Coupled cluster theory for the ground and excited states of two-dimensional quantum dots

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 semianalytic 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.

Automated summary

We conducted a study on the two-dimensional circular quantum dot model Hamiltonian using various quantum chemical ab initio methods. Ground and excited state energies were calculated using different levels of perturbation theories, including the coupled cluster method. We proposed a scheme to compute the required Coulomb integrals in real space and employed a semianalytic solution for the integral over the Coulomb kernel near the singularity. Additionally, we found that the remaining basis set incompleteness error for two-dimensional quantum dots decreases with the inverse number of virtual orbitals, enabling us to extrapolate to the complete basis set limit energy. By adjusting the harmonic potential parameter, we modulated the correlation strength and investigated the predicted ground and excited state energies.