Valence shell electron-pair repulsion (VSEPR) theory is a covalent bond theory that uses the repulsive forces between single electrons and pairs of electrons about the central atom to predict their relative positions around the atomic nuclei. According to VSEPR theory, electron pairs around a central atom repel each other. Because of the repulsion between electrons, the shape with minimum energy is the one in which the distance between electron pairs is maximized. Therefore, the shape with the lowest energy is likely to be the actual form of the molecule. Electron pairs can either be inside a bond between atoms or exist as a lone pair.
There are generally between two and six electron pairs (either in the bonds of bonding atoms or as lone pairs) around any central atom, and the electron pairs can be arranged in either of five ways, each with a different geometry.
Electron-pair geometry is the shape description for all electron pairs (bonding and nonbonding) about a central atom. Electron-pair geometry maximizes the distance between every pair of electrons around a central atom. For example, if there are three pairs of electrons, increasing the angle between two electron pairs in a trigonal planar arrangement would push one of the pairs closer to the third pair, which would increase the potential energy of the third pair. When the distance between all of the electron pairs is maximized, the potential energy of the system is at a minimum. Systems always favor a position of minimum energy, so arrangements that maximize the distance between atoms and/or lone pairs are favored. Generally, large angles represent a greater degree of separation and are more favorable. Angles of 90° are least favorable.
VSEPR Electron-Pair Configurations
|Number of Electron Pairs||Electron-Pair Geometry||Geometry||Geometry Definition||Angle Between Electrons|
|2||Linear||Electron pairs form a straight line with the central atom.||180°|
|3||Trigonal planar||Electron pairs are arranged evenly around the central atom and are in the same plane as the central atom.||120°|
|4||Tetrahedral||Electron pairs are arranged around the central atom such that they are located at the four corners of a tetrahedron.||109.5°|
|5||Trigonal bipyramidal||Electron pairs are arranged such that they are located at the corners of a trigonal bipyramid around the central atom, like two triangular pyramids aligned base to base.||90° and 120°|
|6||Octahedral||Electron pairs are arranged such that they are located at the corners of an octahedron around the central atom, like two square pyramids aligned base to base.||90°|
Consider a molecule with trigonal planar electron-pair geometry with one lone pair of electrons. The molecular geometry of this molecule is bent; it is not trigonal planar. Two atoms are bonded to a central atom at an angle. Furthermore, lone pairs are not constrained by a covalent bond. The electrons in a lone pair have higher energy, which means they can spread out more. Because of the higher energy, lone pairs have a greater repulsive force than bonding pairs. A lone pair–lone pair interaction is the most repulsive (has the highest energy), a bonding pair–bonding pair interaction is the least repulsive (has the lowest energy), and a lone pair–bonding pair interaction is in the middle.
When there is more than one possible location for a lone pair in the molecular geometry, the lone pair settles in the configuration that minimizes the repulsion between the lone pair and other electrons. Consider a central atom with four bonding pairs and one lone pair (AX4E). For this molecule the lone pair is located in the central plane so that there are two 90° lone pair–bonding electron interactions and two 120° lone pair–bonding electron interactions. If the lone pair were at the tip of the pyramid, there would be three 90° lone pair–bonding interactions and one 120° one. This arrangement would be a higher energy state and would be less stable.
VSEPR Molecular Geometries
|Electron Pairs||Electron-Pair Geometry||Lone Pairs||VSEPR Notation||Molecular Geometry||Bond Angles|
||0||AX5||Trigonal bipyramidal||90°, 120°|
Using VSEPR Theory
VSEPR Theory and Polar Covalent Bonds
A polar covalent bond is a covalent bond in which the electron density is more localized on one end of the bond. One end is slightly positive, and one end is slightly negative. A dipole moment () is a vector quantity that defines the extent of the charge on either side of a polar covalent bond, with the direction that points from the positive side of the bond toward the negative side. The negative side is the more electronegative atom, and the positive side is the less electronegative atom. The dipole moment is the product of the charge ( and ) and distance (d). The distance is simply the bond length. The dipole moment is measured in debyes (D), where .The polarity of a molecule is related to its shape. Consider the carbon dioxide (CO2) molecule. Each bond has a dipole moment that has a greater electron density on the oxygen side of the bond, because oxygen is more electronegative than carbon. Schematically, the individual bond dipole moments are represented by a crossed arrow that points toward the side of greater negativity. The plus end of the arrow indicates the positively charged side of the molecule, and the tip of the arrow represents the negatively charged side. Because the dipole moments in carbon dioxide are equal in magnitude but opposite in direction, they cancel each other, and is equal to zero when the molecule is considered as a whole. A molecule with a dipole moment equal to zero is called a nonpolar molecule. Carbon dioxide is nonpolar, and VSEPR theory predicts that carbon dioxide is a linear molecule. If the molecule were bent, there would be a net partial charge on the oxygen atoms and the carbon atom, and the dipole moment would not equal zero.
Water, on the other hand, has a central oxygen atom that is more electronegative than the hydrogen atoms bound to it. In this case, the dipole moments are equal in magnitude but have components that point toward each other, so the entire molecule has a dipole moment greater than zero. A polar molecule, such as water, has a specific dipole moment not equal to zero. Because a water molecule is polar, VSEPR theory predicts that it has a bent structure. The two lone pairs and the hydrogen atoms repel each other, resulting in a bend in the shape of the molecule. In a water molecule, there are net partial charges on the two hydrogen atoms and the oxygen atom.
Consider the known information about the molecule.
The center of the overall dipole moment is located at a point equidistant between the two hydrogen atoms, at the base of an isosceles triangle with an obtuse angle of 104.5°.
The x-components of the dipole moments point in opposite directions and cancel. The y-components of the dipole moments both point in the positive y-direction and do not cancel. The overall dipole moment is therefore the sum of the y-components of the dipole moments.