Assessment of Anharmonicities in Clusters: Developing and Validating a Minimum-Information Partition Function.

Precise thermodynamic calculations are essential for understanding the dynamics of cluster systems and new particle formation. However, the widely employed harmonic statistical mechanical approach often falls short in terms of accuracy. In this study, we present an improved statistical model that incorporates vibrational anharmonicity via a novel partition function that requires only one additional system-specific input parameter. In addition to considering vibrational aspects, we also account for anharmonicity related to the configurational space. The role of anharmonicities is thoroughly examined in the case of general clusters, where the complete sets of conformers, mechanically stable spatial arrangements, are known up to clusters composed of 14 monomers. By performing consistent Monte Carlo simulations on these systems, we benchmark the statistical model's efficacy in reproducing key thermodynamic properties (formation free energy and potential energy) in the classical limit. The model exhibits exceptional alignment with simulations, accurately reproducing free energies within a precision of 2kBT and reliably capturing cluster melting temperatures. Furthermore, we demonstrate the significance and applicability of the model by reproducing thermodynamic barriers in homogeneous gas-phase nucleation of larger clusters. The transferability of our developed approach extends to more complex molecular systems and bears relevance for atmospheric multicomponent clusters, in particular.

Further cautionary tales on thermostatting in molecular dynamics: Energy equipartitioning and non-equilibrium processes in gas-phase simulations.

Molecular dynamics (MD) simulations of gas-phase chemical reactions are typically carried out on a small number of molecules near thermal equilibrium by means of various thermostatting algorithms. Correct equipartitioning of kinetic energy among translations, rotations, and vibrations of the simulated reactants is critical for many processes occurring in the gas phase. As thermalizing collisions are infrequent in gas-phase simulations, the thermostat has to efficiently reach equipartitioning in the system during equilibration and maintain it throughout the actual simulation. Furthermore, in non-equilibrium simulations where heat is released locally, the action of the thermostat should not lead to unphysical changes in the overall dynamics of the system. Here, we explore issues related to both obtaining and maintaining thermal equilibrium in MD simulations of an exemplary ion-molecule dimerization reaction. We first compare the efficiency of global (Nosé-Hoover and Canonical Sampling through Velocity Rescaling) and local (Langevin) thermostats for equilibrating a system of flexible compounds and find that of these three only the Langevin thermostat achieves equipartition in a reasonable simulation time. We then study the effect of the unphysical removal of latent heat released during simulations involving multiple dimerization events. As the Langevin thermostat does not produce the correct dynamics in the free molecular regime, we only consider the commonly used Nosé-Hoover thermostat, which is shown to effectively cool down the reactants, leading to an overestimation of the dimerization rate. Our findings underscore the importance of thermostatting for the proper thermal initialization of gas-phase systems and the consequences of global thermostatting in non-equilibrium simulations.

The missing base molecules in atmospheric acid-base nucleation.

Transformation of low-volatility gaseous precursors to new particles affects aerosol number concentration, cloud formation and hence the climate. The clustering of acid and base molecules is a major mechanism driving fast nucleation and initial growth of new particles in the atmosphere. However, the acid-base cluster composition, measured using state-of-the-art mass spectrometers, cannot explain the measured high formation rate of new particles. Here we present strong evidence for the existence of base molecules such as amines in the smallest atmospheric sulfuric acid clusters prior to their detection by mass spectrometers. We demonstrate that forming (H2SO4)1(amine)1 is the rate-limiting step in atmospheric H2SO4-amine nucleation and the uptake of (H2SO4)1(amine)1 is a major pathway for the initial growth of H2SO4 clusters. The proposed mechanism is very consistent with measured new particle formation in urban Beijing, in which dimethylamine is the key base for H2SO4 nucleation while other bases such as ammonia may contribute to the growth of larger clusters. Our findings further underline the fact that strong amines, even at low concentrations and when undetected in the smallest clusters, can be crucial to particle formation in the planetary boundary layer.

Nonisothermal nucleation in the gas phase is driven by cool subcritical clusters.

Nucleation of clusters from the gas phase is a widely encountered phenomenon, yet rather little is understood about the underlying out-of-equilibrium dynamics of this process. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial. To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics simulations of a supersaturated vapor in the presence of thermalizing carrier gas. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and classical nonisothermal theory. For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes and resolve the apparent contradictions regarding cluster temperatures. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation.

Shells in CO2 clusters.

Abundance spectra of (CO2)N clusters up to N ≈ 500 acquired under a wide range of adiabatic expansion conditions are analyzed within the evaporative ensemble framework. The analysis reveals that the cluster stability functions display a strikingly universal pattern for all expansion conditions. These patterns reflect the inherent properties of individual clusters. From this analysis the size-dependent cluster binding energies are determined, shell and subshell closing sizes are identified, and cuboctahedral packing ordering for sizes above N ≈ 130 is confirmed. It is demonstrated that a few percent variation in the dissociation energies translates into significant abundance variations, especially for the larger clusters.

