The peroxomonosulfate is a hypercoordinated molecule, in which the sulfur appears to exceed Lewis' rule of two, better known as the octet rule. In former times it was believed that d orbitals would contribute to bonding. This is not the case.
Bonding is better represented by
- three equivalent $\ce{S-O}$ single bonds
- sulfur having a formal charge of +2
- these three oxygens having a formal charge of -1
- one $\ce{S-O}$ single bond that leads to the peroxyl oxygen
- this oxygen has a formal charge of zero
- one $\ce{O-O}$ single bond
- and the terminal oxygen having a formal charge of -1
This bonding picture is much more in accordance with quantum chemical calculations and an NBO analysis on the DF-BP86/def2-SVP level of theory. The involvement of d orbitals is minimal (<1%).

It is noteworthy, that this molecule pretty much has the same bonding around the sulphur as in sulphate. It can therefore similarly be described. Have a look at my rant against hypervalency or the bonding picture of the $\ce{PO4^{3-}}$ anion, which is isoelectronic to sulphate.