Radius from bond lengths

The intrinsic molecular volume of monomer units for an amorphous polymer can be calculated from the atomic radius and bond length of the constituent atoms on the basis of the method developed by Slonimskii et al. [24]. When an atom B (atomic radius R) is bound to atom (atomic radius Ri) with bond length d, the atomic volume A.V B) of atom B is given by... 

The covalent radius of an atom is an average value derived from bond lengths in various compounds. The covalent radius of uranium is 142 pm and that of fiuorine is 72 pm. Use these values to estimate the bond lengths in uranium hexafluoride. Calculate the principal moments of inertia of a UFg molecule. Find the energy and the degeneracy of the first excited rotational level of a UFg molecule. 

AB and ABC are the products of the principal moments of inertia. Moments of inertia are calculated from bond angles and bond lengths. Many values are given by Landolt-Bornsteiu. is Avogadro s number, and M is the molecular weight of the molecule. Stuper et al. give a computerized method for prediction of the radius of gyration. 

Each atom makes a characteristic contribution, called its covalent radius, to the length of a bond (Fig. 2.21). A bond length is approximately the sum of the covalent radii of the two atoms (36). The O—H bond length in ethanol, for example, is the sum of the covalent radii of H and O, 37 + 74 pm = 111 pm. We also see from Fig. 2.21 that the covalent radius of an atom taking part in a multiple bond is smaller than that for a single bond of the same atom. 

Because of the occasional occurrence of a difference in hybridization of the bond orbitals involved in bonds of different classes, leading to a difference in single-bond radius, the determination of the bond numbers from experimental values of the bond lengths involves some uncertainty. 

The covalent radii for most of the elements were obtained by taking one-half of the length of a single bond between two identical atoms. For example, the covalent radius of sulfur is obtained from the length of the S—S bond in the S8 molecule ... 

Ionic radii are quoted in Tables 2.3 and 2.5 for a large number of cations including those of the elements in groups 13, 14, 15, and 16, which do not form predominately ionic bonds. These values were obtained by subtracting the fluoride or oxide ion radius obtained from predominantly ionic solids from the length of a bond that is not predominantly ionic. The very small values for the radii of cations obtained in this way do not bear much relation to the real size of the atom in the crystal or molecule. 

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