Molar refractivities

Molar refractivity is related to the size of a molecule. The advantage of using molar refractivity in a model (rather than VA) is that calculation is readily available via for example, the program CMR within the Pomona Medicinal Chemistry Project software [8]. Errors in results from CMR are considered by the present authors to be small compared to the errors in measured D values. 

Calculations of volume based on molecular orbital calculations are possible they are, however, not easily accessible to the non-specialist, so CMR is preferred. 

The electromagnetic wave theory of light enables the definition of the molar refractivity 

It can be shown that R is the volume of the molecules, as distinct from M/p which is the apparent volume [7]. 

R (or CMR) is an additive and constitutive property and has been used widely in determination of molecular structure, before the advent of spectroscopic methods. 

Pauling and Pressman considered the molar refractivity (defined by Equation 56) as a means of assessing polarisability. 

The components of MR are M = molecular weight, d = density of the liquid, and n = refractive index against the D-line of sodium. The molar refractivity is an additive constitutive property of molecules it has been employed extensively in the past as a tool to investigate structural problems such as the constitution of dative bonds, double bonds, aromaticity and the like. Values of MR have been deduced for many substituents (see Table 1 in Appendix 3) and the MR for a molecule calculated from fragmental values usually agrees well with the observed value. 

The MR parameter has the dimensions of volume and can correlate with the hydrophobic substituent constant n it can be used as a crude measure of bulk. However, the parameter has a component proportional to polarisability. These potential complications can be avoided by careful experimental design so that the chosen substituents have tc values which are not linear with their MR parameters. The coefficient of MR in the free energy equation can be used to indicate a steric interaction (-ve) coefficient or an interaction involving dispersion forces (+ve coefficient). 

The parachor,defined in Equation (58), has the dimensions of volume and has been examined as a reference for free energy correlations in much the same way as the molar refractivity.  

The quantity y is the surface tension of the liquid, M is the molecular weight and D and d are respectively the densities of liquid and vapour. The parachor is essentially a molecular volume measured at standard internal pressure and is an additive, constitutive, property because of its molar volume component.  

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Here, k is a factor which converts to units (kcal/mol in this case where the distances are in A and the polarisabilities in A ). G, and Gj are constants chosen to reproduce the well depths for like-with-like interactions. The atomic polarisability values are obtained from an examination of appropriate molecular experimental data (such as measurements of molar refractivity). 

The molar refraction deduced for alkyl derivatives, compared to the value obtained by addition, to the experimental molar refraction of thiazole, of the classical (CH2) increment of Eisenlohr Rch 4.618 cm ), show specific exaltations which are typical for each position of the thiazole ring (Table 1-49). 

TABLE 1-49. SPECIHC EXALTATION OF MOLAR REFRACTION (IN PERCENTAGE OF THE CALCUL-LATED VALUE) (198, 199, 2l5)... 

From the atomic and group refractions in Table 5.19, the molar refraction is computed as follows ... 

Physical Methods of Examination. Physical methods used to examine coals can be divided into two classes which, in the one case, yield information of a stmctural nature such as the size of the aromatic nuclei, ie, methods such as x-ray diffraction, molar refraction, and calorific value as a function of composition and in the other case indicate the fraction of carbon present in aromatic form, ie, methods such as ir and nuclear magnetic resonance spectroscopies, and density as a function of composition. Some methods used and types of information obtained from them are (41) ... 

Parachor is the name (199) of a temperature-independent parameter to be used in calculating physical properties. Parachor is a function of Hquid density, vapor density, and surface tension, and can be estimated from stmctural information. Critical constants for about 100 organic substances have been correlated to a set of equations involving parachors and molar refraction (200). 

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

Trioxolane, 3-ethyl-5-butyI-molar refraction, 6, 865 (55CB1878)... 

Now Pe is numerically equal to the molar refraction R which is an additive property. It has been shown that P is a property which can be calculated by adding the refractions of various electron groups. Six values for such partial molar refractions are given in Table 6.3. 

The additive and constitutive properties of the molar refraction of a substance has been known for nearly a century and the molar refraction is defined by the following equation,... 

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