Heat pumps, which recycle waste heat, are a promising technology for reducing CO₂ emissions. Efficiently using low-grade waste heat remains challenging due to the limitations of standard heat exchangers and the need for more effective working fluids. This work introduces a multi-scale methodology that combines force field-based Monte Carlo simulations, quantum mechanics, and equations of state to explore the potential of formic acid as a new reactive fluid in thermodynamic cycles. Formic acid exhibits dimerization behavior, forming cyclic dimers in the gas phase, which can enhance the thermodynamic efficiency of heat recovery systems. The dimerization reaction of formic acid is crucial because it integrates chemical energy into thermodynamic processes, potentially improving the performance of heat pumps and other energy systems. The study implements umbrella sampling in Monte Carlo simulations to compute the thermodynamic properties of HCOOH dimerization, including equilibrium constants, enthalpy, and entropy. Results from two different methods to study dimer formation, namely the dimer counter method and the potential of mean force method, show strong agreement with the enthalpy of dimerization of −60.46 kJ mol⁻¹ and −62.91 kJ mol⁻¹, and entropy of −137.36 J mol⁻¹K⁻¹ and −146.98 J mol⁻¹K⁻¹, respectively. A very good agreement of the Monte Carlo results with Quantum Mechanics and experimental data validates the accuracy of the simulations. For phase equilibrium properties, the Peng–Robinson equation of state, coupled with advanced mixing rules, was applied and compared to Monte Carlo simulations in the Gibbs ensemble. This approach enabled the determination of the Global Phase Equilibrium of the system, vaporization enthalpy, phase composition, vapor and liquid densities of the coexisting phases, and entropy as a function of temperature. The agreement between the thermodynamic model and Monte Carlo simulations confirms the reliability of the methodology in capturing the phase behavior of the system. The findings demonstrate a promising approach for discovering and characterizing new reactive fluids, contributing to more efficient and sustainable energy technologies.

The use of reactive working fluids in thermodynamic cycles is currently being considered as an alternative to inert working fluids, because of the preliminarily attested higher energy-efficiency potential. The current needs to simulate their use in thermodynamic cycles, which may operate in liquid, vapour or vapour-liquid state, are an accurate real-fluid equation of state and ideal gas thermochemical properties of each molecule constituting the mixture, to calculate the equilibrium constant. To this end, the appeal to a multi-scale theoretical methodology is paramount and its definition represents the objective of the present work. This methodology is applied and validated on the system N₂O₄ ⇌ 2NO₂. Firstly, the equations solved for simultaneous two-phase and reaction equilibrium are presented. Secondly, ideal gas thermochemical properties of N₂O₄ and NO₂ are computed at atomic scale by quantum mechanics simulations. Then, to apply the selected cubic equation of state, pure-component properties of the species forming the reactive mixture (critical point coordinates and acentric factor) are required as input. However, these properties are not measurable, since NO₂ and N₂O₄ do not exist in nature as pure components. To get around this difficulty, the methodology relies on molecular Monte Carlo simulations of the pure N₂O₄ and NO₂, as well as on the reactive N₂O₄ ⇌ 2NO₂, enabling the determination of those missing pure-component properties and thus the calculation, on a macroscopic scale, of the reactive mixture properties. Finally, the comparison of calculated mixture properties with available experimental data leads to validate the accuracy of the proposed methodology.