Chemistry Reference
In-Depth Information
J
′ +
K
′
′
2
K
J
′ -
K
′
J
′
E
′
(sixfold degenerate)
Figure 4.6
Schematic diagram of the energy levels for the excited P(1s2p) state of
the He-like atom
of the energy levels is accomplished only by taking into account spin and
the Zeeman effect in the presence of a magnetic field (Chapter 5). The
schematic diagram of the splitting of the energy levels for the P(1s2p)
state of the He-like atom is given in Figure 4.6. The evaluation in
spherical coordinates of the integrals J, K, J
0
,andK
0
is sketched in the
Appendix.
Variational optimization of the orbital exponent of the 2p functions
(Magnasco, 2007) for He (Z
¼
2) gives
c
p
¼
0
:
4761, which, used in
conjunction with c
0
¼
1
6875 for the 1s AO, yields the following varia-
tional energy bounds (E
0
0
¼
2
:
313 99E
h
, J
0
¼
0
:
:
236 67E
h
):
«
þ
¼
2
:
072 37E
h
«
¼
2
:
082 26E
h
ð
4
:
62
Þ
In this case, too, either the excitation energies from the He ground
state
D«
þ
¼
0
:
7753 E
h
D«
¼
0
:
7654 E
h
ð
4
:
63
Þ
or the splitting
2K
¼
0
:
0099E
h
ð
4
:
64
Þ
are in reasonably good agreement with the experimental values (Moore,
1971) of 0.7796, 0.7703, and 0.0093 respectively. However, from a
quantitative point of view, it is seen that the error in the variational
