Symmetric Group Semiempirical Valence Bond Method for Large Conjugated Molecules

Based on the theory of symmetric group representations, we propose the symmetric group semiempirical valence bond (SGSVB) method for handling large molecular systems. In this approach, the bonded tableau functions are employed to directly construct the VB wave function rather than manipulating a large number of determinants. By truncating the overlap integrals between orbitals in the SGSVB method, efficient calculation of matrix elements is achieved. For the one-electron energy of the Hamiltonian matrix and the overlap matrix elements, the overlap integrals are truncated to first-order terms; for the computation of the two-electron energy, orbital orthogonality is assumed. We applied the SGSVB method to study the vertical excitation energies of the first covalent excited state 2¹A_g of linear polyenes C_2<i>n</i>H_2<i>n</i>+2, and found good agreement with experimental values. Extrapolation to infinite chain length yields limiting energies of ∼1.92 eV, in line with literature estimates. We further demonstrate the applicability of SGSVB by investigating the circumcoronene molecule (C₅₄H₁₈) with an active space of (54<i>e</i>, 54<i>o</i>). The method yields Kekulé structure weights that exhibit strong correlation with those obtained from wave function-based resonance theory (WFRT). The SGSVB method thus offers a novel and efficient computational tool for elucidating the π-electron structure of complex molecular systems using valence bond theory.