Molecules With Trigonal Bipyramidal Shape

Molecules like PCl₅ (phosphorus pentachloride) and PBr₂Cl₃ (phosphorus dibromo-trichloride) possess five covalent bonds whose electron pairs are arranged in a trigonal bipyramidal geometry.

The central atom of these molecules, phosphorus, has only three unpaired electrons out of its five valence electrons as can be seen from its electronic configuration below:

1s2 2s2 2p6 3s2 3px1 3py1 3pz1

ground state configuration

But the Lewis structures of the given molecules, as shown below, indicate that the phosphorus atom uses five unshared electrons to form five covalent bonds.

It is, therefore, assumed that phosphorus uses the empty d orbital to "promote" 1 electron from 3s orbital to d orbital,

1s2 2s2 2p6 3s1 3px1 3py1 3pz1 3dz21

excited configuration

and, through hybridization, form five sp³d hybrid orbitals which are then used to bond with chlorine and bromine atoms.

1s2 2s2 2p6 (sp3d)1 (sp3d)1 (sp3d)1 (sp3d)1 (sp3d)1

excited configuration

Geometry of PCl₅

• shape of molecule: trigonal bipyramidal
• bond angle of axial atoms: 180°
• bond angle of equatorial atoms: 120°
• bond angle between an equatorial atom and an axial atom: 90°

Axial atoms are in white circles; equatorial atoms are in black circles.

A trigonal bipyramid is superimposed on the PCl₅ molecule.

Geometry of PBr₂Cl₃

Due to the different axial and equatorial positions the two bromine atoms can assume, PBr₂Cl₃ (phosphorus dibromo-trichloride) has three geometric isomers as shown below.

Except for the first isomer in which the bromine atoms are in axial positions, the other two geometric isomers of PBr₂Cl₃ are polar.

Geometries of Molecules and Ions

The shapes of compounds, either molecules or polyatomic ions, are very important in helping us understand better their reactions.

Fortunately, the geometries of most molecules and ions can be predicted quite reliably even by considering only their electron-electron pair interactions.

The idea is that the repulsive forces that exist between bonding and non-bonding pairs of electrons of a molecule or an ion cause those pairs of electrons to adapt certain spatial arrangement that allows minimum repulsion.

The spatial arrangement of the electron pairs of a molecule depends on its number of atoms and the number of valence electrons of its central atom.

So, in order to predict the geometry of a molecule or an ion, one needs to know its number of bonding and non-bonding pairs of electrons by determining the following:

• total number of atoms in the molecule or ion
• number of valence electrons of the molecule's central atom
• the Lewis structure of the molecule or ion

In the following illustrations, all of the possible coordination geometries for different compounds are depicted using ball-and-stick models.

In each illustration, information such as number of electron pairs of the compound and the number of its atoms are given.

Linear Geometry

• number of electron pairs: 2
• coordination geometry: linear
• number of atoms: 3 ( 1 central atom, 2 bonding atoms)

Trigonal Planar Geometry

• number of electron pairs: 3
• coordination geometry: trigonal planar
• number of atoms: 4 ( 1 central atom, 3 bonding atoms)

Tetrahedral Geometry

• number of electron pairs: 4
• coordination geometry: tetrahedral
• number of atoms: 4-5 ( 1 central atom, 3-4 bonding atoms)

Trigonal Bipyramidal Geometry

• number of electron pairs: 5
• coordination geometry: trigonal bipyramidal
• number of atoms: 6 ( 1 central atom, 5 bonding atoms)

Octahedral Geometry

• number of electron pairs: 6
• coordination geometry: octahedral
• number of atoms: 7 ( 1 central atom, 6 bonding atoms)

Pentagonal Bipyramidal Geometry

• number of electron pairs: 7
• coordination geometry: pentagonal bipyramidal
• number of atoms: 8 ( 1 central atom, 7 bonding atoms)