Trends of the bonding effect on the performance of DFT methods in electric properties calculations: a pattern recognition and metric space approach on some XY2 (X = O, S and Y = H, O, F, S, Cl) molecules.

A test set of 10 molecules (open and ring forms of ozone and sulfur dioxide as well as water and hydrogen sulfide and their respective fluoro- and chloro-substituted analogs) of specific atmospheric interest has been formed as to assess the performance of various density functional theory methods in (hyper)polarizability calculations against well-established ab initio methods. The choice of these molecules was further based on (i) the profound change in the physics between isomeric systems, e.g., open (C(2v)) and ring (D(3h)) forms of ozone, (ii) the relation between isomeric forms, e.g., open and ring form of sulfur dioxide (both of C(2v) symmetry), and (iii) the effect of the substitution, e.g., in fluoro- and chloro-substituted water analogs. The analysis is aided by arguments chosen from the information theory, graph theory, and pattern recognition fields of Mathematics: In brief, a multidimensional space is formed by the methods which are playing the role of vectors with the independent components of the electric properties to act as the coordinates of these vectors, hence the relation between different vectors (e.g., methods) can be quantified by a proximity measure. Results are in agreement with previous studies revealing the acceptable and consistent behavior of the mPW1PW91, B3P86, and PBE0 methods. It is worth noting the remarkable good performance of the double hybrid functionals (namely: B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties.