Natural minimal basis

Thus, these orbitals can be used to represent exactly any property of the system in localized terms. The NAOs divide naturally into a leading high-occupancy set (the natural minimal basis ) and a residual low-occupancy set (the natural Rydberg basis ), where the occupancies of the latter orbitals are usually quite negligible for chemical purposes. Thus, even if the underlying variational basis set is of high dimensionality (6-311++G for the applications of this book), a perturbative analysis couched in NAO terms has the simplicity of an elementary minimal-basis treatment without appreciable loss of chemical accuracy. 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

We can divide the NAOs into the natural minimal basis (NMB), consisting of only the formal core and valence NAOs of simple bonding theory, and the natural Rydberg basis (NRB), consisting of everything else. With this partitioning, Eq. (3.24a) is expressed as... 

The NAOs will normally resemble the pure atomic orbitals (as calculated for an isolated atom), and may be divided into a natural minimal basis (corresponding to the... 

DMA = distributed multipole analysis ESP = electrostatic potential GAPT = generalized atomic polar tensor NAP = natural atomic population NMB = natural minimal basis NRB = natural Rydberg basis OMM = overlap multipole moments PEOE = partial equalization of orbital electronegativities RESP = restrained electrostatic potential. 

Associated with their strong tendency to condense occupancy in the lowest few orbitals, the NAOs on each center A typically separate into two distinct sets (i) the high-occupancy natural minimal basis (NMB) set, equal in number and type to the nominal minimal basis of occupied Hartree-Fock AOs in the atomic ground-state configuration, and (ii) the low-occupancy natural Rydberg basis (NRB) set, corresponding... 

Natural Atomic Orbitals and the Natural Minimal Basis 29... 

NATURAL ATOMIC ORBITALS AND THE NATURAL MINIMAL BASIS... 

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