Non-localized molecular orbitals

When considering the non-localized forms, it is convenient to form first the two possible group orbitals of the II3 group, viz., Is -j- Is and Is — Is. To do this automatically takes account ot tire, symmetry of the. molecule. The components from which the non-localized molecular orbitals are built may then be written as follows ... 

These m.o.s are symbolically represented in Fig. 9.8. We have non-localized molecular orbitals that are again non-localizable. 

The second situation referred to above, viz systems containing conjugated double bonds, is perhaps more important to the present discussion. The classical example of such a system is benzene. The molecular orbital treatment regards the six G—G bonds and the six G—H bonds as completely localized molecular orbitals compounded out of carbon sp2 hybrid atomic orbitals and the hydrogen s orbital. So far the treatment is identical with the electron pair theory, discussed in Chapter 4. The G—G bonds will be or bonds formed by the overlap of two sp2 hybrid atomic orbitals, one from each carbon atom and the C—H bonds will also be a bonds formed by the overlap of one sp2 hybrid atomic orbital of carbon with the s atomic orbital of hydrogen. The six carbon 2p atomic orbitals that remain will form completely non-localized molecular orbitals. Thus each 2pt electron will be regarded as existing in the field of six nuclei and will possess a wave function of the form ... 

Relationship between localized and non-localized molecular orbital... 

Fig. 9 may be viewed, also, as a localized molecular orbital representation of, e.g., a hydrocarbon (cf. Fig. 13, ref. 7). Thus, replacement of (i) the domains of the Si4+ cations (the atomic cores of silicon atoms) by the domains of C4+ cations (the atomic cores of carbon atoms r = 0.15 A 2>), (ii) the domains of the bridging (i.e., bonding) oxide ions by the domains of the electron-pairs of aliphatic carbon-carbon single bonds (r 0.6e A 40)), and (iii) the domains of the non-bridging oxide ions by the domains of the protonated electron-pairs of carbon-hydrogen bonds... 

The effect of relativity on the bonding in this molecule is so large that even the qualitative features of the bonding cannot be correctly described by non-relativistic theory which (i) fails to predict any 5d-6s hybridization in the localized bonding orbital (ii) seriously underestimates 5d-6s hybridization in one of the nonbonding orbitals (NBOs) (iii) predicts incorrectly that one of the orbitals with mj 1/2 is entirely tt in character and has pure spin and (iv) erroneously predicts that the bond (in AuH) is formed solely from the interaction between the gold 6s and the hydrogen Is atomic orbitals because the non-relativistic molecular orbital (MO) wavefunction constructed from these two atomic orbitals predicts the AuH molecule to be unbound by 0.19 eV. 

Among the 12 occupied m.o.s, the three tt m.o.s - one bonding and two non-bonding - are not only non-localized but also non-localizable. That is, it is not possible to make a unitary transformation with them that leads to three localized molecular orbitals . 

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 residual interactions (12.17) between localized molecular orbitals are important even in the case of coupling between directly bonded atoms, such as and C. The Vch values for the non-strained hydrocarbons CH4, C2H4, and C2H2 are, respectively, 125 Hz, 156 Hz and 248 Hz. These values are almost exactly proportional to the s-character p of the hybrid orbitals sp (p= 1/4), sp p= 1/3) and sp (p= 1/2) ... 

Three equivalent molecular orbitals almost localized in the three N-H bonds and an approximately non-bonding molecular orbital almost localized in the N atom. Since the bond angles (107°) are very close to those for the axes of sp atomic orbitals, the non-bonding orbital can be considered approximately as an sp hybrid orbital of N. Each one of the bonding molecular orbitals is approximately the combination of a Is orbital of H with an sp orbital of N. 

HONDO = bond orbital - neglect of differential overlap (SCF-MO) GIAO = gauge-including atomic orbital L = Lewis-type (or localized) LC-BO = linear combination of bond orbitals LCNBO = linear combination of NBOs LMO = localized molecular orbital MSPNBO = maximum spin-paired NBO NBBP = natural bond-bond polarizability NBO = natural bond orbital NCS = natural chemical shielding NEDA = natural energy decomposition analysis NHO = natural hybrid orbital NL = non-Lewis-type (or... 

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