Chemistry Reference
In-Depth Information
TABLE 3.2 Results from Computing the Total Energy of fcc Cu with
M
3
M
3
Mk
Points Generated Using the Monkhorst Pack Method
M
E/
atom (eV)
No. of
k
Points in IBZ
t
M
=t
1
1
1.8061
1
1.0
2
3.0997
1
1.1
3
3.6352
4
2.3
4
3.7054
4
2.6
5
3.7301
10
5.2
6
3.7541
10
6.0
7
3.7676
20
10.4
8
3.7671
20
11.2
9
3.7680
35
16.9
10
3.7676
35
17.1
11
3.7662
56
31.2
12
3.7665
56
28.5
13
3.7661
84
40.0
14
3.7659
84
39.7
The last column in Table 3.2 lists the computational time taken for the total
energy calculations, normalized by the result for
M
1. Note that getting what
we just defined to be a converged result takes at least 20 times longer than a
calculation involving just one
k
point. An initially curious feature of these
results is that if
M
is an odd number, then the amount of time taken for the cal-
culations with either
M
or (
M รพ
1) was close to the same. This occurs because
the calculations take full advantage of the many symmetries that exist in a
Figure 3.2
Total energies (per atom) for bulk Cu calculated as described in Table 3.2 as a
function of
M
for calculations using
M M Mk
points. Results with even (odd)
M
are
shown with unfilled (filled) symbols.
