Natural atomic orbital analysis

Table 10 Fluorinated methanes mean bond energies MBE) of GEL, and CF4 and C-F thermo-chemical bond energies (TBE) of CEL,. F , = 1 to 3 and net atomic charges obtained by natural atomic orbital analysis (NAO) of calculated electron densities [65]...

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. 

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). 

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... 

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. 

It is instructive to study the vacant atomic orbital population in dimers and trimers. As mentioned in the Introduction, in the 80 s Bauschlicher et al. [10,11] came to the conclusion that the promotion of ns-electrons to np-orbitals leading to sp-hybridization is the main mechanism responsible for binding in alkaline-earth clusters. This conclusion was based on a study of the SCF Mulliken population analysis for tetramers, which are stable at the SCF level. At present, we can perform more precise analysis using the Natural Bond Orbital Analysis and calculate it at the electron correlation level. 

Table VI The net valence population, An , for the isolated atoms and clusters at the equilibrium geometry, obtained by the Natural Bond Orbital Analysis at the SCF and MP4 levels.

It is important to check is the effect of a rather large population of vacant atomic orbitals at the electron correlation level specific for alkaline-earth atoms or it has a general character. In Table VII we present the results of net valence population calculations for noble-gas atoms performed by the Natural Bond Orbital Analysis at the MP4 level. We found non-negligible valence orbital population, especially for the d-orbitals. The results obtained for three different basis sets are quite close. Thus, the population of vacant orbitals in noble-gas atoms is not an artifact of the calculations. From this follows that elements traditionally assumed as closed-shell (noble gases) or closed-subshell (alkaline earths) atoms can to some extent manifest an anisotropic p-or d-symmetry behavior. It would be very interesting to obtain experimental evidence confirming this theoretical prediction. 

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... 

---