• Corpus ID: 244709816

Evaluation of Gaussian integrals for the modeling of two-dimensional quantum systems

@inproceedings{Schoyen2021EvaluationOG,
  title={Evaluation of Gaussian integrals for the modeling of two-dimensional quantum systems},
  author={Oyvind Sigmundson Schoyen and H-P E Kristiansen and Alfred Alocias Mariadason},
  year={2021}
}
We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence schemes for combined position and differential operator integrals, and three-center Gaussian integrals. The Cartesian Gaussian orbitals are isotropic in the exponent, but with arbitrary centers and angular momentum. 

References

SHOWING 1-10 OF 18 REFERENCES

I and J

One- and two-electron integrals over cartesian gaussian functions

Hilbert-space structure of a solid-state quantum computer: Two-electron states of a double-quantum-dot artificial molecule

We theoretically study a double-quantum-dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer, with the electron spins in the dots serving as qubits.

Efficient recursive computation of molecular integrals over Cartesian Gaussian functions

TLDR
The present scheme with a significant saving of computer time is found superior to other currently available methods for molecular integral computations with respect to electron repulsion integrals and their derivatives.

Structure of lateral two-electron quantum dot molecules in electromagnetic fields

The energy levels of laterally coupled parabolic double quantum dots are calculated for varying interdot distances. Electron-electron interaction is shown to dominate the spectra: In the diatomic m

Nonperturbative ab initio calculations in strong magnetic fields using London orbitals.

TLDR
A self-consistent field London-orbital computational scheme to perform gauge-origin independent nonperturbative calculations for molecules in strong magnetic fields is presented and preliminary applications of the newly developed code to the calculation of fourth-rank hypermagnetizabilities for a set of small molecules, benzene, and cyclobutadiene are presented.

Addition and removal energies of circular quantum dots.

TLDR
Several many-body methods as applied to two-dimensional quantum dots with circular symmetry are presented and compared and the approximate ground state energy is calculated using a harmonic oscillator basis optimized by Hartree-Fock theory.

Electronic structure of quantum dots

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly

Coupled quantum dots as quantum gates

We consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We