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

TL;DR

This paper applies coupled cluster and other ab initio methods to study ground and excited states of two-dimensional quantum dots, providing a detailed computational approach and analysis of correlation effects.

Contribution

It introduces a scheme for computing Coulomb integrals in real space and demonstrates basis set extrapolation for accurate energy predictions in 2D quantum dots.

Findings

Coupled cluster method effectively computes energies of 2D quantum dots.

Basis set incompleteness error scales inversely with virtual orbitals.

Tuning harmonic potential parameter reveals correlation effects.

Abstract

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.