Bond orbitals and lone pairs

Bonds interact with one another in molecules. The bond interactions are accompanied by the delocahzation of electrons from bond to bond and the polarization of bonds. In this section, bond orbitals (bonding and antibonding orbitals of bonds) including non-bonding orbitals for lone pairs are shown to interact in a cychc manner even in non-cychc conjugation. Conditions are derived for effective cychc orbital interactions or for a continuous orbital phase. 

Electron-donating orbitals are those occupied by electrons, i.e., bonding orbitals of bonds, non-bonding orbitals of lone pairs, HOMOs of molecnles, gronps and others. Electron-accepting orbitals are vacant orbitals, i.e., antibonding orbitals of bonds, vacant atomic orbitals on cationic centers, LUMOs of molecnles, gronps, etc. 

With accurate calculated barriers in hand, we return to the question of the underlying causes of methyl barriers in substituted toluenes. For simpler acyclic cases such as ethane and methanol, ab initio quantum mechanics yields the correct ground state conformer and remarkably accurate barrier heights as well.34-36 Analysis of the wavefunctions in terms of natural bond orbitals (NBOs)33 explains barriers to internal rotation in terms of attractive donor-acceptor (hyperconjuga-tive) interactions between doubly occupied aCH-bond orbitals or lone pairs and unoccupied vicinal antibonding orbitals. 

The NBOs are an optimized set of localized bonding, antibonding, and lone pair orbitals. The bond orbitals typically have occupancies of 1.98e in molecules with one simple Lewis structure. In C2H6, Weinhold and coworkers36 have shown that the barrier height V3 = 1025 cm-1 can be understood in the NBO terms in the form of aCH — donor-acceptor interactions. When the corresponding off-diagonal... 

Rule 1 Both sigma bonding electrons and lone pairs can occupy hybrid orbitals. The number of hybrid orbitals on an atom is computed by adding the number of sigma bonds and the number of lone pairs of electrons on that atom. 

In order to produce qualitative information about bonding patterns and lone pairs, MO theory has to resort to orbital localisation procedures or more complicated interpretation techniques such as, for example, Bader s Atoms in Molecules (AIM) approach.However, orbital localisation procedures can be applied only to wavefunctions which remain invariant with respect to non-singular linear transformations of the orbitals, i.e. single-configuration and complete-active-space (CAS) MO wavefunctions and even for these, the use of orthogonal localised orbitals is not sufficient to reproduce all of the chemically-important information included in modern VB wavefunctions. Evidence of the superiority of the interpretational facilities offered by VB wavefunctions is provided by the continuing efforts to transform CAS wavefunctions to VB-style... 

Fig. 10.12. The VSEPR model for Sn surrounded by four bonding orbitals, one lone pair orbital (indicated by LP) and two secondary bonds (broken lines)...

In NH, two valence MOs, corresponding to the N-H bond (2a) and lone pair on nitrogen (3a), are occupied by electron pairs. Two more valence electrons must be distributed between two degenerate, nonbonding molecular orbitals (NBMOs), Tlx, Ky, which consist of the 2px and 2py AOs on... 

Fluorine, chlorine, bromine, and iodine are collectively known as the halogens. HF, HCl, HBr, and HI are called hydrogen halides. Bond angles will not help us determine the orbitals involved in a hydrogen halide bond, as they did with other molecules, because hydrogen halides have only one bond. We do know, however, that bonding electrons and lone-pair electrons position themselves to minimize electron repulsion (Section 1.6). If the three lone pairs were in sp orbitals, they would be farther apart than they would be if one pair resided in an s orbital and the other two pairs resided in... 

The exploitation of localized orbitals for dispersion energy calculations has already been proposed since the early works on local correlation methods [41 5]. In classical and semiclassical models most often the atoms are selected as force centers only a few works exploit the advantages related to the use of two-center localized orbitals and lone pairs. A notable exception is the recent work of Silvestrelh and coworkers [46-50], who adapted the Tkatchenko-Scheffler model [16] for maximally localized Wannier functions (MLWF), which are essentially Boys localized orbitals for solids. It is worthwhile to mention that one of the very first use of the bond polarizabilities as interacting units for the description of London dispersion forces has been suggested as early as in 1969 by Claverie and Rein [51] see also [52],... 

For the molecule MeNHj, generate an orbital representation. Label bonds as o or %, and state which orbitals were used to make them (s, p, sp, sp, sp ). Mark empty orbitals and lone pairs, and state their type. 

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