Talk:Chemical bond/Temp
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A chemical bond is a link between atoms in a molecule or in an crystal lattice. The atoms in bonds are electrically neutral and do not attract each other. They are composed of a positively-charged nucleus surrounded by a negatively-charged cloud of electrons. As two atoms approach one another, their lightweight electron clouds repel each other by Coulomb's law of electrostatic forces, and the relatively large weight atoms attract each other by Newton's law of universal gravitation. This weak attraction takes place already at long distances of 100 nanometer, whereas the stronger repulsion only becomes preponderant at distances of 100 picometer, a distance which is similar to atomic radii. The atoms are held together at the distance at which the attractive and repulsive forces cancel out.
A number of different types of chemical bond are usually distinguished. All of these are the result of electrostatic forces operating within the constraints of the quantisation of electron energies but, for historical and practical reasons, their mathematical descriptions can be quite different.
The study of chemical bonds, including formation and rupture, forms a large part of the science of chemistry. The bonds which are observed correspond to the distance between atoms at which repulsion and attraction are in balance.
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[edit] History
The atomists of Ancient Greece recognised the need for a theory of bonding between atoms, which they thought was either the result of geometric constraints or small hooks attached to the atoms. Geometric arguments were used by Dalton at the start of the nineteenth century to explain his Law of partial pressures, in which different gases apperered not to interact. Indeed, the structure of many ionic compounds can be predicted on purely geometric grounds.
The concept of chemical affinity, in which substances are "drawn" to one another, was prevalent in alchemy from at least the twelfth century. The investigations into electricity in the first decades of the nineteenth century lead Berzelius to equate chemical affinity with an electrostatic attraction. Berzelius described the behaviour of ions in solution by his theory, and was close to the modern description of ionic bonding, but he could not explain the existence of bonds between identical atoms. His scientific reputation and conviction that chemical affinity could be explained entirely by the precepts of classical electrostatics led to the oversight of the work of Avogadro, work which implied the existence of O2 molecules.
Avogadro's principle was finally accepted around 1860, sixteen years after the Italian's death and without any great pomp, as a natural consequence of the kinetic theory of gases. Bonds between identical atoms existed, even if they couldn't be explained by the theoretical framework of the time. A consequence of this recognition was the correction of the values of atomic masses, which depended on knowing whether elemental oxygen existed as single atoms or as a diatomic molecule. The newly available, correct, values of atomic masses enabled Mendeleev to propose his periodic table in 1869.
The mid-nineteenth century also saw an explosion in the field of organic chemistry, with thousands of new compounds being described. Although these could only be characterised by their physical properties and by their elemental composition, it became apparent that they could also be classified on the basis of a hypothesis of the number of bonds formed by each element, which was known as its valency. The description of the structure of benzene by Kekulé in 1879 was the apogee of this approach.
Although there was no longer much doubt of the physical reality of chemical bonds, their explanation had to wait until the elucidation of the structure of the atom at the turn of the twentieth century. Gilbert Lewis proposed the concept of the covalent bond based on the sharing of a pair of electrons in 1916, describing the simplest, and by far the most common, case of modern theories.
When Erwin Schrödinger proposed his wave equation in 1926 to describe the behaviour of electrons in atoms, it was immediately apparent that the same approach could be applied to molecules. The following year, Walter Heitler and Fritz London applied the approach to the hydrogen molecule (H2), but ran into difficulties (which still exist today) with the three-body problem. The first mathematically complete solution of the wave equation of a molecule, the hydrogen molecular ion (H2+), was published in 1930 by Edward Teller.
The 1930s saw an explosion in the development and general acceptance of quantum theories of chemical bonding. A great part was played by Linus Pauling and his seminal textbook On the Nature of the Chemical Bond (best known from its third edition published in 1939). To main approached were proposed, the valence bond theory supported by Pauling, and the alternative molecular orbital theory. The latter would prove to be more useful for calculating (and hence predicting) the properties of molecules, although the former has contributed greatly to the vocabulary of chemistry and the description of bonds (e.g. hybridisation). The main limit, even with molecular orbital theory, was the availability of computing power, and calculations on molecules of more than twenty electrons (the size of ethanol) would remain rare until the 1980s.
With the drastic fall in price of compututing power, computational chemistry has become much more widespread, and calculations on molecules the size of proteins are now routine. Many new approaches have become available, such as approximate solutions to the problem of electron correlation, density functional theory (particularly for transition metal compounds) and the electron localisation function to name but three.
[edit] Properties
While each chemical bond has its own characteristics, a certain number of properties are shared by all bonds and can be used to compare them.
