The equilibrium geometry and 48 vibrational normal-mode frequencies of the neutral and cationic ground state and the cationic first excited states of naphthalene isomers were calculated and characterized in the adiabatic representation by using the complete active space self-consistent field (CASSCF) and second order perturbation theory (CASPT2). Photoionization-efficiency (PIE) spectrum of molecular beam conditions in energy range 8 - 11 eV were determined by Kaiser et al. and they were analyzed using time-dependent density functional theory calculations (TDDFT). CASSCF calculations and PIE spectra simulations by one-photon excitation equations were used to optimize the cationic excited (D1) and neutral ground (S0) state structures of naphthalene isomers. The photoionization-efficiency curve was attributed to the S0 D1 electronic transition in naphthalene, and a curve origin was used at 8.14 eV. The ionization-induced geometry changes of the bases are consistent with the shapes of the corresponding molecular orbitals. The displaced harmonic oscillator approximation and Franck-Condon approximation were used to simulate the PIE curve of the D1 S0 transition of naphthalene, and the main vibronic transitions were assigned for the ππ* state. It shows that the vibronic structures were dominated by one of the xxx active totally symmetric modes, with v8 being the most crucial. This indicates that the electronic transition of the D1 state calculated in the adiabatic representation effectively includes a contribution from the adiabatic vibronic coupling through Franck-Condon factors perturbed by harmonic oscillators. The present method can adequately reproduce experimental PIE curve in the molecular beam condition.