Quantum-chemical calculations are combined to a model Frenkel-Holstein Hamiltonian to assess the nature of the lowest electronic excitations in the pentacene crystal. We show that an admixture of charge-transfer excitations into the lowest singlet excited states form the origin of the Davydov splitting and mediate instantaneous singlet exciton fission by direct optical excitation of coherently coupled single and double exciton states, in agreement with recent experiments.