[edit] Bond strength
By definition, the atoms (or ions) involved in a chemical bond have a lower energy than would be the case were they to be completely separated: this difference in energy can be equated to the strength of the bond, and is usually measured by the bond dissociation energy. In a few cases, the bond dissociation energy can be measured directly, but it is usually inferred from other thermodynamic data. Tabulated values are usually averages over a number of similar bonds in different molecules. Values range from 0–1100 kJ/mol (0–260 kcal/mol).
[edit] Bond length
The length of a chemical bond is taken to be the average distance between the two nuclei. For gases it can be determined to a high degree of accuracy by rotational spectroscopy or by electron diffraction. For solids, it is usually measured by X-ray diffraction: however this method cannot measure the length of bonds involving hydrogen, for which neutron diffraction must be used. Average bond lengths (often with standard deviations) for a large number of bond situations in inorganic and organic compounds have been calculated from data in the Cambridge Crystallographic Database. Other factors being equal, a shorter bond is also a stronger bond.
[edit] Force constant
If a chemical bond is stretched or compressed, it will tend to return to its average length. For small displacements, it can be compared to a spring joining the two nuclei, and treated as a simple harmonic oscillator. The vibrations of a bond can be observed by vibrational spectroscopy: for polar bonds infrared spectroscopy is the preferred technique, while for nonpolar bonds Raman spectroscopy must be used. Once the vibrational frequency is known, the force constant can be calculated taking into account the masses of the different atoms. A higher force constant is an indication of a stronger bond (other factors being equal), and can be used for comparison where it is impractical to measure a bond dissociation energy.
[edit] Classification
The following categories of chemical bond should not be taken as exclusive but rather as typical cases which represent various points on a continuum of properties. Two factors should be taken into account in classifying a chemical bond: the symmetry of the electron distribution and the extent to which the electrons are bound to a single pair of atoms. Hence a the electrons are shared equally between two atoms in a perfect covalent bond, while there would be complete transfer of one or more electrons from one atom to the other in a perfect ionic bond (if such a bond existed, see below). Similarly the electrons in a homonuclear diatomic molecule are deemed to be completely localised, while those in a "good" metal are completely delocalised, even though the sharing of electrons is equitable in both cases. However it should be remembered that most chemical bonds have intermediate properties, and the manner in which they are described is often a question of practicality and personal preference.
[edit] Covalent bonds
| Strengths of covalent bonds |
|
|---|---|
| H–H | 436 kJ/mol 104.4 kcal/mol |
| C–C | 245 kJ/mol 58.6 kcal/mol |
| N–N | 84 kJ/mol 20.0 kcal/mol |
| O–O | 145 kJ/mol 34.6 kcal/mol |
| F–F | 265 kJ/mol 63.5 kcal/mol |
| Cl–Cl | 242 kJ/mol 57.8 kcal/mol |
| C–H | 365 kJ/mol 87.3 kcal/mol |
| N–H | 350 kJ/mol 83.7 kcal/mol |
| O–H | 461 kJ/mol 110.2 kcal/mol |
| H–F | 614 kJ/mol 147.5 kcal/mol |
| H–Cl | 429 kJ/mol 102.7 kcal/mol |
| C–O | 293 kJ/mol 70.0 kcal/mol |
| C=C | 420 kJ/mol 100 kcal/mol |
| N=N | 710 kJ/mol 170 kcal/mol |
| C=O | 625 kJ/mol 150 kcal/mol |
| CºC | 515 kJ/mol 123 kcal/mol |
| CºN | 625 kJ/mol 150 kcal/mol |
A covalent bond is characterised by the sharing of electrons (usually a single pair of electrons) between two or more atoms. This arises from the interaction of atomic orbitals on adjacent atoms to form molecular orbitals: this approach is known as the linear combination of atomic orbitals (LCAO).
Consider two hydrogen atoms, labelled A and B, separated by a distance r. The 1s-orbital on atom A is referred to as φA, and that on atom B as φB. The system of the two atoms has D∞h symmetry, and any solution of the Schrödinger wave equation for the system must also have this symmetry. The simplest unique pair of combinations of the two 1s-orbitals which satisfies this condition is:
-
- φ+ = (φA + φB) /√2
- φ− = (φA − φB) /√2
Solving the wave equation to obtain the energies of these combined orbitals shows that their energies differ from those of the isolated 1s-orbitals. In particular, a modifying factor known as the overlap integral, SAB or <A|B>, is introduced.
