Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

TL;DR

This paper investigates how harmonic excitation induces chaotic behavior in the energy and hopping parameters of diatomic molecular cations, revealing that non-linear energy dependence leads to chaos in electronic and ionic dynamics.

Contribution

It introduces a variational approach within second quantization to analyze chaotic evolution of electronic parameters under harmonic excitation in diatomic cations.

Findings

Chaotic dynamics of ionic cores induce chaos in electronic Hamiltonian parameters.

Lyapunov exponents are insensitive to changes in cation mass or charge arrangement.

Harmonic excitation parameters significantly influence the onset of chaos.

Abstract

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.