Bonds formed between atoms and molecules are, quite literally, what holds our world together. Without such intermolecular bonding, we would be surrounded by a formless jumble of swirling gases – save for the fact that we, too, would also be reduced to our component parts. The persistence of solids and liquids fundamentally depends on the existence of intermolecular forces, that is, forces acting between neutral atoms and molecules.
Van der Waals forces result from electrostatic multipole interactions between electrically neutral molecules. The oft-mentioned dipole-dipole interactions, hydrogen bonding, and dispersion forces are special cases of general electrostatic multipole interactions. The foundation of all of these forces is the dipole-dipole interaction, and this will be our first stop along the path.
An electric dipole is a separated pair of equal and opposite charges. The total charge of the pair is zero, but it is surrounded by a dipole electric field. The strength of an electric dipole is the magnitude of the separated charges times the distance of separation. This strength is often measured in Debye units, where the dipole moment of an electron and a proton separated by an Angstrom is about 5 Debye. A pair of electric dipoles each exerts an electrostatic force upon the other. The magnitude of this force depends on the strength of each dipole, on the relative orientation of the dipoles, and follows an inverse-fourth power law.
The electric dipole moment of a molecule, or molecular dipole moment, is a measure of the nonuniformity of the nuclear and electronic charges within the molecule. The molecular dipole moment can be permanent, induced, or instantaneous, but more typically will represent a combination of all three types.
A molecule has a permanent dipole moment (is a ‘polar’ molecule) if electrons are preferentially attracted to some of the atoms which make up the molecule, so that the molecule’s charge distribution is asymmetric. The tendency for an atom in a molecule to attract shared electrons to itself is called electronegativity, which varies from 0.7 to 4.0 Pauling units among the various atoms of the periodic table.
Let’s illustrate how differences in electronegativity create a dipole moment in a two-atom molecule, such as hydrogen chloride (HCl). HCl has a permanent dipole moment of about 1 Debye. The electronegativity of chlorine (3.16) is larger than that of hydrogen (2.2). Accordingly, more of the electrons are located near the chlorine atom, leading to a chlorine atom with a small negative charge and a hydrogen atom with a small positive charge. The electronic redistribution corresponds to the transfer of about 0.16 of an electron from the hydrogen atom to the chlorine. To give a feeling for the size of these interactions, the average dipole-dipole interaction in liquid hydrogen chloride is about 0.025 eV (electron volts), or roughly 20% of the total binding energy of the hydrogen chloride molecules within the liquid (the remainder is mostly dispersion interactions).
An extreme variation of dipole-dipole interactions is called hydrogen bonding. A hydrogen bond is the attractive force between a hydrogen atom attached to a strongly electronegative atom of one molecule and a second atom, from Groups 15 (nitrogen group), 16 (chalcogenide group), or 17 (halogen group) of the periodic table, belonging to a second molecule. These atoms have, respectively, one, two, or three sets of lone pair electrons, which are valence electrons which do not take part in intramolecular bonding.
This seems a very specific set of circumstances, so it is worthwhile to not only explain why the result is a strong bond between molecules, but why it has a special name and an important place in physical chemistry. On the first molecule, a hydrogen atom attached to a strongly electronegative atom will lose most of its charge to the electronegative atom, thereby creating a small but very dense region of positive charge near the hydrogen atom. On the second molecule, an atom with lone pair electrons has a region of large negative charge density along the orientation of the lone pair electrons.
When the positively charged hydrogen atom on the first molecule approaches the negative charge density associated with the lone pair electrons on an atom of the second molecule, they strongly attract each other. The result is called a hydrogen bond, which is clearly a special type of dipole-dipole interaction in which the orientation and proximity of the dipoles results in a rather strong bond.
The strength of a hydrogen bond depends of two major factors. The first is the electronegativity of the atom bonded to the hydrogen atom of the hydrogen bond. The larger the electronegativity, the larger the effective positive charge on the hydrogen atom, and the more concentrated this positive charge becomes. More positive charge concentrated into a smaller volume results in stronger interactions with the lone pair electrons.
The second factor is the period of the atom with the lone pair electrons. The lone pair electrons of the period 2 members of these groups, nitrogen, oxygen, and fluorine, are highly localized, and thus make a large negative charge density available for the hydrogen bond. Accordingly, strong hydrogen bonds (usually the type of which reference is being made) involve nitrogen, oxygen, or fluorine.
As described, a hydrogen bond is a fairly common phenomenon, but some examples offer the potential for dramatic effects. Consider the case where both molecules are water, H2O. Oxygen is highly electronegative and has two lone pairs, so each water molecule offers 2 local concentrations of dense positive charge and 2 local concentrations of dense negative charge.
