Orbitals for bonding

N, 0, F, P, S, and Cl the bond orbitals for normal valence compounds lead to about the same radii as tetrahedral orbitals, whereas in atoms below these in the periodic system normal valence bonds involve orbitals which approach p-orbitals rather closely, and so lead to weaker bonds, and to radii larger than the tetrahedral radii. This effect should be observed in Br, Se, and As, but not in Ge, and in I, Te, and Sb, but not Sn. For this reason we have added 0.03 A to the tetrahedral radii for As and Se and... 

After rising at copper and zinc, the curve of metallic radii approaches those of the normal covalent radii and tetrahedral covalent radii (which themselves differ for arsenic, selenium, and bromine because of the difference in character of the bond orbitals, which approximate p orbitals for normal covalent bonds and sp3 orbitals for tetrahedral bonds). The bond orbitals for gallium are expected to be composed of 0.22 d orbital, one s orbital, and 2.22 p orbitals, and hence to be only slightly stronger than tetrahedral bonds, as is indicated by the fact that R(l) is smaller than the tetrahedral radius. 

It is interesting that a straight line drawn through the tetrahedral radii passes through the metallic radius for calcium this suggests that the metallic bonding orbitals for calcium are sp orbitals, and that those for scandium begin to involve d-orbital hybridization. 

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. 

A simple symmetry-based analysis of the bonding orbitals for the carbene and metal fragments of a trigonal bipyramidal d8 complex suggests that the vertical orientation (i) should be preferred (100) ... 

The use of MO theory to find deep minima in the So surface, or geometries of stable molecules, is well known. A simplified rule would be to choose the geometry so as to allow efficient overlap of valence orbitals of the constituent atoms in a way giving bonding orbitals for all available electrons from pairs or larger sets of suitably hybridized atomic orbitals. No atomic orbitals occupied by one electron should be left over dangling free and unable to interact with others, since that would give radicals, biradicals, etc. Chemical intuition allows one to proceed almost automatically in cases of molecules of familiar types. 

TABLE 3. Hybridizations of bonding orbitals for cr-bonds from NBO (Natural Bond Orbital) analyses based on MP2/6-31G(d,p) optimized structures... 

We have outlined in the previous Section an efficient solution to the problem posed in (1). For the second point, one quickly realizes that the space 0 0 must take a full Cl (or, CASSCF) form, if no particular restrictions are to be placed on the valence bond orbitals. For the single-configuration spin-coupled wavefunction, there is for this reason an important link to N, N, A) CASSCF wavefunctions. 

The high electrical conductivity of lithium (and metals in general) indicates considerable electron mobility. This is consistent with the MO treatment of an infinite three-dimensional array of atoms, in which the 2s orbitals are completely delocalized over the system with the formation of a band of nil bonding orbitals and nil anti-bonding orbitals for the n atoms concerned. Figure 7.3 shows a simple representation of the... 

The first-row atoms can form no more than four stable bond orbitals. For the second-row atoms the and p orbitals of the M shell are much more stable than the d orbitals, and in general contribute preponderantly to the bond orbitals, but the promotion energy for the d orbitals (which also are in the M shell) is small enough to permit these orbitals to take a larger part in bond formation than for the first row atoms. 

The existence of compounds such as PF, PFiClj, PCI, [PF ] and SF suggests that one or two 3d orbitals are here being used together with the 3 orbital and the three dp orbitals (all hybridized to bond orbitals) for bond formation. It seems probable, however, that for fluo-... 

The molecule IF7 has the configuration of a pentagonal bipyramid five fluorine atoms are arranged in a belt in the equatorial plane about the iodine atom, and the other two are in the axial positions.84 The I—F bond lengths are about 1.85 A. Bond orbitals for this configuration have been reported by Duffey.86 The equatorial sp d orbitals have strength 2.976 and the axial orbitals have strength 2.920. 

For all three the cyanate group would be expected to be linear. Expected values of the H—N—C bond angle (unstrained) are 116° for A, 108° for B, and 180° for C (Sec. 4-8). Resonance among the three structures would lead to an averaged value of this angle. (The fourth structure, like A but with the double bond in the alternative planes, is not considered because it does not provide a bond orbital for the N—H bond.)... 

For a simple MO picture of molecular electronic structure, the same procedures can be followed to classify the symmetries spanned by bond and lone-pair orbitals. For instance, we can envisage the electronic structure of BF3 as involving sp2 hybridization of the atoms. We would then have B and three F Is core orbitals, two sp2 and one jr symmetry lone pair on each F atom, and three sp2 bond orbitals for the three BF bonds. Our analysis above shows that the four core orbitals comprise 2 a and a doubly degenerate e orbital the in-plane lone-pairs transform as a, a 2, and 2 e orbitals the out-of-plane lone pairs transform as a"2 and e" and the three BF bonds as a and e. ... 

LBO Localized bond orbital. For a given molecule, the LBOs can be obtained from the canonical MOs (CMOs) by a unitary transformation that does not change either the total energy or the total wave function. (See Chapter 3.)... 

The bond orbitals for graphite can accommodate three electrons per carbon atom. The remaining electrons go into p states oriented perpendicular to the plane in Fig. 3-10 and are analogous to the a states of diatomic molecules, as discussed in Chapter 1. The tc states are coupled by small matrix elements and broaden into a rather narrow band. There are enough electrons to half-fill this band (because of the two spin states). By filling only the lower half of the band these electrons... 

Bond orbitals for the SiOj bonding unit. All are doubly occupied. The antibonding combinations A. and A, obtained by reversing the sign of the p states in B and arc empty. 

By comparison of Eqs. (19-34) and (19-35) we. sec that the calculation based upon the chemical grip corresponds to the form we obtained from consideration of bond orbitals for tetrahedral solids with A equal to 7/12. In particular, we obtain the V2 0c dependence suggested in Eq. (8-15). 

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