Computational Chemistry

Gmay now be calculated. From Eqs. (5.106)–(5.108), using the above values of
Pand the integrals of Eq. (5.110), and recalling that integrals like (11j12) and
(21j11) are equal (Eq. (5.109)) we get:

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 : 1240 ð 0 : 3642 Þþ 0 : 4318 ð 0 : 1709 Þ

þ 0 : 4318 ð 0 : 1709 Þþ 1 : 5034 ð 0 : 4754 Þ¼ 0 : 9075

ð 5 : 124 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 : 1240 ð 0 : 1709 Þþ 0 : 4318 ð 0 : 1096 Þ

þ 0 : 4318 ð# 0 : 0733 Þþ 1 : 5034 ð 0 : 2184 Þ¼ 0 : 3652

ð 5 : 125 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 : 1240 ð 0 : 4754 Þþ 0 : 4318 ð 0 : 2184 Þ

þ 0 : 4318 ð 0 : 2184 Þþ 1 : 5034 ð 0 : 4964 Þ¼ 0 : 9938

ð 5 : 126 Þ

From the G values based on the initial guessc’s the initial-guess electron repulsion
matrix is

G 0 ¼

0 :9075 0: 3652

0 :3652 0: 9938



ð 5 : 127 Þ

The initial-guess Fock matrix is (Eqs (5.116), (5.120) and (5.126))

F 0 ¼TþVðHÞþVðHeÞþG 0 ¼HcoreþG 0

¼

# 1 : 6606 # 1 : 3160

# 1 : 3160 # 2 : 3030



þ

0 :9095 0: 3652

0 :3652 0: 9938



¼

# 0 : 7511 # 0 : 9508

# 0 : 9508 # 1 : 3092



ð 5 : 128 Þ

The zero subscripts in Eqs. (5.127) and (5.128) emphasize that the initial-guessc’s,
with no iterative refinement, were used to calculateG; in the subsequent iterations
of the SCF procedureHcorewill remain constant whileGwill be refined as thec’s,

5.2 The Basic Principles of the ab initio Method 223