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# Molecular Dipole Moment

Permanent dipole occurs when a charge separation is found to be omnipresent in a molecule, even when there is no external electric fields. An induced dipole is a charge separation that arises only in the presence of an applied electric field. But yes, we also could come across molecules where both permanent and induced dipole moments are seen.

Usually the permanent dipole is characterised by its dipole moment, $\mu$ = q d, where q is the distance between the charges. These dipole moments are measured in Debye units (D). These are concepts which arise from the fact that any molecule with a strong electronegative element has definite dipole moments and molecules with equal or no electronegative elements do not exhibit any type of dipole activity.

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## Molecular Dipole Moment Definition

The concept of bond dipoles are basically an extended idea about electronegativity, along with molecular dipole considered to be intrinsic property of molecule. A molecule has a dipole moment whenever the center of positive charge within the molecule is not coincident with the center of negative charge. The charge separation of these centers makes it possible to calculate the molecular dipole moments. These values actually help us understand the intensity of the field around such molecules or how strong a molecule is approaching another and also of how the charge can differentiate one end of the molecule from the other.

Like in case of methane or tetra chloro methane, a molecule with zero dipole moment can essentially come across the same electric field. In contrast to this, the electric field experienced by a molecule approaching a structure with a high dipole is definitely different depending upon the direction from which it is approaching. In high symmetry cases, all the local bond dipoles cancel and the overall molecule has no molecular dipole as a molecular dipole is nothing but a vector sum of bond dipoles. Hence, the absence of a molecular dipole cannot rule out the existence of bond dipoles and the presence of bond dipoles does not guarantee the existence of molecular dipole.

The more chlorines attached to methane from $CH_{3}Cl$ to $CCl_{4}$, the lower the dipole becomes and this trend might at first seem to counter to the idea itself as we are adding more electronegative elements to the molecule. But when we consider the vector part to this trend we get to observe that the individual bond dipoles increasingly cancel out as the number of electronegative elements increase. This incorporation of nitro or Cyano groups into molecules results in a very large molecular dipoles when there are no other bond dipoles to cancel these out.

Let us consider another situation, where $CH_{3}Br$ and $CH_{3}F$ have same dipole. This is irrespective of the fact that C-F bond would have greater polarisation effect as compared to C-Br. But in this case the C-Br bond is relatively longer than the C-F bond and even though the charge separation is smaller, the distance is large. Both these phenomenon affect the molecular dipole and leads to same dipole moment for the two different molecules.

The polar dielectrics are understood to have asymmetrical molecules in which the center of gravity of both positive and negative charges are located at some distance from one another and hence form an electric dipole. Thus, nonpolar molecules do not possess a dipole moment in the absence of a field, while polar molecules have a permanent dipole moment independent of the field. Under applied electric field a process of polarisation takes place not only any small volume of dielectric but also of each individual molecule, irrespective of permanent dipole moment in the absence of a field.

The action of a field leads to appearance in the molecule of some induced dipole moment proportional to the strength of the mean macroscopic field. Water has no net charge and has a permanent dipole moment due to partial negative charge on Oxygen and partial positive charge on two hydrogens.

## Molecular Dipole Moment Examples

The experimentally determined dipole moments of molecules are as follows.

 Compound Molecular dipole Compound Molecular dipole Carbon tetra chloride Zero 1 butene 0.34 Mono chloro methane 1.9 Water 1.8 Di methyl ether 1.3 Methanol 1.7 Mono fluoro methane 1.8 Mono bromo methane 1.8 Di chloro methane 1.6 1 propyne 0.8 Tri chloro methane 1.0 Acetic acid 1.7 Methyl ethanoate 2.9 Propanoic acid 1.7

## Molecular Dipole Moment Calculation

Better approach to the calculation of dipole moments is by taking the position and magnitudes of the partial charges of all the participating atoms. These partial charges are included in the output of many molecular structures. The dipole moments are calculated for each molecule by using the electric dipole moment vector value and taking into account the direction as well with the help of µx, µy and µz.

The µ helps in getting the direction of the orientation of dipole in molecule and also the length of vector magnitude. The magnitude is related to three components relationship given out by:

$\mu$ = $(\mu x + \mu y + \mu z) \frac{1}{2}$

## How to Determine Dipole Moment From Lewis Structure?

In all of the lewis structures the bonds are formed by the sharing of one or more electron pairs, in which half the electrons come from each bonding atoms. For each participating atoms in a compound the whole criteria lies in reaching the nearest octet. These structure has octet about each atom and exhibits the exact shared number of electrons and the ones without pairing.
• The participating atoms show the exact lewis electron dot symbols which are assigned half the shared electrons to each of the participating atoms.
• When these are separated from the shared electrons point of view, they yield lewis symbol for valence electrons, where the lone pairs and shared electrons are taken into account.
• The lewis structure is written with formal charge which are assigned to each atoms in the structure assuming that the shared electrons are divided equally between the participating bonded atoms.
• Formal charges are written next to the atoms and inside a circle. If lewis structure have atoms with formal charges, then only non-zero values are written.
• The assigning of formal charge is one method of electron counting. A neutral species needs to have a formal charge of zero.
• The sum of the formal charges on an ion must be equal to the charge of the overall ion.
• Most lewis structures yield zero form formal charges of atoms and the non-zeros formal charges can be recognized by the number of bonds made by atoms.
• If the lewis structure shows bonds that differ from these numbers, the atom will have a formal charge.
• Atoms with more bonds have positive formal charges and atoms with lesser bonds have a negative formal charge.
• Formal charge = (number of valence electrons in atom) – (number of lone pair electrons) – (½ number of shared electrons)
These formal charges can give the dipole moment of the compound.

## How to Determine Molecular Dipole Moment?

The magnitude of dipole depends on the difference of the magnitude or product value of electronegativity of these bonding atoms. The bigger existing difference in electronegativity gives even bigger dipole moment and the more polar is covalent bond.

Dipole moment is vector and has both magnitude as well as direction. To determine if a molecule is polar, two criteria is fulfilled:
• Existence of polar bonds between molecules
• Existence of net dipole moment for the molecule
Ebertâ€™s method:
This method is based mainly on the fact that gases and to an extent liquids, the molecules have free movements. Unlike solids, where the molecules remains almost stationary in space lattice.

Polar molecules in liquid and gaseous state suffer orientation and distortion polarisation when exposed to electric field. This shows, that in a polar molecule the total polarisation in gaseous and solid state will be markedly different.

Total molar polarisation will be represented as:

$P_{gas}$ = $Pi + P_{M}$

$P_{solid}$ = Pi, $P_{M}$ = $P_{gas} â€“ P_{solid}$

$\mu$ = $\sqrt \frac{9KT}{4 \pi N P gas â€“ P_{solid}}$

Vapour temperature method:
The Debye equation is specifically meant for gases and hence, this method is considered to be most perfect.

The Debye equation:

$P_{M}$ = $A + \frac{B}{T}$

Where, A = $\frac{4 \pi N \alpha D}{3}$ B =$\frac{4 \pi N}{3} * \frac{\mu^{2}}{3 KT}$

From the Debye equation, it is clear that if a graph is plotted between the total polarisations (PM) and $\frac{1}{T}$, a straight line could be drawn. In case itâ€™s a polar molecule, the slope of line will provide the value of the constant B which finally determines the dipole moment $\mu$.

B = $[(PM_{1}) â€“ (PM_{2})]$  $\frac{T_{2} - T_{1}}{T_{2} T_{1}}$.

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