Using molecular similarity to construct accurate semiempirical electronic structure theories

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structure theories with parameters for the transferable characteristics of functional groups. We propose that high-level calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various small-molecule environments, and "mine" this data to build a sophisticated model for the group's behavior in large environments. This work details such a model for electron correlation: a semiempirical, subsystem-based correlation functional that predicts a subsystem's two-electron density matrix as a functional of its one-electron density matrix. This model is demonstrated on two small systems: chains of linear, minimal-basis (H-H)(5), treated as a sum of four overlapping (H-H)(2) subsystems; and the aldehyde group of a set of HOC-R molecules. The results provide an initial demonstration of the feasibility of the approach.