  Locally noncentrosymmetric CeRh$_{2}$As$_{2}$ exhibits characteristic
two-phase unconventional $H$--$T$ superconducting phase diagram. The transition
from even- to odd-parity superconducting phase is supported by the P4/nmm
crystal structure and it can be induced by the external magnetic field. Dual
nature of the Ce $f$ electrons and competition between their itinerant and
localized nature can be important for its physical proprieties. The existing
electronic band structure in this material is still under debate. Energy scale
occurring in the system can be important for adequate theoretical description
of its supercomputing properties. In this paper, we discuss electronic band
structure obtained from {\it ab initio} calculations. We analyze electronic
surface states which can be compared with recently obtained angle-resolved
photoemission spectroscopy measurement (ARPES). Additionally, we present the
analyses of the hopping parameters obtained from the electronic band structure.
The As-Rh layers are characterized by much more significant hopping parameters
between atoms than these obtained for the Ce-Ce atoms. This suggests need of a
revision of the tight binding model necessary for adequate description of the
physical properties of CeRh$_{2}$As$_{2}$.
