The orbitals defined (P. Lowdin) as the eigenfunctions of the spinless one-particle
electron density matrix. For a configuration interaction wave-function constructed from orbitals
,
the
electron density function,
,
is of the form:
where the coefficients
are a set of numbers which form the density matrix. The
NOs reduce the density matrix
to a diagonal form:
where the coefficients
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
basis set and the subsequent diagonalisation of the density matrix
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.
Source:
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.