The recombination of ions in the gas-phase plays an important role in the chemical composition, energy and charge balance of partially ionized gas environments such as flames, plasmas, inter-planetary gas clouds and ultra-cold (~few K) systems like cryogenics and quantum computers. Motivated by the lack of robust theoretical models of gas-phase ion-ion recombination, a holistic approach to modeling the recombination rate constant β_r that takes into account the ion-ion electrostatic interactions, ion-neutral gas molecule collisions and ion number concentration is proposed here.

The modeling of elementary recombination reactions between a cation and an anion in the presence of a neutral gas is proposed here through the use of Langevin Dynamics and ion-pair specific potentials developed using the widely used Generalized AMBER Force Field (GAFF) combination rules. The use of translational and rotational Langevin equations to describe ion-ion motion implicitly captures the interaction between ions and neutral gas molecules through a systematic drag and thermal fluctuations due to diffusion, as well as explicitly accounts for ion-ion electrostatic interactions (force and torque on each other). This allows the reduction of a many body simulation (recombining cation, anion, and background gas molecules) to that of a two-body simulation (cation and anion) in the electrostatic and hydrodynamic force field (due to the gas molecules). A computationally inexpensive approach is described to obtain the recombination rate constant  and to parameterize the same using scaling analysis for a wide range of gas pressures and temperatures of interest to aforesaid applications (p≥100 Pa, T≥1 K). Lastly, the effect of ion concentration n_± will be systematically explored from the dilute limit (n_± < 10¹⁵ cm^-3) to the dense or strongly coupled regimes (10¹⁵ cm^-3< n_± < 10²⁷ cm^-3 such as those found in fusion plasmas or solar winds), investigating the electrostatically correlated motion of ions and implications for the recombination process.

This computational research project will summarize Langevin Dynamics calculations of the recombination rate constant β_r into accurate predictive models that take into account the gas density (pressure and temperature), ion structure, ion-specific potential interactions, and ion number concentration to describe the chemical physics of ion recombination. To provide accurate inputs to the Langevin Dynamics calculation of β_r , the ionic structures will be determined using the Gaussian16® commercial package. The ion mobility or diffusion coefficient will be obtained from published experimental data or calculated using the IMoS ion mobility calculation package (developed by Prof. Carlos Larriba, IUPUI). The analysis procedure described in the proposal allows the parameterization of Langevin-inferred β_r  into accurate expressions that converge to the high-pressure (p→∞  or continuum) and low-pressure (p→0 or kinetic) limits of ion recombination. The β_r models developed as part of this project will be validated against the experimentally measured recombination rate constants from published experimental datasets identified in the project narrative. In this project, one graduate student will be involved (for the entire project period) and one undergraduate student will be involved (for three months a year for all three project years), supervised by the PI.