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# Polyatomic Molecules

The polyatomic molecules are composed of a bound stable state which are mainly comprised of than three atoms or more. The polyatomic molecules formula shows the composition in various forms depending upon the position and bracketing of participating atoms.

Although the polyatomic molecules are arranged in various forms but the overall empirical formula most often remain same. The complexity of the molecules and their structure increase with the increase in number of participating atoms. The possibilities of various isomeric forms and configurations of such polyatomic molecules makes the study of polyatomic molecules very challenging.

## Polyatomic Molecules Definition

Nearly all molecules are represented by a schematic structural formula with chemical symbols or a figure with circles representing atoms. If the molecules are combination of more than three or at the least three atoms then the designation of the molecules becomes a poly form and hence is called polyatomic molecule.

These are in general based on those given in the original form and are consistent with those used in respective tables and also with international recommendation. The line structures connecting atoms in structural formulae need not necessarily represent correct bond orders or bond types in order to check with free radical or a molecule in an electronically excited state and could be ambiguous, contentious but although perfectly characterized by potential function.

The presence of double bonds and triple bonds in structural formulae represent the bond nature. In polyatomic molecules due to large number of degree of freedom for the internal motions either by rotations or vibrations of the atoms present in the molecule, the dynamics of such a system of atomic nuclei the role of electron become very important as compared to in diatomic molecules.

## Molecular Orbital Theory for Polyatomic Molecules

With the localised electron pair concept, it is much easier to visualise the shape of polyatomic molecules than with the delocalised or molecular orbital concept of electron pair bond. The concept of directed valence is a direct consequence of the localised electron pair or valence bond theory.

For any chemical bonding the orbitals of atoms which are participating in bond formation must overlap and the direction of the bond is determined by direction in which the two orbitals overlap as much as possible.

The modern views of molecular structure are mainly depended on applying wave mechanics to molecules. While the Schrödinger equation is written to describe the behaviour of electrons in molecules and is solved only by means of approximation techniques. The two methods are applied to understand better the approximation for polyatomic molecules. One is valence bond and the other is molecular orbital theory.
• The molecular orbital theory designates electrons to molecular orbitals similar to atomic orbitals each containing two or more nuclei.
• The molecular orbital theory that are applied to diatomic molecules provides a logical starting point for understanding polyatomic system.
• The general method of constructing molecular wave functions for polyatomic molecules is to use un hybridized atomic orbitals in linear combinations or to use localised two atom orbitals which provides a simple framework for discussion of ground state properties especially molecular geometry.
The electrons in these molecular orbitals are not localised between two atoms of a polyatomic molecule but are delocalised among several atoms of the polyatomic form.

When we deal with heteronuclear species where two atoms have different orbitals available for possible bond formation. When we consider combination of 1s atomic orbitals on two different atoms the shapes of the orbitals are plots of electron density as these orbitals are occupied by electrons.
• In bonding orbital the two 1s orbitals have been placed with each other in the region between two nuclei by electron waves overlap.
• While in anti-bonding orbital these cancel each other by out of phase or destructive overlap of their electron waves.
• We assign both the molecular orbitals as sigma (σ) molecular orbitals as they are found to have cylindrical symmetry about inter-nuclear axis. The asterix (*) classifies an antibonding orbital.
• All sigma antibonding orbitals have nodal planes bisecting inter-nuclear axis.
• For diatomic specis the σ2p orbital is higher in energy as compared to two π2p orbitals and the occupation of electrons in molecular orbital as per the same rules applied for atomic orbitals as they follow same Aufbau principal and Hund’s rule.

## H2O Molecule

During the formation of $H_{2}O$ molecule the two 1s orbitals of the two H atoms and the four valence orbitals $2s 2p_{x} 2p_{y} 2p_{z}$ of the oxygen atom as the two 1s electrons in the inner shell of the O atom do not contribute to the binding energy.

The oxygen atom electronic configuration in the valence shell stands as: $2s^{2} 2p_{x} 2p_{y} (2p_{z})^{2}$

The first approximation involves two unpaired electrons in 2px and 2py atomic orbitals are used to form molecular orbitals with two 1s atomic orbitals of the two H atoms. Each of the two molecular orbitals contain one electron from H atom and one from O atom. This leads to increase in electron density between the O atom and H atoms and hence the attraction between the atoms implying that there is a decrease in total energy.

