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A means to take advantage of molecular similarity to lower the computationalcost of electronic structure theory is explored, in which parameters areembedded into a low-cost, low-level (LL) ab initio model and adjusted to obtainagreement with results from a higher-level (HL) ab initio model. A parametrizedLL (pLL) model is created by multiplying selected matrix elements of theHamiltonian operators by scaling factors that depend on element types. Variousschemes for applying the scaling factors are compared, along with the impact ofmaking the scaling factors linear functions of variables related to bondlengths, atomic charges, and bond orders. The models are trained on ethane andethylene, substituted with -NH2, -OH and -F, and tested on substituted propane,propylene and t-butane. Training and test datasets are created by distortingthe molecular geometries and applying uniform electric fields. The fittedproperties include changes in total energy arising from geometric distortionsor applied fields, and frontier orbital energies. The impacts of includingadditional training data, such as decomposition of the energy by operator orinteraction of the electron density with external charges, are also explored.The best-performing model forms reduce the root mean square (RMS) differencebetween the HL and LL energy predictions by over 85% on the training data andover 75% on the test data. The argument is made that this approach has thepotential to provide a flexible and systematically-improvable means to takeadvantage of molecular similarity in quantum chemistry.

Embedding parameters in ab initio theory to develop approximations based on molecular similarity