As a result, an arbitrary number of water molecules can each be bound to four neighboring molecules by identical hydrogen bonds. These hydrogen bonds are quite strong, having a binding energy of about 0.2 eV – not as strong as most chemical bonds, but quite large within the collection of intermolecular forces. The magnitude of the bond strength is the source for most of the astounding properties of water, including the high boiling point, large heat capacity, extraordinary solvation properties, and a solid form (ice) which is less dense than the liquid. The hydrogen bonding of water is the main reason that this variation of the dipole-dipole interaction merits a special scientific status.
A molecule having an induced dipole moment can participate in dipole-dipole intermolecular interactions in just the same manner as molecules with a permanent dipole moment. But what is an induced dipole moment?
Earlier, we discussed the dipole moment of HCl. What happens if an argon atom is placed next to an HCl molecule? The electrons of an argon atom are distributed about the nucleus with spherical symmetry, so argon has no permanent dipole moment. However, the argon electrons can shift around under the influence of external electrostatic interactions.
When argon is placed near an HCl molecule, the electric field associated with the permanent dipole moment of the HCl slightly distorts the initially symmetric distribution of the argon electrons. For example, if the positively charged hydrogen atom of the HCl molecule is closer to the argon atom than the negatively charged chlorine atom, the argon electrons will be slightly attracted to the hydrogen, and the argon nucleus will be slightly repelled therefrom. This electronic distortion generates (or induces) a small dipole moment on the argon atom.
Now that both the argon atom and the HCl molecule have electric dipole moments, they are weakly attracted through standard dipole-dipole interactions. Because the magnitude of the induced electric dipole moment depends on how close the argon atom is to the HCl molecule, the bonding interaction is much shorter in range than are dipole-dipole interactions between molecules having permanent dipole moments. The binding energy between the HCl molecule and the argon atom is about 10 millielectron volts.
Finally, we take a look at the dispersion force, the one form of intermolecular interaction which is universally considered a ‘van der Waals’ interaction. Although often presented with some degree of mystery, the mechanism turns out to be another version of the dipole-dipole interaction.
In our previous discussion of induced dipole moments, it was made clear that an electric dipole moment is induced in a molecule as the result of electron redistribution caused by a nearby electric dipole. A symmetrical molecule such as carbon tetrachloride or benzene has no permanent dipole moment. However, the laws of quantum mechanics, as applied to atomic and molecular electrons, tell us that there will be quantum fluctuations of the electron distribution. These quantum fluctuations produce a small, rapidly changing dipole moment on the symmetrical molecule.
Now this quantum dipole moment will produce an induced dipole moment in neighboring molecules. The result is an induced dipole-induced dipole interaction between the neighboring molecules. This is the phenomenon usually referred to as dispersion forces.
A somewhat controversial topic involves the strength of dispersion forces. The example of liquid helium is often advanced to support the notion that dispersion forces are extremely weak. Owing to the spherically symmetric distribution of helium’s 1s electrons, the only attractive forces between helium atoms are dispersion forces. The magnitude of these forces is indicated by the 4 degrees Kelvin boiling point of liquid helium, which corresponds to a helium-helium bond strength of about 0.8 millielectron volts, which is very small indeed.
Remember that the dipole moment is equivalent to a pair of opposite charges separated by a distance. Because helium is a very small atom having only 2 electrons, it cannot form a large induced dipole moment. However, there are large molecules with many delocalized electrons, but no permanent dipole moment, which might be expected to exhibit larger dispersion forces.
A group of organic molecules which have particularly favorable characteristics for larger dispersion forces is the planar aromatic hydrocarbons, such as benzene, naphthalene, and anthracene. These molecules are completely nonpolar, so that again the only attractive intermolecular forces will be the dispersion forces.
As before, we can get a feel for the magnitude of the dispersion forces from the boiling point of the aromatic hydrocarbons. Benzene boils at 80 degrees Centigrade, indicating a dispersion bond strength around 100 times larger than that between helium atoms. Anthracene boils at 354 degrees Centigrade, corresponding to double the dispersion bonding strength as appears between benzene molecules. The intermolecular bond strength for these examples is roughly 0.1 to 0.2 electron volts – a magnitude comparable to hydrogen bonds. Dispersion forces can dominate intermolecular interactions even in relatively small polar molecules, such as HCl, where the dispersion forces are about 4 times larger than those of the dipole-dipole interaction.
The theory of van der Waals forces is still a subject of very active research, much of it based on rather subtle quantum electrodynamical analysis. Despite the subtleties, these forces determine most of the structure of our everyday world.