J. C. Polanyi

Energy Distribution Among Products of Exothermic Reactions. II. Repulsive, Mixed, and Attractive Energy Release

A series of two‐dimensional classical kinematic computer calculations have been made on the hypothetical exothermic exchange reaction A+BC→AB+C, −ΔH=48.5 kcal mole−1. Product energy distribution (vibration, rotation, and translation; Evib, Erot, Etrans) was obtained as a function of initial position, impact parameter, and kinetic energy (αi, b, and Ekini). All eight different combinations of light (L=1 amu) and heavy (H=80 amu) masses were examined. Eight different potential‐energy hypersurfaces were explored. All were obtained from an empirical extension of the London—Eyring—Polanyi—Sato (L.E.P.S.) method. The hypersurfaces were categorized in terms of the percentage attraction, A⊥, and percentage repulsion R⊥, read off the collinear three‐dimensional surface. This categorization was shown to be helpful in arriving at a qualitative understanding of the product energy distribution to be expected from all the mass combinations reacting on these extended L.E.P.S. hypersurfaces. However, it was also shown th...

Mechanism of Rotational Relaxation

It has been known for some time from infrared chemiluminescence experiments that a nonthermal rotational distribution of hydrogen halide peaked initially at high rotational quantum number, J, relaxes to a thermal distribution without generating a peak at intermediate J [Discussions Faraday Soc. 44, 183 (1967)]. It is shown in the present study that this characteristic pattern of relaxation is well described by a model according to which ΔJ is unrestricted, except for the relation PJ−ΔJJ=N exp (— CΔE), where PJ−ΔJJ is the probability of a collision−induced transfer from J to J — ΔJ, ΔE is the energy difference between these two rotational states, and N and C are constants. This expression for PJ−ΔJJ ascribes a very much lower probability of rotational deactivation to the higher J levels. Three other, contrasting, models were tested; they were rejected since they failed to describe the observed pattern of relaxation adequately. Upper limits were ascribed to PJ−ΔJJ for ΔJ=1–5 in HCl–H2 collisions. This study...

Location of Energy Barriers. I. Effect on the Dynamics of Reactions A + BC

The dynamics of exchange reactions A+BC→AB+C have been examined on two types of potential‐energy hypersurfaces that differed in the location of the energy barrier along the reaction coordinate. On “surface I” the barrier was in the entry valley of the energy surface, along the approach coordinate. On “surface II” the barrier was in the exit valley of the energy surface, along the retreat coordinate. The classical barrier height was Ec = 7.0 kcal mole−1 on both surfaces, and was displaced from the corner of the energy surface by the same amount; on surface I, r1‡ = 1.20 A, r2‡ = 0.80 A; on surface II, r1‡ = 0.80 A, r2‡ = 1.20 A (r1 ≡ rAB, r2 ≡ rBC, and the superscript ‡ refers to the location of the crest of the barrier). Three‐dimensional (3D) classical trajectory calculations were performed for the mass combination mA = mB = mC at several reagent energies. The reagent energy took the form of translation, vibration or an equilibrium distribution of the two. The main findings were that translation was mark...

Some Concepts in Reaction Dynamics

The objective in this work has been one which I have shared with the two other 1986 Nobel lecturers in chemistry, D. R. Herschbach and Y. T. Lee, as well as with a wide group of colleagues and co-workers who have been responsible for bringing this field to its current state. That state is summarized in the title; we now have some concepts relevant to the motions of atoms and molecules in simple reactions, and some examples of the application of these concepts. We are, however, richer in vocabulary than in literature. The great epics of reaction dynamics remain to be written. I shall confine myself to some simple stories.

Location of Energy Barriers. II. Correlation with Barrier Height

In Paper I of this series a hypothetical potential‐energy surface was used in order to examine the effect on the dynamics of exchange reactions A + BC→AB + C of moving the energy barrier from an “early” to a “late” position along the reaction coordinate (i.e., from the entry valley to the exit valley of the energy surface). In the present work an attempt has been made to correlate barrier location with other properties of the energy surface, as a step toward the application of the generalizations of Paper I to real cases. Related families of reactions have been examined in the London–Eyring–Polanyi–Sato (LEPS) and bond‐energy bond‐order (BEBO) approximations. The principal generalizations may be summarized as follows: (1) For substantially exothermic reactions the barrier is in the entry valley, and for substantially endothermic reactions the barrier is in the exit valley. In the light of Paper I this implies that the cross sections for these exothermic reactions will rise most steeply with increasing tra...

Ab Initio SCF–MO–CI Calculations for H−, H2, and H3+ Using Gaussian Basis Sets

Fixed‐center Gaussian‐type functions (GTF) have been used as basis sets in an extensive SCF–MO–CI study on H−, H2, and H3+. An accurate description requires 4 or 5 s‐GTF on each center, plus at least one set of p‐GTF, which are essential for the reproduction of reliable potential curves; d‐GTF are, however, of minor importance. A constant p exponent may be used successfully in a wide variety of nuclear configurations. Variational energies of − 1.3397 and − 1.2765 hartree were calculated for the most stable equilateral and collinear geometries of H3+. A potential‐energy surface has been computed for the reaction H+ + H2, to an accuracy of about 2 kcal mole−1 over its important regions. In the computation of the proton affinites of H− and H2, little accuracy was lost when a limited basis set was used in SCF calculations.

Formation of Vibrationally Excited OH by the Reaction H + O(3).