The integral of overlap and binding energy also becomes large and this also implies that the two electrons must have opposite spins as they are in the same molecular orbital.

Oxygen atomic orbitals of valence electrons.

Formation of water molecule without hybridization. Now compared to the polyatomic molecules the diatomic molecules like hydrogen, helium or boron molecular orbitals are as follows:

Hydrogen molecule: the overlap of the 1s orbitals of two hydrogen atom produce σ1s and σ*1s molecular orbitals where the two electrons of the molecule occupy the lower energy $\sigma 1s$ orbital. In hydrogen only two electrons are in a bonding orbital and hence bond order is one.

The energy associated with two electrons in $H_{2}$ molecule is lower than that associated with same two electrons in separate 1s atomic orbitals. The lower the energy of a system the more stable it is.

For boron molecule $B_{2}$, the atoms have configuration $1s^{2} 2s^{2} 2p^{1}$. Here the p electrons participate in the bonding, and hence πp molecular orbitals are lower in energy than the $\sigma 2p$ for boron molecule. The electronic configuration for boron is $\sigma1s^{2} \sigma *1s^{2} \sigma2s^{2} \sigma * 2s^{2} \pi 2py^{1} \pi 2pz^{1}$

## CO2 Molecule

The molecular orbitals of CO2 molecule have 12 atomic valence orbitals 2s, 2px, 2py and 2pz for each of the three atoms of the molecule. The orthogonal linear combinations of these atomic orbitals are 12 molecular orbitals ordered in increasing energy where two electrons occupy each orbital.

With 16 valence electrons for CO2 molecule there are only eight lowest orbitals are filled in by electrons. The overlap of electron wave functions between the participating atoms reach maximum with the total energy of the CO2 molecule tend to be minimum.

In carbon atom the 2s orbital is occupied by 2 electrons with each of the 2px and 2py orbitals having one electron. If no hybridization takes place then only two 2p orbitals of each oxygen atoms and two p orbitals of carbon atom are available for molecule formation.

Large overlap could be obtained by the sp hybridization with one each of 2s and 2p from the participating atoms combine to form the six atomic hybrid orbitals. The binding energy contribution is from molecular orbitals which are formed as linear combinations of the Spz hybrid orbitals from the oxygen atom and either S or pz orbitals of the carbon atom.

Molecules with more than three atoms. These triatomic molecules have planar structure and anything more than these have linear, planar or non-planar which gives isomeric forms. The geometry of these molecules depend upon the electronic structure of the molecule and these are definitely different for both excited and ground electronic state.

## NH3 Molecule

The nitrogen atom consist of three unpaired electrons with three Px, Py and Pz orbitals. Three directed bonds with 1s orbitals of hydrogen atoms (perpendicular to each other). The overlap of the 1s orbitals of the H atoms and nitrogen atomic orbitals become large with sp hybrid atomic orbitals instead of only p orbitals of the N atom. The non-planar $NH_{3}$ molecule has a pyramid structure with similarity of equilateral triangle as the basis. The valence electrons of N atom sp hybrid orbitals.

Methane CH4 molecule

The methane molecule shows $sp^{3}$ hybridization which explains the combination of 2s orbitals with all existing three p orbitals of px, py and pz with four normal orthogonal hybrid functions comprising of linear combinations of four atomic orbitals.

Apart from the combinations of s and p orbitals the formation of hybrid orbitals could be carried out by linear combinations which include atoms occupied orbitals of atoms involved in molecular binding.

These represent directional bonds resulting in various geometrical molecular structures.

## Polyatomic Molecules List

Polyatomic Molecules List:
 Molecule name Molecule formula Methane $CH_{4}$ Water $H_{2}O$ Nitrogen dioxide $NO_{2}$ Di nitrogen tetra oxide $N_{2}O_{4}$ Hydrogen peroxide $H_{2}O_{2}$ Ethane $C_{2}H_{6}$ Sulphur dioxide $SO_{2}$ Ammonia $NH_{3}$ Phosphine $PH_{3}$ Butane $C_{4}H_{10}$ Carbon di oxide $CO_{2}$

## Polyatomic Molecules Examples

The best five examples of polyatomic molecles would be methane $CH_{4}$, Nitrogen dioxide $NO_{2}$, water $H_{2}O$, ammonia $NH_{3}$ and sulphur dioxide $SO_{2}$.