Low-temperature chemistry using the R-matrix method

Abstract

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.

Momentum space calculations of the binding energies of argon dimer

“…For the angle integration x in Equation ( Our numerical results for all 174 vibrational and rotational energy levels of argon dimer using potential models I and II are listed in Tables 2 and 3, respectively. In Tables 4 and 5, however, our vibrational levels of argon dimer, for the rotational states j = 0, 1, 2, are compared with those of previous studies by Tennyson et al using R-matrix method [9,10] and also with the findings of Ref. [11].…”

“…It should be pointed out that the argon mass used in our calculations and also in Refs. [9,10] corresponds to pure 40 Ar mass of 39.9623831225 amu, whereas the results of Ref. [11] are obtained by 40 Ar mass of 39.962384 amu.…”

The ExoMol project: Software for computing large molecular line lists

“…A first release of DUO has just been published [24] and the reader is refered to this article and an associated topical review [62] this has the effect of discretizing the continuum and allowing localized, resonance states to be identified. [63] Second, the energy levels of open shell molecules are sensitive to the effects of magnetic fields. The behavior of molecules in a magnetic field provides a spectroscopic tool as well as being important in fields as diverse as molecular trapping [64] and astrophysics.…”

“…This possibility is currently being explored. [63] Another development in progress is the extension of TROVE for molecular dynamics in the presence of external time dependent electric fields. For example, recently the TROVE has been extended to allow time-dependent solutions of Schr€ odinger equations for polyatomic molecules exposed by electric fields of arbitrary shapes and polarizations, [135] where the flexibility of the ExoMol format [50] is explored for the transition dipole and polarizability moments required to simulate the laser-driven molecular dynamics.…”

Perspective: Accurate ro-vibrational calculations on small molecules

“…The idea of using variational rotation-vibration calculations extending above the dissociation limit as a basis for theoretical studies of cold and ultra-cold reactions is currently being explored within my group. 169 …”