Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.Comment: Presented at Faraday Discussion on the Theory of Chemical Reactions Published in Faraday Discussion

ExoMol line lists XVIII. The high temperature spectrum of VO

An accurate line list, VOMYT, of spectroscopic transitions is presented for hot VO. The 13 lowest electronic states are considered. Curves and couplings are based on initial {\it ab initio} electronic structure calculations and then tuned using available experimental data. Dipole moment curves, used to obtain transition intensities, are computed using high levels of theory (e.g. MRCI/aug-cc-pVQZ using state-specific or minimal-state CAS for dipole moments). This line list contains over 277 million transitions between almost 640,000 energy levels. It covers the wavelengths longer than 0.29 $\mu$m and includes all transitions from energy levels within the lowest nine electronic states which have energies less than 20,000 \cm{} to upper states within the lowest 13 electronic states which have energies below 50,000 \cm{}. The line lists give significantly increased absorption at infrared wavelengths compared to currently available VO line lists. The full line lists is made available in electronic form via the CDS database and at www.exomol.com.Comment: MNRAS in pres

Ab initio calculations to support accurate modelling of the rovibronic spectroscopy calculations of vanadium monoxide (VO)

Accurate knowledge of the rovibronic near-infrared and visible spectra of vanadium monoxide (VO) is very important for studies of cool stellar and hot planetary atmospheres. Here, the required ab initio dipole moment and spin-orbit coupling curves for VO are produced. This data forms the basis of a new VO line list considering 13 different electronic states and containing over 277 million transitions. Open shell transition, metal diatomics are challenging species to model through ab initio quantum mechanics due to the large number of low-lying electronic states, significant spin-orbit coupling and strong static and dynamic electron correlation. Multi-reference configuration interaction methodologies using orbitals from a complete active space self-consistent-field (CASSCF) calculation are the standard technique for these systems. We use different state-specific or minimal-state CASSCF orbitals for each electronic state to maximise the calculation accuracy. The off-diagonal dipole moment controls the intensity of electronic transitions. We test finite-field off-diagonal dipole moments, but found that (1) the accuracy of the excitation energies were not sufficient to allow accurate dipole moments to be evaluated and (2) computer time requirements for perpendicular transitions were prohibitive. The best off-diagonal dipole moments are calculated using wavefunctions with different CASSCF orbitals.Comment: Molecular Physics, 201

Low temperature scattering with the R-matrix method: argon-argon scattering

Results for elastic atom-atom scattering are obtained as a first practical application of RmatReact, a new code for generating high-accuracy scattering observables from potential energy curves. RmatReact has been created in response to new experimental methods which have paved the way for the routine production of ultracold atoms and molecules, and hence the experimental study of chemical reactions involving only a small number of partial waves. Elastic scattering between argon atoms is studied here. There is an unresolved discrepancy between different argon-argon potential energy curves which give different numbers of vibrational bound states and different scattering lengths for the argon-argon dimer. Depending on the number of bound states, the scattering length is either large and positive or large and negative. Scattering observables, specifically the scattering length, effective range, and partial and total cross-sections, are computed at low collision energies and compared to previous results. In general, good agreement is obtained, although our full scattering treatment yields resonances which are slightly lower in energy and narrower than previous determinations using the same potential energy curve.Comment: 26 pages, 9 figures, 3 table

General Mathematical Formulation of Scattering Processes in Atom-Diatomic Collisions in the RmatReact Methodology

Accurately modelling cold and ultracold reactive collisions occuring over deep potential wells, such as \ce{D+ + H2 -> H+ + HD}, requires the development of new theoretical and computational methodologies. One potentially useful framework is the R-matrix method adopted widely for electron-molecule collisions which has more recently been applied to non-reactive heavy particle collisions such as Ar-Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photo-association, photo-dissociation, charge exchange and reactive scattering using the R-matrix method. Of particular note is that the inner region, of central importance to calculable R-matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. % The choice of coordinate set and basis function is these cases becomes more complexThis introduces substantial challenges to the basis sets utilised in practical calculations as integrals over finite domains are often much more challenging than over infinite domains for this problem.Comment: Submitted as part of the issue of Phil. Trans. Roy. Soc. A special issue on "Advances in hydrogen molecular ions: H3+, H5+ and beyond

The {\it ab initio} calculation of spectra of open shell diatomic molecules

The spectra (rotational, rotation-vibrational or electronic) of diatomic molecules due to transitions involving only closed-shell ($^1\Sigma$) 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 perturbations with even larger 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 \emph{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 Schr\"odinger equation for open-shell diatomic molecules, with a focus on molecules containing a transtion metal. It considers four aspects of the problem: 1. The electronic structure problem, 2. Non-perturbative treatments of the curve couplings, 3. The solution of the nuclear motion Schr\"odinger equation, 4. The generation of accurate electric dipole transition intensities. Examples of applications are used to illustrate these issues.Comment: Topical Revie

Full Spectroscopic Model and Trihybrid Experimental-Perturbative-Variational Line List for ZrO

Zirconium monoxide (ZrO) absorption lines define rare S-type stars and are currently being sought on exoplanets. Successful detection is dependent on an accurate and comprehensive line list, with existing data not ideal for many applications. Specifically, the Plez \etal{} line list is near-complete but has insufficient accuracy for high-resolution cross-correlation, while the Sorensen \& Bernath data has high accuracy but only considers a small number of spectral bands. This article presents a novel spectroscopic model, variational line list and trihybrid line list for the main \ZrO{} isotopologue, as well as isotopologue-extrapolated hybrid line lists for the \isoa{}, \isob{}, \isoc{}, \isod{}~and \isoe{} isotopologues. These were constructed using \DUO{} based on icMRCI-SD/CASSCF~\abinitio{} electronic data calculated using \MOLPRO{}, experimental energies obtained from a previous \Marvel{} data compilation and perturbative energies from Sorensen \& Bernath. The new \ZrO{} \EXOMOL{}-style trihybrid line list, \LLname{}, comprises \noenergies{} energies (\noMaenergies{} experimental) and \notransitions{} transitions up to 30,000~\cm{} (333~nm) between ten low-lying electronic states (\ZrOX{}, \ZrOaa{}, \ZrOA{}, \ZrObb{}, \ZrOB{}, \ZrOC{}, \ZrOdd{}, \ZrOee{}, \ZrOff{} and \ZrOF{}). The inclusion of experimental energy levels in \LLname{} means ZrO will be much easier to detect using high-resolution ground-based telescopes in the 12,500 -- 17,500~\cm{} (571 -- 800~nm) spectral region. The inclusion of variational energy levels means that the ZorrO line list has very high completeness and can accurately model molecular absorption cross-sections even at high temperatures. The \LLname{} data will hopefully facilitate the first detection of ZrO in the atmosphere of a hot Jupiter exoplanet, or alternatively more conclusively exclude its presence