The optical absorption spectra of magnesium oxide (MgO) nanoparticles, along with the atomic centres responsible, are studied using a combination of time-dependent density functional theory (TD-DFT) and coupled-cluster methods. We demonstrate that TD-DFT calculations on MgO nanoparticles require the use of range-separated exchange-correlation (XC-)functionals or hybrid XC-functionals with a high percentage of Hartree-Fock like exchange to circumvent problems related to the description of charge-transfer excitations. Furthermore, we show that the vertical excitations responsible for the experimentally studied range of the spectra of the MgO nanoparticles typically involve both 3-coordinated corner sites and 4-coordinated edge sites. We argue therefore that to label peaks in these absorption spectra exclusively as either corner or edge features does not provide insight into the full physical picture.