Biomedical Engineering Reference
In-Depth Information
14
The Orbital Model
Our next step is to consider a many-electron atom, such as that illustrated in Figure 14.1.
1
r
1
r
12
Nucleus
r
2
2
Figure 14.1
Many-electron atom
I am going to make the 'infinite nuclear mass' approximation, and only consider the
electronic problem. The atom is therefore fixed in space with the nucleus at the centre
of the coordinate system. The
n
electrons are at position vectors
r
1
,
r
2
, ...,
r
n
and the
scalar distance between (say) electrons 1 and 2 is
r
12
in an obvious notation. The elec-
tronic wavefunction will depend on the coordinates of all the electrons, and I will write it
Ψ (
r
1
,
r
2
, ...,
r
n
) If the nuclear charge is
Ze
, we have to consider three contributions to the
electronic energy: the kinetic energy of each electron, the Coulomb attraction between the
nucleus and the electrons and finally the Coulomb repulsion between pairs of electrons. We
therefore write the Hamiltonian operator as
