Natural resonance theory

Finally, we show an illustrative open-shell CHOOSE key list for the alternative spin-flipped structure of ozone [Section 4.5 cf. (4.29)]  

Of course, this merely returns an identical structure to that shown in Section 4.5 (but with oc and spin output sections interchanged), corresponding to the equivalent weightings that such spin-flipped resonance structures are expected to have in a resonance-hybrid picture. 

Once you have gained some practice, the CHOOSE format will be found to offer convenient expression for Lewis structures of quite general form, including the exotic high-order (quadruple and higher) metal-metal bonds of transition metal 

Strictly speaking, Pauling s mathematical formulation of resonance theory did not behave as its author intended (Sidebar 5.3). However, the theory was initially applied only in a qualitative empirical fashion that obscured these difficulties. Nearly a half-century elapsed before reliable polyatomic calculations allowed a rigorous test of Pauling s approximations, by which time the qualitative concepts of Pauling s resonance theory had become firmly entrenched in chemistry textbooks in more or less present form. Although some theorists continue to believe that resonance concepts 

Performing NRT analysis of a modem wavefunction is typically as simple as inserting the NRT keyword into the NBO keylist. For formamide, for example, the NRT keyword leads first to summary search diagnostics, as shown in 1/0-5.12  

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Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

The natural resonance theory (NRT) method53 offers a convenient ab initio means to calculate such resonance weights from the D(true) density matrix for a [Pg.32]

Natural resonance theory (NRT) allows these conflicting pictures of the oxyan-ion electron distributions to be tested quantitatively.149 Table 3.36 compares the geometries, NRT bond orders, atomic charges, and d-orbital occupancies for a representative variety of first- and second-row XOm"+ species,... 

Natural resonance theory (Section 1.6) provides a quantitative gauge of the contributions of various resonance structures to the total electronic density. The results are shown in Table 4.41 demonstrating the remarkable intermediacy in the nature of metal-alkene interaction relating metallacycle, nonbonded, and carbanion-type resonance forms. 

Because we are both computational chemistry researchers, we have naturally directed the book also to specialists in this field, particularly those wishing to incorporate natural bond orbital (NBO) and natural resonance theory (NRT) analysis into their methodological and conceptual toolbox. Researchers will find here a... 

Quantum-chemical calculations for pyrylium including one, two, or three water molecules using DFT and 6-31 + G(d,p) basis set revealed that the aromaticity (estimated by harmonic oscillator stabilization energy, HOSE natural resonance theory, NRT harmonic oscillator model of aromaticity, HOMA and nucleus-independent chemical shifts, NICS) is not influenced by water molecules [82],... 

Natural resonance theory (NRT) is an optimal ab initio realization of the resonance weighting concepts expressed in Equation 7.10 and Equation 7.11. The necessary and sufficient condition that Equation 7.10 be satisfied for all possible density-related (one-electron) properties p is that the first-order reduced density operator be expressible as such a weighted average of localized density operators t... 

There has been a NPA analysis of the delocalization in amides. Both the planar and rotated forms of formamide and its =S, =Se, and =Te analogs were smdied by NPA and natural resonance theory. HF/6-31+G, MP2/6-31+G, and B3LYP/6-31+G calculations were employed. At the MP2/6-31+G level, the transfer of charge noted on going from the planar to rotated form of formamide was +0.105 at N, —0.088 at O, and -0.033 at C. This charge transfer is consistent with the resonance formulation. The shifts were in the same direction but somewhat larger for the heavier elements. 

The model most widely used to explain hypervalence is the three-center, four-electron (3c-4e) model of Rundle and Pimentel [5]. Coulson [31] analyzed the 3c-4e model and suggested a valence bond resonance model that shares some similarities with the MO model. Under this model, the bond is posited to arise primarily from resonance between F-X F and F X -F charge structures (with contributions from other charge configurations). Weinhold and Landis [32] incorporated natural bond orbital analysis and natural resonance theory in what is perhaps the most... 

Bean, G. 1998. Application of natural bond orbital analysis and natural resonance theory to delocalization and aromaticity in five-memhered heteroaromatic compounds. J. Org. 

SOME BASICS OF NATURAL RESONANCE THEORY VERSUS PAULING RESONANCE THEORY... 

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