Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method

Arie Landau,Uzi Kaldor,Lucas Visscher,Ephraim Eliav

doi:10.3390/i3050498

Abstract

Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3Πu is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the Λ = 1, 2 states lying 32.5 and 66.1 cm−1, respectively, above the Λ = 0 minimum (experimental values are 30.4 and 63.4 cm−1). The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 ˚A, and ωe 21 cm−1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations.

Highlights

The aluminum dimer, a light molecule with only two valence electrons, exhibits interesting features in its bonding
The accuracy and convergence of the Fock-space coupled cluster method discussed above depends on an appropriate partitioning of the function space into P and Q subspaces
Results were corrected for basis set superposition errors (BSSE) by the counterpoise method [23]

Summary

Introduction

The aluminum dimer, a light molecule with only two valence electrons, exhibits interesting features in its bonding. The Ω = 0 state itself is split into 3Π0−u and 3Π0+u, separated by 0.087 cm−1 These splittings were not accounted for in previous calculations, which were nonrelativistic and did not include spin-orbit coupling. The purpose of the present work is to apply the relativistic Fock-space coupled cluster method to the low states of Al2. This method has proved highly accurate for energy levels of heavy atoms, reproducing transition energies (ionization potentials, excitation energies, electron affinities) within a few hundredths of an eV in most cases and providing reliable predictions for super-heavy elements, where ground and excited state configurations are often different from those of lighter homologs (for a recent review see [5]). This work should be regarded as preliminary, with a modest-size basis, and is expected to pave the way to more complete applications in the future

The relativistic Hamiltonian

The Fock space coupled cluster method

The intermediate Hamiltonian coupled cluster method

Calculations

Results and Discussion