Optimization of long range potential interaction parameters in ion mobility spectrometry

Abstract

The problem of optimizing Lennard-Jones (L-J) potential parameters to perform collision cross section (CCS) calculations in ion mobility spectrometry has been undertaken. The experimental CCS of 16 small organic molecules containing carbon, hydrogen, oxygen, nitrogen, and fluoride in N2 was compared to numerical calculations using Density Functional Theory (DFT). CCS calculations were performed using the momentum transfer algorithm IMoS and a 4-6-12 potential without incorporating the ion-quadrupole potential. A ceteris paribus optimization method was used to optimize the intercept σ and potential well-depth ϵ for the given atoms. This method yields important information that otherwise would remain concealed. Results show that the optimized L-J parameters are not necessarily unique with intercept and well-depth following an exponential relation at an existing line of minimums. Similarly, the method shows that some molecules containing atoms of interest may be ill-conditioned candidates to perform optimizations of the L-J parameters. The final calculated CCSs for the chosen parameters differ 1% on average from their experimental counterparts. This result conveys the notion that DFT calculations can indeed be used as potential candidates for CCS calculations and that effects, such as the ion-quadrupole potential or diffuse scattering, can be embedded into the L-J parameters without loss of accuracy but with a large increase in computational efficiency.