Atomic natural orbital

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

Natural Atomic Orbital and Natural Bond Orbital Analysis... 

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. 

The Natural Atomic Orbitals for atom A in the molecular environment may be defined as those which diagonalize the block, NAOs for atom B as those which diagonalize the D block etc. These NAOs will in general not be orthogonal, and the orbital oecupation numbers will therefore not sum to the total number of electrons. To achieve a well-defined division of the electrons, the orbitals should be orthogonalized. 

NATURAL ATOMIC ORBITAL AND NATURAL BOND ORBITAL ANALYSIS... 

Ab initio calculations (MP2/6-31G ) of the parent compound of 8 revealed that the most stable arrangement of the dimer adopts Dih symmetry (Fig. 5). Interestingly, the four Li ions and the two phosphorus centers constitute an octahedral skeleton with relatively short Li-Li and Li-P distances of 2.645 and 2.458 A, respectively. Charge analysis (22) undoubtedly supports the electrostatic bonding model for this system because of the high net charges of the natural atomic orbitals (NBO) at Li (+0.768) and P (-1.583), while NBO-Lewis resonance structures support stabilization through delocalization (Fig. 5). 

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. 

Selected Natural Atomic Orbital Occupancies of re-Type Orbitals Calculated by Natural Orbital Population Analysis"... 

Natural Atomic Orbital and Natural Bond Orbital Analysis 230 9.7 Computational Considerations 232 9.8 Examples 232 References 234 10 Molecular Properties 235 104 Examples 236 References 294 12 Transition State Theory and Statistical Mechanics 296 12.1 Transition State Theory 296 12.2 Statistical Mechanics 298 12.2.1 ans 299 12.2.2 300... 

WAVE FUNCTION ANALYSIS Qfl NATURAL ATOMIC ORBITAL AND NATUFIAL BOND ORBITAL ANALYSIS 231... 

The Natural Atomic Orbitals for atom A in the molecular environment may be defined as those which diagonalize tire block, NAOs for atom B as lliose which diagonalize... 

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. 

By analogy, the natural atomic orbitals are the atomic orbitals having maximal occupancy and are obtained as eigenfunctions of atomic subblocks of the density matrix, instead of the entire density matrix. The trick is to define these subblocks and then obtain eigenfunctions that are orthonormal not only within the subblock, but with all other eigenfunaions. 

The approach to the parameters of the ligand field is not restricted to the DFT method. The procedure in The LFDFT- an attempt to revive LFT can instead be combined with any method for electronic structure, supposing that it is able to yield (after some averaging) reasonable LF orbitals and effective LF matrix elements. Thus DFT failed badly for rare earths [32, 88, 89]. For that purpose we applied a spectroscopically adjusted extended Htickel model [90]. Alternatively, one can proceed beyond LFT and take average natural atomic orbitals resulting from an average multi-configurational procedure, such as SORCI, and calculate all matrix elements of both one- and two-electron operators. 

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]. 

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