Symmetry-Adapted Orbitals for Polyatomic Molecules · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Matching orbitals by symmetry

Science · Chemistry · ages 19-20
Name ______________________   Date ____________

  1. What does a ligand SALC's symmetry label tell you?

    • It identifies symmetry-compatible central-atom partners.
    • It fixes the electron count in every resulting energy level.
    • It gives the final orbital energies without any calculation.

  2. In the symmetry-adapted method for water, what comes before matching hydrogen combinations to oxygen orbitals?

    • Replace the oxygen valence orbitals with four local hybrids.
    • Form and label combinations of the hydrogen 1s orbitals.
    • Assign electrons to the highest empty molecular levels first.

  3. Water lies in yz with z bisecting H-O-H. C2 exchanges H1 and H2. Which correctly labelled hydrogen SALC changes sign under this exchange?

    • H1 + H2, labelled a1, changes sign when the H atoms swap.
    • H1 + H2, labelled b2, changes sign when the H atoms swap.
    • H1 - H2, labelled b2, changes sign when the H atoms swap.

  4. Use water's oxygen 2s/2p and hydrogen 1s basis, with the molecule in yz and z bisecting H-O-H. Which oxygen orbital has no hydrogen SALC partner?

    • Oxygen 2py, labelled b2, has no matching hydrogen SALC.
    • Oxygen 2px, labelled b1, has no matching hydrogen SALC.
    • Oxygen 2pz, labelled a1, has no matching hydrogen SALC.

  5. For water in yz with z bisecting H-O-H, which oxygen valence orbitals are symmetry-compatible with the a1 hydrogen SALC?

    • Oxygen 2s and 2pz, both with the a1 label
    • Oxygen 2px and 2py, both with the a1 label
    • Oxygen 2py and 2pz, both with the b2 label

  6. Methane's hydrogen 1s basis gives one a1 SALC and a t2 set containing three independent SALCs. How many hydrogen SALCs are there in total?

    Answer: ______________

  7. Water's valence MO order is 2a1 < 1b2 < 3a1 < 1b1 < 4a1 < 2b2. The counts 2a1(2), 1b2(2), 3a1(2), 1b1(0), 4a1(2), 2b2(0) give its ground state. Parentheses count electrons.

    Circle one:   True   False

  8. Maya says, 'Both lone-pair MOs in water are strictly nonbonding because neither has a hydrogen partner.' What corrects this claim in the minimal valence model?

    • Both occupied lone-pair MOs must be pure oxygen 2px functions.
    • The occupied 1b1 MO mixes with the hydrogen a1 SALC to make an O-H bond.
    • Occupied 3a1 has some O-H bonding character in a matched block.
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Answer key

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Matching orbitals by symmetry W1-mt_llEYzYuutf-s1

  1. It identifies symmetry-compatible central-atom partners. · Matching labels permit mixing. The label does not determine its strength, the final energies or the electron count.
  2. Form and label combinations of the hydrogen 1s orbitals. · This method forms ligand SALCs and assigns their symmetry labels before comparing them with central-atom orbitals.
  3. H1 - H2, labelled b2, changes sign when the H atoms swap. · The exchange turns H1 - H2 into H2 - H1 = -(H1 - H2). In this axis convention, the difference is b2.
  4. Oxygen 2px, labelled b1, has no matching hydrogen SALC. · Hydrogen supplies a1 and b2 SALCs but no b1 SALC. Oxygen 2px is b1 and forms the nonbonding 1b1 MO in this basis.
  5. Oxygen 2s and 2pz, both with the a1 label · Oxygen 2s and 2pz have a1 symmetry in this convention. Oxygen 2px is b1 and 2py is b2.
  6. 4 · Count each independent combination: one a1 plus three t2 components gives 1 + 3 = 4 SALCs.
  7. False · The counts total eight electrons, but place a pair in 4a1 while lower 1b1 is empty. The ground state fills 1b1 and leaves 4a1 empty.
  8. Occupied 3a1 has some O-H bonding character in a matched block. · Only 1b1 is symmetry-unmatched in this minimal basis. The largely lone-pair 3a1 MO belongs to the interacting a1 block and has some bonding character.
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