Point group symmetry

Forte takes advantage of symmetry, so it important to specify both the symmetry of the target electronic state and the orbital spaces that define a computation (see below). Forte supports only Abelian groups (\(C_1\), \(C_s\), \(C_i\), \(C_2\), \(C_{2h}\), \(C_{2v}\), \(D_2\), \(D_{2h}\)). If a molecule has non-Abelian point group symmetry, the largest Abelian subgroup will be used. For a given group, the irreducible representations (irrep) are arranged according to Cotton’s book (Chemical Applications of Group Theory). This ordering is reproduced in the following table and is the same as used in Psi4:

Point group	Irrep 0	Irrep 1	Irrep 2	Irrep 3	Irrep 4	Irrep 5	Irrep 6	Irrep 7
\(C_1\)	\(A\)
\(C_s\)	\(A'\)	\(A''\)
\(C_i\)	\(A_{g}\)	\(A_{u}\)
\(C_2\)	\(A\)	\(B\)
\(C_{2h}\)	\(A_{g}\)	\(B_{g}\)	\(A_{u}\)	\(B_{u}\)
\(C_{2v}\)	\(A_{1}\)	\(B_{1}\)	\(A_{2}\)	\(B_{2}\)
\(D_2\)	\(A\)	\(B_{1}\)	\(B_{2}\)	\(B_{3}\)
\(D_{2h}\)	\(A_{g}\)	\(B_{1g}\)	\(B_{2g}\)	\(B_{3g}\)	\(A_{u}\)	\(B_{1u}\)	\(B_{2u}\)	\(B_{3u}\)

By default, Forte targets a total symmetric state (e.g., \(A_1\), \(A_{g}\), …). To specify a state with a different irreducible representation (irrep), provide the ROOT_SYM option. This option takes an integer argument that indicates the irrep in Cotton’s ordering.