Page 42 - 71 the abc of dft_opt

10.3. IONIZATION ENERGIES AND ELECTRON AFFINITIES 83 84 CHAPTER 10. PROPERTIES
0
-20

v S (r) -40
-60
-80 Ne atom
exact
LDA
-100
0 0.2 0.4 0.6 0.8 1
atom LSDX X LSD exact
r
h 12.40 13.61 13.00 13.61
Figure 10.3: Kohn-Sham potential of Ne atom, both exactly and in LDA.
he 22.01 23.45 24.28 24.59
40
Ne atom li 5.02 5.34 5.46 5.39
35 exact
LDA be 7.63 8.04 9.02 9.32
30
b 7.52 7.93 8.57 8.30
25
v H (r) 20 c 10.72 10.81 11.73 11.26
15 n 13.91 14.00 14.93 14.55
o 11.78 11.87 13.85 13.62
10
f 16.14 15.66 17.98 17.45
5
ne 20.35 19.81 22.07 21.62
0
0 0.5 1 1.5 2 2.5 3 3.5 4 na 4.84 4.94 5.32 5.13
mg 6.48 6.59 7.70 7.64
r
al 5.14 5.49 5.99 5.99
Figure 10.4: Hartree potential of Ne atom, both exactly and in LDA.
si 7.40 7.65 8.26 8.16
p 9.63 10.04 10.51 10.53
The LDA exchange-correlation potential, however, looks very different from the exact
s 8.79 9.03 10.52 10.37
quantities for any finite systems, as shown in Fig. 10.5. This in turn means that the
orbital eigenvalues can be very different from exact Kohn-Sham eigenvalues. Thus ionization cl 11.67 11.77 13.22 12.98
ar 14.42 14.76 15.90 15.84
potentials from orbital energy differences are very poor. This will be discussed in great detail
in chapter X. Table 10.2: Ionization energies of first twenty atoms, non-relativistic, using exact-exchange densities, in eV. The X results
use Engel’s code, and the LSD results are evaluated on those densities. The ’exact’ results are from Davidson.
10.3 Ionization energies and electron affinities
In Table ??, we list ionization potentials for the first twenty atoms. There are many things
to see in this table:
• Comparing the exchange results (which are essentially identical to HF) with the exact
results, we find that HF underestimates ionization potentials by about 1 eV . In fact, the
mean error is -0.9 eV.
• Repeating with the LSD numbers, we find that the errors vary in sign. Now we must