It is shown that a one-electron Hamiltonian that defines the Rydberg orbitals of many-electron atoms can be related to an equivalent Hamiltonian defining molecular Rydberg orbitals in a perturbation theory manner. The perturbational potential is the difference between the atomic and molecular forms of the one-electron electrostatic potential in which the Rydberg electron moves. The molecular Rydberg orbital wavefunction can therefore be expanded as a linear combination of atomic orbitals (LCAO), which provides a method of calculating the spatial distributions of the molecular Rydberg orbitals. The potential is separated into its attractive and repulsive components and it is shown that the attractive part can be represented by the Coulombic attraction of the Rydberg electron to the cationic charge whilst the repulsive part can be represented by a charge–multipole interaction. Appropriate models for both parts of the potential are proposed. Mathematical representations of the atomic orbitals are obtained by non-linear least-squares fitting of the output of ab initio calculations of the atomic orbitals. The orbital energies of a variety of diatomic molecules are calculated and compared with experiment and a number of general features of the energies of molecular Rydberg orbitals are discussed.