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Part 1
Improving Self-consistent Field Convergence
energy increase in other iterations. In short, the identification of µ from the overlap requirement
a
orb
min
orb
min
= A appears to be a good and secure way to control the step sizes in the optimization.
orb
a min
1.0
0.8
orb
A min = 0.975
orb
a min
1.0
0.8
orb
A min = 0.98
0.6
0.6
0.4
0.2
0.0
A
0 2 4 6 8 10
µ
0.4
0.2
0.0
A
0 2 4 6 8 10
µ
40.0
20.0
RH
∆E HF
40.0
20.0
RH
∆E LDA
∆E / a.u.
0.0
-20.0
-40.0
RH
∆E
0 2 4 6 8 10
µ
Fig. 1.4 HF/6-31G, iteration 7. (A) The overlap
orb
RH
a
min
and (B) the changes in the HF energy ∆ E HF
RH
and in the RH energy model ∆ E as a function of
the level shift µ.
B
∆E / a.u.
0.0
-20.0
-40.0
∆E RH
0 2 4 6 8 10
µ
Fig. 1.5 LDA/6-31G, iteration 7. (A) The overlap
orb
a
min
and (B) the changes in the LDA energy
RH
RH
∆ E LDA
and in the RH energy model ∆ E as a
function of the level shift µ.
B
1.4.1.3 DIIS and Dynamically Level Shifted RH
For accelerating the SCF convergence, DIIS is a simple and in general very successful scheme. We
would expect to get an even better performance and improve the stability of the scheme if DIIS was
combined with a dynamically level shifted RH step like TRRH instead of the standard RH with no
control of the step. To investigate how a combination of DIIS and TRRH performs, we carried out a
number of DIIS-TRRH optimizations. A typical example is seen in Fig. 1.7 and an extraordinary
example is seen in Fig. 1.8.
Fig. 1.6 Cd 2+ complexed with an
imidazole ring.
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