1. The problem statement, all variables and given/known data What terms are generated by the configuration (e1g)2(e2u)2 in D6h symmetry? 2. Relevant equations configuration (χd)2 gives terms 1(symmetric product) + 3(antisymmetric product) where χ=symmetry of an orbital and d = degenerate (e1g)x(e1g) = A1g + [A2g] + E2g (e2u)x(e2u) = A1g + [A2g] + E2g where brackets [ ] indicate antisymmetric product s=singlet, d=doublet, t=triplet, q=quartet, qu=quintet sxs = s sxd = d sxt = t sxq = q dxd = s + t dxt = d+q dxq = t+qu txt = s+t+qu txq = d+q+sextet qxq = s+t+qu +septet 3. The attempt at a solution So first I found the terms generated by e1gxe1g and e2uxe2u seperately (e1g)2x(e1g)2 = 1A1g + 3A2g + 1E2g (e2u)2x(e2u)2 = 1A1g + 3A2g + 1E2g Then find direct product of [(e1g)x(e1g)]x[(e2u)x(e2u)] 1A1g 1A1g 3A2g x 3A2g = 1E2g 1E2g 1A1gx1A1g + 1A1gx3A2g + 1A1gx 1E2g 3A2gx1A1g + 3A2gx3A2g + 3A2gx 1E2g = 1E2gx1A1g + 1E2gx3A2g + 1E2gx 1E2g 1A1g + 3A1g + 2A2g + 4A2g + 2E2g 1A1g + 3A1g + 5A1g + 2A2g + 4A2g + 3E2g 1A1g + 1A2g + 1E2g + 2E2g + 3E2g = 31A1g + 23A1g + 5A1g +1A2g +22A2g +24A2g + 1E2g + 22E2g + 23E2g The correct answer is 31A1g + 3A1g + 5A1g +1A2g +23A2g + 31E2g + 23E2g I assume I'm messing up in when doing this direct product: [(e1g)x(e1g)]x[(e2u)x(e2u)]. but I'm not sure exactly what i'm doing wrong. Any help is really appreciated!