Orbitals different criteria

Symmetry and stability analysis. The semi-empirical unrestricted Hartree-Fock (UHF) method was used for symmetry and stability analysis of chemical reactions at early stage of our theoretical studies.1,2 The BS MOs for CT diradicals are also expanded in terms of composite donor and acceptor MOs to obtain the Mulliken CT theoretical explanations of their electronic structures. Instability in chemical bonds followed by the BS ab initio calculations is one of the useful approaches for elucidating electronic structures of active reaction intermediates and transition structures.2 The concept is also useful to characterize chemical reaction mechanisms in combination with the Woodward-Hoffman (WH) orbital symmetry criterion,3 as illustrated in Figure 1. According to the Woodward-Hoffmann rule,3 there are two types of organic reactions orbital-symmetry allowed and forbidden. On the other hand, the orbital instability condition is the other criterion for distinguishing between nonradical and diradical cases.2 The combination of the two criteria provides four different cases (i) allowed nonradical (AN), (ii) allowed radical (AR), (iii) forbidden nonradical (FN), and (iv) forbidden radical (FR). The charge and spin density populations obtained by the ab initio BS MO calculations are responsible for the above classifications as shown in Fig. 1. 

A two-dimensional Httckel molecular orbital (HMO) theory approach to acetylenic systems yielded n-bond orders of P = 0.894 for the central C—C bond and P = 1.788 for the C C triple bonds in 1,3-butadiyne (209, 210). For comparison, P = 1 for ethylene and P = 2 for acetylene. A different criterion for determining the relative strengths of chemical bonds was used by Politzer and Ranganathan (17). Starting from STO-3G geometries and force constants, they calculated a bond order of 1.34 for the central C-C bond in diacetylene. This corresponds to a bond dissociation energy of 150 kcal/mol [211], which compares with bond orders and bond dissociation energies of 1.14 and 88 kcal/mol for ethane and 1.85 and 163 kcal/mol for ethylene. 

The calculation mixes all single determinant wavefunctions that can be obtained from the ground state by exciting electrons from a subset of the occupied orbitals (of the ground state) to a subset of the unoccupied orbitals. The subsets are specified as a fixed number (highest occupied or lowest unoccupied) or by an energy criterion associated with the energy difference between the occupied orbital and the unoccupied orbital. 

Del Re and coworkers [131] were concerned with the relation of s character in hybrids to bond angles and have considered hybridization as described by local orbitals, determined by requiring that hybrids on different atoms have minimal overlap unless they participate in the same bond. Alternate approaches are provided by the bond index of Wiberg [132] and by the Trindle-Sinanoglu procedure [133] for the application of the physical criterion of Lennard-Jones and Pople [134,135], requiring that an electron in a localized orbital interact maximally with the electron sharing that orbital. 

The first criterion really related to the content of this book is the analysis of T and 72. As the dominant contribution to nuclear relaxation is dipolar in nature, Tfl and linewidths will decrease as we move farther from the paramagnetic center. Even the contact contribution to relaxation often decreases with the number of chemical bonds from the paramagnetic center. A caveat, however, should be given. Spin density transfer causes ligand-centered relaxation. Significant spin density on ax orbital of an sp2 carbon may relax an attached proton more than the paramagnetic center itself, owing to the different distances and to the sixth power dependence on distance. 

For media more complicated than hydrogen, where the electrons may have different orbital velocities, the Bohr criterion alone is not enough. At present we have no good theory that would explain the influence of a... 

D. Dohnert, J. Koutecky, J. Am. Chem. Soc. 102, 1789 (1980). Occupation Numbers of Natural Orbitals as a Criterion for Biradical Character. Different Kinds of Biradicals. 

The g-values of most organic free radicals are within 2% of the free electron value and thus do not provide a potentially powerful criterion for radical identification. However, Norman and Pritchett (115) have noted that substitution of hydroxy or alkoxy groups on the a-carbon in simple hydrocarbon radicals increases the g-value by about 0.001, while a-aldehydic or ketonic groups increase the value still higher, about 0.002. It has already been mentioned in Section II.B.2 that because of large spin-orbit coupling, most radicals with spin localized or heteroatoms, such as oxygen and sulfur, have g-values appreciably different from that of a free electron. These... 

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