Natural Rydberg 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. 

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... 

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... 

The Natural Bond Orbital analysis of Weinhold [Foster and Weinhold, 1980 Reed, Weinstock etal., 1985 Reed, Curtiss etal., 1988] generates, departing from canonical MOs, a set of localized one center (core, lone pairs) and two center (jt and a bonds) strongly occupied orbitals, and a set of one center (Rydberg) and two center (a, Jt ) weakly occupied orbitals the NBOs. The Natural Bond Orbitals (NBOs) are obtained by a sequence of transformations from the input basis to give, first, the Natural Atomic Orbitals (NAOs), then the Natural Hybrid Orbitals (NHOs), and finally the Natural Bond Orbitals (NBOs). For NAOs, atomic charges can be calculated as a summation of contributions given by orbitals localized on each atom moreover, from NBOs, bond order can be also calculated. 

It is, however, also clear that quantitative results can be obtained only when the basis sets are large enough to treat the different types of excited states on a comparable level of accuracy. This means that the basis set must be able to describe equally well valence and Rydberg states, and flexible enough to cover states of an ionic nature at the same time as less diffuse covalent states. 

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