LAUSR

The computational efficiency of local correlation methods is strongly dependent on the size of the domain of functions used to expand local correlating orbitals such as orbital specific or pair natural orbitals. Here we define a principal domain of order $m$ as the subset of $m$ one-particle functions that provides the best support for a given $n$-electron wavefunction by maximising the partial trace of the one-body reduced density matrix. Principal domains maximise the overlap between the wavefunction and its approximant for two-electron systems and are the domain selection equivalent of L\"owdin's natural orbitals. We present an efficient linear scaling greedy algorithm for obtaining principal domains of projected atomic orbitals and demonstrate its utility in the context of pair natural orbital local correlation theory. We numerically determine thresholds such that the projected atomic orbital domain error is an order of magnitude smaller than the pair natural orbital truncation error.