European Physical Journal D, Volume 16 , Issue 1-3 : 373-380(2001) https://doi.org/10.1007/s100530170133

## Coupling and dissociation in artificial molecules

• PublishedJul 19, 2021
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### References

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[17] Within the terminology adopted here, the simple designation Hartree-Fock (HF) in the literature most often refers to our restricted HF (RHF), in particular in atomic physics and the physics of the homogeneous electron gas. In nuclear physics, however, the simple designation HF most often refers to a space (S)-UHF. The simple designation unrestricted Hartree-Fock (UHF) in Chemistry most often refers to our s-UHF. Google Scholar

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[29] Refs. [15,16] have studied, as a function of the magnetic field, the behavior of the singlet-triplet splitting of the QD H2 by diagonalizing the two-electron Hamiltonian inside the minimal four-dimensional basis formed by the products $\phi_L({\bf r}_1)\phi_L({\bf r}_2)$ , $\phi_L({\bf r}_1)\phi_R({\bf r}_2)$ , $\phi_R({\bf r}_1)\phi_L({\bf r}_2)$ , $\phi_R({\bf r}_1)\phi_R({\bf r}_2)$ of the 1s orbitals of the separated QD's. This Hubbard-type method [15] (as well as the refinement employed by Ref. [16] of enlarging the minimal two-electron basis to include the p orbitals of the separated QD's) is an improvement over the simple HL method (see Ref. [15]), but apparently it is only appropriate for the weak-coupling regime at sufficiently large distances and/or interdot barriers. Our method is free of such limitations, since we employ an interdot-distance adjustable basis (see section 2) of at least 66 spatial TCO molecular orbitals when solving for the sS-UHF ones. Even with consideration of the symmetries, this amounts to calculating a large number of two-body Coulomb matrix elements, of the order of 106. Google Scholar

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