### The Use of Natural Orbitals in Predicting Molecular Properties

#### Abstract

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 natural orbitals a logical choice for a one-electron basis as they facilitate the truncation of orbitals. Yet traditional methods for generating natural orbitals are incompatible with the computation of global potential energy surfaces and the prediction of transition state geometries that are difficult to characterize experimentally. The procedure advocated here overcomes this shortcoming by including multiple electronic configurations as references and fixing the number of retained orbitals after considering both occupation numbers and molecular symmetries. The accuracy and robustness of the method is assessed by modeling simple bond cleavage and triatomic reactions. When compared to calculations employing standard (and large) basis sets, this selection scheme yields potential energy surfaces with high accuracy at a significantly reduced computational cost.

#### Keywords

Electron correlation, natural orbitals, electronic structure

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