New Particle Formation from the Vapor Phase: From Barrier-Controlled Nucleation to the Collisional Limit.

Studies of vapor phase nucleation have largely been restricted to one of two limiting cases-nucleation controlled by a substantial free energy barrier or the collisional limit where the barrier is negligible. For weakly bound systems, exploring the transition between these regimes has been an experimental challenge, and how nucleation evolves in this transition remains an open question. We overcome these limitations by combining complementary Laval expansion experiments, providing new particle formation data for carbon dioxide over a uniquely broad range of conditions. Our experimental data together with a kinetic model using rate constants from high-level quantum chemical calculations provide a comprehensive picture of new particle formation as nucleation transitions from a barrier-dominated process to the collisional limit.

Homogeneous nucleation of carbon dioxide in supersonic nozzles II: molecular dynamics simulations and properties of nucleating clusters.

Large scale molecular dynamics simulations of the homogeneous nucleation of carbon dioxide in an argon atmosphere were carried out at temperatures between 75 and 105 K. Extensive analyses of the nucleating clusters' structural and energetic properties were performed to quantify these details for the supersonic nozzle experiments described in the first part of this series [Dingilian et al., Phys. Chem. Chem. Phys., 2020, 22, 19282-19298]. We studied ten different combinations of temperature and vapour pressure, leading to nucleation rates of 1023-1025 cm-3 s-1. Nucleating clusters possess significant excess energy from monomer capture, and the observed cluster temperatures during nucleation - on both sides of the critical cluster size - are higher than that of the carrier gas. Despite strong undercooling with respect to the triple point, most clusters are clearly liquid-like during the nucleation stage. Only at the lowest simulation temperatures and vapour densities, clusters containing over 100 molecules are able to undergo a second phase transition to a crystalline solid. The formation free energies retrieved from the molecular dynamics simulations were used to improve the classical nucleation theory by introducing a Tolman-like term into the classical liquid-drop model expression for the formation free energy. This simulation-based theory predicts the simulated nucleation rates perfectly, and improves the prediction of the experimental rates compared to self-consistent classical nucleation theory.

Homogeneous nucleation of carbon dioxide in supersonic nozzles I: experiments and classical theories.

We studied the homogeneous nucleation of carbon dioxide in the carrier gas argon for concentrations of CO2 ranging from 2 to 39 mole percent using three experimental methods. Position-resolved pressure trace measurements (PTM) determined that the onset of nucleation occurred at temperatures between 75 and 92 K with corresponding CO2 partial pressures of 39 to 793 Pa. Small angle X-ray scattering (SAXS) measurements provided particle size distributions and aerosol number densities. Number densities of approximately 1012 cm-3, and characteristic times ranging from 6 to 13 µs, resulted in measured nucleation rates on the order of 5 × 1017 cm-3 s-1, values that are consistent with other nucleation rate measurements in supersonic nozzles. Finally, we used Fourier transform infrared (FTIR) spectroscopy to identify that the condensed CO2 particles were crystalline cubic solids with either sharp or rounded corners. Molecular dynamics simulations, however, suggest that CO2 forms liquid-like critical clusters before transitioning to the solid phase. Furthermore, the critical clusters are not in thermal equilibrium with the carrier gas. Comparisons with nucleation theories were therefore made assuming liquid-like critical clusters and incorporating non-isothermal correction factors.

Deviation from equilibrium conditions in molecular dynamic simulations of homogeneous nucleation.

We present a comparison between Monte Carlo (MC) results for homogeneous vapour-liquid nucleation of Lennard-Jones clusters and previously published values from molecular dynamics (MD) simulations. Both the MC and MD methods sample real cluster configuration distributions. In the MD simulations, the extent of the temperature fluctuation is usually controlled with an artificial thermostat rather than with more realistic carrier gas. In this study, not only a primarily velocity scaling thermostat is considered, but also Nosé-Hoover, Berendsen, and stochastic Langevin thermostat methods are covered. The nucleation rates based on a kinetic scheme and the canonical MC calculation serve as a point of reference since they by definition describe an equilibrated system. The studied temperature range is from T = 0.3 to 0.65 ϵ/k. The kinetic scheme reproduces well the isothermal nucleation rates obtained by Wedekind et al. [J. Chem. Phys. 127, 064501 (2007)] using MD simulations with carrier gas. The nucleation rates obtained by artificially thermostatted MD simulations are consistently lower than the reference nucleation rates based on MC calculations. The discrepancy increases up to several orders of magnitude when the density of the nucleating vapour decreases. At low temperatures, the difference to the MC-based reference nucleation rates in some cases exceeds the maximal nonisothermal effect predicted by classical theory of Feder et al. [Adv. Phys. 15, 111 (1966)].

