Anisotropic van der Waals Radii

Structural studies of crystalline iodine show that the intermolecular distance depends on the crystallographic direction and the difference equals 0.9 A [116,117]. This result at first was also confirmed by Jdanov and Zvonkova [118] for the longitudinal (/ i) and transverse (/ t) vdW radii of Br and H later this effect has been studied in numerous structural works (see for example [88]). 

Nyburg [119, 120] determined the anisotropic vdW radii of halogens (Table 4.7) in the structures ofX2 molecules we calculated [121,122] the analogous 

The longitudinal vdW radii of H in gas-phase Rg HX molecules were computed from stmctural data in [128]. However, in these complexes the HX axis forms a certain angle (6) with the Rg- H direction and therefore the latter separation corresponds to the intermediate (between R and Rt) value of R(H). Using the dependence / (H) =/(180° — 6) [106], the following values of 7 i(H) in Rg HX were obtained 

The transverse and longitudinal vdW radii have been also determined experimentally in other gas-phase molecules. Thus, in T-shaped vdW complexes Rg A2 (Rg = He, Ne, Ar, Kr, Xe A = H, O, N or a halogen) the radii of A (perpendicular to the A-A bond line) were calculated from structural data [99] such complexes are rigid and Rt(A) does not depend (within 0.05 A) on the type of Rg. In some (A2)2 dimers the A2 molecules contact side-to-side and thus Ri is equal to one-half of the (experimentally determined) separation between the molecular centers of mass. These Rt values are close to the corresponding radii of A in Rg A2 complexes the former radii exceed the latter by 0.05 A on average, due to different modes of molecular packing projection into hollow in Rg A2 or projection against projection in (A2)2 [121, 122]. 

To determine the longitudinal radii in bonds or molecules, one can use the experimental anisotropy of the bond or molecular electronic polarizability (01/ and a,). Polarizability being the optical volume of a molecule, the expression y = (ai/at) corresponds to the ratio between the length and thickness of this molecule  

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