How hot are weakly-bound cluster ions in a blackbody field? Insights from master equation modeling

Abstract

Measuring accurate energetics in mass spectrometry thermochemical and calorimetry experiments depends on detailed knowledge of the energetics of the ion populations. For example, in cases where blackbody infrared radiative dissociation (BIRD) kinetics are not in the rapid energy exchange (REX) limit, threshold dissociation energies obtained directly from experiment will be too low. When ions are not in the REX limit, the ion internal energy distributions can be modeled using a master equation (ME). The ME allows evaluation of ion internal energies over time with a set of rate equations that describe the transfer of energy from one energy state to another. Here, ME modeling that accounts for the radiative absorption and emission, and dissociation rate constants is performed to determine the energetics of two model systems, M²⁺(H₂O)_n with n = 24, 55, 96, 178 and H⁺(AlaGly)_n with n = 4, 8, 16, 32, activated by a blackbody field at temperatures between 120 and 200 K. The hydrated cluster and oligopeptide sizes are chosen such that respective ions have comparable number of internal degrees-of-freedom. The effects of blackbody temperature and inherent properties, such as frequencies and infrared (IR) intensities, molecule size, and dissociation parameters (threshold dissociation energy, E₀, and high-pressure pre-exponential factor, A^∞) on the resulting ion effective temperatures, steady-state energy distributions, and BIRD kinetics are explored. ME results show that at low blackbody temperatures (<∼140 K), the steady-state internal energy distributions of the ion populations resemble those of Boltzmann distributions at the blackbody temperature. At higher blackbody temperatures (>∼140 K), rapid dissociation causes the steady-state internal energy distributions to equilibrate to lower energies where absorption and emission are competitive with dissociation. This results in ion effective temperatures that deviate from and are “colder” than the blackbody temperatures. The temperature where this transition occurs depends on the competition among absorption, emission, and dissociation, and is controlled by the dissociation parameters, vibrational frequencies, and IR intensities, as illustrated for M²⁺(H₂O)_n and H⁺(AlaGly)_n. This work shows that, under certain conditions, the ion effective temperatures can deviate significantly from those of the blackbody field temperatures. ME modeling can be used to determine the energy content of ion complexes in mass spectrometry experiments to improve the accuracy of thermochemical and calorimetry measurements of weakly-bound clusters and for more confident assignments of conformations and structures in action spectroscopy.