Local softness, softness dipole, and polarizabilities of functional groups: Application to the side chains of the 20 amino acids

The values of molecular polarizabilities and softnesses of the 20 amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the softness of the side chain of the 20 amino acids are clustered in groups reflecting their biochemical classification, namely: aliphatic, basic, acidic, sulfur containing, and aromatic amino acids. The present findings are in agreement with previous results using different approximations and partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126, 145105 (2007)]. In addition, we show that the polarizability of the side chain of an amino acid depends mainly on its number of electrons (reflecting its size) and consequently cannot be used to cluster the amino acids in different biochemical groups, in contrast to the local softness. Our results also demonstrate that the global softness is not simply proportional to the global polarizability in disagreement with the intuition that "a softer moiety is also more polarizable." Amino acids with the same softness may have a polarizability differing by a factor as large as 1.7. This discrepancy can be understood from first principles as we show that the molecular polarizability depends on a "softness dipole vector" and not simply on the global softness.