# Valence-Shell Electron-Pair Repulsion (VSEPR) Model

## Molecular Geometry

The water molecule consists of an oxygen atom covalently bound to two hydrogen atoms.
What is the shape of the water molecule?
Do the atoms lie on a straight line (linear geometry)?
Is the molecule V-shaped?

The shape of a molecule has important implications for its properties and reactivity. If the water molecule has the shape of a V (with the oxygen at the lower vertex and hydrogens at the upper left and right), the molecule will be polar. The lower part of the molecule will have a partial negative charge (because the oxygen strongly attracts shared electrons to itself), while the top part of the molecule will have a partial positive charge (because hydrogen atoms have a weaker pull than oxygen on shared electrons). If the water molecule is linear, the molecule will be non-polar. That is, there will not be a negative end and positive end of the molecule.

Many properties of a compound, such as its ability to serve as a solvent, the melting and boiling points, and heats of fusion and vaporization, depend strongly upon its polarity.

An essential tool for chemists is a simple, reliable strategy for determining the shapes of small molecules and portions of larger molecules. This tool is called the Valence-Shell Electron-Pair Repulsion Model (VSEPR Model). The key concept in the VESPR model is that electrons, each having a negative charge, repel each other. The molecule will adopt whatever geometry minimizes the energy of these repulsions.

Determining the geometry or shape of a molecule using the VSEPR model involves four steps:

1. Write the best Lewis structure for the molecule.
2. Determine the number of Electron Groups (NEG) around the central atom.
3. Use NEG to determine the geometry of the Electron Groups.
4. Identify which Electron Groups are associated with bonds and determine the molecular geometry.

## Lewis Structure

### 1. Write the best Lewis structure for the molecule.

The starting point for the VSEPR Model is to determine the connectivity of the atoms and write a good Lewis structure for the molecule. Most stable molecules contain an even number of electrons and the electrons occupy orbitals as pairs (one electron spin-up and the other spin-down). Thus the Lewis structure depicts electrons as pairs, either in bonds or as lone pairs (sometimes called nonbonding pairs). Also recall that a Lewis structure shows only the valence electrons (no core electrons).

## Electron Pairs

### 2. Determine number of electron groups (NEG) around the central atom.

With a good Lewis structure in hand, identify the central atom (for water this is oxygen) and determine the number of Electron Groups around the central atom. An Electron Group is a pair of electrons in a σ bond or a nonbonding pair. Pairs of electrons in π bonds do not count as Electron Groups in VSEPR. The number of Electron Groups equals the total number of lone pairs (NLP) and σ bonds (Nσ) around the central atom. For the purpose of determining the number of Electron Groups, an entire bond (single, double, or triple) counts as a one Electron Group.

NEG = NLP + Nσ

## Electron Group Geometry

### 3. Use NEG to determine the geometry of the Electron Groups.

Once the number of Electron Groups (NEG) is known, one can predict the geometry of the Electron Groups. The electron groups (lone pairs and σ bonding pairs) will assume whatever geometry minimizes their mutual repulsion (Coulomb's law). With a knowledge of trigonometry and calculus, one can solve this minimization problem. The results are shown in the following table. For all but the largest atoms (when bound to small groups), there is insufficient space to accommodate more than six Electron Groups around the central atom. Thus the table accounts for all commonly encountered geometries.

Note! The Electron Group Geometry is NOT the Molecular Geometry. The molecular geometry describes the arrangements of atoms around the central atoms and does not include the positions of lone pairs.

NEG Electron Group Geometry
2linear
3trigonal planar
4tetrahedral
5trigonal bipyramidal
6octahedral

## Molecular Geometry

### 4. Identify which Electron Groups are associated with bonds and determine the Molecular Geometry.

Once the Electron Group geometry is determined, one can finally predict the molecular geometry. The molecular geometry describes the relative positions of the atoms in the molecules. Thus one must determine which Electron Groups are from a σ bond, and thus associated with a peripheral atom, and which are not. Electron Groups attributable to lone (nonbonding) pairs of electrons (NLP) are not associated with any other atom. Recall that

NEG = NLP + Nσ

## Hybridization

In Valence Bond Theory, a chemical bond between two atoms is regarded as the result of overlap of one atomic orbital from each atom. In order to provide optimal overlap, each atomic orbital should be directional and point towards the other atom. Therefore, a set of hybrid atomic orbitals should have the same geometry as the Electron Groups from the VSEPR Model.

The various possible combinations NEG and Nσ are tabulated below. In each case, an example is provided.

## Exercise

1. Select a molecule from the rightmost column. Draw the best Lewis Structure for the molecule.
2. Identify the central atom and count the number of σ bonds (Nσ) and number of lone pairs (NLP) associated with the central atom. Add these numbers to obtain the number of Electron Groups (NEG). These values should be consistent with the row entries from the table.
3. Click on the chemical formula to display the molecule. The geometry of the molecule should be similar to the description in the table. (The geometry shown in the viewer is based upon experimental data. The VSEPR geometry is a simplified geometry.)

Carefully examine the molecular geometry where NEG = Nσ (highlighted in blue) to visualize the Electron Group geometry. In this case all Electron Groups are associated with atoms and the Electron Group geometry is identical to the molecular geometry.

Then look at examples where NEG > Nσ. In this case some of the Electron Groups are lone pairs, and the molecular geometry differs from the Electron Group geometry. (In most cases where NEG > Nσ, it does not matter which site is occupied by an atom. The exceptions are for NEG = 5 or 6.

As a technique for determining molecular geometry, the VSEPR Model is simplistic and lacks a rigorous theoretical foundation. Nonetheless, the VSEPR Model is remarkably good at predicting actual molecular geometries. The geometries shown in the table represent idealized geometries. Real molecules often show deviations from the ideal bond angles listed below.

NEG Nσ NLP Molecular Geometry Ideal Bond Angle(s) Hybridization Example
220linear 180° sp CO2
321V-shaped 120° sp2 O3
330trigonal planar 120° sp2 BF3
422V-shaped 109.5° sp3 H2O
431trigonal pyramidal 109.5° sp3 NH3
440tetrahedral 109.5° sp3 CH4
523linear 180° dsp3 I3-
532T-shaped 90° dsp3 ClF3
541see-saw 90°, 120° dsp3 SF4
550trigonal bipyramidal 90°, 120° dsp3 PCl5
642square planar 90° d2sp3 ICl4-
651square pyramidal 90° d2sp3 BrF5
660octahedral 90° d2sp3 PF6-

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