Explicit Models for Condensed Phases

At the heart of chemistry are atoms and molecules - they are the basis set in which chemical events are expressed. While the continuum models described in Chapter 11 can be very efficient and powerful in situations where the molecular nature of a surrounding condensed phase is superfluous to the question at hand, they are unsuitable when knowledge of the explicit behavior of the surroundings is deemed to be as important as its effect on some system embedded therein. 

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Thus, in contrast to preceding MM approaches explicit treatment of electronic polarisability is integral to a semi-empirical QM approach and promises excellent prospects for quantitative theoretical modelling of carbohydrates across a range of condensed phase environments. The results of the PM3CARB-1 model do however indicate in line with classical force field approaches [65, 73] that perhaps greater... 

One variation on this theme that should be borne in mind when analyzing actual chemical situations is tliat certain species in the real system may be buffered . That is, their concentrations may be held constant by external means. A good example of this occurs in condensed phases, where solvent molecules may play explicit roles in chemical equilibria but tlie concentration of the free solvent is so much larger than that for any other species that it may be considered to be effectively constant. Modeling solvation phenomena in general is covered in detail in the next two chapters, but it is instructive to consider here a particular case as it relates to computing equilibria. Consider such a reaction as... 

Molecular dynamics simulations are attractive because they can provide not only quantitative information about rates and pathways of reactions, but also valuable insight into the details of ho y the chemistry occurs. Furthermore, a dynamical treatment is required if the statistical assumption is not valid. Yet another reason for interest in explicit atomic-level simulations of the gas-phase reactions is that they contribute to the formulation of condensed-phase models and, of course, are needed if one is to include the initial stages of the vapor-phase chemistry in the simulations of the decomposition of energetic materials. These and other motivations have lead to a lot of efforts to develop realistic atomic-level models that can be used in MD simulations of the decomposition of gas-phase energetic molecules. 

It is well known that ROKS systematically underestimates excitation energies, this has also been reported for other nucleobases [43 15, 47, 56], Typically, however, the shape of the ROKS potential landscape, which determines the excited state dynamics, has been found to be surprisingly accurate [16,20, 21, 56], An indication for this are the Stokes shifts obtained with ROKS. The experimental Stokes shift of 0.91 eV measured in aqueous solution [30] is much smaller than the gas phase ROKS results (Table 10-1). TDDFT calculations taking into account solvent effects through a polarizable continuum model seem to confirm that the Stokes shift is significantly reduced (by 0.4 eV) due to the solvent [30], Nieber and Doltsinis [64] have calculated the Stokes shift in explicit water solvent using ROKS/DFT we shall discuss these condensed phase simulations in detail below (see Section 10.3.1.2). 

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

Deviations from OGM were recognized early on spectroscopic properties of molecular crystals Davydov shifts and splittings of absorption bands in molecular crystals are clear deviations from OGM and were rationalized based on the excitonic model (EM) [10, 14, 15, 16, 17]. This same model proved extremely successful to describe the complex and technologically relevant spectroscopy of molecular aggregates, i.e. of clusters of molecules that spontaneously self-assemble in solution or in condensed phases [IS]. Much as it occurs in molecular crystals, due to intermolecular electrostatic interactions the local bound electron-hole pair created upon photoexcitation travels in the lattice and the corresponding wave function describes an extended delocalized object called an exciton. We explicitly remark that the Frenkel picture of the exciton, as a bound electron-hole pair, both residing on the same molecule, survives, or better is the basis for the excitonic picture. The delocalization of the exciton refers to the fact that the relevant wave function describes a Frenkel exciton (a bound e-h pair) that travels in the lattice, and this is of course possible even when electrons and/or holes are, separately, totally localized. In other terms, the EM describes localized charges, but delocalized excitations. 

The models (photochemical and thermal) can be subdivided into volume and surface models. The processes responsible for ablation in surface models only take place within several monolayers of the surface. As a result, the velocity of the interface between the gaseous and condensed phase depends explicitly on the surface temperature or laser intensity. With volume models, the processes resulting in ablation take place within the bulk of the material. The volume and surface models are ... 

The two phases are coupled explicitly with mass flux and energy flux preserved. Thermal radiation from gas phase reaction is neglected in this model only laser radiation and conductive heat feedback from adjacent gas phase grids are taken into account as energy source terms for the condensed phase, which is critical to realize the pressure dependence of the mass burning rate. 

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