-
- SAB = <A|B> = ∫ φAφB* dτ
As its name suggests, the overlap integral is a measure of the degree of overlap between the two atomic orbitals: it can vary between zero and one and depends, among other factors, on the interatomic distance. The effect is that φ+ is stabilised (lower energy) in comparison to an isolated 1s-orbital while φ− is destabilised (higher energy). φ+ is known as a bonding orbital, while φ− is known as an antibonding orbital. Each molecular orbital can accept two electrons: each hydrogen atom provides one electron which goes into the lower-energy bonding orbital. The total energy of the system is lower than that of the two isolated hydrogen atoms, and a hydrogen molecule is formed.
The lowering in energy of the bonding orbital is due to the fact that the electrons spend part of their time between the two nuclei, and so experience a greater positive charge than in the isolated atom. The presence of electron density between the nuclei also reduces their mutual repulsion, which lowers the energy of the system as whole.
In the case of the hydrogen molecule, the two atoms are identical and the elctron density is shared equally between them, as is required by the molecular symmetry. Where the two atoms forming a bond are not strictly identical, the electron density is not shared equally, and the bond which is formed is said to be polar. The form of the bonding orbital in this case is:
-
- φ+ = c1φA + c2φB
where c12 + c22 = 1. The atom having the larger coefficient has the larger share of the electron density, and hence has a partial negative charge (denoted δ−). In many cases, the whole molecule will have a net dipole moment, but this is not always the case: each of the bonds in sulfur hexafluoride is polar (with the fluorine atoms carrying partial negative charges), but the charges cancel each other out to leave the molecule with no overall dipole moment.
The tendency of an atom in a molecule to attract a larger share of the electron density is called electronegativity: the concept was originally proposed by Pauling on the basis of a comparison of bond energies in homonuclear and heteronuclear molecules, and has been shown to correlate with a wide variety of atomic and molecular properties.
Unfortunately it is not possible to measure the polarity of an individual bond. An estimation can be made on the basis of the orbital coefficients, but this is only as accurate as the model used to calculate the coefficients and cannot be verified experimentally. Dipole moments can only be measured for whole molecules, and include the contributions not only of bonds but also of any lone pairs present. Pauling presented a formula for estimating the proportion of ionic character based on the difference in electronegativity between the two atoms.
-
- pionic = 1 − exp[−(χA−χB)2/4]
[edit] Multiple bonds
The covalent bond in the hydrogen molecule is formed by a single pair of electrons, as is the case for the majority of covalent bonds. The electron density is evenly distributed around the bond axis (with no nodal plane), and the bond is termed a σ-bond by analogy with s-orbitals which are spherically symmetrical and also have no angular nodes.
In certain circumstances a pair of atoms may be connected by more than one pair of electrons: this is the case, for example, between the two carbon atoms of ethylene, which are linked by two pairs of electrons forming what is termed a double bond. One pair of electrons forms a σ-bond similar to that in ethane, while the second pair forms a π-bond between the two atoms above and below the plane of the molecule. A π-bond has a single nodal plane in the same manner as a p-orbital. In valence bond theory, π-bonds are formed by the side-to-side overlap of two p-orbitals (an end-to-end overlap forms a σ-bond). In appropriate circumstances, a second π-bond can be formed, leading to an overall triple bond, as is the case in acetylene or dinitrogen (N2).
Double bonds are stronger (and shorter) than single bonds, and triple bonds are stronger and shorter still. Together, the two π-bonds in a triple bond have overall cylindrical symmetry (as do σ-bonds), but the electron density precisely along the bond axis is zero: as such, they are less efficient at shielding the internuclear repulsion than σ-bonds. Double bonds do not have cylindrical symmetry, and this leads to a barrier to rotation around the bond. For this reason, double-bonded compounds such as alkenes may show cis-trans isomerism.
Quadruple bonds are also known in a handful of transition metal compounds, particularly in those of chromium and molybdenum. A quadruple bond consists of a σ-bond, two π-bonds and a δ-bond. The latter may be thought of as two d-orbitals overlapping face-to-face.
The total number of bonds formed between two atoms is known as the bond order. Fractional bond orders are also known, and are associated either with unpaired electrons, as in nitric oxide (bond order 2.5) or the superoxide ion (bond order 1.5), or with conjugation (see below).
[edit] Conjugation and aromaticity
Where two double bonds are separated by a single bond, as in butadiene, the intervening single bond shows partial double bond character as if the π-bonding system extended along the whole length of the molecule. This phenomenon is known as conjugation, and is usually explained by Hückel theory, a particularly simple form of molecular orbital theory which deals only with π-bonds and similar interactions. The electrons in the π-bonds effectively have more space available to them, which reduces both the electrostatic repulsion between them and their zero point energy (a quantum-mechanical energy which results from their relative confinement).
