Monte Carlo Simulations of Small Sulfuric Acid−Water Clusters

Abstract

Effective atom-atom potentials are developed for binary sulfuric acid-water clusters and applied in a Bennett Metropolis Monte Carlo calculation to determine free energy differences for small neighboring sized clusters of fixed composition at 298 K. The atom-atom pair potentials consist of Lennard-Jones short-range and Coulombic long-range terms and assume rigid SO 4 2δ-with two unconstrained H δ+ and rigid H 2 O molecules interacting via revised central force (RSL2) potentials. The potential parameters are determined from both ab initio studies and tests of the potential using the statistical mechanical formalism for binary cluster size distributions. In the potential tests, fixed composition free energy differences, δf km,m , for [H 2 O] km [H 2 SO 4 ] m clusters are plotted versus (km + m) -1/3 , and the resulting slope and intercept (in the large cluster regime) are used to extract model dependent binary liquid surface tension and partial vapor pressures at 298 K. The potential parameters are adjusted to obtain approximate agreement with experimental surface tension and partial vapor pressures for k ) 1 and 4 (84% and 57% weight percent H 2 SO 4 , respectively). The free energy differences for m e 15 are presented, together with internal cluster energy contributions, snapshots of cluster structure, and evidence for onset of the large cluster regime near m ) 5. The long-range goals have been to test the free energy difference procedure for studying binary cluster properties and to develop model potentials appropriate for the simulation of small binary clusters at low temperatures characteristic of stratospheric sulfuric acid-water aerosols.

Nucleation and the Solid–Liquid Interfacial Free Energy

“…Hale et al [38][39][40] performed Monte Carlo simulations on the cluster energetics of water clusters, unary and binary LJ systems, and binary sulfuric acid-water. They found that when the differential Helmholtz energy, F n -F n-1 , is plotted versus n -1/3 [essentially n 2/3 -(n -1) 2/3 ], the data points fit well to a straight line down to n as small as 5-10, which suggests that even very small clusters already exhibit bulklike behavior.…”

Scaling of the Nucleation Rate and a Monte Carlo Discrete Sum Approach to Water Cluster Free Energies of Formation

“…Values of -δf n are determined after equilibration from Monte Carlo runs of length 30 to 50 million steps, using different initial configurations. The values of -δf n are also generated from two independently developed codes, one of which was used for binary clusters 61 and moved all of the molecules at each step.…”

A density functional study on water‐sulfuric acid‐ammonia clusters and implications for atmospheric cluster formation

“…Thus liquid drop models describe them very inaccurately. Classical simulations [ Kathman and Hale , 2001; Kusaka et al , 1998] capture the true nature of newly formed particles as molecular clusters, but suffer from the lack of transferable interaction potentials able to describe correctly the various binding states of, for example, water and sulfuric acid. Quantum chemical methods are needed to understand properties of these clusters, where proton transfer is an essential part of bond formation.…”