Intermolecular force

From Wikipedia, the free encyclopedia

Intermolecular forces are electromagnetic forces that act between molecules or between widely separated regions of a macromolecule. These forces can be cohesive between like molecules in for example surface tension or adhesive between unlike molecules for example in capillary action. Listed in order of decreasing strength, these forces are:

• Ionic interactions
• Hydrogen bonds
• dipole-dipole interactions
• London dispersion forces (Van der Waals force)

Contents 1 Description and strength 1.1 Ionic interactions 1.2 Hydrogen bonding 1.3 Dipole-dipole interactions 1.4 London dispersion forces 1.5 Quantum mechanical theory of dispersion forces 1.6 Anisotropy and non-additivity of intermolecular forces 1.7 Software for calculation of intermolecular forces 1.8 See also

[edit] Description and strength

These are fundamentally electrostatic interactions (ionic interactions, hydrogen bond, dipole-dipole interactions) or electrodynamic interactions (Van der Waals force/London dispersion forces). Electrostatic interactions are classically described by Coulomb's law; the basic difference between them is the strength of their charge. Ionic interactions are the strongest with integer level charges, hydrogen bonds have partial charges that are about an order of magnitude weaker, and dipole-dipole interactions also come from partial charges another order of magnitude weaker.

A very approximate strength order would be:

Bond type	Relative strength
Ionic bonds	1000
Hydrogen bonds	100
Dipole-dipole	10
London (Van der Waals) Forces	1

[edit] Ionic interactions

These are interactions that occur between charged species (ions). Like charges repel, while opposite charges attract. These bonds form when the electronegativities between two atoms are large enough that one steals an electron from the other. The now oppositely charged ions are attracted. Ionic compounds have high melting and boiling points due to the large amount of heat required to break the forces between the charged ions. When molten they are also good conductors of heat and electricity, due to free or delocalised electrons.

[edit] Hydrogen bonding

Hydrogen bonding occurs when a hydrogen atom is covalently bonded to a small highly electronegative atom such as nitrogen, oxygen, or fluorine. The result is a dipolar molecule. The hydrogen atom has a partial positive charge δ+ (see unit: Debye) and can interact with another highly electronegative atom in an adjacent molecule (again N, O, or F). This results in a stabilizing interaction that binds the two molecules together. An important example is water:

         δ+                δ+
          H               H
           \             /
            O | | | H - O      
           / δ-    δ+    δ-
          H
         δ+

Hydrogen bonds are found throughout nature. They give water its unique properties that are so important to life on earth. Hydrogen bonds between hydrogen atoms and nitrogen atoms of adjacent base pairs provide the intermolecular force that bind together the two strands in a molecule of DNA.

The critical difference between hydrogen bonding and dipole-dipole interactions is that the hydrogen is partially transferred to the second molecule - the second molecule's lone pair of electrons forms a covalent bond and the pair becomes somewhat like:

H₂O⁺-H ^-O-H

The effect is twofold: The bonding is stronger and is directional. The directional nature of hydrogen bonding requires the two molecules to adopt a specific relative geometry.

[edit] Dipole-dipole interactions

Dipole-dipole interactions, also called Keesom interactions or Keesom forces after Willem Hendrik Keesom who produced the first mathematical description in 1921, are the force that occur between two molecules with permanent dipoles (spatially oriented δ+ within a molecule). These work in a similar manner to ionic interactions, but are weaker because only partial charges are involved. They result from the angle-averaged dipole-dipole interaction between two atoms or molecules and its potential. An example of this can be seen in hydrochloric acid:

(+)(-)   (+)(-)
 H--Cl----H--Cl

Note added by other author: Usually the dipole-dipole interaction between two atoms is zero, because atoms rarely carry a permanent dipole, see atomic dipoles.

[edit] London dispersion forces

Also called London forces, instantaneous dipole (or multipole) effects (spatially variable δ+) or Van der Waals forces, these involve the attraction between temporarily induced dipoles in nonpolar molecules (often disappear within an instant). This polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in nonpolar molecules. An example of the former is chlorine dissolving in water:

                 (+)(-)(+)  (-) (+)
[Permanent Dipole] H-O-H-----Cl-Cl [Induced Dipole]

Note added by other author: Sketched is an interaction between the permanent dipole on water and an induced dipole on chlorine. The latter dipole is induced by the electric field offered by the permanent dipole of water (see field from an electric dipole). This permanent dipole-induced dipole interaction is referred to as induction (or polarization) interaction and is to be distinguished from the London dispersion interaction. The latter is sometimes described as an interaction between two instantaneous dipoles, see molecular dipole. The Cl₂—Cl₂ interaction that now follows is an example of a proper London dispersion interaction.

