An ab initio study is carried out to investigate the anionic aerogen bonds in complexes of KrO3, XeO3 and XeOF2 with F, Cl, Br, CN, NC, N-3, SH, SCN, NCS, OH and OCH3 anions. All of the anionic aerogen bonds analyzed here have a partial covalent character. Charge transfer from the anion to the Kr-O or Xe-O o-* orbital stabilizes these complexes and leads to a sizable redshift in the corresponding stretching frequencies. The J(Kr-O) or J(Xe-O) spin-spin coupling constants can be regarded as a useful tool for the characterization of strength of the anionic aerogen-bonded complexes. (C) 2016 Elsevier B.V. All rights reserved.