  We present a study of the two dimensional circular quantum dot model
Hamiltonian using a range of quantum chemical ab initio methods. Ground and
excited state energies are computed on different levels of perturbation
theories including the coupled cluster method. We outline a scheme to compute
the required Coulomb integrals in real space and utilize a semi-analytic
solution to the integral over the Coulomb kernel in the vicinity of the
singularity. Furthermore, we show that the remaining basis set incompleteness
error for two dimensional quantum dots scales with the inverse number of
virtual orbitals, allowing us to extrapolate to the complete basis set limit
energy. By varying the harmonic potential parameter we tune the correlation
strength and investigate the predicted ground and excited state energies.
