Journal of Aerosol Science 162 105974 (2022)
A consistent formation free energy definition for multicomponent clusters in quantum thermochemistry
Roope Halonen
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 92 Weijin Road, Tianjin, 300072, China
E-mail address: roope@tju.edu.cn
Abstract
Quantum chemical calculations have proven to describe the thermodynamics of sub-nanometre clusters more accurately than the liquid drop model used in classical nucleation theory (CNT). However, the standard quantum chemical free energies of multicomponent clusters are fundamentally incompatible with the quantity appearing in the exponential of the CNT expression for the nucleation rate. The origin of this incompatibility is known to be in the statistical thermochemistry, but it is also connected to a much debated issue of self-consistency within CNT. Although these issues do not affect the main results of previous theoretical studies of nucleation, a thorough analysis and discussion about the nature of free energy in quantum chemistry of cluster formation has been missing. In this study, we present a consistent definition for the formation free energy using the law of mass action and a general equilibrium cluster distribution function, and apply this definition to gas-phase quantum thermochemical calculations. This internal consistency allows us to integrate the high-level thermochemical data to the basic framework of CNT and the liquid drop model contained therein. Moreover, based on our analysis, we derive a simple analytical expression for the steady-state nucleation rate compatible with the widely used numerical acdc model. As an illustrative example, the consistent formation free energies and nucleation rates are presented and analysed for atmospherically relevant H2SO4–NH3 clusters at various temperature and monomer vapour pressure conditions.
