For larger molecules

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... 

The difference between the energy of a molecule at 0 K and its enthalpy at 298 depends on the thermal contr ibution due to vibration at the two temperatures. If the molecule in question is rigid, with few vibrational degrees of freedom, this contribution will be small, as it is for propene and cyclopropane. For larger molecules with a good deal of vibrational freedom, the difference will be conespondingly larger. 

For conditions in industrial production reactors and in corresponding recycle reactors, the mass transfer coefficients of Gamson et al (1943) will be used. These are approximately correct and simple to use. There may be better correlations for specific cases and especially for larger molecules, where diffiisivity is low and Schmidt number is high. In such cases literature referring to given conditions should be consulted. 

In small-molecule crystallography the phase problem was solved by so-called direct methods (recognized by the award of a Nobel Prize in chemistry to Jerome Karle, US Naval Research Laboratory, Washington, DC, and Herbert Hauptman, the Medical Foundation, Buffalo). For larger molecules, protein aystallographers have stayed at the laboratory bench using a method pioneered by Max Perutz and John Kendrew and their co-workers to circumvent the phase problem. This method, called multiple isomorphous replacement... 

Similar prediction can be made for larger molecules. It must be pointed out that the contributions of excited structures become important for bonds with small double bond character, inasmuch as in conjugated systems excited structures alone may lead to as much as 20% double bond character it is probable that the maximum carbon-carbon bond distance in aromatic hydrocarbons is about 1.46 A., the minimum being the double bond distance 1.38 A. 

In a rigorous treatment, one replaces the one-electron operator h by the four-component Dirac-operator hjj and perhaps supplement the two-electron operator by the Breit interaction term [15]. Great progress has been made in such four-component ab initio and DPT methods over the past decade. However, they are not yet used (or are not yet usable) in a routine way for larger molecules. 

The abundant expression of a variety of transporters in Caco-2 cells also makes it attractive to apply functional genomics tools, such as cDNA arrays in order to map the expression [31] and relative abundance of these transporters [32], Also, genomic mapping of surface receptors on Caco-2 cells can be performed to study receptor-mediated endocytosis and other endocytotic pathways for larger molecules in enterocytes [33-36]. 

The results of this test of the TDB-FMS method are encouraging, and we expect the gain in efficiency to be more significant for larger molecules and/or longer time evolutions. Furthermore, as noted briefly before, the approximate evaluation of matrix elements of the Hamiltonian may be improved if we can further exploit the temporal nonlocality of the Schrodinger equation. 

We have shown that theoretical calculations are a complementary tool to experiment in the comprehension of the behavior of such systems. In certain aspects, specially for the smaller systems, quantum chemical calculations already provide sufficiently accurate results. However, for larger molecules and time-dependent phenomena the results have not yet achieved the same level of accuracy. 

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