Exchange and correlation energies of ground states of atoms and molecules in strong magnetic fields

Abstract

Using a Hartree-Fock mesh method and a configuration interaction approach based on a generalized Gaussian basis set we investigate the behaviour of the exchange and correlation energies of small atoms and molecules, namely the helium and lithium atom as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B = 0 − 100a.u. In general the importance of the exchange energy to the binding properties of atoms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions and in particular due to the contributions of the tightly bound hydrogenic states which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.

Physics of strongly magnetized neutron stars

“…In strong magnetic fields, the electron spins are in the ground state all aligned antiparallel to the magnetic field, the spatial wavefunction is antisymmetric with respect to the interchange of two electrons. Thus the error in the Hartree-Fock approach is expected to be significantly smaller than the 1% accuracy characteristic of zero-field Hartree-Fock calculations (Neuhauser et al 1987;Schmelcher et al 1999).…”

High-field impurity magneto-optics of Si:Se

“…4(c)-is not surprising, as it has been theoretically predicted for the helium molecule that this change become visible only at the fields higher than 5 B 0 [7]. It should be mentioned that in comparison to the helium molecule, the electron-electron interaction in the Se 2 center is expected to be magnified due to the fact that the separation (and consequently, the overlap of the electron wave functions) between the selenium atoms in silicon is 1 order of magnitude smaller in units of the electron ground-state orbital radius than in the case of the helium.…”

“…The triplet ground state 1 3 (−1) + demonstrates an increase of exchange energy by approximately 2 orders of magnitude when the field is changed from 0 to 100 B 0 , because of the constriction of the wave function by the field [7]. The spin singlet states, such as the ground state 1 1 0 + , do not produce exchange energy changes with field.…”

“…The spin singlet states, such as the ground state 1 1 0 + , do not produce exchange energy changes with field. However, the correlation energy of the 1 1 0 + state monotonically increases by a factor of 2 with the field strength up to 100 B 0 [7]. In what follows the ground state is always the singlet, and we investigate only electric dipole transitions that conserve spin.…”

“…For example, there are no theoretical reports of the excited states with magnetic quantum number M = +1 (presumably because in astrophysical situations where the field is inhomogeneous, states that tune rapidly with field are less interesting). The electron-electron effects make the calculations hard but they produce an interesting phase transition at very high field; the ground state of helium at low field is a singlet state 1 1 0 + (with spins antiparallel, known as parahelium, see Table II), but at B ∼ 0.76 B 0 the lowest triplet state 1 3 (−1) + (orthohelium, spins parallel) drops below it [7]. The resulting dipole can produce a new type of bond that is magnetic in origin rather than electric [8].…”