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Valence Shell Electron Pair Repulsion Theory

Valence Shell Electron Pair Repulsion Theory

VSEPR Theory is one method that chemists use to predict the shapes of molecules. This theory predicts that electron pairs, whether involved in bonds or as non-bonding pairs, will adopt a geometry in which they maximize the distance from one another in order to minimize repulsions. This will result in a geometry with the lowest possible energy.

Valence Shell Electron Pair Repulsion theory (VSEPR) is a set of rules whereby the chemist may predict the shape of an isolated molecule. It is based on the premise that groups of electrons surrounding a central atom repel each other, and that to minimize the overall energy of the molecule, these groups of electrons try to get as far apart as possible. Groups of electrons can refer to electrons that participate in a bond (single, double, or triple) to another atom, or to non-bonding electrons (e.g. lone pair electrons).

The ideal electronic symmetry of a molecule consisting of a central atom surrounded by a number of substituents (bonded atoms and non-bonding electrons) is characteristic of the total number of substituents, and is determined solely by geometric considerations — the substituents are arranged so as to maximize the distances amongst them. VSEPR is useful for predicting the shape of a molecule when there are between 2 and 6 substituents around the central atom (the case of one substituent is not discussed because it is trivial — the only possible shape for such a molecule is linear). That means that there are only five unique electronic geometries to remember. For each electronic geometry, there may be a number of different molecular geometries (the shape of the molecule when only bonded atoms, not non-bonding electrons are considered). Molecular geometries are really just special cases of the parent electronic geometry — this will hopefully be evident from the models shown on the pages linked to this one.

Since the molecular geometry is determined by how many bonding and non-bonding electron groups surround the central atom, the first thing one needs to do is count how many of each there are. There is a notation that simplifies this bookkeeping:

Valence Shell Electron Pair Repulsion theory, VSEPR theory, starts with the simple axiom that electrons repel each other. Since a bond is a concentration of electron density between two nuclei, they will repel each other also. Bonds and unshared pairs all involve these regions of electron density called domains. If you have a central atom and a set of bonds or unshared electron pairs around it, you would expect them to get as far as possible away from each other to minimize the repulsion. That means the angle between say any two bonds needs to be as large as practical to minimize the energy of the molecule.

The steps to applying VSEPR theory to a molecule are:

Draw a Lewis structure for the molecule.

Determine the number of domains around the central atom.

Determine the geometry and hybridization around the central atom.

Determine the bond angles and shape of the molecule.

Consider the molecule BeCl2. Figure 1 is the Lewis structure. Note that there are no unshared pairs on be and only two single bonds. Therefore there are two domains around be. The best geometry for two domains is shown in figure 2. In order for the two domains to be as far as possible from each other, they must be on opposite sides in a line. This is called the linear geometry. The bond angle is 180o.

How is this linear geometry achieved? The beryllium atom has two valence electrons in a 2s orbital. To form two bonds we need two orbitals with one electron each. We can promote one of the 2s electrons to a 2p orbital to get that. However if we form sigma bonds to chlorine using two different kinds of orbitals on the beryllium we will get two different bonds. Beryllium chloride has two equivalent bonds. That requires two equivalent orbitals. How can we use the existing orbitals to get that? Also how do we insure the linear geometry?

Since we need to convert two different orbitals into two equivalent orbitals, and since the orbitals are just mathematical functions, we should mathematically average the functions. Averaging a 2s function and a 2p function gets us two hybrid functions. These hybrid orbitals are called sp orbitals, 2s + 2p = 2 sp. When the two sp orbitals on beryllium are plotted in 3D space we see that they have two lobes pointing in opposite directions, perfect for linear geometry.

Consider BF3. Figure 3 shows the Lewis structure. It has only three bonds to the boron which makes three electron domains. The best geometry for three repulsive domains is shown in figure 4. The three bonds are in a plane and oriented 120o from each other. This is called trigonal planar geometry.

Boron has two valence electrons in a 2s orbital and one in a 2p. Promotion of one 2s to a 2p gives three singly occupied orbitals but with the wrong geometry. Hybridizing the 2s and the two 2p’s give three sp2 hybrid orbitals and one empty 2p left over. The sp2 orbitals have the required trigonal planar geometry as shown in figure 5.

Consider CH4. The Lewis structure for methane is shown in figure 6. It has four bonds to the central carbon which is four domains. The best geometry for four domains in 3D space is oriented toward the vertices of a tetrahedron. Thus methane has tetrahedral geometry. The tetrahedral bond angle is about 109.5o.

Carbon has two valence electrons in a 2s orbital and one each in two 2p orbitals. Promotion of one’s electron to the 2p gives four singly occupied orbitals for bonding. Hybridizing the 2s and three 2p’s gives four sp3 hybrid orbitals (figure 7). These sp3 orbitals are arranged in a tetrahedral geometry.

Consider phosphorus pentachloride, PCl5. Figure 8 is the Lewis structure and shows five domains around phosphorus. The best geometry for five repulsive centers is called trigonal bypyramidal, i. e. three in a planar trigonal orientation at 120o and two more at 90o to those to form two pyramids base-to-base (figure 9).

