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- Spherium abstract "The "spherium" model consists of two electrons trapped on the surface of a sphere of radius . It has been used by Berry and collaborators to understand both weakly and strongly correlated systems and to suggest an "alternating" version of Hund's rule. Seidl studies this system in the context of density functional theory (DFT) to develop new correlation functionals within the adiabatic connection.The electronic Hamiltonian in atomic units iswhere is the interelectronic distance.For the singlet S states, it can be then shown that the wave function satisfies the Schrödinger equationBy introducing the dimensionless variable , this becomes a Heun equation with singular points at . Based on the known solutions of the Heun equation, we seek wave functions of the formand substitution into the previous equation yields the recurrence relationwith the starting values . Thus, the Kato cusp condition is . The wave function reduces to the polynomial (where the number of roots between and ) if, and only if, . Thus, the energy is a root of the polynomial equation (where ) and the corresponding radius is found from the previous equation which yieldsis the exact wave function of the -th excited state of singlet S symmetry for the radius .We know from the work of Loos and Gill that the HF energy of the lowest singlet S state is . It follows that the exact correlation energy for is which is much larger than the limiting correlation energies of the helium-like ions or Hooke's atoms . This confirms the view that electron correlation on the surface of a sphere is qualitatively different from that in three-dimensional physical space.".
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- Spherium subject Category:Quantum_chemistry.
- Spherium subject Category:Quantum_mechanics.
- Spherium subject Category:Quantum_models.
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- Spherium comment "The "spherium" model consists of two electrons trapped on the surface of a sphere of radius . It has been used by Berry and collaborators to understand both weakly and strongly correlated systems and to suggest an "alternating" version of Hund's rule.".
- Spherium label "Spherium".
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