Two-electron Diatomic Molecules Research Articles

Signatures of magnetic-field effects in nonsequential double ionization manifesting as backscattering for molecules versus forward scattering for atoms

For two-electron diatomic molecules, we investigate magnetic field effects in non-sequential double ionization where recollisions prevail. We do so by formulating a three-dimensional semi-classical model that fully accounts for the Coulomb singularities and for magnetic field effects during time propagation. Using this model, we identify a prominent signature of non-dipole effects. Namely, we demonstrate that the recolliding electron back-scatters along the direction of light propagation. Hence, this electron escapes opposite to the direction of change in momentum due to the magnetic field. This is in striking contrast to strongly-driven atoms where the recolliding electron forward-scatters along the direction of light propagation. We attribute these distinct signatures to the different gate that the magnetic field creates jointly with a soft recollision in molecules compared to a hard recollision in atoms. These two different gates give rise, shortly before recollision, to different momenta and positions of the recolliding electron along the direction of light propagation. As a result, we show that the Coulomb forces from the nuclei act to back-scatter the recolliding electron in molecules and forward-scatter it in atoms along the direction of light propagation.

Strictly-correlated-electron approach to excitation energies of dissociating molecules

In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation based on adiabatic SCE (ASCE) theory which was shown to display a particular feature of the exact Hxc kernel, namely, a spatial divergence as function of the bond distance. This makes the ASCE kernel a candidate for correcting a notorious failure of the commonly used adiabatic local density approximation (ALDA) in the calculation of excitation energies of dissociating molecules. Unlike the ALDA, we obtain nonzero excitation energies from the ASCE kernel in the dissociation regime but they do not correspond to those of the true spectrum unless the interaction strength is taken to be very large such that the SCE theory has the right regime of validity, in which case the excitation energies become exact and represent the so-called zero-point oscillations of the strictly correlated electrons. The commonly studied physical dissociation regime, namely, large molecular separation at intermediate interaction strength, therefore remains a challenge for density functional approximations based on SCE theory.

Evaluation of electron repulsion integral of the explicitly correlated Gaussian-nuclear orbital plus molecular orbital theory

This Letter proposes two schemes for the efficient evaluation of electron repulsion integrals required for the explicitly correlated Gaussian-nuclear orbital plus molecular orbital (ECG-NOMO) theory, which offers accurate descriptions for electrons and nuclei. Two schemes, i.e., fully analytical and hybrid schemes for analytical and numerical integrations, for the ECG-NOMO/Hartree–Fock theory are assessed. Illustrative applications of these schemes to two-electron diatomic molecules demonstrate that the ECG-NOMO/HF theory provides significantly accurate zero-point energies within 123.5cm−1 deviation when compared with the experimental data.

Few-particle systems: quasi-exactly solvable models

Several quasi-exactly solvable models of few-particle systems are discussed. In particular, the Hooke atom (also known as harmonium) and its extensions appropriate to a description of non-Born-Oppenheimer one- and two-electron diatomic molecules are presented. Also several methods of construction of quasi-exactly solvable Schrodinger equations are described.

Stability of two-electron diatomic molecules

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.

Exactly Solvable Model Mimicking the H2 Molecule in the Limit of Large Nuclear Masses

Avoiding the limitations of the Born-Oppenheimer approximation remains an issue of continuing importance in molecular physics. If we take the H 2 molecule as a prototype, then one uses, in some sense, the ratio of electron mass in to nuclear mass M as an expansion parameter, sometimes cited to be explicitly (m/M) 1/4 . Here, we employ a model of such a two-electron diatomic molecule set up by Makarewicz [Am. J. Phys. 54 (1986) 178] to study the exact ground-state wave function obtained by treating electrons and nuclei on the same footing, Of course, to obtain such a wave function analytically means adopting model force laws, both for confinement and for the interelectronic interaction. From the exact wave function and ground-state energy, contact is finally established with the large nuclear mass limit.

