Natural Atomic Orbital NAO

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

MacDonald s theorem, 408 Natural Atomic Orbital (NAO), 230 Pauli spin matrices, 205 (QM-MM) methods, 50 ... 

TABLE 4. Natural atomic orbital (NAO) occupancies, natural population of the MOs, summary of natural population analysis and MuUiken atomic charges of the electronic ground state of phenol... 

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. 

G and 6-31G basis sets [Ig], pp. 337-339). Other approaches to partitioning elecuons among orbitals and thus calculating charges and bond orders are the Lowdin method [167] and the natural atomic orbitals (NAO) population analysis of Weinhold [168]. 

Until recently the primary interest in the electronic stmcture calculations has been to derive partial charges on the imidazohum cation for use in classical simulations [11,13,14,16,62,83]. The charge distribution however depends strongly on the method of analysis. The Natural Atomic Orbital (NAO) [84-88] and MuUiken population analysis methods have been apphed to the imidazolium cations [16,64]. A number of methods have been used to determine partial charges from the electrostatic potential these also show significant variation. There is an especially large... 

Natural bond orbital (NBO) analysis The NBO analysis transforms the canonical delocalized Hartree-Fock (HF) MOs and non-orthogonal atomic orbitals (AOs) into the sets of localized natural atomic orbitals (NAOs), hybrid orbitals (NHOs), and bond orbital (NBOs). Each of these localized basis sets is complete, orthonormal, and describes the wavefunction with the minimal amount of filled orbitals in the most rapidly convergent fashion. Filled NBOs describe the hypothetical, strictly localized Lewis structure. NPA charge assignments based on NBO analysis correlate well with empirical charge measures. ... 

Table 8.1. Atomic charges in the 21 heteronuclear diatomic molecules formed hy comhination of H, the alkali metal Li, Na or K, and the halogen F, Cl or Br atoms experimental and calculated ionic characters, q Q atomic charges calculated by natural atomic orbital (NAO) analysis, and by topological analysis of the electron densities (AIM) [2]. All charges in atomic units. Note that the chemical formulae have been written in such a way that the atom carrying net positive charge is listed first.

An improvement on Mulliken population analysis (MPA) is natural population analysis (NPA) [A. E. Reed, R. B. Weinstcx k, and F. Weinhold, J. Chem. Phys., 83, 735 (1985)], which uses ideas related to natural orbitals (Pilar, Section 10-7). Here, one first calculates a set of orthonormal natural atomic orbitals (NAOs) from the AO basis set Xr The NAOs are then used to compute a set of orthonormal natural bond orbitals (NBOs), where each occupied NBO is classifiable as a core, lone pair, or bond orbital. Using these NBOs, one carries out a population analysis. NPA net atomic charges show less basis-set dependence than those from Mulliken population analysis. Other methods of assigning net atomic charges are discussed in the next section. Still another method of population analysis that yields net atomic charges is Lowdin population analysis (Cramer, Section 9.1.3.2). 

A more elaborate formalism, called natural population analysis (NPA), has been advanced by Weinhold and coworkers. In this formalism, atomic charges are computed as differences between nuclear charges and the respective sums of populations of natural atomic orbitals (NAOs). The NAOs, which form orthonormal sets, ate obtained from the... 

Narcissistic reaction, 420 Natural Atomic Orbital (NAO), 230 Natural bond length, 11 Natural Bond OrbiM (NBO), 230 Natural internal coordinates, for optimization, 327... 

Immediately below is the NATURAL POPULATIONS table of Natural Atomic Orbital (NAO) labels and occupancies (I/0-2.2). 

As before, the Natural Atomic Orbitals (NAOs) serve as the optimal effective atom-like orbitals for describing the overall electron density distribution of the molecular wavefunction, so that finding the atomic electrons in NBO output is not more difficult than in Chapter 2. We shall first examine how the NAOs within the molecular environment differ from the free-space forms encountered in Chapter 2. We use the experience gained there to anticipate the breathing ... 

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