Jean Brocas

Comments on Kinetic Equation for Autocorrelation Functions

The non‐Markoffian kinetic equation for the one‐particle momentum autocorrelation function, derived by Zwanzig and studied in great detail recently by Berne, Boon, and Rice, is analyzed in the weak coupling limit. It is shown that, in this limit, this kinetic equation remains non‐Markoffian because the kernel which determines the memory effects only decays very slowly. More precisely, it tends to zero over times of the order of the relaxation time itself and not, as could be expected, over the much shorter collision time. The comparison with the more traditional approach, based on the solution of a transport equation, is also discussed.

On the spectroscopic consequences of different tunnelling mechanisms in non-rigid phosphorus pentafluoride (II)

In this paper the spacings between the non-rigid molecule levels for each conceivable tunnelling pathway of phosphorus pentafluoride are parametrized. The theoretical spectra corresponding to each isomerization mode of this molecule are obtained and are shown to lead to new ways of discriminating the various isomerization modes.

The reaction graph of the Cope rearrangement in bullvalene

The concept of mode of rearrangement is used to analyse the connectedness of the reaction graph for the Cope rearrangement in bullvalene.

NMR line-shape analysis and modes of rearrangements

We classify the possible permutational isomerizations of a given molecular skeleton in NMR-modes. Such a mode is the set of permutations which are indistinguishable from the point of view of NMR-line shape analysis. The present classification is compared to earlier ones and its advantages are underlined.

On the equivalence between the master equation and the functional approaches to the generalized transport equation

Abstract We prove the complete equivalence between the two long-time generalized transport equations as obtained respectively by the functional approach and by the master equation approach. We first show that the collision operator as obtained by E. Cohen using a functional method may be rewritten in a compact form in terms of Ursell non-equilibrium operators only; we then show that a similar transformation is possible on the collision operator obtained by I. Prigogine and coworkers. The identity of the two transport equations becomes then obvious.

Classification of rearrangement mechanisms and dynamic stereochemistry

We review some aspects of dynamic stereochemistry related to the classification theory of rearrangement mechanisms. This classification is based on the symmetry of the molecular skeleton and has been widely used in connection with nuclear magnetic resonance line shape analysis. It is also related to the Longuet-Higgins approach to nonrigidity and may be used to predict the consequences of various tunneling mechanisms in rotation or vibration spectroscopy.

Semi-invariants in irreversible statistical mechanics

Abstract We stress the differences that exist between the equilibrium semi-invariants and the analogous operators which have been recently introduced out of equilibrium. By an example, we show that these operators, in contrast with their equilibrium analogs, are not the sum of all irreducible Mayer graphs. They are now related to the Husimi operators introduced by Cohen who showed for a different case that the Husimi operators can play the same role out of equilibrium as the irreducible graphs in the equilibrium theory. We study also the relation between the semi-invariant operators and the Ωψ operator appearing in the kinetic equations derived by Prigogine and his coworkers. We show - up to the sixth order in the coupling parameter - that both formalisms give equivalent results for long times but, because of the operator character of Ωψ and the semi-invariants, no trivial relation seems to exist between the quantities involved in the two theories. Another consequence of the fact that semi-invariants are operators - their complicated asymptotic time dependence (0, t1, t2, ..) - is also studied for a simple case.

The dsd model in heptacoordinate stereochemistry: a comparison with experiment

The diamond-square-diamond or dsd model provides a simple description for heptacoordinate interconversion. We compare it to NMR information. It appears that the model is almost always compatible with experimental facts, at least when the dsd processes do not lead to isomerization.

Permutational character of dsd mechanisms in heptacoordinate chemistry

The permutational character of degenerate single and double dsd and of degenerate 4, 5-pyramidal processes is obtained for the heptacoordinate deltahedra. The symmetry properties of the paths of steepest descent and transition states of these rearrangements are derived. From this Permutational character, it would be possible to investigate the compatibility of these processes with the results of NMR line shape analysis of the dynamics of heptacoordinate complexes. This possibility is briefly discussed.

Modes of rearrangements and reaction graphs for XeF6

Abstract Chemical graphs for the rearrangements of XeF6 are represented and discussed in terms of the corresponding Longuet-Higgins groups of this molecule. Some properties of these graphs are related to the previous permutational analysis of the XeF6 dynamics.