Step 9– Beginning the second SCF cycle: using thec’s ofC 1 to calculate a new
Fock matrixF 1 (cf. Step 4, (b))
The first Fock matrixF 0 used c’s from our initial guess (Step 4, (b)). An
improvedFmay now be calculated using thec’s from the first SCF cycle. Calcu-
latingG 1 as we did in Step 4, (b) forG 0 , but using the newP’s:
G 11 ¼P 11 ð 11 j 11 Þ#
1
2
ð 11 j 11 Þ
þP 12 ð 11 j 12 Þ#
1
2
ð 12 j 11 Þ
þP 21 ð 11 j 21 Þ#
1
2
ð 11 j 21 Þ
þP 22 ð 11 j 22 Þ#
1
2
ð 12 j 21 Þ
¼ 0 : 1885 ð 0 : 3642 Þþ 0 : 4973 ð 0 : 1709 Þ
þ 0 : 4973 ð 0 : 1709 Þþ 1 : 3122 ð 0 : 4754 Þ¼ 0 : 8624
ð 5 : 137 Þ
G 12 ¼G 21 ¼P 11 ð 12 j 11 Þ#
1
2
ð 11 j 12 Þ
þP 12 ð 12 j 12 Þ#
1
2
ð 12 j 12 Þ
þP 21 ð 12 j 21 Þ#
1
2
ð 11 j 22 Þ
þP 22 ð 12 j 22 Þ#
1
2
ð 12 j 22 Þ
¼ 0 : 1885 ð 0 : 1709 Þþ 0 : 4973 ð 0 : 1096 Þ
þ 0 : 4973 ð# 0 : 0733 Þþ 1 : 3122 ð 0 : 2184 Þ¼ 0 : 3369
ð 5 : 138 Þ
G 22 ¼P 11 ð 22 j 11 Þ#
1
2
ð 21 j 12 Þ
þP 12 ð 22 j 12 Þ#
1
2
ð 22 j 12 Þ
þP 21 ð 22 j 21 Þ#
1
2
ð 21 j 22 Þ
þP 22 ð 22 j 22 Þ#
1
2
ð 22 j 22 Þ
¼ 0 : 1885 ð 0 : 4754 Þþ 0 : 4973 ð 0 : 2184 Þ
þ 0 : 4973 ð 0 : 2184 Þþ 1 : 3122 ð 0 : 4964 Þ¼ 0 : 9582
ð 5 : 139 Þ
From theGvalues based on the first-cyclec’s the electron repulsion matrix is
G 1 ¼
0 :8624 0: 3369
0 :3369 0: 9582
ð 5 : 140 Þ
and the Fock matrix from this is
F 1 ¼HcoreþG 1 ¼
# 1 : 6606 # 1 : 3160
# 1 : 3160 # 2 : 3030
þ
0 :8624 0: 3369
0 :3369 0: 9582
¼
# 0 : 7982 # 0 : 9791
# 0 : 9791 # 1 : 3448
ð^5 :^141 Þ
226 5 Ab initio Calculations