Theab initiocalculation of spectra of open shell diatomic molecules

Abstract

The spectra (rotational, rotation–vibrational or electronic) of diatomic molecules due to transitions involving only closed-shell (1Σ ) electronic states follow very regular, simple patterns and their theoretical analysis is usually straightforward. On the other hand, open-shell electronic states lead to more complicated spectral patterns and, moreover, often appear as a manifold of closely lying electronic states, leading to perturbed spectra of even greater complexity. This is especially true when at least one of the atoms is a transition metal. Traditionally these complex cases have been analysed using approaches based on perturbation theory, with semi-empirical parameters determined by fitting to spectral data. Recently the needs of two rather diverse scientific areas have driven the demand for improved theoretical models of open-shell diatomic systems based on an ab initio approach; these areas are ultracold chemistry and the astrophysics of ‘cool’ stars, brown dwarfs and most recently extrasolar planets. However, the complex electronic structure of these molecules combined with the accuracy requirements of high-resolution spectroscopy render such an approach particularly challenging. This review describes recent progress in developing methods for directly solving the effective Schrödinger equation for open-shell diatomic molecules, with a focus on molecules containing a transtion metal. It considers four aspects of the problem: (i) the electronic structure problem; (ii) non-perturbative treatments of the curve couplings; (iii) the solution of the nuclear motion Schrödinger equation; (iv) the generation of accurate electric dipole transition intensities. Examples of applications are used to illustrate these issues.

Uncertainty estimates for theoretical atomic and molecular data

“…the diagonal dipole moments, there are technical issues with their use that still need to be overcome [70,71].…”

Quantum‐Mechanical Calculations of Cross Sections for Electron Collisions With Atoms and Molecules

“…Sophisticated quantum chemical methods are available for treating electronically excited states for small molecules, largely based on procedures such as multi‐reference configuration interaction . At present, however, these wavefunctions cannot be used directly as the input for electron‐molecule scattering calculations, for several reasons: (a) the formulation given in Equation (5) requires a single set of orbitals for all states while the best results are obtained with orbital sets optimised for each state; (b) it is difficult to create a balanced model for electron scattering based on an MRCI target wavefunction; (c) excited states of molecules rapidly become very diffuse and are therefore hard to treat, at least within the confines of an R ‐matrix procedure; and (d) treatments involving electron collisions with complicated target wavefunctions rapidly become prohibitively computationally expensive. See Halmová et al for an illustrative discussion of this last point.…”

Spectroscopy of YO from first principles

“…(for the discussion, see, e.g., Refs. 59,60). In the openshell TM-containing species, these problems are exacerbated by stronger relativistic effects than those in the molecules made up of relatively light main group elements, and greater number of electronic excited states governing the spectroscopic behaviour of a molecule and hence deserving to be taken into account in a study aimed at accurate description of its spectroscopy.…”