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# Trigonal Pyramidal

The molecular geometry of trigonal pyramidal has electron pair geometry of tetrahedral arrangement. With overall electron pair of four and with one lone pair the structure makes an interesting topic to discuss about. The valence state electron pair repulsion theory suggest that the axial position of the lone pair makes it trigonal pyramidal geometry whereas the equatorial position leads to another form.

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## Trigonal Pyramidal Geometry

For valence state electron pair repulsion the idea of local geometry anticipation about an atom in a molecule requires the number of electron pairs which surrounds the atom, which are either bonded or lone in nature.

The VSEPR theory is based on two simple rules. One that the electron pairs (either lone pair or bonded) try to seek and avoid each other as much as possible. These electron pairs will lead to many forms. If there are two then it’s a linear geometry, three leads to trigonal planar, four pairs lead to tetrahedral and five leads to trigonal bipyramidal.

The tetrahedral form again has three option. If the arrangement has no lone pair then its plain tetrahedral, if it has got 1 lone pair then we get to see axial position with trigonal pyramidal geometry and if it has 2 lone pairs then it will show equatorial position with seesaw geometry.

The lone pairs take up more space than bonds and clarifies the situation. The trigonal pyramidal geometry results in which three bonds 90$^{\circ}$ to the lone pair, but though VSEPR theory is easy to apply but the utilisation is of limited value and is strictly qualitative. The structures that we finally get to see is definitely has the minimum energy and these are optimized to form the resonance structure with minimum energy.

## Trigonal Pyramidal Hybridization

Hybrid orbitals are formed when atomic orbitals on the same atom interfere and specific hybridization schemes correspond to each local molecular geometry. For a tetrahedral electron pair geometry.

Tetrahedral description of bonding in $AB_4$ the molecule of group 14 is still incomplete as it appears to imply the presence of three sigma bonds of one type and a fourth sigma bond of a distinctly different character points to the equivalence of all four A-B bonds as in case of methane $CH_4$.

This is overcome by realizing that the electron density distribution in the promoted atom is equivalent to the electron density in which each electron occupies a hybrid orbital formed by interference or rather mixing between A2s and A2p orbitals.

The origin of hybridisation can be appreciated by thinking of the four atomic orbitals which are waves centred on a nucleus and these waves either constructively or destructively in different regions give rise to either tetrahedral, trigonal pyramidal or seesaw molecular arrangement.

The specific linear combination that give rise to four equivalent hybrid orbitals are as follows:
For $h_{1}$ = s + Px + Py + Pz
For $h_{2}$ = s – Px – Py + Pz
For $h_{3}$ = s – Px + Py – Pz
For $h_{4}$ = s + Px – Py – Pz

Due to the interference between the component orbitals each hybrid orbital consists of a large lobe pointing in the direction of one corner of a regular tetrahedron and a smaller lobe pointing in the opposite direction.

The angle between the axis of the hybrid orbitals is the tetrahedron angle as each hybrid is built from one ‘s’ orbital and three ‘p’ orbitals and is termed as $sp^3$ hybrid orbital.

In this type of hybridisation a hybrid orbital has pronounced directional character with an enhanced amplitude in inter nuclear region.
The hybridisation of the lone pair in trigonal pyramidal will be different from that of the bonding pairs.

Most of the hybridisation result in equivalent hybrid orbitals or hybrid orbitals are identical in composition and also in spatial orientation with respect to each other.

They have very high symmetrical composition and end up in tetrahedral electron pair geometry as well as octahedral symmetry. If the arrangement of tetrahedral is in axial then we get to see the trigonal pyramidal molecular geometry.

The lewis dot formula predicts four regions of high electron density around the central atom, a tetrahedral electronic geometry and a pyramidal molecular geometry. The central atom will have a sp3 hybridisation with the three dimensional structure showing a single peak of central atom.

The valence bond theory shows that the central atoms of the molecular formula $AB+_{2}E_{2}$ and $AB_{3}E$ will undergo $sp_{3}$ hybridisation with a predicted angle of 109.5$^{\circ}$ and if no hybridisation occur then the bonds would be formed by the use of p orbitals.

Since the p orbitals are oriented at 90o from each other the bond angles would be 90o and moreover, the hybridisation is applied only in case the actual molecular geometry necessitates it.

## Trigonal Pyramidal Shape

For any B-A-B form of molecular geometry, the shape depends upon the number of electron pairs. The presence of bonded and lone electron pairs give the overall shape of the molecule.

The strategy to draw the shapes of molecules or ions is to draw the lewis dot structures for each.
• Draw the lewis dot structure
• Count each number of lone and bonded pairs around the central atom
• Decide the electron pair geometry
• Find the bonded and lone pairs which gives the geometry of the molecules or ions based on the atoms or ions location
• In case of hydronium ion (H3O+), three of the four pairs are used to bond terminal atoms, while the centrally placed oxygen atom and three H atoms form a trigonal pyramidal molecular shape.
The molecular geometries of methane, ammonia and water have four electron pairs around the central atom and hence all have a tetrahderal electron pair geometry.
• Methane has four bond pairs with no lone pair showing tetrahedral but not a pyramidal shape.
• Ammonia has three bond pairs and one lone pair and has got a trigonal pyramidal molecular shape.
• Water has two bond pairs and two lone pairs resulting in a bent shape tetrahedral molecular shape but since there is no point axis so the shape is not considered as pyramidal
• Hydronium has three bond pairs and one lone pair and has a trigonal pyramidal molecular shape
• Nitrogen trifluoride NF3 has three bond pairs and one lone pair resulting in single axis point which shows a trigonal pyramidal molecular shape.
• The basic idea is that if an atom is removed from one corner of the tetrahedron then the remaining fragment gets a trigonal pyramidal geometry.