Initial molecular motion

Molecular transport concerns the mass motion of molecules in condensed and gaseous phases. The mass motions are driven primarily by temperature. As time progresses, the initial mass motion results in concentration gradients. In the condensed phase, dow along concentration gradients is described by Fick s law. 

These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

To determine molecular motions in real time necessitates the application of a time-ordered sequence of (at least) two ultrafast laser pulses to a molecular sample the first pulse provides the starting trigger to initiate a particular process, the break-up of a molecule, for example whilst the second pulse, time-delayed with respect to the first, probes the molecular evolution as a function of time. For isolated molecules in the gas phase, this approach was pioneered by the 1999 Nobel Laureate, A. H. Zewail of the California Institute of Technology. The nature of what is involved is most readily appreciated through an application, illustrated here for the photofragmentation of iodine bromide (IBr). 

I propose to develop and apply such methods, based on ultrafast X-ray absorption spectroscopy, to study the ultrafast molecular motions of organometallics in solutions. In particular, initial studies will focus on photo-induced ligand dissociation and substitution reactions of transition metal carbonyls and related compounds in various solvent systems. 

One of the most interesting applications of Femtochemistry is the stroboscopic measuring of observables related to molecular motion, for instance the vibrational periods or the breaking of a bond [1], Because femtosecond laser fields are broadband, a wave packet is created by the coherent excitation of many vibrational states, which subsequently evolves in the electronic potential following mostly a classical trajectory. This behavior is to be contrasted to narrow band selective excitation, where perhaps only two (the initial and the final) states participate in the superposition, following typically a very non-classical evolution. In this case one usually is not interested in the evolution of other observables than the populations. 

Note that many of these surface reactions involve the conversion of a hydrophophic polymer to one with a hydrophilic surface or vice versa. For example, the replacement of trifluoroethoxy groups at the interface by hydroxyl units changes a non-adhesive, highly hydrophobic surface to an adhesive hydrophilic one. Variations in the reaction conditions allow both the depth of transformation and the ratios of the initial to the new surface groups to be controlled. A possible complication that needs to be kept in mind for all of these surface transformations is that polymer molecular motions may bury the newly introduced functional units if the polymer comes into contact with certain media. For example, a hydrophilic surface on a hydrophobic polymer may become buried when that surface is exposed to dry air or a hydrophobic liquid. But this process can be reversed by exposure to a hydrophilic liquid. 

In the case of vibrations of solvated molecules the same two-term partition can be assumed, but in this case the slow term will account for the contributions arising from the motions of the solvent molecules as a whole (translations and rotations), whereas the fast term will take into account the internal molecular motions (electronic and vibrational) [42], After a shift from a previously reached equilibrium solute-solvent system, the fast polarization is still in equilibrium with the new solute charge distribution but the slow polarization remains fixed to the value corresponding to the solute charge distribution of the initial state. 

With the large number of motional theories being touted the need for multi-frequency relaxation studies becomes critical. At one frequency most theories can satisfactorily predict the behavior because of the many adjustable parameters. By initiating multifield and multitemperature and NOEF studies, more subtle features of molecular motion can be probed. Although the motional model used by us is adequate, it may not be the best model. Indeed, Howarth has had better results with our preliminary data using internal librational motion. This enforces the need for measuring as many relaxation parameters as possible, under as many different conditions as possible. 

Selective inversion recovery experiments i.e. only select frequencies within the powder pattern are excited, have also been performed on 2H for the purposes of studying molecular motion. Initial experiments were performed on deuterated dimethylsulfone (DMS) to demonstrate the utility of the experiment.46 Selective inversion recovery curves were fitted to a suitable motional model, a two-site jump model in the case of DMS, to yield the motional rates as a function of temperature. A significant feature of this work is that the activation energy for the motion so obtained differs markedly from that obtained from earlier 13C chemical shift anisotropy lineshape studies. 

Similar modelling has been performed for both of these systems, based on the cube model. Following Hand and Harris, the molecular motion was coupled to the surface oscillator via a rigid shift of the Z-coordinate in the PES, i.e. V(Z, r,. .., y) = V(Z — y, r...), where y is the oscillator coordinate. For the H2/Pd system [80], six molecular degrees-of-freedom were included in a classical treatment, while four molecular degrees-of-freedom were included in a quantum solution for the H2/Cu system [81, 82]. In the classical calculations, the surface temperature dependence was introduced by sampling the surface vibration from a Boltzmann distribution. In quantum calculations, this is not possible, and many calculations were required, each in a different initial surface oscillator state. The results... 

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