Hybrid orbitals water

To improve our model we note that s- and /7-orbitals are waves of electron density centered on the nucleus of an atom. We imagine that the four orbitals interfere with one another and produce new patterns where they intersect, like waves in water. Where the wavefunctions are all positive or all negative, the amplitudes are increased by this interference where the wavefunctions have opposite signs, the overall amplitude is reduced and might even be canceled completely. As a result, the interference between the atomic orbitals results in new patterns. These new patterns are called hybrid orbitals. Each of the four hybrid orbitals, designated bn, is formed from a linear combinations of the four atomic orbitals ... 

For example, we can construct hi and h2, two hybrid orbitals for describing the bonds in the water molecule, by taking the two combinations... 

Let us consider the simplest possible case of a system which consists of two orbitals, XA( 1) and / (I), with energies eA and which can interact. It should be emphasized here that these may be orbitals of any kind, atomic orbitals, group orbitals, or complicated MOs. We wish to investigate the results of the interaction between them, that is, what new wave functions are created and what their energies are. Let us also be clear about what the subscripts A and represent. The subscripts denote orbitals belonging to two physically distinct systems the systems, and therefore the orbitals, are in separate positions in space. The two systems may in fact be identical, for example two water molecules or two sp3 hybrid orbitals on the same atom or on different but identical atoms (say, both C atoms). In this case, eA = - Or the two systems may be different in... 

In hybridizations involving nonequivalent hybrid orbitals, such as sp tl, it is usually possible to resolve the set of hybrid orbitals into subsets of orbitals that are equivalent within the subset, as the sp2 subset and the dp subset. We have seen (Chapter 5) that the nonequivalent hybrids may contain fractional s and p character, e.g., the water molecule which uses bonding orbitals midway between pure p and sp3 hybrids. For molecules such as this, we can divide the four orbitals into the bonding subset (the bond angle is 1041°) and the nonbonding subset (angle unknown). We can then apply Eq. 6.1 to each subset of equivalent orbitals. In water, for example, the bond angle is 1041°, so... 

The carbon-oxygen double bond in aldehydes and ketones is similar and can be described in either of these two ways. If we adopt the iocalised-orbital description, formaldehyde will have two directed lone pairs in place of two of the C-H bonds in ethylene. In this case the axes of these hybrid orbitals will be in the molecular plane (unlike the oxygen lone pairs in water). Either the components of the double bond or the lone pairs can be transformed back into symmetry forms. The alternative description of the lone pairs would he one er-type along the 0-0 direction and one jr-type with axis perpendicular to the 0-0 bond hut in the molecular plane. It is the latter orbital which has the highest energy, so that an electron is removed from it in. ionisation or excitation to the lowest excited state. 

The values of 6 are estimated by methods described in the Appendix this gives 6 = 0.455 for the sp oxygen hybrid orbital and 8 = tt/4 for the sd vanadium hybrid orbital The tetrahedral hybrid, 6 — 7r/6, is used for the water oxygen c orbital... 

Note the differences between crystal field theory and valence bond theory. In crystal field theory, there are no covalent bonds, no shared electrons, and no hybrid orbitals—just electrostatic interactions within an array of ions. In complexes that contain neutral dipolar ligands, such as H20 or NH3, the electrostatic interactions are of the ion-dipole type (Section 10.2). For example, in [Ti(H20)g]3+, the Ti3+ ion attracts the negative end of the water dipoles. 

We conclude this section by discussing systems where there are two types of hybrid orbitals. One such example is NIH, where there are three equivalent bond hybrids and one lone pair hybrid. Another example is the water molecule. As shown in Fig. 3.4.11, hybrids hi and/12 are lone pairs orbitals, while hybrids... 

Both the nitrogen atom in ammonia and the oxygen atom in water form sp3 hybrid orbitals. 

Unlike carbon, which has four valence electrons to be distributed among the four equal hybrid orbitals, nitrogen has five electrons to fill those orbitals. That means one of the orbitals has a complete pair of electrons. The extra repulsion that results from that complete pair of electrons pushes the other bonds slightly away. If there were no such extra repulsion, the angle between Fi H< e3.32 the hybrid orbitals would be 109.5 degrees (refer back to the discussion of water molecules in this chapter). 

There are two alternative approaches to hybridization for the water molecule. For example, the electron pairs around the oxygen atom in water can be considered as having nearly tetrahedral symmetry (counting the two lone pairs and the two bonds equally). All four valence orbitals of oxygen are used, and the hybrid orbitals are sp. The predicted bond angle is then the tetrahedral angle of 109.5° compared with the experimental value of 104.5°. Repulsion by the lone pairs, as described in the VSEPR section of Chapter 3, is one explanation for this smaller angle. 

The concept of hybridization of atomic orbitals was subsequently introduced, in an attempt to interpret the difference between the actual bond angle for the water molecule and the value of 90° considered in the previous model. This concept had already been introduced to interpret, for example, the tetrahedral geometry of the methane molecule. We shall come back to this subject later in the chapter, to conclude that, although it is possible to establish a correlation between molecular geometry and hybrid orbitals, it is not correct to take the latter as the basis of an explanation of the former. This distinction is very important in teaching. 

FIGURE 8.32 Overlap of metal orbitals with ligand orbitals to form a bonds. The ligand orbitals can be either p or hybrid orbitals (e.g., sp for water), and thus they are represented only schematically. 

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