Question

The water molecule belongs to a C2v point group (the corresponding character table is presented below). Consider the following linear combination of atomic orbitals consisting of 2py orbital of oxygen and 1s orbitals of hydrogen atoms:

Φ=c1*O2py+c2*(H1s-H'1s)

This linear combination can also be presented schematically as:

	E	C2	σv(xz)	σv(yz)
A1	1	1	1	1
A2	1	1	-1	-1
B1	1	-1	1	-1
B2	1	-1	-1	1

Is this linear combination of atomic orbitals symmetry-adapted? Explain.

Answer 1

In non-linear H₂O molecule point group symmetry given is C_2v. Hydrogen atom consist only 1s orbital to take part. In oxygen atom there are many other orbitals to take part. The 1s orbital of oxygen is clearly non bonding core orbital. The oxygen 2s and 2p orbitals are of valence type. They adapted symmetry adapted linear combination it is clear from the group table. Symmetry adapted groups are a1 and b2 in C2v table. Oxygen 2s and 2p_z belong to the a1 table and 2p_x is b1 and 2p_y belong to the b2 group.

There is only one non bonding orbital 2p_x. The bonding and antibonding b2 orbital (the O-H bond and antibond formed by 2p_y orbital). And 2s and 2p_z form lone pair of water molecule.