Diagrammatic valence bond (DVB) theory is a general approach to electron correlations in quantum cell models that conserve total spin. VB diagrams are a convenient many-electron basis for combining spin, point-group, and other symmetries in oligomers with a large but finite basis. Half-filled Hubbard or Pariser-Parr-Pople (PPP) models with 16 sites have similar to-34.7x10(6) singlet diagrams. Improved DVB methods yield exact low-lying states of the 16-site polyene in C-2h symmetry and of pyrene in D-2h symmetry. Several generalizations of symmetry adaptation are necessary for large bases, including new rules for linearly independent basis vectors and an iterative method for Hamiltonian matrix elements that avoids overlap and inversion. The number and dimensions of the. disjoint invariant subspaces S-m encountered in symmetry adaptation depend on the connectivity. D-2h symmetry adaptation is much simpler for acenes than for pyrene, linear stilbene, or polyphenyls. Standard PPP parameters account well for the 11 pyrene states identified in linear and two-photon spectra. Polyenes to N=16 show systematic deviations, with the 2 (1)A(g) threshold decreasing less rapidly with N than experiment. We discuss perturbations that break electron-hole, parity, or point-group symmetry on the low-energy states, test the second pi-electron approximation for pyrene, and comment on the feasibility of DVB for N=18 or 20 sites.