An earlier study [Chem. Phys. Lett. 1, 619 (1968)] concluded that the reaction H + O(3) ? OH + O(2) forms OH predominantly in the highest accessible vibrational levels, upsilon = 8 and 9. We have extended this earlier work (1) by using fourier transform spectroscopy which is capable of giving more precise values for the relative vibrational populations at low intensities, (2) by recording emission down to lower background pressures (1 x 10(-4) Torr), and (3) by treating the vessel walls so as to remove OHdagger (vibrationally excited OH in it ground (2)II electronic state) more effectively. This involved using a room temperature vessel coated with silica gel. Under these conditions (provided that the values available for the radiational lifetime of OHdagger are correct) vibrational relaxation of OHdagger should have been largely arrested. We conclude that the relative rate constants for formation of OHdagger in levels upsilon are k(upsilon = 6) < 0.4, k(upsilon = 7) asymptotically equal to 0.4, k(upsilon = 8) asymptotically equal to 0.8, and k(upsilon = 9) = 1.00.

Energy Distribution Among Reagents and Products of Atomic Reactions

A simple valence bond resonance description of the activated complex in exothermic reactions A+BC→AB+C, coupled with experimental and theoretical evidence concerning the efficiency of transfer of vibrational energy at a collision, leads to the prediction that almost the entire heat of reaction will be contained in vibration of the bond being formed. The predicted activated complex configuration, which involves extended internuclear separation in the bond being formed, may be connected with increased collision diameters. The high efficiency of association reactions A+A+M→A2+M requires that in these reactions also the product contains almost the entire heat of reaction in vibration of the bond being formed. An attempt is made to account for the hitherto unexplained negative activation energy of these reactions in terms of the collisional redissociation of the highly vibrating product; a value for Eact of the required order of magnitude is obtained. The rate of the endothermic processes which constitute the ...

Energy distribution among reaction products. IX. F + H2, HD and D2

Abstract The infrared chemiluminescence technique has been used to obtain detailed rate constant k ( V ′, R ′, T ′) ( V ′, R ′, T ′ are product vibrational, rotational and translational energies) for four isotopic reactions; (1a) F + HD → HF + D (−Δ H 0 0 = 31.1 kcal mole −1 ), (1b) F + HD → DF + H (−Δ H 0 0 = 32.8 kcal mol −1 ), (2) F + H 2 → HF + F (−Δ H 0 0 = 31.9 kcal mole −1 ), and (3) F + D 2 → DF + D (−Δ H 0 0 = 31.8 kcal mole −1 ). The mean fraction of the available energy which becomes vibration and rotation in the molecular product, 〈 f » V 〉 and 〈 f » R 〉, listed in this sequence for the four reactions is: (1a) 0.59 and 0.125; (1b) 0.63 and 0.066; (2) 0.66 and 0.083; (3) 0.67 and 0.076. The changes in mean product rotational excitation along the series are correctly predicted by (prior) classical trajectory studies. These studies do not, however, account for 〈 f » V 〉 1a f » V 〉 1b . The “anomalously” low vibrational excitation for reaction (1a) is likely to be linked to the fact that this reaction liberates an energy barely sufficient to populate the (highest) vibrational level, HF(υ′ = 3); classical mechanics is unsuited to the study of processes near to threshold. The effect of the product vibrational and rotational distributions of variation in the temperature of the molecular reagent in the range from 77—1315 K, has been determined for reactions (1a), (2) and (3). The changes in the mean product distributions are in accord with our earlier finding, based on both theory and experiment, that enhanced reagent translation results in enhanced product translation and rotation, 〈Δ T 〉 → 〈Δ T ′〉 + 〈Δ R ′〉. The detailed rate constant k (υ′ = 3) for the HF product of F + HD [reaction (1a)] showed a marked increase with reagent energy at low energy (77—400 K), levelling off at higher reagent energy (⪆ 600 K). This threshold-type behaviour contrasts with that observed in the other systems for highly vibrationally excited product. For (1a) the energy release measured off the energy surface, E a − Δ H 0 0 , (where E a is the activation energy) exceeds the energy of HF (υ′ = 3) by only ∼0.2 kcal mole −1 . For reactions (2) and (3) E a - Δ H 0 0 exceeds the energy of the highest-populated υ′-level by ⪆ 1 kcal mole −1 . Triangle plots, recording k ( V ′, R ′, T ′), are given for both paths of F + Hd [i.e., (1a) and (1b) proceeding in the exothermic direction] and for both paths (HF + D and DF + H, each yielding F + HD) in the endothermic direction.

Infrared‐Emission Studies of Electronic‐to‐Vibrational Energy Transfer. II. Hg*+CO

Electronic‐to‐vibrational transfer has been observed in the system Hg*(63P1,0)+NO. Both Hg*(63P1) and Hg*(63P0) have been found to be effective in bringing this about. A set of rate constants, kv (or cross sections σv2) for electronic‐to‐vibrational transfer were derived according to various models from an observed set of steady‐state concentrations, Nv. The set of kv bear a qualitative resemblance to those for Hg*+CO (Part II). Hg*+NO exhibits a significant but slowly diminishing probability for vibrational excitation into vibrational levels up to v=16 or 17, and an insignificant probability for vibrational excitation into higher levels than v=16–17, corresponding to ⅔ of the electronic energy converted into vibration. The qualitative similarity of these results to those obtained for Hg*+CO suggests that a similar mechanism may be applicable here: Hg*+NO→HgNO*→HgNO→Hg+NO†. However, there exists in the present system an alternative mechanism which would involve electronic‐to‐electronic transfer: Hg*+NO(X ...