  (abridged) We analyse the evolution of the fractional ionisation in a
steady-state protoplanetary disc with a vertical temperature gradient and with
gas-grain chemistry including surface reactions. The ionisation due to stellar
X-rays, stellar and interstellar UV radiation, cosmic rays and radionuclide
decay is taken into account. Using our reduction schemes as a tool for the
analysis, we isolate small sets of chemical reactions that reproduce the
evolution of the ionisation degree at representative disc locations with an
accuracy of 50%-100%. Column densities of key molecules are calculated and
compared to the results of other recent studies and observational data.
