The potential-energy surfaces of the 1 (1)A(g), 2 (1)A(g), and 1 B-1(u) states of trans-1,3,5-hexatriene (THT) are explored in the vicinity of the ground state equilibrium structure. The S-0 geometry optimization and force field calculation have been carried out with the restricted Hartree-Fock plus Moller-Plesset second-order perturbation theory method. Vibronic coupling constants for the normal coordinates of a(g) and b(u) symmetry were computed with the complete-active-space self-consistent-field (CASSCF) and single state multiconfigurational second-order perturbation theory (CASPT2) electronic structure models. The CASSCF/CASPT2 method unequivocally places the vertical excitation energy of the dark 2 (1)A(g) "phantom state" below the 1 B-1(u) level and predicts an energy difference of ca. 0.5 eV. The results are consistent with time-resolved photoionization yield and photoelectron spectroscopy experiments that indicate the existence of a low lying S-1-S-2 conical intersection which induces rapid 1 B-1(u)--> 2 (1)A(g) internal conversion on a time scale of 40 fs to 50 fs [Cyr and Hayden, J. Chem. Phys. 104, 771 (1996)]. Based on the vibronic coupling constants five totally symmetric vibrations with high Franck-Condon and/or tuning activity have been identified. The S-1 and S-2 states interact primarily via the two b(u) normal modes nu(24) and nu(26). Other a(g) and b(u) normal vibrations do not appear to couple significantly to the lowest lying pi -->pi(*) transition. The modeling of the ultrafast relaxation processes following optical excitation of the 1 B-1(u) state of THT and the calculation of absorption and resonance Raman spectra are discussed in the following paper.