the deactivator in the relaxation process exists.

Collisional Transition Probabilities for Deactivation of Highly Vibrationally Excited Cyclopropane and Dimethylcyclopropane

Collisional deactivation of vibrationally excited cyclopropane and dimethylcyclopropane molecules, in their ground electronic states, has been studied with ethylene and cis‐butene as the respective deactivators. Activation is to an energy region just above 100 kcal mole—1, which is reached by chemical activation. The activated molecules may isomerize, and the measurable cascade is to a reaction threshold at 60–65 kcal; below the threshold the excited molecules are stable with respect to reaction. The principle and characteristics of this steady‐state method has been described in detail in Ref. 5.The two substrate molecules offer an interesting difference in internal rotational degrees of freedom. Cyclopropane was investigated at 298°, 598°, and 723°K, and dimethylcyclopropane at 573° and 673°K. The observed behavior was compared with model calculations for various assumed functional forms of collisional transition probabilities pij which include stepladder, Gaussian, and skewed distributions. The data, un...

Vibrational Energy Transfer from a Homologous Series of Chemically Activated Radicals

The relative collisional efficiencies β of several inert bath molecules for the collisional deactivation of a homologous series of highly vibrationally excited species have been measured. The inert gases were H2, and N2 CH4, and CF4, The excited species were 2‐butyl, 2‐methyl‐2‐butyl,2‐pentyl, 2‐hexyl, and 2‐octyl radicals. The relative efficiency of a particular bath gas was roughly constant for all members of the series. This finding is discussed and compared with theoretical results on a stochastic model. The approximate values of β are: 0.22, 0.53, 0.78, and 1.0 for H2, N2, CH4, and CF4, respectively. These correspond to average values of the mean energy decrement per collision, 〈ΔE〉 = 1.3, 2.3, 4.3, and >9 kcal mole−1, respectively, for a stepladder model of transition probabilities, and to somewhat larger average values for an exponential distribution of the sizes of energy decrements.