Atmospheric Fate of Monoethanolamine: Enhancing New Particle Formation of Sulfuric Acid as an Important Removal Process.

Monoethanolamine (MEA), a potential atmospheric pollutant from the capture unit of a leading CO2 capture technology, could be removed by participating H2SO4-based new particle formation (NPF) as simple amines. Here we evaluated the enhancing potential of MEA on H2SO4-based NPF by examining the formation of molecular clusters of MEA and H2SO4 using combined quantum chemistry calculations and kinetics modeling. The results indicate that MEA at the parts per trillion (ppt) level can enhance H2SO4-based NPF. The enhancing potential of MEA is less than that of dimethylamine (DMA), one of the strongest enhancing agents, and much greater than methylamine (MA), in contrast to the order suggested solely by their basicity (MEA < MA < DMA). The unexpectedly high enhancing potential is attributed to the role of -OH of MEA in increasing cluster binding free energies by acting as both a hydrogen bond donor and acceptor. After the initial formation of one H2SO4 and one MEA cluster, the cluster growth mainly proceeds by first adding one H2SO4, and then one MEA, which differs from growth pathways in H2SO4-DMA and H2SO4-MA systems. Importantly, the effective removal rate of MEA due to participation in NPF is comparable to that of oxidation by hydroxyl radicals at 278.15 K, indicating NPF as an important sink for MEA.

Formation of atmospheric molecular clusters consisting of sulfuric acid and C8H12O6 tricarboxylic acid.

Using computational methods, we investigate the formation of atmospheric clusters consisting of sulfuric acid (SA) and 3-methyl-1,2,3-butanetricarboxylic acid (MBTCA), identified from α-pinene oxidation. The molecular structure of the clusters is obtained using three different DFT functionals (PW91, M06-2X and ωB97X-D) with the 6-31++G(d,p) basis set and the binding energies are calculated using a high level DLPNO-CCSD(T)/Def2-QZVPP method. The stability of the clusters is evaluated based on the calculated formation free energies. The interaction between MBTCA and sulfuric acid is found to be thermodynamically favourable and clusters consisting of 2-3 MBTCA and 2-3 SA molecules are found to be particularly stable. There is a large stabilization of the cluster when the amount of sulfuric acid-carboxylic acid hydrogen bonded interactions is maximized. The reaction free energies for forming the (MBTCA)2-3(SA)2-3 clusters are found to be similar in magnitude to those of the formation of the sulfuric acid-dimethylamine cluster. Using cluster kinetics calculations we identify that the growth of the clusters is essentially limited by a weak formation of the largest clusters studied, implying that other stabilizing vapours are required for stable cluster formation and growth.

Effect of Conformers on Free Energies of Atmospheric Complexes.

In this article we show how to calculate free energies for atmospherically relevant complexes when multiple conformers and/or isomers are present. We explain why the thermal averaging methods used in several published works are incorrect. On the basis of our two sample cases, the sulfuric acid-pinic acid complex and the (H2SO4)3(NH3)3(H2O)4 cluster, we provide numerical evidence that the use of these incorrect formulas can result in errors larger than 1 kcal/mol. We recommend that if vibrational frequencies and thus Gibbs free energies of the individual conformers are unavailable, one should not attempt to correct for the presence of multiple conformers and instead use only the global minimum conformers for both reactants and products. On the contrary, if the free energies for the conformers are calculated for both reactants and products, their effect can be accounted for by the statistical mechanical methods presented in this article.

Coupled Cluster Evaluation of the Stability of Atmospheric Acid-Base Clusters with up to 10 Molecules.

We investigate the utilization of the domain local pair natural orbital coupled cluster (DLPNO-CCSD(T)) method for calculating binding energies of atmospherical molecular clusters. Applied to small complexes of atmospherical relevance we find that the DLPNO method significantly reduces the scatter in the binding energy, which is commonly present in DFT calculations. For medium sized clusters consisting of sulfuric acid and bases the DLPNO method yields a systematic underestimation of the binding energy compared to canonical coupled cluster results. The errors in the DFT binding energies appear to be more random, while the systematic nature of the DLPNO results allows the establishment of a scaling factor, to better mimic the canonical coupled cluster calculations. Based on the trends identified for the small and medium sized systems, we further extend the application of the DLPNO method to large acid - base clusters consisting of up to 10 molecules, which have previously been out of reach with accurate coupled cluster methods. Using the Atmospheric Cluster Dynamics Code (ACDC) we compare the sulfuric acid dimer formation based on the new DLPNO binding energies with previously published RI-CC2/aug-cc-pV(T+d)Z results. We also compare the simulated sulfuric acid dimer concentration as a function of the base concentration with measurement data from the CLOUD chamber and flow tube experiments. The DLPNO method, even after scaling, underpredicts the dimer concentration significantly. Reasons for this are discussed.