Natural localized molecular orbitals

Abstract

The method of natural localized molecular orbitals (NLMOs) is presented as a novel and efficient technique for obtaining LMOs for SCF and CI wave functions. It is an extension of the previously developed natural atomic orbital (NAO) and natural bond orbital (NBO) methods, and uses only the information contained in the one-particle density matrix. Results are presented for methane and cytosine to indicate that NLMOs closely resemble LMOs obtained by the Boys and Edmiston–Ruedenberg methods, with the exception that the NLMO procedure automatically preserves the MO σ–π separation in planar molecules. The computation time is modest, generally only a small fraction of the SCF computation time. In addition, the derivation of NLMOs from NBOs gives direct insight into the nature of the LMO ‘‘delocalization tails,’’ thus enhancing the role of LMOs as a bridge between chemical intuition and molecular wave functions.

On Dipole Moments and Hydrogen Bond Identification in Water Clusters

“…For that reason, we have used four quite different localization procedures. Two of them were standard ones: Boys localization 32 and calculation of the "natural localized orbitals" (NLOs) of Weinhold group 33 . The other two represented generalizations of our approach applied for determining effective atomic orbitals [34][35][36][37] .…”

A theoretical study on the spectroscopy, structure, and stability of C2H3NS molecules

“…This supplied harmonic (ω B3LYP ) and anharmonic (ν B3LYP ) frequencies, as well as vibration-rotation coupling constants and quartic centrifugal distortion constants. Raman intensities and natural bond orbitals [37][38][39] (NBO) were also calculated at the same level of theory.…”

Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals

“…From eq (14) we see that a PAO (|µ P ) is an AO (|µ ) with a correction that depends on the density matrix elements through the AO overlap matrix. Hence, |µ P will only be local if the Hartree-Fock density matrix is local, whereas the PAOs will have a poor locality for systems with a non-local density matrix.…”

“…However, more objective measures which more directly reflects the spatial extent of an orbital have to be used. Many different measures have been introduced, ranging from general measures such as the second 14,24,30,32,90,91 and fourth 34 moment orbital spreads, charge populations, 18,92,93 and MO coefficient sparsity, 12,29,31 to more specific measures directly related to a particular localization scheme 36 and to a purely visual presentation. 89,94 We will discuss orbital locality in a context where an orbital is local if it is confined to a small volume in space.…”

“…A widely used orbital locality measure is the square root of the orbital's second central moment, 14,24,30,32,90,91,113 commonly referred to as the orbital spread. The second central moment (the variance) of an orbital φ p , |p , in one dimension is defined as,…”