What is SALCs of atomic orbitals? Explain the formation of molecular orbitals in water molecule.
What are SALCs of Atomic Orbitals?
SALCs (Symmetry Adapted Linear Combinations) are linear combinations of atomic orbitals (or other basis functions) constructed so that they transform according to the irreducible representations of a molecule's symmetry group. These combinations are created using group theory and serve as the group orbitals that can then combine with central atom orbitals of same symmetry to form molecular orbitals. SALCs are foundational in molecular orbital theory for describing bonding in polyatomic molecules, especially when considering symmetry and molecular shape.
Formation of Molecular Orbitals in Water Molecule
The water molecule (H2O) belongs to the C2v point group. The valence atomic orbitals are:
Oxygen: 2s, 2px, 2py, 2pz
Hydrogen: Two 1s orbitals
Oxygen 2s and 2pz orbitals: A1 symmetry
Oxygen 2pxorbital: B1 symmetry
Oxygen 2py orbital: B2 symmetry
Two SALCs can be formed by the combination of two equivalent 1s orbital of hydrogen atoms, one is a symmetric combination Ψ(A1) = c1(ϕH1 + ϕH2) with respect to all symmetry operations of the C2v point group, so it has A1 symmetry. And the other is an antisymmetric combination Ψ(B2) = c1(ϕH1 − ϕH2) which is is symmetric with respect to rotation about the C2 axis and reflection in the σv(yz) plane, but is antisymmetric with respect to reflection in the σv(xz) plane, so it has B2 symmetry.
Now, molecular orbitals are formed by combining the atomic orbitals of oxygen and the group orbitals (SALCs) of the hydrogens having the same symmetry.
A1 Combinations: 2s and 2pz orbitals of oxygen combine with the hydrogen A1 SALC to form three molecular orbitals of A1 symmetry. One is a bonding molecular orbitals, one is a non-bonding molecular orbital, and the third is an antibonding molecular orbital.
B2 Combinations: The oxygen 2py orbital and the hydrogen B2 SALC both have B2 symmetry and can combine. This forms one bonding and one antibonding molecular orbital, both of B2 symmetry.
B1 Combinations: 2px orbital of oxygen has B1 symmetry. There is no corresponding SALC from the hydrogen atoms with B1 symmetry. Therefore, the oxygen 2px orbital remains a non-bonding molecular orbital with B1symmetry.
The water molecule has 8 valence electrons. These electrons fill the Molecular Orbitals starting from the lowest energy level. In order to filling these electrons, electron fills in two bonding orbitals and two non-bonding orbitals. The two non-bonding orbitals correspond to the two lone pairs on the oxygen atom, and the two bonding orbitals form the two O-H covalent bonds. This explains the bent geometry and the presence of lone pairs in the water molecule.
Test Your Knowledge
1. What is the primary role of Symmetry Adapted Linear Combinations (SALCs) in molecular orbital theory?
a) To construct only antibonding molecular orbitals.
b) To create group orbitals that transform according to the molecule’s symmetry and combine with orbitals of matching symmetry.
c) To mix orbitals regardless of symmetry.
d) To increase the number of molecular orbitals formed.
View Answer
b) To create group orbitals that transform according to the molecule's symmetry and combine with orbitals of matching symmetry.
2. For the water molecule (H2O), which atomic orbitals of oxygen possess A1 symmetry in the C2v point group?
a) 2px and 2py
b) 2s and 2pz
c) 2s and 2py
d) 2pz and 2px
View Answer
b) 2s and 2pz
3. Which hydrogen SALC interacts with the oxygen 2py orbital in H2O to form molecular orbitals of B2 symmetry?
a) Symmetric combination Ψ(A1) = c1(ϕH1 + ϕH2)
b) Antisymmetric combination Ψ(B2) = c1(ϕH1 − ϕH2)
c) Both symmetric and antisymmetric combinations
d) None of the above
View Answer
b) Antisymmetric combination Ψ(B2) = c1(ϕH1 − ϕH2)
4. Why does the oxygen 2px orbital in H2O remain non-bonding according to group theory?
a) It has the same symmetry as hydrogen SALCs.
b) There is no hydrogen SALC with B1 symmetry to combine with.
c) It always forms bonding molecular orbitals.
d) It is energetically unfavorable to bond.
View Answer
b) There is no hydrogen SALC with B1 symmetry to combine with.
5. How do the electrons fill molecular orbitals in water according to symmetry-adapted combinations?
a) All electrons fill only bonding orbitals.
b) Two electrons fill bonding orbitals, and two electrons fill non-bonding orbitals.
c) Only antibonding orbitals are filled.
d) Electrons fill only lone pair orbitals.
View Answer
b) Two electrons fill bonding orbitals, and two electrons fill non-bonding orbitals.
6. Why SALCs are used instead of combining all atomic orbitals at once?
a) It simplifies the calculations and ensures only orbitals of the correct symmetry interact.
b) It increases the number of molecular orbitals formed.
c) It only works for diatomic molecules.
d) It helps to identify the geometry of the molecule before bonding.
View Answer
a) It simplifies the calculations and ensures only orbitals of the correct symmetry interact.
7. Which symmetry operation in the C2v point group is responsible for the out-of-phase combination of hydrogen 1s orbitals having B2 symmetry?
a) C2 rotation
b) Reflection in the σv(xz) plane
c) Reflection in the σv(yz) plane
d) The identity operation (E)
View Answer
b) Reflection in the σv(xz) plane. The out-of-phase combination is antisymmetric with respect to this reflection, which is a key characteristic of the B2 irreducible representation.