  We analysed the dynamics of the positively charged ions of diatomic molecules
(${\rm X_{2}^{+}}$ and ${\rm XY^{+}}$), in which the bond is realised by the
single electron. We assumed that the atomic cores separated by the distance $R$
were subjected to the external excitation of the harmonic type with the
amplitude $A$ and frequency $\Omega$. We found the ground states of ions using
the variational approach within the formalism of second quantization (the
Wannier function was reproduced by means of Gaussian orbitals). It occurred
that, on the account of the highly non-linear dependence of the total energy on
$R$, the chaotic dynamics of cores induced the chaotic evolution of the
electronic Hamiltonian parameters (i.e. the energy of the electron orbital
$\varepsilon$ and the hopping integral $t$). Changes in cation masses or in the
charge arrangement does not affect qualitatively the values of Lyapunov
exponents in the $A$-$\Omega$ parameter space.
