Alg,A2g Big,B2g,Eig E2g Alu A2u Blu B2us Elu E2u 8.2 The SCF MO Treatment of Polyatomic Molecules The purely electronic nonrelativistic Hamiltonian for a polyatomic molecule is(in atomic units): 户=-Σ：-∑Σ2+2Σ1 (8.3) Best possible variation function-Hartree-Fock SCF function:The form of an antisymmetrized product of spin-orbitals.The MOs are usually expressed as linear combinations of basis functions,the coefficients being found by solution of the Roothaan equations. A sufficiently large basis set-Accurate approximations to the Hartree-Fock MO's. A minimal basis set->only rough approximations to the Hartree-Fock MO's,still referred to as SCF molecular orbitals. Classification of Molecular Orbitals As might be expected,the MOs of a polyatomic molecule show the same kinks of possible symmetry behavior as the electronic wavefunction does.The MOs are therefore classified according to the symmetry species of the molecular point group. For example,the MOs of H2O have the possible symmetry species a,a2, b1,and b2.Lowercase letters are used for MO symmetry species.To distinguish MOs of the same symmetry species,we number them in order of increasing energy.1a,2a,3a,1b,2b1,. For benzene C6H6,there are some doubly degenerate symmetry species, so some of the benzene MOs occur in having the same energy. Specification of the number of electrons in each MO specifies theA1g, A2g, B1g, B2g, E1g, E2g A1u, A2u, B1u, B2u, E1u, E2u 8.2 The SCF MO Treatment of Polyatomic Molecules The purely electronic nonrelativistic Hamiltonian for a polyatomic molecule is (in atomic units): ∑ ∑∑ ∑∑ > ∧ = − ∇ − + i i i i i j ij i el r r Z H 1 2 1 2 α α α (8.3) Best possible variation function — Hartree-Fock SCF function: The form of an antisymmetrized product of spin-orbitals. The MOs are usually expressed as linear combinations of basis functions, the coefficients being found by solution of the Roothaan equations. A sufficiently large basis set → Accurate approximations to the Hartree-Fock MO’s. A minimal basis set → only rough approximations to the Hartree-Fock MO’s, still referred to as SCF molecular orbitals. Classification of Molecular Orbitals As might be expected, the MOs of a polyatomic molecule show the same kinks of possible symmetry behavior as the electronic wavefunction does. The MOs are therefore classified according to the symmetry species of the molecular point group. For example, the MOs of H2O have the possible symmetry species a1, a2, b1, and b2. Lowercase letters are used for MO symmetry species. To distinguish MOs of the same symmetry species, we number them in order of increasing energy. 1a1, 2a1, 3a1, …; 1b1, 2b1, … For benzene C6H6, there are some doubly degenerate symmetry species, so some of the benzene MOs occur in having the same energy. Specification of the number of electrons in each MO specifies the