Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads.

In previous works, we have introduced an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonian with the identity on the rotational degrees of freedom. The convergence of our method for the methane vibrational ground state was very satisfactory and our predictions were quantitative. In the present article, we provide further details on the implementation of the method in the degenerate and quasi-degenerate cases. The quasi-degenerate version of the method is tested on excited polyads of methane, and the results are assessed with respect to a variational treatment. The optimal choice of the size of quasi-degenerate spaces is determined by a trade-off between speed of convergence of the perturbation series and the computational effort to obtain the effective super-Hamiltonian.

Precise adjustment of nanometric-scale diffusion layers within a redox dendrimer molecule by ultrafast cyclic voltammetry: an electrochemical nanometric microtome.

Performing cyclic voltammetry at scan rates into the megavolt per second range allows the exploration of the nanosecond time scale as well as the creation of nanometric diffusion layers adjacent to the electrode surface. This latter property is used here to adjust precisely the diffusion layer width within the outer shell of a fourth-generation dendrimer molecule decorated by 64 [Ru(II)(tpy)2] redox centers (tpy = terpyridine). Thus the shape of the dendrimer molecule adsorbed onto the ultramicroelectrode surface can be explored voltammetrically in a way reminiscent of an analysis with a nanometric microtome. The quantitative analysis developed here applied to the experimental voltammograms demonstrates that in agreement with previous scanning tunneling microscopy (STM) studies the adsorbed dendrimer molecules are no more spherical as they are in solution but resemble more closely hemispheres resting onto the electrode surface on their diametrical planes. The same quantitative analysis gives access to the apparent diffusion coefficient featuring electron hopping between the [Ru(II)/ Ru(III)(tpy)2] redox centers distributed on the dendrimer surface. Based on the electron hopping rate constant thus measured and on a Smoluchowski-type model developed here to take into account viscosity effects during the displacement of the [Ru(II)/Ru(III)(tpy)2] redox centers around their equilibrium positions, it is shown that the [Ru(II)/Ru(III)(tpy)2] redox centers are extremely labile in their potential wells so that they may cross-talk considerably more easily than they would do in solution at an equivalent concentration.

Ultrafast voltammetry of adsorbed redox active dendrimers with nanometric resolution: an electrochemical microtome.

Megavolt-per-second cyclic voltammetry is used to control the expansion with time of a diffusion layer created within the redox outer shell of a fourth generation dendrimer molecule adsorbed onto an electrode; one quarter of the dendrimer is shown in the picture. This allows the measurement of the degree of communication between the ruthenium(II/III) bis(terpyridyl) ("LRuL") redox centers borne at the extremity of the dendrimer tethers, as well as the characterization of the shape of the adsorbed dendrimer molecule.

Interplay between membrane dynamics, diffusion and swelling pressure governs individual vesicular exocytotic events during release of adrenaline by chromaffin cells.

Release of adrenaline by chromaffin cells occurs through a process involving docking and then fusion of a secretory vesicle to the cytoplasmic membrane of the cell. Fusion proceeds in two main stages. The first one leads to the creation of a stable fusion pore passing through the two membranes and which gives a constant release flux of neurotransmitter (pore-release stage). After a few milliseconds, this initial stage which is not investigated here proceeds through a sudden enlargement of the initial pore (full-fusion stage) up to the complete incorporation of the vesicle membrane into that of the cell and total exposure of the initial matrix vesicle core to the extracellular fluid. The precise time-resolved dynamics of the release and of the vesicle membrane during the full-fusion phase can be extracted with a precision never achieved so far by de-convolution of experimental chronoamperometric currents monitored during individual exocytotic secretion events. The peculiar dynamics of the vesicle membrane proves that exocytotic events are powered by the swelling of the matrix polyelectrolyte core of the vesicle, although they are kinetically regulated by diffusion in the matrix and by the dynamics of the vesicle and cell membranes. Two simple theoretical models based on the dynamics of pores are developed to account for these dynamics and are shown to predict behaviors which are essentially identical to the experimental ones. This offers a new view of the kinetic grounds which control the full-fusion stage, and therefore provides a new interpretation of the sudden transition between the pore-release and the full-fusion stages. This transition occurs when the increasing membrane surface tension energy due to the refrained internal swelling pressure overcomes the edge energy of the pore, so that the initial fusion pore becomes unstable and is disrupted. This new view predicts that secretory vesicles which contain matrixes energetically similar to those of the adrenal cells investigated here can be separated into two classes according to their radius and catecholamine content. Small vesicles (less than ca. 25 nm radius, and containing less than ca. 20000 molecules) should always release through pores. Larger vesicles should always end into fusing except if another mechanism closes the pore before ca. 10000 molecules of catecholamines have been released.