I am familiar with the many-electron Hamiltonian of electrons in a positive jellium. But e.g. surface electrons move in a positive jellium plus a negative jellium from the bulk electrons. The system would not be charged. I want to use Hartree-Fock methods to solve the SE. The surface electrons are additionally confined by an infinite potential.
It is appropriate to consider problems of the kind discussed above in terms of electrons in some external potential. The jellium model in its original form assumes a rigid uniform external potential to which electrons are exposed. Charge neutrality is taken into account by explicitly discounting some unbounded energy contributions in the Hamiltonian when interaction of charged particles (whether the electron-electron interaction or the electron-background interaction) is mediated by the long-range Coulomb potential. In describing surface physics in terms of some extended jellium model, one merely uses piece-wise uniform external potentials, one piece describing the bulk, and the other piece describing the vacuum (one can also consider spherical models for describing surface physics, whereby the isotropy of the model considerably simplifies the treatment of the problem.
In short, there is no need to consider what you call "positive jellium plus negative jellium". All that is required is using a piece-wise constant potential that models one's physical problem of interest. The relevant many-electron Hamiltonian is different from the many-electron Hamiltonian of the traditional jellium model only in the form of its underlying external potential. Regarding surface physics, the following paper contains one of the earliest application of the jellium model:
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.12.5585
A more recent relevant publication:
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.77.245107
Note added: In particular in the latter publication, the external potential is described as the electrostatic (Hartree) potential arising from a rigid (piece-wise constant) positive charge distribution n_+(r) (see Eq. (15) herein), to be contrasted with the electronic charge distribution n(r). As a consequence, the external potential is, while rigid, not piece-wise constant. This does not alter my above argument, that the relevant many-body Hamiltonians only differ in respect of their underlying external potentials.
Many thanks for your fast reply. This is a possible pathway for me.
Best regards,
KFB
In order to deal with the surface properties, you terminate the positive background of jellium at x=0. then on the left you have uniform positive charge and for x>0 you have 0 charge. Next you solve the HF hamiltonian with a test potential the electrostatic part of which goes to zero asymptotically, since your electrons cancel the positive charge. On the right asymtotically you get a constant electrostatic potential. Bardeen was the first to deal with this problem. Lang and Kohn applied DFT to deal with this problem and myself and Modinos considered external electric fields to deal with field emission and field ionization. Mine was a DFt version, considering a model background potential for the neutral metal. All papers are in Phys. Rev. but I do not have handy the date.
I shall wellcome any other questions.
REgards
Andreas K. Theophilou
Would it be a valid approximation to use the profile of the surface electron wavefunctions perpendicular to the surface from a DFT calculation as part of my laterally confined wavefunction for the HF calculation ? The effect of the positive/negative jellium should then already (approximately) be included through the shape of the z-part of the wavefunction.
Yes, you can start with DFT wave functions and some local potential. However, we do not know the asymptotic form on the right since we do not know the asymptotic form of the potential, taking as zero the potential far inside the metal. The potential on the right must be found by the self consisten solutions of the KS equation. In using a local exchange potential, you will get a constant exchange inside the metal and thus you cannot consider this equal to zero. I shall try to find the papers and send them to you.
For details you can look into the paper cle: An analytic estimate of the field penetration into metal surfaces
A K Theophilou
[Show abstract]
Journal of Physics F Metal Physics 03/2001; 2(6):1124.
See also
Article: Metallic-Field Effect and Its Consequences in Field Emission, Field Ionization, and the Capacitance of a Capacitor
A. K. Theophilou, A. Modinos
[Show abstract]
Physical Review B 07/1972; 6(3). · 3.77 Impact Factor ,
This is not for neutral atoms and it is worth doing it with a full Hartree-Fock.
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