Partition Theory

Partition Theory (PT) is a quantum chemistry method for simplifying a molecular calculation by breaking it down into fragment calculations. This “fragmentation” can lead to more efficient and/or more accurate results. The work in this thesis concerns studying fundamental aspects of PT and exact properties of energy functionals used in PT. We hope that these properties can be used for the development of feasible approximations to PT functionals.

We implemented PT so that it can be solved numerically exactly for model systems in 1D. We used this implementation to study exact properties of the partition potential (a fictitious one-body potential used in PT to recover inter-fragment interactions). Our implementation can be used to study non-interacting and interacting electrons in 1D. We extended PT to systems supporting continuous electronic states (e.g., metals and metal

surfaces) and demonstrated this method using a model system in 1D. We derived an exact virial relation for fragment energies and tested it on simple diatomic molecules in 3D. Finally, we studied properties of the partition potentials obtained through numerical inversions of formic acid dimer systems in 3D.