# Ab initio and AIM theoretical analysis of hydrogen-bond radius of HD (D = F, Cl, Br, CN, HO, HS and CCH) donors and some acceptors

Raghavendra, B and Mandal, Pankaj K and Arunan, E (2006) Ab initio and AIM theoretical analysis of hydrogen-bond radius of HD (D = F, Cl, Br, CN, HO, HS and CCH) donors and some acceptors. In: Physical Chemistry Chemical Physics, 8 (45). pp. 5276-5286.

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Recently, we defined ‘hydrogen-bond radii’ for various hydrogen-bond donors, DH where D=F, Cl, Br, CN, HO or CCH from an empirical analysis. It was shown that the $A^{...} H$ distances in $B^{...}HD$ complexes could be written as a sum of hydrogen bond radius for DH and a constant acceptor radius for A, which is the bonding atom/centre in B. This manuscript reports the determination of the hydrogen-bond radii for these molecules and $H_2S$ from ab initio and atoms in molecules (AIM) theoretical calculations. The results from ab initio calculations are consistent with the empirical estimates for the six molecules noted above and provide the first estimate for hydrogen bond radius (1.08 \pm 0.16 \AA ) for $H_2S$ donor. The results from AIM theoretical analysis are in qualitative agreement with ab initio results. However, AIM analysis indicates that both hydrogen bond donor and acceptor radii vary in a systematic way from the strong to weak hydrogen bonds. Irrespective of the method used, the hydrogen bond donor radius increases in the order HF<HCl<$H_2O$<HBr<HCN<HCCH<$H_2S$, but mostly lie between Pauling’s covalent and van der Waals radii of H atom. Interestingly, the acceptor radii for A in $A^{...}HD$ also increase in the same order. The AIM theoretical results on about 100 complexes have been reduced to suggest radii for H, F, O, N, C and S that are appropriate for strong, medium and weak hydrogen bonds. It is suggested that the use of a single van der Waals radius for D, H or A in determining the presence/absence of $D-H^{...}A$ hydrogen bonding be discontinued.