We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a fourcomponent relativistic framework. The first is based on the full semi-classical light-matter interaction operator and the two others on a truncated interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl 4 , when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter interaction.
The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas–Kroll–Hess Hamiltonian. Spin–orbit coupling was addressed with the Breit–Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin–orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.
High level multireference calculations were performed for LuF for a total of 132 states, including four dissociation channels Lu(2D) + F(2P), Lu(2P) + F(2P), and two Lu(4F) + F(2P). The 6s, 5d, and 6p orbitals of lutetium, along with the valence 2p and 3p orbitals of fluorine, were included in the active space, allowing for the accurate description of static and dynamic correlation. The Lu(4F) + F(2P) channel has intersystem spin crossings with the Lu(2P) + F(2P) and Lu(2D) + F(2P) channels, which are discussed herein. To obtain spectroscopic constants, bond lengths, and excited states, multi-reference configuration interaction (MRCI) was used at a quadruple-ζ basis set level, correlating also the 4f electrons and corresponding orbitals. Core spin–orbit (C-MRCI) calculations were performed, revealing that 13Π0− is the first excited state closely followed by 13Π0+. In addition, the dissociation energy of LuF was determined at different levels of theory, with a range of basis sets. A balance between core correlation and a relativistic treatment of electrons is fundamental to obtain an accurate description of the dissociation energy. The best prediction was obtained with a combination of coupled-cluster single, double, and perturbative triple excitations /Douglas–Kroll–Hess third order Hamiltonian methods at a complete basis set level with a zero-point energy correction, which yields a dissociation value of 170.4 kcal mol−1. Dissociation energies using density functional theory were calculated using a range of functionals and basis sets; M06-L and B3LYP provided the closest predictions to the best ab initio calculations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.