  A means to take advantage of molecular similarity to lower the computational
cost of electronic structure theory is proposed, in which parameters are
embedded into a low-cost, low-level (LL) ab initio theory and adjusted to
obtain agreement with a higher level (HL) ab initio theory. This approach is
explored by training such a model on data for ethane and testing the resulting
model on methane, propane and butane. The electronic distribution of the
molecules is varied by placing them in strong electrostatic environments
consisting of random charges placed on the corners of a cube. The results find
that parameters embedded in HF/STO-3G theory can be adjusted to obtain
agreement, to within about 2 kcal/mol, with results of HF/6-31G theory.
Obtaining this level of agreement requires the use of parameters that are
functions of the bond lengths, atomic charges, and bond orders within the
molecules. The argument is made that this approach provides a well-controlled
means to take advantage of molecular similarity in quantum chemistry.
