In order to be able to accurately model chemical systems, knowledge of the system’s electronic energy and electron distribution is essential. However, in order to find the electronic energy and electron density distribution, one must use the principles of quantum mechanics and find approximate solutions to a complicated differential equation called the Schrödinger equation, in particular the electronic Schrödinger equation for a fixed set of nuclear coordinates. Usually, this equation cannot be solved exactly but useful approximate solutions can be obtained. Methods for finding these approximate solutions (to various degrees of accuracy, depending on the system size and complexity) exist, but their computational cost often increases drastically even with small increases in system size. For example, for some of the approximation schemes of interest, the cost increases by a factor of 128 when the size of a large system is doubled. Therefore, fragment-based methods have been introduced to try to reduce the rate at which the cost of an electronic structure calculation increases with system size. Fragment-based methods require the user to break a large system into fragments (called monomers or subsystems or fragments); in the fragment method this group will use, the approximate solution to the Schrödinger equation is found for each monomer in the system and for small groups of monomers (in particular dimer and trimers), each in the presence of some representation of the electrostatic potential due to the other monomers. A linear combination of the energies of the monomers and groups of monomers is then taken as an approximation of the total energy of the entire system. The electrostatically embedded many-body (EE-MB) is the particular fragment-based method used. A major application of fragment-based methods and, in particular, the EE-MB approximation, is for the simulation of atmospheric nucleation processes. In order to model atmospheric nucleation, it is essential that the chosen method be capable of handling proton transfer reactions that occur within the molecular clusters. A proton transfer reaction requires that a single atom (or, more specifically, ion) breaks free from one molecule and joins another. This poses a challenge for fragment-based methods because each monomer is typically defined as a single molecule. If a proton transfer reaction occurs, the definition of each monomer changes.

The goal of this project is to get a baseline understanding of how well the EE-MB approximation captures a simple potential energy curve of a proton transfer reaction within a small atmospherically-relevant cluster relative to a conventionally calculated energy curve at a given level of electronic structure theory. Specifically, the pairwise additive (PA), electrostatically embedded pairwise-additive (EE-PA), three-body (3B), and electrostatically embedded three-body (EE-3B) approximations will be used.