The Use of Natural Orbitals in Predicting Molecular Properties

Pragmatic modeling of a chemical system requires a method that will produce results of desirable accuracy while avoiding excessive computational cost. This process begins by specifying the size and type of atomic orbital basis set to be used. In general, as the number of orbitals increases so does the accuracy of the computed energies. Unfortunately, this increase in basis set size comes with severe memory and time requirements. Yet it is possible to truncate the number of orbitals and defray costs, while retaining a high level of accuracy, if an appropriate type of orbital is chosen. While it seems appropriate to choose a molecular orbital basis that is optimized with regards to energy considerations, their slow convergence when modeling the instantaneous repulsion between electrons makes them effete for truncation purposes. As an alternative, natural orbitals have enjoyed considerable popularity. Of course, before natural orbitals can be used to model a chemical system, they must first be generated. While expensive in the exact case, an approximate one-electron reduced density matrix can be quickly constructed with the aid of multi-reference Møller-Plesset perturbation theory. Once the density matrix is diagonalized, the acquired eigenvectors represent the desired natural orbitals and each associated eigenvalue corresponds to the probability of finding an electron in that orbital. These probabilities have the desirable property of providing an intuitive scheme for ordering the orbitals according to their importance in the electronic wave function, making the acquired natura