Refractivity MR

Another vital and equally important criterion to measure the steric factor is adequately provided by a parameter called as molar refractivity (MR). It is usually designated as a simple measure of the volume occupied either by an individual atom or a cluster (group) of atoms. However, the MR may be obtained by the help of the following expression  

Molar refractivity is specifically significant in a situation when the substituent possesses either n electron or lone pairs of electrons. 

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A table of correlations between seven physicochemical substituent parameters for 90 chemical substituent groups has been reported by Hansch et al. [39]. The parameters include lipophilicity (log P), molar refractivity MR), molecular weight MW), Hammett s electronic parameters (a and o ), and the field and resonance parameters of Swain and Lupton F and R). 

The molecular refractivity, MR, has been successfully utilized in QSAR studies 3). This parameter is, in a way, an index for the molecular volume. However, since it is originally defined as a measure of the polarizability related to dispersion forces, it is not included. 

The physicochemical properties that correlate with the biological property are likely to be related to the mechanism by which the chemicals cause the biological activity, and are often referred to as descriptors of the biological activity. Examples of physicochemical properties that often correlate with biological activity and used in the quantification of SARs include octanol-water partition coefficient (logP0/w), dissociation constant (p/<,), and molar refractivity (MR), among others. 

A correlation for less structurally related compounds was also developed by Amalric et al. (1996). To develop this correlation, meta- and para-substituted anisoles were studied. These aromatic compounds were substituted with F, Cl, N02, OH, and NH2 groups. The first-order degradation rate constant, kapf was predicted with the octanol/water partition coefficient (log Kow), Brown s constant (o+), and molar refractivity (MR) used as descriptors. The following correlation was developed ... 

In Eq. [20], Ri is the excess molar refraction (MR), which is the MR of the solute less the MR of the alkane with the same characteristic volume, V 2, as the solute. The 7t symbol is the dipolarity/polarizability, and X) P2 3re the so-called overall LIB acidity and basicity descriptors, respectively. The summation sign is used to emphasize that these are overall HB properties designed to be appropriate to situations where the solute molecule is surrounded by an excess of solvent molecules. These descriptors are in contrast to the HB descriptors 0.2 and p2 employed in Eq. [19], which are derived from 1 1 complexation constants. Equation [20] has also been used with the Vx2 term replaced by a log (L ) term, where is the equilibrium constant... 

For in vitro data, Eq. 35 was derived. Parabolic dependence on CMR (molar refractivity) provided an optimum value for molar refractivity. MR represents the molar refractivity of the molecules. IDN is an indicator variable, which takes the value of 1 for the compounds that contain an heterocycUc ring with nitrogen. It seems that this type of ring is the best substituent compared to the... 

One of the most widely used steric parameters is molar refraction (MR), which has been aptly described as a "chameleon" parameter by Tute (160). Although it is generally considered to be a crude measure of overall bulk, it does incorporate a polarizability component that may describe cohesion and is related to London dispersion forces as follows MR = 4TrNa/By where N is Avogadro s number and a is the polarizability of the molecule. It contains no information on shape. MR is also defined by the Lorentz-Lorenz equation ... 

It is interesting to note that by analogy with chromatographic retention parameters, the values of some other properties of organic compounds may be pre-2 sented in the linear interpolated form relative to the set of reference compounds. These equivalent to indices forms are known for boiling points [6], molecular I weights [7], and molar refractions, MR , = (MW/d)(n -1 l)/( + 2), where MW is the molecular weight, is the... 

The connectivity indices x and xv (102, 103), quantitatively characterize the size of the molecule and the degree of branching. In that sense, and also because they are derived from a theoretical procedure (104), they lack the usual extrathermodynamic meaning. The strong correlation of X with molar refractivity, MR,... 

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

The subset of compounds showing activity LC5q< 5 ppm (all para substituted) were submitted to regression analysis. Plots of log(l/LC5o) vs each physicochemical parameter (it, a, F, R, molar refractivity (MR), L, Bl, B4) (20) revealed several promising relationships, and it appeared that a was important although the 4-SCF3 compound was identified as an "outlier" in the analysis. (21)... 

Another measure of the steric factor is provided by a parameter known as molar refractivity (MR). This is a measure of the volume occupied by an atom or group of atoms. The molar refractivity is obtained from the following equation ... 

Another parameter that is related to molecular volume and steric effects is the molar refractivity (MR). Experimentally, it is obtained from the equation... 

Table L4 Ghose-Crippen atomic contributions to logP and molar refractivity (MR).

A property for which generally good experimental data are available is molar refraction (MR), a composite of refractive index, density, and molecular weight. Because of its relation to polarizability, it has been used in many QSAR relations as a regression variable. It is observed that the relation between MR and skeletal variation is very different from the relation between heat of atomization and structure. The heat of atomization for a set of alkane isomers is generally ranked rather well by the x index the most stable isomer in a set generally has the smallest value of the chi-one index. Such is not the case with MR the MR values in an isomer set follow a much different pattern with x- We expect, then, a rather different QSAR for MR than for AH.,. For alkanes the following QSAR is obtained ... 

When a molecule is represented as an object with well-defined boundaries, geometric methods of analysis may be applied. Several steric parameters have been derived from the model in w hich atoms, hence molecules, are represented as geometric objects with surfaces and volumes. The boundary of an atom is usually determined by its van der Waals radius. Surface area and volume of groups and molecules can be estimated. Bondi,Hermann, and Pearlman are among those who have studied surface area and volume. Molar refractivity (MR), calculated from density and refractive index, has frequently been used to estimate the bulk or global volume of a molecule or group. A more recent trend is to use MR as a model for dispersion interactions. 

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