natural orbital (NO)
The orbitals defined (P. Lowdin) as the eigenfunctions of the spinless one-particle @E01986@ matrix. For a configuration interaction wave-function constructed from orbitals \(\varPhi \), the @ET07024@, \(\unicode[Times]{x3C1}\), is of the form: \[\unicode[Times]{x3C1} = \sum_{i}\sum _{j}a_{ij}\,\varPhi_{i}^{*}\,\varPhi_{j}\] where the coefficients \(a_{ij}\) are a set of numbers which form the density matrix. The NOs reduce the density matrix \(\unicode[Times]{x3C1}\) to a diagonal form: \[\unicode[Times]{x3C1} = \sum _{k}b_{k}\mathit{\Phi}_{k}^{*}\mathit{\Phi}_{k}\] where the coefficients \(b_{k}\) are occupation numbers of each orbital. The importance of natural orbitals is in the fact that CI expansions based on these orbitals have generally the fastest convergence. If a CI calculation was carried out in terms of an arbitrary @BT06999@ and the subsequent diagonalisation of the density matrix \(\text{a}_{ij}\) gave the natural orbitals, the same calculation repeated in terms of the natural orbitals thus obtained would lead to the wave-function for which only those configurations built up from natural orbitals with large occupation numbers were important.
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1954 [Terms] [Paper]