The intermolecular interaction that is dependent on the inverse cube of distance between molecules is:

  1. hydrogen bond
  2. ion-ion interaction
  3. ion-dipole interaction
  4. London force

Inverse cube of distance I think means an ion-dipole interaction, since we know force due to a dipole on a charge is inversely proportional to the cube of distance. But I don't understand why the answer given is hydrogen bond. What is the distance dependence of the hydrogen bond? Shouldn't the answer be (3)?


2 Answers 2



The ion-ion or charge-charge interaction is given by

$$ V_{\text{cc}} = \frac{Z_{i}Z_{j}e^{2}}{4\pi\epsilon_{0}} \frac{1}{|\mathbf{R}_{i} - \mathbf{R}_{j}|} $$

and is therefore proportional to $R^{-1}$.


The ion-dipole or charge-(permanent) dipole interaction is given by

$$ V_{\text{cd}} = \frac{Z_{i}e}{4\pi\epsilon_{0}} \frac{\mathbf{R}_{ij} \cdot \vec{\mu}_{j}}{R_{ij}^{3}} $$

and is therefore proportional to $R^{-2}$.


"London force" is often meant to encapsulate any of the van der Waals forces (here, here), but in particular the dispersion force. All of the above have a $R^{-6}$ dependence.

Here is a general table that covers each of the interactions so far:

\begin{array}{lll} \hline \text{type of molecular unit} & \text{type of force} & n~\text{in}~R^{-n} \\ \hline \text{ions} & \text{coulombic} & 1 \\ \text{ion - polar molecule} & \text{ion - dipole} & 2 \\ \text{two polar molecules} & \text{dipole - dipole} & 3 \\ \text{ion - nonpolar molecule} & \text{ion - induced dipole} & 4 \\ \text{polar and nonpolar molecule} & \text{dipole - induced dipole} & 6 \\ \text{nonpolar molecules} & \text{dispersion} & 6 \\ \hline \end{array}


From Wikipedia:

The hydrogen bond is often described as an electrostatic dipole-dipole interaction. However, it also has some features of covalent bonding: it is directional and strong, produces interatomic distances shorter than the sum of the van der Waals radii, and usually involves a limited number of interaction partners, which can be interpreted as a type of valence. These covalent features are more substantial when acceptors bind hydrogens from more electronegative donors.

This implies that hydrogen bonding interactions may not behave exactly as $R^{-3}$. Consider the water dimer:

which is a prototypical example of a hydrogen-bonded complex. From Stone, using density functional-based symmetry-adapted perturbation theory (SAPT-DFT) in the aug-cc-pVQZ basis, \begin{array}{lr} \hline \text{Type of interaction} & \text{Energy (kJ/mol)} \\ \hline \text{Electrostatic} & -33.4 \\ \text{Exchange-repulsion} & 31.5 \\ \text{Dispersion} & -12.2 \\ \text{Induction} & -8.0 \\ \text{Charge transfer} & -5.9 \\ \text{Exchange-dispersion} & 2.3 \\ \text{Exchange-induction} & 7.8 \\ \delta_{\text{HF}}~\text{correction} & -3.4 \\ \hline \text{Total} & -21.5 \\ \hline \end{array} the electrostatic component is clearly the largest contributor, but after taking the absolute value of all interaction terms, is about 32% of the total interaction. Another approach for decomposing the interaction energy is based on absolutely localized molecular orbitals (ALMO-EDA), which at the $\omega$B97M-V/def2-QZVPP level gives \begin{array}{lr} \hline \text{Type of interaction} & \text{Energy (kJ/mol)} \\ \hline \text{Electrostatics} & -65.7 \\ \text{Pauli repulsion} & 65.0 \\ \text{Dispersion} & -7.7 \\ \text{Polarization} & -4.6 \\ \text{Charge transfer} & -7.9 \\ \hline \text{Total} & -20.9 \\ \hline \end{array} SAPT-DFT and ALMO-EDA are in good agreement, though charge transfer is more important in ALMO-EDA primarily due to the lackluster definition of charge transfer within SAPT. Electrostatics are now about 44% of the total interaction. For reference, here is how the additional terms decay (Stone, Table 1.2): \begin{array}{lccl} \hline \text{Contribution} & \text{Additive?} & \text{Sign} & \text{Comment} \\ \hline \textbf{Long-range}~(U \sim R^{-n}) & & & \\ \text{Electrostatic} & \text{Yes} & \pm & \text{Strong orientation dependence} \\ \text{Induction} & \text{No} & - & \\ \text{Dispersion} & \text{approx.} & - & \text{Always present} \\ \text{Resonance} & \text{No} & \pm & \text{Degenerate states only} \\ \text{Magnetic} & \text{Yes} & \pm & \text{Very small} \\ \hline \textbf{Short-range}~(U \sim e^{-\alpha R}) & & & \\ \text{Exchange-repulsion} & \text{approx.} & + & \text{Dominates at very short range} \\ \text{Exchange-induction} & \text{approx.} & - & \\ \text{Exchange-dispersion} & \text{approx.} & - & \\ \text{Charge transfer} & \text{No} & - & \text{Donor-acceptor interaction} \\ \hline \end{array}


Although components of hydrogen bonding interactions may have a $R^{-3}$ distance dependence, there are significant contributors to the hydrogen bond interaction other than electrostatics that do not decay as $R^{-3}$; in general, it is a complex interaction and its definition is still hotly debated. For that reason, the best answer is (3), the ion-dipole interaction.



Simple Google search led me to the content at Wikipedia page:

The energy of a Keesom interaction depends on the inverse sixth power of the distance, unlike the interaction energy of two spatially fixed dipoles, which depends on the inverse third power of the distance.

  • $\begingroup$ so this ion-dipole interaction comes under which one exctly?? keesom interactiom?? or two fixed dipoles?? i thought it comes under the interaction between a charge and a dipole in space $\endgroup$ Commented Apr 20, 2015 at 10:32
  • $\begingroup$ This answer does not seem to fit any of the given options. $\endgroup$ Commented May 14, 2018 at 1:38
  • $\begingroup$ @GaurangTandon only if hydrogen bond is considered dipole-dipole interaction... $\endgroup$
    – user43021
    Commented May 14, 2018 at 23:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.