Phosphorus has five valence electrons, two in a 2s orbital and three in 2p’s. Promotion of a 2s to 3d gives five singly occupied orbitals for bonding. Hybridization gives five sp3d hybrid orbitals and four empty 3d’s left over. The sp3d orbitals have the required trigonal bipyramidal geometry.

Consider sulfur hexafluoride, SF6. The Lewis structure (figure 11) has six domains around the sulfur. This gives it an octahedral geometry with all six bonds at 90o from each other (figure 12).

The six valence electrons on sulfur occupy 2s and 2p orbitals. Promotion of 2 electrons to 3d orbitals gives six singly occupied orbitals. A 2s, three 2p’s, and two 3d’s give six sp3d2 hybrid orbitals. These have the required octahedral geometry.

5 Trigonal Bipyramidal 90o, 120o SP3D

Consider the water molecule. The Lewis structure has two bonds and two unshared pairs. That makes four repulsive centers. That requires a tetrahedral geometry. However unshared electron pairs are not visible in terms of molecule shape. Remember that the electrons really have only a high probability in that particular region not a real presence as localized particles. Thus only the nuclei of the atoms count in terms of shape. The water molecule is therefore a bent or angular molecule with a bond angle of about 109.5o. Since unshared pairs represent a higher electron density than bonding pairs, they are more repulsive. Thus we can expect that the bond angle would be compressed slightly less than 109.5o. In water the actual bond angle is about 104.5o.

The Lewis structure for ethylene is shown in figure 14. Each carbon has two single bonds and a double bond attached. Note that since a double bond is two electron pairs localized in the same region, they count as one domain. Therefore each carbon has three domains around it.

Three domains means that the carbons are trigonal planar sp2 hybridized. One sp2 orbital from each carbon can be used to form a sigma bond between them. Sigma overlap between the other four sp2 orbitals and the 1s orbitals on the hydrogens completes the sigma framework of the molecule (figure 15). Due to trigonal planar geometry all six atoms of the molecule lie in the same plane and the H-C-H bond angle is about 120o.

Three sp2 hybrid orbitals on each carbon accounts for three valence electrons used in bonding. However there are four valence electrons on a carbon. Where did the fourth one go?

Remember that when the three sp2 orbitals were formed it left one p orbital remaining. The fourth electron in each carbon will be found there. If one looks at the sigma framework from the side, one sees that the 2p’s on carbon are perpendicular to the plane of the molecule. The two 2p orbitals on the carbons can overlap to form a pi bond (Figure 16). Thus we see that the double bond between the carbons consists of one sigma bond due to sp2 overlap and one pi bond due to orbital overlap.

The VSEPR Theory of Molecular Geometry

VSEPR stands for Valence Shell Electron Pair Repulsion. That’s a real mouthful for what is really a rather simple idea.

The whole concept revolves around the idea that the electrons in a molecule repel each other and will try and get as far away from each other as possible. VSEPR explains a lot about molecular geometry and structure, BUT NOT EVERYTHING!!

The electrons (both in pairs and singles as you will see) are “attached” to a central atom in the molecule and can “pivot” freely on the atom’s surface to move away from the other electrons.

Electrons will come in several flavors:

a) Bonding pairs – this set of two electrons is involved in a bond, so we will write the two dots BETWEEN two atoms. This applies to single, double, and triple bonds.

b) Nonbonding pairs – this should be rather obvious.

c) Single electrons – in almost every case, this single electron will be nonbonding.

Almost 100% of the examples will involve pairs, but there are a significant number of examples that involve a lone electron.

VSEPR uses a set of letters to represent general formulas of compounds. These are:

a) A – this is the central atom of the molecule (or portion of a large molecule being focused on).

b) X – this letter represents the ligands or atoms attached to the central atom. No distinction is made between atoms of different elements. For example, AX4 can refer to CH4 or to CCl4.

c) E – this stands for nonbonding electron pairs.

d) E – this stands for lone nonbonding electrons.

Each area where electrons exist is called an “electron domain” or simply “domain.” It does not matter how many electrons are present, from one to six, it is still just one domain. Now a domain with six electrons in it (a triple bond) is bigger (and more repulsive) than a lone-electron domain. However, it is still just one domain.

This is an IMPORTANT point to remember in VSEPR. The more electrons in a domain, the more repulsive it is and it will push other domains farther away than if all domins were equal in strength. Keep in mind that the domains are all attached to the central atom and will pivot so as to maximize the distance between domains.

Another important point to mention in this introduction is that an element’s electronegativity will play an important role is determining its role in the molecule.

For example, the least electronegative element will be the central atom in the molecule. The more electronegative the element, the more attractive it is to its bonding electrons this will play a very important role, especially in five domains.

The most important domain numbers at the introductory level are 3, 4, 5, and 6. Domains of 1 and 2 exist, but are simple to figure out. Domains up to 9 exists, but become progressively more complex. If you decide you MUST study those domains, seek out this book:

The VSEPR Model of Molecular Geometry (1991) by Ronald J. Gillespie and Istvàn Hargittai. Published by Allyn & Bacon. ISBN 0-205-12369-4.

Gillespie coined the term VSEPR and has been active in this field since it was established in the early 1940’s. Except where noted, all bond angles and bond lengths have been taken from this book.

Bibliography:

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