Computational Chemistry

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