**iii. The Alavi and Waldeck theory (AW)**

Alavi and Waldeck theory (Alavi and Waldeck, 1991a), proposes that it is rather the charge distribution of the solute than the dipole moment that is used to calculate the friction experienced by the solute molecule. Not only the dipole moment of the solute, but also the higher order moments, contribute significantly to the dielectric friction. In other words, molecules having no net dipole moment can also experience dielectric friction. AW theory has been successful compared to NZ and ZH theories in modeling the friction in nonassociative solvents (Dutt and Ghanty, 2003). The expression for the dielectric friction according to this model is given by (Alavi and Waldek, 1991a)

$$
\sigma\_{\rm DF} = P \frac{(\varepsilon\_0 - 1)}{(2\varepsilon\_0 + 1)^2} \sigma\_D \tag{33}
$$

where

$$P = \frac{4}{3akT} \sum\_{j=1}^{N} \sum\_{l=1}^{N} \sum\_{L=1}^{l\_{\text{max}}} \sum\_{M=1}^{L} \left(\frac{2L+1}{L+1}\right) \frac{(L-M)!}{(L+M)!} \times$$
 
$$M^2 q\_i q\_j \left(\frac{r\_i}{a}\right)^L \left(\frac{r\_j}{a}\right)^L P\_L^M(\cos\theta\_i) P\_L^M(\cos\theta\_j) \cos M\phi\_{ji} \tag{34}$$

where ( ) *MP x <sup>L</sup>* are the associated Legendre polynomials, *a* is the cavity radius, *N* is the number of partial charges, *qi* is the partial charge on atom *i*, whose position is given by ( , , *iii r* θ φ ), and φ *ji* = − φ φ *<sup>j</sup> <sup>i</sup>* . Although the AW theory too treats solvent as a structureless continuum like the NZ and vdZH theories, it provides a more realistic description of the electronic properties of the solute.
