  We introduce a computational method developed for study of long-range
molecular Rydberg states of such systems that can be approximated by two
electrons in a model potential of the atomic cores. Only diatomic molecules are
considered. The method is based on a two-electron \rmath approach inside a
sphere centered on one of the atoms. The wave function is then connected to a
Coulomb region outside the sphere via multichannel version of the Coulomb
Green's function. This approach is put into a test by its application to a
study of Rydberg states of the hydrogen molecule for internuclear distances $R$
from 20 to 400 bohrs and energies corresponding to $n$ from 3 to 22. The
results are compared with previous quantum chemical calculations (lower quantum
numbers $n$) and computations based on contact potential models (higher quantum
numbers $n$).