The modified electronic mass approach for the adiabatic corrections in H2

A theory of the modified (distance dependent) electronic mass effect for two-electron diatomic molecules is presented. The modified electronic mass correction is compared with the diagonal Born-Oppenheimer correction to the potential energy curves of H2, suggesting that the adiabatic correction is almost exactly accounted for by this effect.

Representation of the electronic continuum of with B-spline basis

We present an integrable method with B-spline basis to describe the electronic continuum of two-electron diatomic molecules. The method is applied to obtain (i) energy positions and widths of the lowest doubly-excited states of the molecule, and (ii) photoionization cross sections of in the fixed-nuclei approximation. Our results are compared with existing theoretical and experimental works. We show the existence of avoided crossings between two series of doubly-excited states, and , converging to the ionization threshold of .

Large-Dimension Limit Yields Generic Reduced Potential Curves for H2+, H2, HHe+, and He22+

Analytic expressions for the D [yields] [infinity] limit previously evaluated for one- and two-electron diatomic molecules are compared with the familiar D = 3 potentials as functions of the internuclear distance R for H[sub 2][sup +], H[sub 2], HHe[sup +], and He[sub 2][sup 2+]. We find that the D = 3 potential can be obtained from the large-D limit simply by E[sub 3](R) = E[sub [infinity]](R)/G(R), to good approximation, where the function G(R) has the same form for the four molecules. Furthermore, 1. G(R) has a corresponding-states property; when reduced by two parameters, it becomes the same function for all four molecules, nearly proportional to x[sup 2]e[sup [minus]2x], with x the scaled internuclear distance. This suggests that the pseudoclassical D [yields] [infinity] limit may provide a useful reference for analysis of intermolecular potentials. 21 refs., 3 figs., 1 tab.

Simple correlated wavefunction for two-electron diatomic molecules. Application to H 2 and He 2+2 systems

In the present work we show that one can build accurate wavefunctions depending upon few variational parameters for ground and excited states of two-electron diatomic systems. Such simple wavefunctions could be useful in collisional problems. A convenient expression to compute the energy is also given using the first Green theorem.

Electron repulsion potentials of diatomic molecules in the adiabatic basis

General expressions are obtained for the calculation of the matrix elements of the Coulomb repulsion between electrons in two-electron diatomic molecules using the adiabatic basis. Based on these formulae, the algorithm for calculating these matrix elements for a hydrogen molecule in a wide range of internuclear distances is realised. The authors' results are compared with the asymptotic calculations and the previous calculations (1979) in the vicinity of the equilibrium position.

Bounds to dissociation energy of exciton-neutral donor complexes

From numerical computations based on the Born-Oppenheimer and the adiabatic approximations for the two-electron diatomic molecules, rigorous upper and lower bounds of the dissociation energy of the exciton-neutral impurity complexes are obtained.

Large Z Asymptotic Wavefunction for the Ground State of a Two-Electron Diatomic Molecule

The asymptotic large Z method is applied to the ground state of a two-electron homonuclear diatomic molecule with total nuclear charge Z and internuclear separation R and the first-order basic asymptotic wavefunction is obtained. As R goes to zero, the molecular wavefunction is shown to go over to the atomic (united atom) result obtained previously. Electron–electron correlation effects are explicitly exhibited.

Euler-Angle Reduction for Two-Electron Diatomic Molecules

We give a complete Euler-angle reduction of the Schrödinger equation for two-electron diatomic molecules. Explicit account is taken of the electron and nuclear symmetries, and the motion of the nuclei is accounted for exactly. This work is an extension of a previous analysis for three-electron atoms.

On the importance of correlation effects for the parameters of semi-empirical molecular orbital calculations

The one- and two-center coulomb repulsion parameters of semi-empirical molecular orbital calculations are commonly assumed to incorporate some correlation effects. It is shown that the horizontal correlation energy in a two-electron diatomic molecule can indeed be combined with the one- and two-center coulomb integrals to yield “correlated parameters”. However, the theoretical expressions for these parameters show a dependence on the internuclear separation which is strongly at variance with the common assumptions. The results indicate that a theoretical elucidation of the semi-empirical parameters is not likely to be found by consideration of correlation effects in a single electronic state.