### 21.6 ROHF of Two Open Shells

#### Extracts from control for O2 in D3d Symmetry

# HF-SCF/SVP

# Reference: triplet-sigma in D3d
# This is a Roothaan case (as is D-infinity-h).
#
\$coord
0.0             0.0               1.08597397921317       o
0.0             0.0              -1.08597397921317       o
\$symmetry d3d
\$closed shells
a1g     1-3                         (2)
a2u     1-2                         (2)
eu      1                           (2)
\$open shells type=1
eg      1                           (1)
\$roothaan         1
a = 1      b = 2
\$energy      SCF               SCFKIN            SCFPOT
1   -149.4774402753    149.4799190239   -298.9573592992

# Reference: singlet-delta in D3d
# This is a Roothaan case (as is D-infinity-h).
#
\$coord
0.0             0.0               1.08597397921317       o
0.0             0.0              -1.08597397921317       o
\$symmetry d3d
\$closed shells
a1g     1-3                         (2)
a2u     1-2                         (2)
eu      1                           (2)
\$open shells type=1
eg      1                           (1)
\$roothaan       1
a = 1/2   b = 0
\$energy      SCF               SCFKIN            SCFPOT
1   -149.4297623470    149.4298692899   -298.8596316369

#### Extracts from control for O2 in D2h Symmetry

# HF-SCF/SVP

# Triplet-sigma in D2h
#
\$coord
0.0             0.0               1.08597397921317       o
0.0             0.0              -1.08597397921317       o
\$symmetry d2h
\$closed shells
ag      1-3                         ( 2 )
b1u     1-2                         ( 2 )
b2u     1                           ( 2 )
b3u     1                           ( 2 )
\$open shells type=1
b2g     1                           ( 1 )
b3g     1                           ( 1 )
\$roothaan          1
a = 1    b = 2
\$energy      SCF               SCFKIN            SCFPOT
1   -149.4774402750    149.4798706643   -298.9573109393

# Singlet-delta in D2h : xx-yy component
# where x = b2g and y = b3g.  In D-infinity-h, b2g and b3g combine to eg.
#
\$coord
0.0             0.0               1.08597397921317       o
0.0             0.0              -1.08597397921317       o
\$symmetry d2h
\$closed shells
ag      1-3                         ( 2 )
b1u     1-2                         ( 2 )
b2u     1                           ( 2 )
b3u     1                           ( 2 )
\$open shells type=1
b2g     1                           ( 1 )
b3g     1                           ( 1 )
\$roothaan          2
\$rohf
1b2g-1b3g    a = 0      b = 2
1b2g-1b2g    a = 1      b = 0
1b3g-1b3g    a = 1      b = 0
\$energy      SCF               SCFKIN            SCFPOT
1   -149.4297623516    149.4298351805   -298.8595975321

# Singlet-delta in D2h : xy+yx component
# (an example of the general type: [xy]-singlet)
# where in D2h x = b2g and y = b3g are of different symmetry.
# In D-infinity-h, b2g and b3g combine to eg; see the reference
# calculation in D3d above.
#
\$coord
0.0             0.0               1.08597397921317       o
0.0             0.0              -1.08597397921317       o
\$symmetry d2h
\$closed shells
ag      1-3                         ( 2 )
b1u     1-2                         ( 2 )
b2u     1                           ( 2 )
b3u     1                           ( 2 )
\$open shells type=1
b2g     1                           ( 1 )
b3g     1                           ( 1 )
\$roothaan          2
\$rohf
1b2g-1b3g    a = 1      b = -2
1b2g-1b2g    a = 0      b =  0
1b3g-1b3g    a = 0      b =  0
\$energy      SCF               SCFKIN            SCFPOT
1   -149.4297623501    149.4298391833   -298.8596015334