Mechanisms in Condensed Phases

The manual interpretation of a mass spectrum - nature and origin of the fragmentation peaks - is a difficult but interesting exercise. Organic chemists are usually familiar with these methods of interpretation since they retrieve different types of transient ions considered to explain reaction mechanisms in condensed phases. The difference here is that these ions move in a vacuum and do not collide. The very short period of time between ion formation and ion detection (a few pis), allows to observe the existence of very unstable species that are unstable under normal conditions. 

VIII. Mechanisms in Condensed Phases A. Alkanes, Alkenes and Alkynes... 

Molecules are sufficiently heavy that their motions can be described quite accurately by classical mechanics. In condensed phases (solution or solid state), there is a strong interaction between molecules, and a reasonable description can only be attained by having a large number of individual molecules moving under the influence of each other s repulsive and attractive forces. The forces in this case are complex and cannot be written in a simple form such as the Coulomb or gravitational interaction. No analytical solutions can be found in this case, even for a two-particle (molecular) system. Similarly, no approximate solution corresponding to a Hartree-Fock model can be constructed. The only method in this case is direct simulation of the full dynamical equation. 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

Understanding VER in condensed phases has proven difficult. The experiments are hard. The stmcturally simple systems (diatomic molecules) involve complicated relaxation mechanisms. The stmctures of polyatomic molecules are obviously more complex, but polyatomic systems are tractable because the VER mechanisms are somewhat simpler. 

On several occasions, the reader will notice a direct connection between the topics covered in the book and other, related areas of statistical mechanics, such as the methodology of computer simulations, nonequilibrium dynamics or chemical kinetics. This is hardly a surprise because free energy calculations are at the nexus of statistical mechanics of condensed phases. 

On the other hand, one has to take into account the influence of the surrounding which must induce an irreversible evolution of the H-bond system when its fast mode is excited the fast mode may be directly damped by the medium that is the direct relaxation mechanism. It may be also damped through the slow mode to which it is anharmonically coupled, that is the indirect relaxation mechanism. A schematical illustration of these two damping mechanism is given in Fig. 2. Of course, the role played by damping must be more important for H bonds in condensed phase. 

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera< where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

Although the traditional approach of transition structure determination and reaction path following is perfectly suited for gas phase reactions, which can also provide major insight into the mechanism of condensed phase reactions, (14-16) it is also important to specifically consider the fluctuation and collective solvent motions accompanying the chemical transformation in solution.(17, 18) One approach that has been used to address this problem is the use of an energy-gap reaction coordinate, A. -... 

In consideration of the kinetic law obtained, Rp i0 of magnitude range, one can conclude that the common polymerization mechanism, based on bimolecular termination reactions, is no longer valid for these multifunctional systems when irradiated in condensed phase. Indeed, for conventional radical-induced polymerizations, the termination step consists of the interaction of a growing polymer radical with another radical from the initiator (R), monomer (M) or polymer (P) through recombination or disproportionation reactions ... 

This conclusion is borne out by kinetic evidence which shows that the intensity of emission is proportional to [02(1A9)]3. Since [02(1H9+)] oc [Oz(1A9)]a in the discharge-flow system, the result indicates that [N02 ] oc [02(1A9)][02(1S9+)]. The experimental evidence does not allow description of the detailed mechanism for reaction (32). Two possibilities are (a) that a low-lying excited state of N02 is excited from one or other of the excited 02 species before a second energy-transfer reaction produces the emitting state of N02, or (b) that direct transfer to N02 takes place from an 02(1Afl) 02(1S9+) dimol. Although emission from this latter dimol is not observed in the gas phase, since [02(1S9+)] is normally very small, it has been seen in condensed phase systems.20... 

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