  The interaction of ionizing and far-ultraviolet radiation with the
interstellar medium is of great importance. It results in the formation of
regions in which the gas is ionized, beyond which are photodissociation regions
(PDRs) in which the gas transitions to its atomic and molecular form. Several
numerical codes have been implemented to study these two main phases of the
interstellar medium either dynamically or chemically. In this paper we present
TORUS-3DPDR, a new self-consistent code for treating the chemistry of
three-dimensional photoionization and photodissociation regions. It is an
integrated code coupling the two codes TORUS, a hydrodynamics and Monte Carlo
radiation transport code, and 3D-PDR, a photodissociation regions code. The new
code uses a Monte Carlo radiative transfer scheme to account for the
propagation of the ionizing radiation including the diffusive component as well
as a ray-tracing scheme based on the HEALPix package in order to account for
the escape probability and column density calculations. Here, we present the
numerical techniques we followed and we show the capabilities of the new code
in modelling three-dimensional objects including single or multiple sources. We
discuss the effects introduced by the diffusive component of the UV field in
determining the thermal balance of PDRs as well as the effects introduced by a
multiple sources treatment of the radiation field. We find that diffuse
radiation can positively contribute to the formation of CO. With this new code,
three-dimensional synthetic observations for the major cooling lines are
possible, for making feasible a detailed comparison between hydrodynamical
simulations and observations.
