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Journal of Physics B Atomic Molecular and Optical Physics

Stability of two-electron diatomic molecules

Alejandro Ferrón, Pablo Serra

Published Feb 19, 2007• 3 citations
Publisher

Abstract

We present a detailed study of the ground state behaviour of two-electron diatomic molecules. The ground state stability diagram for diatomic molecules in the Born–Oppenheimer approximation is obtained and the behaviour of the ground state near the stability line is studied. Two different cases are analysed: the homonuclear two-centre two-electron molecule with the internuclear distance as a free parameter and the diatomic two-electron molecule (in this case, the internuclear distance is determined by equilibrium conditions). Analytical and numerical results for these systems are presented.

DOI
10.1088/0953-4075/40/5/014

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We present a detailed study of the ground state behaviour of two-electron diatomic molecules. The ground state stability diagram for diatomic molecules in the Born–Oppenheimer approximation is obtained and the behaviour of the ground state near the stability line is studied. Two different cases are analysed: the homonuclear two-centre two-electron molecule with the internuclear distance as a free parameter and the diatomic two-electron molecule (in this case, the internuclear distance is determined by equilibrium conditions). Analytical and numerical results for these systems are presented.
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The vibrational motion equations of both homo- and hetero-nuclei diatomic molecules are here derived for the first time. A diatomic molecule is first considered as a quantum mechanics oscillator. The second- and third-order Hamiltonian operators are then formed by substituting the number operator for the quantum number in the corresponding energy eigenvalues. The temporal variations of relative position and linear momentum of two oscillating atoms are calculated by solving Heisenberg's equations of motion. The results indicate that the oscillatory behaviour of diatomic molecules are described by the wave packets which consisted of two different frequencies. The stability theory of optical oscillators (lasers) is then exploited to determine the stability conditions of an oscillating diatomic molecule in the different energy levels of Morse potential. It peculiarly turned out that the diatomic molecules are exactly dissociated at the energy level in which their equations of motion become unstable. We also determine the minimum oscillation frequency (cut-off frequency) of a diatomic molecule at the dissociation level of Morse potential.
We explore the electronic structure of ultralong-range penta-atomic Rydberg molecules from a merger of a Rydberg atom and two ground-state heteronuclear diatomic molecules. Our focus is on the interaction of Rb(23s\mathrm{Rb}(23sRb(23s) and Rb(n=20\mathrm{Rb}(n=20Rb(n=20, $l\ensuremath{\ge}3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the penta-atomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and orientation of the polar diatomic molecules.
A theorem on differential inequalities is proved. By means of this theorem the following result is established. Let psi (r 1 ,r 2 ,r 12 ) denote the ground-state wavefunction of a two-electron atom; then psi (r 1 ,r 2 r 12 )<or= psi (r 1 ,r 1 ,r' 12 ) for r' 12 <or=r 12 . Furthermore, a different proof is given, for the hydrogenic molecular ion, of a recent result of Lieb and Simon (1978) on the monotonicity of the electronic part of the Born-Oppenheimer energy with respect to the internuclear distance.
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 RRR-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a 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 RRR from 20 to 400 bohrs and energies corresponding to nnn from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers nnn) and computations based on contact-potential models (higher quantum numbers nnn).
The paper deals with the interaction of strong and pulsed radiation fields with a two-electron-state molecule. The light pulses under discussion are shorter than a vibrational period. The molecule is treated within the framework of the Born-Oppenheimer approximation. The nuclear degree of freedom is modeled as displaced harmonic potentials for the ground and the excited electronic states, respectively. Using coherent states as expansion tools for the nuclear motion, analytical expressions are given for the short-pulse region defined by the duration of the light pulse and the displacement of the potentials. The resonance condition is derived for this region. It is shown that within the short-pulse region the two-electron-state molecule mimics the behavior of a two-electron-state atom. Longer pulses are treated with numerical methods. The concept of resonance is discussed for the longer-pulse case. Limitations on population inversion are considered.