Photodissociation is one of the main destruction pathways for dicarbon (C$_{2}$) in astronomical environments such as diffuse interstellar clouds, yet the accuracy of modern astrochemical models is limited by a lack of accurate photodissociation cross sections in the vacuum ultraviolet range. C$_{2}$ features a strong predissociative $F\,^1\Pi_u - X\,^1\Sigma_g^+$ electronic transition near 130 nm originally measured in 1969; however, no experimental studies of this transition have been carried out since, and theoretical studies of the $F\,^1\Pi_u$ state are limited. In this work, potential energy curves of excited electronic states of C$_{2}$ are calculated with the aim of describing the predissociative nature of the $F\,^1\Pi_u$ state and providing new ab initio photodissociation cross sections for astrochemical applications. Accurate electronic calculations of 56 singlet, triplet, and quintet states are carried out at the DW-SA-CASSCF/MRCI+Q level of theory with a CAS(8,12) active space and the aug-cc-pV5Z basis set augmented with additional diffuse functions. Photodissociation cross sections arising from the vibronic ground state to the $F\,^1\Pi_u$ state are calculated by a coupled-channel model. The total integrated cross section through the $F\,^1\Pi_u$ $v=0$ and $v=1$ bands is 1.198$\times$10$^{-13} $cm$^2$cm$^{-1}$, giving rise to a photodissociation rate of 5.02$\times$10$^{-10}$ s$^{-1}$ under the standard interstellar radiation field, much larger than the rate in the Leiden photodissociation database. In addition, we report a new $2\,^1\Sigma_u^+$ state that should be detectable via a strong $2\,^1\Sigma_u^+-X\,^1\Sigma_g^+$ band around 116 nm.