                      (+) (-)    (+) (-)
[instantaneous dipole] Cl-Cl------Cl-Cl [instantaneous dipole]

Note added by other author: It must be pointed out that the London interaction is not the only interaction between two chlorine molecules in the region where the overlap between the respective charge distributions may be neglected. Each chlorine molecule carries permanent multipole moments of even order, the first one being a permanent quadrupole moment (order 2). The interaction between two permanent multipole moments also contributes to the intermolecular force and the first term (quadrupole-quadrupole) is as important as the London dispersion force.

London dispersion forces exist between all atoms. London forces are the only reason for rare-gas atoms to condense at low temperature.

[edit] Quantum mechanical theory of dispersion forces

The first explanation of the attraction between noble gas atoms was given by Fritz London in 1930 ^[1]. He used a quantum mechanical theory based on second-order perturbation theory. The perturbation is the Coulomb interaction V between the electrons and nuclei of the two monomers (atoms or molecules) that constitute the dimer. The second-order perturbation expression of the interaction energy contains a sum over states. The states appearing in this sum are simple products of the excited electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included and the Pauli exclusion principle is only partially satisfied. London developed the perturbation V in a Taylor series in , where R is the distance between the nuclear centers of mass of the monomers. This Taylor expansion is known as the multipole expansion of V because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer. Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles somewhat an expression describing the interaction between instantaneous multipoles (see the qualitative description above). Additionally an approximation, named after Albrecht Unsöld, must be introduced in order to obtain a description of London dispersion in terms of dipole polarizabilities and ionization potentials. In this manner the following approximation is obtained for the dispersion interaction between two atoms A and B. Here α^A and α^B are the dipole polarizabilities of the respective atoms. The quantities I_A and I_B are the first ionization potentials of the atoms and R is the intermolecular distance.

Note that this final London equation does not contain instantaneous dipoles (see molecular dipoles). The "explanation" of the dispersion force as the interaction between two such dipoles was invented after London gave the proper quantum mechanical theory. See the authoritative work ^[2] for a criticism of the instantaneous dipole model and ^[3] for a modern and thorough exposition of the theory of intermolecular forces.

The London theory has much similarity to the quantum mechanical theory of light dispersion, which is why London coined the phrase "dispersion effect" for the interaction that we described in this lemma.

References:

1. ^ F. London, Zeitschrift für Physik, vol. 60, p. 245 (1930) and Z. Physik. Chemie, vol. B11, p. 222 (1930). English translations in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000).
2. ^ J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954
3. ^ A. J. Stone, The Theory of Intermolecular Forces, 1996, (Clarendon Press, Oxford)

[edit] Anisotropy and non-additivity of intermolecular forces

Consider the interaction between two electric point charges at position and . By Coulomb's law the interaction potential depends only on the distance between the particles. For molecules this is different. If we see a molecule as a rigid 3-D body, it has 6 degrees of freedom (3 degrees for its orientation and 3 degrees for its position in R³). The interaction energy of two molecules (a dimer) in isotropic and homogeneous space is in general a function of 2x6-6=6 degrees of freedom (by the homogeneity of space the interaction does not depend on the position of the center of mass of the dimer, and by the isotropy of space the interaction does not depend on the orientation of the dimer). The analytic description of the interaction of two arbitrarily shaped rigid molecules requires therefore 6 parameters. (One often uses two Euler angles per molecule, plus a dihedral angle, plus the distance.) The fact that the intermolecular interaction depends on the orientation of the molecules is expressed by stating that the potential is anisotropic. Since point charges are by definition spherical symmetric, their interaction is isotropic. Especially in the older literature, intermolecular interactions are regularly assumed to be isotropic (e.g., the potential is described in Lennard-Jones form, which depends only on distance).

Consider three arbitrary point charges at distances r₁₂, r₁₃, and r₂₃ apart. The total interaction U is additive, i.e., it is the sum

U = u(r₁₂) + u(r₁₃) + u(r₂₃).

Again for molecules this can be different. Pretending that the interaction depends on distances only—but see above— the interaction of three molecules takes in general the form

U = u(r₁₂) + u(r₁₃) + u(r₂₃) + u(r₁₂,r₁₃,r₂₃),

where u(r₁₂,r₁₃,r₂₃) is a non-additive three-body interaction. Such an interaction can be caused by exchange interactions, by induction, and by dispersion (the Axilrod-Teller triple dipole effect).

[edit] Software for calculation of intermolecular forces

Quantum 3.2
An ab initio quantumchemical package: SAPT

[edit] See also

• Hydrophobic effect
• Polymer