# Intermolecular force

Intermolecular forces are forces of attraction or repulsion which act between neighboring particles (atoms, molecules or ions). They are weak compared to the intramolecular forces, the forces which keep a molecule together. For example the covalent bond, involving the sharing of electron pairs between atoms is much stronger than the forces present between the neighboring molecules. They are an essential part of force fields used in molecular mechanics.

The investigation of intermolecular forces starts from macroscopic observations which point out the existence and action of forces at a molecular level. These observations include non-ideal gas thermodynamic behavior reflected by virial coefficients, vapor pressure, viscosity, superficial tension and adsorption data.

The first reference to the nature of microscopic forces is found in Alexis Clairaut's work Theorie de la Figure de la Terre.[1] Other scientists who have contributed to the investigation of microscopic forces include: Laplace, Gauss, Maxwell and Boltzmann.

Attractive intermolecular forces are considered by the following types:

Information on intermolecular force is obtained by macroscopic measurements of properties like viscosity, PVT data. The link to microscopic aspects is given by virial coefficients and Lennard-Jones potentials.

## Dipole-dipole interactions {{safesubst:#invoke:anchor|main}}

Dipole-dipole interactions are electrostatic interactions between permanent dipoles in molecules. These interactions tend to align the molecules to increase attraction (reducing potential energy). An example of a dipole-dipole interaction can be seen in hydrogen chloride (HCl): the positive end of a polar molecule will attract the negative end of the other molecule and influence its position. Polar molecules have a net attraction between them. Examples of polar molecules include hydrogen chloride (HCl) and chloroform (CHCl3).

Often molecules contain dipolar groups, but have no overall dipole moment. This occurs if there is symmetry within the molecule that causes the dipoles to cancel each other out. This occurs in molecules such as tetrachloromethane. Note that the dipole-dipole interaction between two individual atoms is usually zero, since atoms rarely carry a permanent dipole. See atomic dipoles.

## Van der Waals forces

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The vdW forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical adsorption of gases, but also to a universal force of attraction between macroscopic bodies.[4]

### Keesom (permanent-permanent dipoles) interaction

The first contribution to Van der Waals forces is due to electrostatic interactions between charges (in molecular ions), dipoles (for polar molecules), quadrupoles (all molecules with symmetry lower than cubic), and permanent multipoles. It is referred to as Keesom interactions(named after Willem Hendrik Keesom).[5] These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent.[6]

They consists in attractive interactions between dipoles that are ensemble averaged over different rotational orientations of the dipoles. It is assumed that the molecules are constantly rotating and never get locked into place. This is a good assumption, but at some point molecules do get locked into place. 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. The Keesom interaction can only occur among molecules that possess permanent dipole moments aka two polar molecules. Also Keesom interactions are very weak Van der Waals interactions and do not occur in aqueous solutions that contain electrolytes. The angle averaged interaction is given by the following equation:

Where m = charge per length, ${\displaystyle \varepsilon _{o}}$ = permitivity of free space, ${\displaystyle \varepsilon _{r}}$ = dielectric constant of surrounding material, T = temperature, ${\displaystyle k_{b}}$ = Boltzmann constant, and r = distance between molecules.

### Debye (permanent-induced dipoles) force

The second contribution is the induction (also known as polarization) or Debye force, arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles). These induced dipoles occur when one molecule with a permanent dipole repels another molecule’s electrons. A molecule with permanent dipole can induce a dipole in a similar neighboring molecule and cause mutual attraction. Debye forces cannot occur between atoms. The forces between induced and permanent dipoles are not as temperature dependent as Keesom interactions because the induced dipole is free to shift and rotate around the non-polar molecule. The Debye induction effects and Keesom orientation effects are referred to as polar interactions.[7]

The induced dipole forces appear from the induction (also known as polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced (by the former di/multi-pole) multipole on another.[8][9][10][11] This interaction is called the Debye force, named after Peter J.W. Debye.

One example of an induction-interaction between permanent dipole and induced dipole is the interaction between HCl and Ar. In this system, Ar experiences a dipole as its electrons are attracted (to the H side of HCl) or repelled (from the Cl side) by HCl.[8][10] The angle averaged interaction is given by the following equation.

Where ${\displaystyle \alpha }$= polarizability

This kind of interaction can be expected between any polar molecule and non-polar/symmetrical molecule. The induction-interaction force is far weaker than dipole-dipole interaction, but stronger than the London dispersion force.

