The sulfate ion can act as a ligand attaching either by one oxygen (monodentate) or by two oxygens as either a chelate or a bridge. An example is the neutral metal complex PtSO4P(C6H5)32 where the sulfate ion is acting as a bidentate ligand. The metal-oxygen bonds in sulfate complexes can have significant covalent character.
The first description of the bonding in modern terms was by Gilbert Lewis in his groundbreaking paper of 1916 where he described the bonding in terms of electron octets around each atom, i.e. no double bonds and a formal charge of 2+ on the sulfur atom.
Later, Linus Pauling used valence bond theory to propose that the most significant resonance canonicals had two π bonds (see above) involving d orbitals. His reasoning was that the charge on sulfur was thus reduced, in accordance with his principle of electroneutrality. The double bonding was taken by Pauling to account for the shortness of the S-O bond (149 pm).
Pauling's use of d orbitals provoked a debate on the relative importance of π bonding and bond polarity (electrostatic attraction) in causing the shortening of the S-O bond. The outcome was a broad consensus that d orbitals play a role, but are not as significant as Pauling had believed. A widely accepted description involves pπ - dπ bonding, initially proposed by D.W.J Cruickshank, where fully occupied p orbitals on oxygen overlap with empty sulfur d orbitals (principally the dz2 and dx2-y2). In this description, while there is some π character to the S-O bonds, the bond has significant ionic character. This explanation is quoted in some current textbooks. The Pauling bonding representation for sulfate and other main group compounds with oxygen is a common way of representing the bonding in many textbooks.
The first indirect effect is also known as the Twomey effect. Sulfate aerosols can act as cloud condensation nuclei and this leads to greater numbers of smaller droplets of water. Lots of smaller droplets can diffuse light more efficiently than just a few larger droplets.
The second indirect effect is the further knock-on effects of having more cloud condensation nuclei. It is proposed that these include the suppression of drizzle, increased cloud height, to facilitate cloud formation at low humidities and longer cloud lifetime. Sulfate may also result in changes in the particle size distribution, which can affect the clouds radiative properties in ways that are not fully understood. Chemical effects such as the dissolution of soluble gases and slightly soluble substances, surface tension depression by organic substances and accommodation coefficient changes are also included in the second indirect effect.
The indirect effects probably have a cooling effect, perhaps up to 2 W/m2, although the uncertainty is very large. Sulfates are therefore implicated in global dimming, which may have acted to offset some of the effects of global warming.