A dynamical theory which accounts for all microscopic one-electron processes is used to study the spectral function of the 1D Hubbard model for the whole (k,ω)-plane, beyond previous studies which focused on the weight distribution in the vicinity of the singular branch lines only. While our predictions agree with those of the latter studies concerning the tetracyanoquinodimethane (TCNQ) related singular features in photoemission of the organic compound tetrathiafulvalene–tetracyanoquinodimethane (TTF–TCNQ) metallic phase, the generalized theory also leads to quantitative agreement concerning the tetrathiafulvalene (TTF) related finite-energy spectral features, which are found to correspond to a value of the on-site repulsion U larger than for TCNQ. Our study reveals the microscopic mechanisms behind the unusual spectral features of TTF–TCNQ and provides a good overall description of those features for the whole (k,ω)-plane.