Molecular volume difference method

MVD (molecular volume difference) method presented here was based on MCD method and on MTD multi-conformational method. MVD allows a logical construction of a start map of receptor, S, and assures the differentiation of the vertices in hypermolecule H, translating all the ligands into their vdW space. 

The energetic, geometric, and electronic differences of the meso and chiral form of oxirane 1 and cyclobutene 2 derivatives were studied using DFT methods (Fig. 3.12) [34], The partition of several molecular characteristics (energy, charge, and volume) into atomic contributions was carried out within the AIM framework. The energetic analysis shows that the main contribution to the energy differences came from the chiral carbon atom where the substituents X are attached. The molecular volume differences can be explained based on the results obtained for the substituents in both dispositions. 

The molecular size and shape descriptors may indicate if a ligand molecule, L, does not fit the active site. Unfortunately, in many cases the receptor site cannot be described in simple terms of large , width , and depth . The MTD (minimal topologic difference) method allows a receptor site mapping in the frame of a series of bioactive compounds. The MVD (minimal volume difference) method is an improved variant of the MTD method, which takes into account the 3D extension of a molecule. These two methods are described here in some detail. The results obtained in the study of anti-carcinogenic activity of some retinoids and in the inhibition of carbonic-anhydrase (CA) by a series of sulfonamides are also presented in this chapter. 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

The basic principles are described in many textbooks [24, 26]. They are thus only sketchily presented here. In a conventional classical molecular dynamics calculation, a system of particles is placed within a cell of fixed volume, most frequently cubic in size. A set of velocities is also assigned, usually drawn from a Maxwell-Boltzmann distribution appropriate to the temperature of interest and selected in a way so as to make the net linear momentum zero. The subsequent trajectories of the particles are then calculated using the Newton equations of motion. Employing the finite difference method, this set of differential equations is transformed into a set of algebraic equations, which are solved by computer. The particles are assumed to interact through some prescribed force law. The dispersion, dipole-dipole, and polarization forces are typically included whenever possible, they are taken from the literature. 

Volume additivity methods generally do not take into account crystal packing efficiency or molecular conformation effects and thus will afford identical calculated densities for positional and conformational isomers and for compounds that possess different multiples of the same functional group composition. As an example, a volume additivity calculation predicts that l,3,5-trinitro-l,3,5-triazacyclohex-ane (RDX), l,3,5,7-tetranitro-l,3,-5,7-tetraazacyclooctane (a-HMX), and /3-HMX all will possess the same crystal density, 1.783 g/cm [32]. In fact, the experimentally observed densities of these three compounds differ markedly (i.e., 1.806 [33], 1.839 [34], and 1.902 [35], respectively). 

Dead Volume. The dead volume difference between the viscometer and DRI must be accounted for. Otherwise systematic errors in Mark-Houwink parameters K and u can occur. In the previous paper (16), a method developed by Lesec and co-workers (38) based on injecting a known amount of a very high molecular weight polystyrene standard onto low porosity columns was used. From the viscometer and DRI chromatograms, the apparent intrinsic viscosity [h] was plotted against retention volume V. A series of [n] vs. V plots are then constructed assuming a range of dead volume, AV. 

The 47i-comparator method 23,24) represents a qualitative version of the above two methods. One used CPK molecular models and the computer generates the six projections corresponding to the faces of the cube containing the respective pair of molecules. These projections reveal shape and volume differences among the molecules considered. 

The mechanical properties of polyelectrolyte multilayer capsules have been subject of several studies using different methods. Baumler and co-workers [7] have used the micropipette technique and found that PMCs are not conserving their volume if pressure differences are applied between inside and outside of the shell. This is expected, since the shells can only be formed in first place because the membrane is permeable to low molecular weight species, the core dissolution products. They found no deformation up to a critical pressure followed by an irreversible collapse, showing that shells deform not elastically but plastically for large deformations. First quantitative estimates of the Young s modulus of the shell material were obtained by Gao and coworkers, using osmotic pressure differences between inside and outside of the shell [8,9], These authors monitored the onset of the buck-... 

Immersion of dry samples in liquids of different molecular size This method is designed to take advantage of molecular sieving. The basic data are simply in the form of a curve of the specific energy of immersion versus the molecular size of the immersion liquid. This provides immediate information on the micropore size distribution. For room-temperature experiments one can use the liquids listed in Table 8.1, which are well suited for the study of carbons. Because of the various ways of expressing the critical dimension of a molecular probe or its molecular size , one must be careful to use a consistent set of data (hence the two separate lists in Table 8.1). Again, one can process the microcalori-metric data to compare either the micropore volumes accessible to the various molecules (see Stoeckli et a ., 1996), or the micropore surface areas, as illustrated in Figure 8.5. 

That the alteration in the vapour pressure is a small quantity is at once shown by the ratio v/Y Thus in the case of water at xoo° C, the molecular volume of the liquid may be taken to be 18 c c approximately, and the molecular volume of the vapour as 20,000 c c approximately Hence v/Y = o 0009 approximately This small fraction denotes the increase in the saturated vapour pressure expressed in atmospheres, due to increasing the external pressure by one atmosphere The change is of the order of one part in 1000 and is therefore a negligible quantity It follows, however, that in vapour pressure measurements the static method gives the true value whilst the dynamic or streaming method gives the vapour pressure at an external pressure of one atmosphere The difference between the two values is, however, often undetectable... 

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