Localized molecular orbitals valence bonds

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

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 ... 

All lone pair orbitals have a node between the two atoms and, hence, have a slightly antibonding character. This destabilizing effect of the lone pair localized molecular orbitals corresponds to the nonbonded repulsions between lone pair atomic orbitals in the valence bond theory. In the MO theory all bonding and antibonding resonance effects can be described as sums of contributions from orthogonal molecular orbitals. Hence, the nonbonded repulsions appear here as intra-orbital antibonding effects in contrast to the valence-bond description. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

The complete active space valence bond (CASVB) method [1,2] is a solution to this problem. Classical valence bond (VB) theory is very successful in providing a qualitative explanation for many aspects. Chemists are familiar with the localized molecular orbitals (LMO) and the classical VB resonance concepts. 

We have proposed two types of CASVB method. The first one is a method where the valence bond structures are constructed from orthogonal localized molecular orbitals (LMOs) [1], and the second is one from nonorthogonal localized molecular orbitals [2]. 

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

Considering B4H8 or B R in terms of localized molecular orbitals (LMO), the 24 available atomic orbitals and the 20 available valence electrons must be organized in four (3c2e) and six (2c2e) molecular bonds. The only bicyclobutane-type structure in accord with these simple requirements is the one found by theory and by experiment (Fig. 5). 

Certainly one of the first conceptual problems which arises if one describes the ground state of a molecule in terms of Q-bonds is how to obtain a compatible description of the excited states and ion states which may have B, IT, or A symmetries. A discussion of how a compatible description is obtained has been given recently 11). However, since it is important for later discussions in this work, especially with respect to the connection between valence bond theory, localized molecular orbitals (LMOs) and canonical molecular orbitals (CMOs), a brief account is provided here. 

We now outline two approaches to a description of valence in the boron hydrides. The first employs three-center bonds. This particular kind of localized molecular orbital seems most suitable for the smaller, more open hydrides. Its use in the more complex hydrides will require delocalization of the bonding electrons either by a molecular orbital modification or a resonance description. The second approach is simply that of molecular orbitals, which is particularly effective in the more condensed and symmetrical hydrides. These approaches merge as the discussion becomes more complete. It is an important result that filled orbital descriptions are obtainable for the known boron hydrides. Also some remarks about charge distribution in the boron hydrides are possible. But the incompleteness of this valence theory in this nontopological form is indicated by the lack of a large number of unknown hydrides, whose existence would be consistent with these assumptions. 

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. 

In Chapter 9, we found that some geometrical arrangements of nuclei do not allow an equivalent set of localized molecular orbitals to be defined. In such cases, there are non-localizable canonical m.o.s these structures are presented as resonant hybrids in the classical valence-bond description. 

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 ... 

The canonical m.o.s of diamond are delocalized over the entire crystal. However, as we have seen in Chapter 8 for other systems, the occupied m.o.s can be the object of a unitary transformation leading to a set of equivalent and quasi-localized molecular orbitals . This is why the structure of diamond can (for some purposes) be described in terms of the overlap of sp hybrid orbitals, four for each C atom. As we have seen in Chapter 8, we must stress that such an alternative description cannot be used to infer information about electron energies. In particular, the localized bond description of the structure of diamond does not imply that all valence electrons have the same energy. This would be the case only if the sp -sp bonds were independent. It is because of residual interactions such as f and (3"... 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

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