Orbitals and Hybridization States

To determine the geometry of a molecule, we need to know how atoms bond with each other three dimensionally, so it makes sense for our discussion to start with orbitals. After all, bonds come from overlapping atomic orbitals. 

A bond is formed when an electron of one atom overlaps with an electron of another atom. The two electrons are shared between both atoms, and we call that a bond. Since electrons exist in regions of space called orbitals, then what we really need to know is what are the locations and angles of the atomic orbitals around every atom It is not so complicated, because the number of possible arrangements of atomic orbitals is very small. You need to learn the possibilities, and how to identify them when you see them. So, we need to talk about orbitals. 

There are two simple atomic orbitals i and p orbitals (we don t really deal with d and/orbitals in organic chemistry), i orbitals are spherical and p orbitals have two lobes (one front lobe and one back lobe)  

Atoms in the second row (such as C, N, O, and F) have one s orbital and three p orbitals in the valence shell. These orbitals are usually mixed together to give us hybridized orbitals (sp, sp, and sp). We get these orbitals by mixing the properties of i and p orbitals. What do we mean by mixing  

To truly understand the geometry of bonds, we need to understand the geometry of these three different hybridization states. The hybridization state of an atom describes the type of hybridized atomic orbitals (ip, sp, or sp) that contain the valence electrons. Each hybridized orbital can be used either to form a bond with another atom or to hold a lone pair. 

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The theory of chemical bonding is overwhelmed by a host of insurmountable obstacles the real orbitals and hybrids of LCAO have no physical, chemical or mathematically useful attributes - certainly not in the quantum-mechanical sense the distribution of electron density between atoms, in the form of spin pairs, is an overinterpretation of the empirical rules devised to catalogue chemical species the structures, assumed in order to generate free-molecule potential fields, are only known from solid-state diffraction experiments the assumption of directed bonds is a leap of faith, not even supported by crystal-structure analysis. The list is not complete. 

Ethylene is planar with bond angles close to 120° (Figure 2 15) therefore some hybridization state other than sp is required The hybridization scheme is determined by the number of atoms to which carbon is directly attached In sp hybridization four atoms are attached to carbon by ct bonds and so four equivalent sp hybrid orbitals are required In ethylene three atoms are attached to each carbon so three equivalent hybrid orbitals... 

FIGURE 2 16 sp Hybridization (a) Electron configuration of carbon in its most stable state (b) Mixing the s orbital with two of the three p orbitals generates three sp hybrid orbitals and leaves one of the 2p orbitals untouched The axes of the three sp orbitals lie in the same plane and make angles of 120 with one another... 

Section 2 20 Carbon is sp hybridized in ethylene and the double bond has a ct com ponent and a rr component The sp hybridization state is derived by mix mg the 2s and two of the three 2p orbitals Three equivalent sp orbitals result and their axes are coplanar Overlap of an sp orbital of one car bon with an sp orbital of another produces a ct bond between them Each carbon still has one unhybridized p orbital available for bonding and side by side overlap of the p orbitals of adjacent carbons gives a rr bond between them... 

All of these trends can be accommodated by the orbital hybridization model The bond angles are characteristic for the sp sp and sp hybridization states of carbon and don t require additional comment The bond distances bond strengths and acidities are related to the s character m the orbitals used for bonding s Character is a simple concept being nothing more than the percentage of the hybrid orbital contributed by an s orbital Thus an sp orbital has one quarter s character and three quarters p an sp orbital has one third s and two thirds p and an sp orbital one half s and one half p We then use this information to analyze how various qualities of the hybrid orbital reflect those of its s and p contributors... 

The total electron density contributed by all the electrons in any molecule is a property that can be visualized and it is possible to imagine an experiment in which it could be observed. It is when we try to break down this electron density into a contribution from each electron that problems arise. The methods employing hybrid orbitals or equivalent orbitals are useful in certain circumsfances such as in rationalizing properties of a localized part of fhe molecule. Flowever, fhe promotion of an electron from one orbifal fo anofher, in an electronic transition, or the complete removal of it, in an ionization process, both obey symmetry selection mles. For this reason the orbitals used to describe the difference befween eifher fwo electronic states of the molecule or an electronic state of the molecule and an electronic state of the positive ion must be MOs which belong to symmetry species of the point group to which the molecule belongs. Such orbitals are called symmetry orbitals and are the only type we shall consider here. 

Here, the bonding between carbon atoms is briefly reviewed fuller accounts can be found in many standard chemistry textbooks, e.g., [1]. The carbon atom [ground state electronic configuration (ls )(2s 2px2py)] can form sp sp and sp hybrid bonds as a result of promotion and hybridisation. There are four equivalent 2sp hybrid orbitals that are tetrahedrally oriented about the carbon atom and can form four equivalent tetrahedral a bonds by overlap with orbitals of other atoms. An example is the molecule ethane, CjH, where a Csp -Csp (or C-C) a bond is formed between two C atoms by overlap of sp orbitals, and three Csp -Hls a bonds are formed on each C atom. Fig. 1, Al. 

Thus the bonding in sulfur hexafluoride SF6 has for a long time been considered to involve two of the 3d orbitals of sulfur, with the sulfur in a sp3d2 hybridized state and... 

If the assumption is made that the bond orbitals and one metallic orbital (except for the state with maximum valence, which has no metallic orbital) have the same hybrid character, values of the radii for the various pure valence states of the metals of the first ascending branch, from copper to germanium, can be calculated by use of equations (10c) and (10d). These values are given in table 6. There are also given the values interpolated for resonance between the state of maximum valency (with no metallic orbital) and the next state (with valency two less, and with a metallic orbital) in the ratio 25 75, the number of orbitals being included in the calculation as a weight factor. 

Answer First, we need to determine the hybridization state. We did this for this molecule earlier in this chapter and found that the hybridization state is sp (there are 3 atoms connected and no lone pairs, so we need three hybridized orbitals therefore,... 

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