Jumat, 09 Oktober 2009

VSEPR Theory

Molecular Shapes


Now that you understand the basics of covalent bonding, we are in a position to consider another aspect of molecular structure- molecular shape. It's important to understand at the outset what organic chemists mean when they use the word shape. At the most basic level shape refers to the spatial disposition of two or more atoms about another atom. The other atom is referred to as the central atom. Figure 1 shows five of the most common molecular shapes of interest to organic chemists. (If you hold down the Shift key while dragging the mouse, you can change the size of the models.)

Figure 1

Trigonal Planar
carbon dioxide
boron trifluoride

Organic chemists discuss molecular shapes in terms of two theories, Valence Shell Electron Pair Repulsion (VSEPR) theory and Hybridization theory.

VSEPR Theory

In our discussion of Coulomb's Law we encountered the adage "like charges repel", and we added a phrase to indicate that this repulsion produced a more stable system. VSEPR theory is merely a restatement of this version of Coulomb's Law: areas of electron density will be arrayed around a central atom in such a way as to minimize the repulsions between them. Minimizing electron-electron repulsions is achieved by maximizing the distance between the regions of electron density. Maximum distance means maximum angles between bonds. By "areas of electron density" we generally mean electron pairs, either bonding or non-bonding. In the case of carbon dioxide, the carbon is doubly bonded to each oxygen atom. Thus there are two regions of electron density around the carbon, and the repulsions between them are minimized when they are 180o apart, i.e. when the O-C-O bond angle is 180o. In contrast, there are four areas of electron density around the oxygen atom in a water molecule, two bonding electron pairs and two non-bonding electron pairs. The best way to mimimize the repulsions between four regions of electron density is to distribute them in a tetrahedral array about the central atom. The tetrahedral bond angle is 109.5o. The H-O-H bond angle in water is 104.5o. The decrease from the tetrahedral value is rationalized by assuming that repulsions between the two non-bonding pairs are greater than those between the two bonding pairs, thus forcing the bonded pairs to compress slightly in order to allow the non-bonded pairs to get slightly farther apart. In methane, CH4, where the four C-H bonds are identical, the H-C-H angle is 109.5o.

In order to master VSEPR theory you have to be able to draw correct Lewis structures. The most common errors that students make are drawing incorrect Lewis structures and forgetting to include lone pairs of electrons. Practice and you won't make these mistakes. If you'd like to see a web page with VSEPR models that display lone pairs of electrons, click here.

Hybridization Theory

VSEPR theory adequately describes all of the situations we will encounter in this course. Unfortunatley, organic chemists still use the language of an older theory, hybridization theory, in the literature and in textbooks. We will take a pragmatic approach to hybridization theory: if there are two regions of electron density around a central atom, that atom is said to be sp hybridized; if there are three regions of electron density around a central atom, that atom is said to be sp2 hybridized; if there are four regions of electron density around a central atom, that atom is said to be sp3 hybridized. If you recognize that sp is an abbreviation for s1p1, then the sum of the superscipts, either implicit or explicit, in the smpn designation is equal to the number of regions of electron density around a central atom. If (m+n) = 2 for a given atom, the shape about that atom is linear; if (m+n) = 3, the shape is trigonal planar; if (m+n) = 4, the shape is either bent, pyramidal, or tetrahedral, depending on the number of atoms attached to the central atom.

In our discussion of the periodic table we saw how measurements of the ionization energies of atoms led to the idea of shells and sub-shells. For most of the compounds of interest in this course, we will focus on the s and p sub-shells of the n=2 shell, i.e. the 2s and 2p sub-shells. As you know, the 2s orbital is spherical; it has no directional properties. The three 2p orbitals, however, are mutually perpendicular; they are directed along the x, y, and z axes of a Cartesian coordinate system. Consider Figure 2 for a moment. Both panels are meant to suggest the formation of bonds between a central atom, X, and two other atoms, A. If the overlap occurs as depicted in the left panel, then the A-X-A angle should be 180o . The overlap shown in the right panel implies an angle of 90o. The fact that the bond angles found in most organic molecules are not 90o or 180o forced chemists to assume that the orbitals in molecules were different than the orbitals in isolated atoms. The idea

Figure 2

Alternative Atomic Orbital Overlap

was that each atom would "mix" its s and p orbitals to form "hybrid" orbitals which would lead to better orbital overlap as the atoms came together. Hybridization theory lacks intuitive simplicity of VSEPR theory. Nonetheless, the language of organic chemistry is peppered with terms that demand an awareness of hybridization theory. So we must persist a bit longer.

According to hybridization theory, there are two types of bonds, sigma (s) and pi (p). Sigma bonds are single bonds. They are formed by the head-to-head overlap of hybridized orbitals. Multiple bonds are combinations of one sigma bond and one or two pi bonds. The pi bonds are formed by the side-to-side overlap of unhybridized p orbitals. Thus a double bond is considered to be a combination of one sigma bond and one pi bond, while a triple bond is formed from one sigma bond and two pi bonds. Figure 3 animates the way organic chemists envision the formation of a double bond between two sp2 hybridized carbon atoms. Only the sp2 orbitals that are involved in the formation of the C-C sigma bond are shown explicitly.

Figure 3

Imagining the Formation of a Double Bond

Since head-to-head overlap localizes the electron pair in the internuclear region more than side-to-side overlap does, the electrons in a sigma bond experience greater nuclear attraction than the electrons in a pi bond. Hence, electrons in sigma bonds have lower energy than electrons in pi bonds. Both sigma-bonded electrons and pi-bonded electrons are lower in energy than non-bonded electrons because non-bonded electrons are localized on a single atom and therefore experience the nuclear attraction of only that atom.

Table 1 summarizes the bonding arrangements that are possible for the three most common hybridizations. Each entry in columns 1-5 of the table refers to a single carbon atom. After you have considered the information in the table, you may want to review the summary of bonding options in Table 3 of our discussion of Lewis structures. You should be certain you understand the relationships between the information in these two tables.

Table 1

A Summary of Hybridization and Bonding

Hybridizing Orbitals
Unhybridized Orbitals
s Bonds
p Bonds
s + p = 2 sp
2 p
s + 2p = 3 sp2
1 p
s + 3p = 4 sp3

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