Orbital hybridization notation

A. Structure, Bonding, and Nomenclature — Lewis structures, orbital hybridization, configuration and stereochemical notation, conformational analysis, systematic IUPAC nomenclature, spectroscopy (IR and 3H and 13 C NMR)... 

Figure 6. Top 1-4 interactions between hybrid orbitals on neighboring Si atoms. Bottom The frontier orbitals of three conformers of SiJ0H<2 in the notation of Figure...

The VSEPR notation for the Cl2F+ ion is AX2E3. According to Table 11.1, molecules of this type exhibit an angular molecular geometry. Our next task is to select a hybridization scheme that is consistent with the predicted shape. It turns out that the only way we can end up with a tetrahedral array of electron groups is if the central chlorine atom is sp3 hybridized. In this scheme, two of the sp3 hybrid orbitals are filled, while the remaining two are half occupied. 

The possible donor-acceptor interactions among the valence hybrids are constrained by diatomic symmetry to the five possible combinations shown in Table 3.14. For simplicity, we shall temporarily suppress the subscript atoms in the NBO symbols (which are now simply indicated as a, nx,...). We also introduce a special typographic convention to denote each type of NBO (curved bonds for 7tx and ny, opposed arrows for complementary y and y, and so forth), as shown in Table 3.14. (The corresponding typographic convention for nonbonded NBOs will consist of a short bar on the atomic symbol, A for hn, A for pA, and A for py.) We also employ the convention of attaching an asterisk ( ) to denote an unfilled orbital, i.e., an orbital that is formally serving as an acceptor in a donor-acceptor interaction (the star says I m empty ). Thus, the notation px —> pf denotes an interaction from a filled pA orbital on the first atom to an unfilled pA on the second atom.46... 

In the previous section we used quaternions to construct a convenient parameterization of the hybridization manifold, using the fact that it can be supplied by the 50(4) group structure. However, the strictly local HOs allow for the quaternion representation for themselves. Indeed, the quaternion was previously characterized as an entity comprising a scalar and a 3-vector part h = (h0, h) = (s, v). This notation reflects the symmetry properties of the quaternion under spatial rotation its first component ho = s does not change under spatial rotation i.e. is a scalar, whereas the vector part h — v — (hx,hy,hz) expectedly transforms as a 3-vector. These are precisely the features which can be easily found by the strictly local HOs the coefficient of the s-orbital in the HO s expansion over AOs does not change under the spatial rotation of the molecule, whereas the coefficients at the p-functions transform as if they were the components of a 3-dimensional vector. Thus each of the HOs located at a heavy atom and assigned to the m-th bond can be presented as a quaternion ... 

We now apply our model to investigate the formation of four C-H bonds in the methane molecule CH4 of symmetry Tc (Magnasco, 2004a). For this molecule, tetrahedral sp3 hybridization is completely determined by molecular symmetry. We use the usual notation for the eight valence AOs, callings, x, y, zthe2s and 2p orbitals on C, and h, h2,h3, h4 the Is orbitals on the H atoms at the vertices of the tetrahedron (Figure 2.14). Molecular... 

The notation sp means that one s atomic orbital and one p atomic orbital mix to form a set of two hybrid orbitals with different directional properties. 

Recall the shorthand notation used for benzene.) (a) What is the hybridization at the N atom in each of the substances (b) How many unhybridized atomic orbitals are there on the N and the C atoms in each of the substances (c) Predict the N — N — C angles in each of the substances, (d) Azobenzene is said to have greater delocalization of its Tr electrons than hy-drazobenzene. Discuss this statement in light of your answers to (a) and (b). (e) All the atoms of azobenzene lie in one plane, whereas those of hydrazobenzene do not. Is this observation consistent with the statement in part (d) (f) Azobenzene is an intense red-orange color, whereas hydrazobenzene is nearly colorless. Which molecule would be a better one to use in a solar energy conversion device (See the Chemistry Put to Work box for more information about solar cells.)... 

Fe—NO complexes also exhibit unique electronic structures due to the noninnocent nature of the nitrosyl ligand. The electrons in the Fe—NO bond are highly delocahzed and thus assignment of oxidation state in these systems is challenging and resonance structures are often proposed. For example, a complex may be described as a resonance hybrid between Fe(II)-NO <-> Fe(III)—NO a total of six electrons in the Fe 3d and NO Jt orbitals. In light of the extent of electron delocalization and difficulty in assigning oxidation state, Enemark and Feltham devised the generic notation (or EF notation) MNO, where x is the total sum of the Md and... 

The approximation method of choice is the LCAO-MO method, which is an acronym that stands for linear combinations of atomic orbitals to make molecular orbitals. Unlike VBT, however, the linear combinations used to construct MOs derive from the AOs on two or more different nuclei, whereas the linear combinations used to make hybrid orbitals in VBT involved only the valence orbitals on the central atom. Using the variation theorem, the energy of a particle can be determined from the integral in Equation (I0.I2), which is also written in its Dirac (or bra-ket) notation. 

Fig. 29 (a) The molecular structure of [Cp2Rh3(CO)4] . The electronic structures of (b) [Rh(t-CO)2(RhCp)2] and (c) [Cp2Rh3(CO)4] . Only unused hybrid orbitals are presented and the exact order of occupied orbitals could be different, (d) Visualized HOMO and HOMO-1 of [Cp2Rh3(CO)4] . The notations AB and B refer to bonding and antibonding interactions between Rhi and Rh2. The notations and d 2 refer to the orbitals dominated by the respective atomic orbitals of Rhs. Ip (in-plane) and op (out-of-plane) orbitals are w.r.t. RhiRh2CO plane... 

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