Generalized Born term

The cubic amphiphilic mesophases (Sic, Vi, and V2) from their interposition in the succession of mesophases Sic, Mi, Vi, G, V2, and M2, have generally been termed liquid crystalline like the optically anisotropic amphiphilic mesophases Mi, G, and M2. The cubic mesophases formed by non-amphiphilic globular molecules have however usually been termed plastic crystals. This nomenclature has obscured the fact that these plastic crystals are fundamentally liquid crystals rather than solid cyrstals and bear a relationship to the optically anisotropic non-amphiphilic smectic and nematic liquid crystals similar to that born by the amphiphilic cubic mesophases to the optically anisotropic neat (G) and middle (Mi and M2) liquid crystalline phases. 

This is a generalization of the Onsager reaction field model for a point dipole inside a spherical cavity. For charged solutes, one should also include an ionic Born term, derived by... 

The CDS parameters, on the other hand, are expected neither to be solvent-independent nor to be clearly related to any particular solvent bulk observable, especially insofar as they correct for errors in the NDDO wavefunc-tion and its impact on the ENP terms. The CDS parameters also make up empirically for the errors that inevitably occur when a continuous charge distribution is modeled by a set of atom-centered nuclear charges and for the approximate nature of the generalized Born approach to solving the Poisson equation. Hence, the CDS parameters must be parameterized separately against available experimental data for every solvent. This requirement presents an initial barrier to developing new solvent parameter sets, and at present, published SMx models are available for water only (although a hexadecane parameter seH will be available soon). 

The Gpoi term is calculated by the generalized Born equation (Eq. (15))... 

Implicit solvation models developed for condensed phases represent the solvent by a continuous electric field, and are based on the Poisson equation, which is valid when a surrounding dielectric medium responds linearly to the charge distribution of the solute. The Poisson equation is actually a special case of the Poisson-Boltzmann (PB) equation PB electrostatics applies when electrolytes are present in solution, while the Poisson equation applies when no ions are present. Solving the Poisson equation for an arbitrary equation requires numerical methods, and many researchers have developed an alternative way to approximate the Poisson equation that can be solved analytically, known as the Generalized Born (GB) approach. The most common implicit models used for small molecules are the Conductor-like Screening Model (COSMO) [96,97], the Dielectric Polarized Continuum Model (DPCM) [98], the Conductor-like modification to the Polarized Continuum Model (CPCM) [99], the Integral Equation Formalism implementation of PCM (lEF-PCM) [100] PB models and the GB SMx models of Cramer and Truhlar [52,57,101,102]. The newest Miimesota solvation models are the SMD (universal Solvation Model based on solute electron Density [57]) and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [103-105] with semiempirical terms that account for local electrostatics [106]. Further details on these methods can be found in Chapter 11 of reference 52. 

However, the influence of long-range interactions has to be taken into account by a term describing the Debye-Hiickel theory. For this term, in the general case the density and the dielectric constant of the mixed solvent have to be determined (see Eq. (7.49)). As the reference state of the electrolyte components refers to the infinitely diluted solution in pure water, the Debye-Hiickel term must be corrected by the so-called Born term, which takes into account the difference between the dielectric constants of water and the solvent mixture [14] ... 

An especially interesting model, termed the generalized Born model, has been developed primarily for water as a solvent. We will describe it briefly here, because it nicely illustrates in a quantitative way some of the topics we have discussed in this chapter. The approach is a parameterized method that produces Gsoiv, the solvation free energy for a molecule or ion. First, Gsoiv is divided into three terms (Eq. 3.32). 

The first requirement is the definition of a low-dimensional space of reaction coordinates that still captures the essential dynamics of the processes we consider. Motions in the perpendicular null space should have irrelevant detail and equilibrate fast, preferably on a time scale that is separated from the time scale of the essential motions. Motions in the two spaces are separated much like is done in the Born-Oppenheimer approximation. The average influence of the fast motions on the essential degrees of freedom must be taken into account this concerns (i) correlations with positions expressed in a potential of mean force, (ii) correlations with velocities expressed in frictional terms, and iit) an uncorrelated remainder that can be modeled by stochastic terms. Of course, this scheme is the general idea behind the well-known Langevin and Brownian dynamics. 

This is a rough calculation, based on direct capital cost and not on interest rates, and needs to be analysed in terms of the general plant economics. It should also be borne in mind that this is based on present-day electricity costs, and a greater saving will be made as fuel costs rise. 

A second simplihcation results from introducing the Born-Oppenheimer separation of electronic and nuclear motions for convenience, the latter is most often considered to be classical. Each excited electronic state of the molecule can then be considered as a distinct molecular species, and the laser-excited system can be viewed as a mixture of them. The local structure of such a system is generally described in terms of atom-atom distribution functions t) [22, 24, 25]. These functions are proportional to the probability of Ending the nuclei p and v at the distance r at time t. Building this information into Eq. (4) and considering the isotropy of a liquid system simplifies the theory considerably. 

Over the past decades the term device quality has come to refer to intrinsic PECVD hydrogenated amorphous silicon that has optimum properties for application in a certain device. Of course, depending on the type of device, different optimum values are required nevertheless the properties as listed in Table I are generally accepted, e.g. [6, 11]. Many of these properties are interrelated, which has to borne in mind when attempting to optimize only one of them. 

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