### London dispersion force (induced-induced dipoles interaction)

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The third and dominant contribution is the dispersion or London force (fluctuating dipole-induced dipole), due to the non-zero instantaneous dipole moments of all atoms and molecules. Such polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in non-polar molecules. Thus, London interactions are caused by random fluctuations in electron density in an electron cloud. An atom with a large number of electrons will have a greater associated London force than a smaller atom. The dispersion (London) force is the most important component because all materials are polarizable, whereas Keesom and Debye forces require permanent dipoles. The London interaction is universal and is present in atom-atom interactions as well. For various reasons, London interactions (dispersion) have been considered relevant for interactions between macroscopic bodies in condensed systems. Hamaker developed the theory of vdW between macroscopic bodies in 1937 and showed that the additivity of these interactions renders them considerably more long-range.[12]

## Relative strength of forces

Bond type Dissociation energy (kcal/mol)[13]
Ionic Lattice Energy 250-4000 [14]
Covalent Bond Energy 30-260
Hydrogen Bonds 1-12 (about 5 in water)
Dipole–Dipole 0.5–2 {{ safesubst:#invoke:Unsubst \$B=

{{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

London Dispersion Forces <1 to 15 (estimated from the enthalpies of vaporization of hydrocarbons)[15]

Note: this comparison is only approximate – the actual relative strengths will vary depending on the molecules involved. Ionic and covalent bonding will always be stronger than intermolecular forces in any given substance.

## Quantum mechanical theories

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Intermolecular forces observed between atoms and molecules can be described phenomenologically as occurring between permanent and instantaneous dipoles, as outlined above. Alternatively, one may seek a fundamental, unifying theory that is able to explain the various types of interactions such as hydrogen bonding, van der Waals forces and dipole-dipole interactions. Typically, this is done by applying the ideas of quantum mechanics to molecules, and Rayleigh–Schrödinger perturbation theory has been especially effective in this regard. When applied to existing quantum chemistry methods, such a quantum mechanical explanation of intermolecular interactions, this provides an array of approximate methods that can be used to analyze intermolecular interactions.

## References

1. H. Margenau, N Kestner, Theory of intermolecular forces, International Series of Monographs in Natural Philosophy, Pergamon Press
2. Dr. Michael Blaber, 1996. Intermolecular Forces. http://www.mikeblaber.org/oldwine/chm1045/notes/Forces/Intermol/Forces02.htm
3. Template:GoldBookRef
4. “Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy”, Fabio L. Leite, Carolina C. Bueno, Alessandra L. Da Róz, Ervino C. Ziemath and Osvaldo N. Oliveira Jr., Int. J. Mol. Sci. 2012, 13 12777 (p.1)
5. Keesom, W.H. The second virial coefficient for rigid spherical molecules whose mutual attraction is equivalent to that of a quadruplet placed at its center. Proc. R. Acad. Sci. 1915, 18, 636–646
6. “Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy”, Fabio L. Leite, Carolina C. Bueno, Alessandra L. Da Róz, Ervino C. Ziemath and Osvaldo N. Oliveira Jr., Int. J. Mol. Sci. 2012, 13 12777 (p.2)
7. “Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy”, Fabio L. Leite, Carolina C. Bueno, Alessandra L. Da Róz, Ervino C. Ziemath and Osvaldo N. Oliveira Jr., Int. J. Mol. Sci. 2012, 13 12777 (p.3)
8. Blustin PH, 1978. A Floating Gaussian Orbital calculation on argon hydrochloride (Ar • HCl). Theoret. Chim. Acta 47, 249–257.
9. Nannoolal Y, 2006. Development and critical evaluation of group contribution methods for the estimation of critical properties, liquid vapour pressure and liquid viscosity of organic compounds. University of Kwazulu-Natal PhD Thesis.
10. Roberts JK and Orr WJC, 1938. Induced dipoles and the heat of adsorption of argon on ionic crystals. Trans. Faraday Soc. 34, 1346–1349.
11. Sapse AM, Rayez-Meaume MT, Rayez JC and Massa LJ, 1979. Ion-induced dipole H-n clusters. Nature 278, 332–333.
12. “Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy”, Fabio L. Leite, Carolina C. Bueno, Alessandra L. Da Róz, Ervino C. Ziemath and Osvaldo N. Oliveira Jr., Int. J. Mol. Sci. 2012, 13 12777 (p.3-4)
13. Organic Chemistry: Structure and Reactivity by Seyhan Ege, pp.30–33, 67
14. Template:Cite web
15. Majer, V. and Svoboda, V., Enthalpies of Vaporization of Organic Compounds, Blackwell Scientific Publications, Oxford, 1985.}