Localized molecular orbital/generalized valence

Localized molecular orbital/generalized valence bond (LMO/GVB) method, direct molecular dynamics, ab initio multiple spawning (AIMS), 413-414 Longuet-Higgins phase-change rule conical intersections ... 

Molecular-orbital- versus valence-bond-type descriptions Let us now examine the connection between localized and delocalized descriptions in somewhat more formal terms, using the actual numerical energy levels of PtH42 to illustrate the formal connections. Inevitably, this discussion entails somewhat more technical detail concerning computational MO methodology than required elsewhere in this book, and we assume a general familiarity with Sections 1.4 and 1.5, Appendix A, and other sections mentioned below. 

The Fermi hole for the reference electron at a bonded maxima in the VSCC of the carbon atom has the appearance of the density of a directed sp hybrid orbital of valence bond theory or of the density of a localized bonding orbital of molecular orbital theory. Luken (1982, 1984) has also discussed and illustrated the properties of the Fermi hole and noted the similarity in appearance of the density of a Fermi hole to that for a corresponding localized molecular orbital. We emphasize here again that localized orbitals like the Fermi holes shown above for valence electrons are, in general, not sufficiently localized to separate regions of space to correspond to physically localized or distinct electron pairs. The fact that the Fermi hole resembles localized orbitals in systems where physical localization of pairs is not found further illustrates this point. 

It should be borne in mind that the resemblance of a Fermi hole density to that of a localized valence orbital is obtained only when the reference electron is placed in the neighbourhood of a local maximum in the VSCC. The Fermi hole and hence the density of the reference electron are much more delocalized for general positions throughout the valence region (see Fig. E7.4(f)). Localized molecular orbitals thus overemphasize electron localiz-ability and do not provide true representations of the extent to which electrons are spatially localized. 

A complete study of the molecular orbitals for an octahedral complex sue as [Cr(CN)6] or [Co(NH3)6] " " would require linear combinations of all the valence atomic orbitals of the metal and of the ligands. An approximation isl to take the metal valence a.o.s (nine a.o.s for a metal of the first transition series (five 3d orbitals, one 4s and three 4p orbitals)) together with six a.o.s from the ligands, one for each atom directly bonded to the metal atom. Ini general, these six a.o.s are quasi-localized molecular orbitals (see Chapter 8), which point from the ligand to the metal and have essentially non-bonding character ... 

To explain this type of structure we have chosen sodiiam chloride. The sodium atom has one valence electron and the chlorine atom, seven electrons. Each atom is surrounded by six neighbors of the other element. Consequently, in classical theory, it is impossible, with the eight available electrons, to build two electron bonds between the sodium and chlorine atoms and still respect the equivalence between the neighboring atoms. The situation is the same for localized molecular orbitals, doubly utilized. In return, it is possible to describe the system by means of four delocalized molecular orbitals, constructed on the s and p orbitals of each chlorine atom, as well as on the sp d2 hybrid orbitals of the neighboring sodium atoms pointing toward the chlorine atom. The delocalized system is constructed from ten atomic orbitals (hybrid or not). This structure is a generalization of the case of where each of two molecular... 

On a more qualitative level, the bonding in the more stable isomer lb can be explained on the basis of the general molecular orbital scheme for bent (C2v) metallocenes containing 14 valence electrons, as shown in Fig. 5. The localization of three electron pairs in bonding orbitals (lal, 2 i, 2b2) is primarily responsible for the Si-Cp interaction the absence of a silicon orbital of a2 symmetry imposes the presence of a ligand-based non-bonding orbital. Structural adjustment from D5d (ferrocene type) to C2v... 

Fig. 2. CASSCF, orthogonal localized, non-orthogonal localized, and generalized valence bond molecular orbitals for the hydrogen molecule.

As the next step, using a generalized version of Little s original propxal, we have to take into account that the atomic cores of the TCNQ molecules (containing besides the nuclei and the Is electrons also the valence shell electrons in the PFP approximation) provide a localized polarizable "side chain" electron system which may substantially reduce through its screening the repulsion between the Jtf -electrons. For the description of these electrons we applied LCAO molecular orbitals localized each on... 

The first quantum-mechanical treatment of the hydrogen molecule was by Heitler and London in 1927. Their ideas have been extended to give a general theory of chemical bonding, known as the valence-bond (VB) theory. The valence-bond method is more closely related to the chemist s idea of molecules as consisting of atoms held together by localized bonds than is the molecular-orbital method. The VB method views molecules as composed of atomic cores (nuclei plus inner-shell electrons) and bonding valence electrons. For H2, both electrons are valence electrons. 

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