The effect is most striking in cyclic systems which contain 2n+2 π-electrons (n = 0, 1, 2...). In such systems, which are known as aromatic, the bonds are all equivalent and do not show the normal chemistry associated with double bonds (such as electrophilic addition). The best known example of an aromatic compound is benzene, which has six π-electrons (n = 1): it is stabilised by 163 kJ/mol (39 kcal/mol) compared its hypothetical unconjugated isomer. The condition of 2n+2 π-electrons, known as Hückel's rule, is very important, at least for small values of n: cyclic compounds with 2n electrons, such as cyclooctatetraene, are not aromatic and are even destabilised ("antiaromatic").
[edit] Three centre-two electron bonds
One of the legacies of the valence bond theory championned by Pauling is a tendency to consider chemical bonds as being restricted to a single pair of adjacent atoms. This is simplistic to say the least, and not even a correct statement of intricacies of valence bond theory (merely of a popular view of it). As the phenomena of conjugation and aromaticity show, the effects of a chemical bond can extend to more than two atoms.
The most striking examples are to be found in the boranes (hydrides of boron), of which the simplest which can be isolated and studied experimentally is diborane, B2H6. Diborane has eight boron–hydrogen bonds but only twelve electrons (six pairs), insufficient to form normal two-electron bonds throughout the molecule. Although valence bond theory can provide a description of the bonding, the approach of molecular orbital theory is much simpler. The four terminal hydrogens are bound to their respective boron atoms by normal two-electron bonds, while there are two bonding orbitals each of which covers the two boron atoms and one of the bridging hydrogens and each of which is filled with a pair of electrons. Hence there are six bonding orbitals for six pairs of electrons, but two of the orbitals cover three atoms ("centres") for two electrons. This approach can be extended to the higher boranes, and forms the theoretical basis for Wade's rules which describe the structure of boranes.
In boranes there are insufficient electrons to form two centre-two electron bonds throughout the molecule, but there are also molecules which appear not to have enough atomic orbitals available to form the observed number of bonds. Such molecules are termed hypervalent, and their theoretical treatment is still the subject of some controversy. Sulfur hexafluoride contains six sulfur–fluorine bonds, but sulfur normally uses only four orbitals in its bonding—one 3s-orbital and three 3p-orbitals. Pauling proposed that, in such cases, sulfur also uses two of its five 3d-orbitals to form bonds, a phenomenon known as sp3d2-hybridisation. An alternative view based on molecular orbital theory is that the four bonding orbitals cover the six obeserved bonds, giving a bond order of 2/3 for each. As with many of the best scientific controversies, there is no way on unequivocally testing the two hypotheses, and there is no reason to suppose that the reality might not be somewhere in between the two points of view.
[edit] Other bond types
[edit] Ionic bonds
| Strengths of ionic bonds |
||
|---|---|---|
| Na–Cl | 281.4 pm | 107 kJ/mol 25.5 kcal/mol |
| Calculated per bond for dissociation to neutral atoms. | ||
If one were to bring a sodium atom and a chlorine atom together, one would not expect to observe a transfer of one electron from the sodium to the chlorine, as the reaction is strongly endothermic:
-
- Na + Cl = Na+ + Cl−, ΔU = +114 kJ/mol (+27.3 kcal/mol)
However the resulting ions would be attracted to one another by classical electrostatic forces, at least until they became so close that the repulsion between their electron shells became preponderant. The sodium ion would also be attracted to any other chloride ions which happened to be present (and vice versa), again until the repulsion of the electron shells overcame the attraction between the oppositely-charged ions. Kossel realised in 1916 that this attraction stabilises the ions in solids and liquids compared to the gas phase.
The theory of ionic bonding treats the ions as hard spheres of fixed charge which are attracted to one another by Coulomb's law but which cannot overlap with one another. The electrical field around the ion is spherically symmetrical, and so such bonds do not have any preferred direction: the structure is determed only by geometrical principles, notable the radius ratio rule. These predict that each sodium ion in solid sodium chloride should be surrounded by six chloride ions at the vertices of an octahedron (and vice versa), as is observed in practice. The strength of an ionic bond, known as the lattice energy, may be inferred from experimental measurements (using the Born-Haber cycle) or calculated from Coulomb's Law: in cases such as sodium chloride, there is good agreement between calculation and experiment.
In fact the "pure" ionic bonding of the classical model does not, and cannot, exist, and this for reasons of classical physics as much as quantum mechanics. A sodium chloride molecule (sodium chloride exists as NaCl molecules in the gas phase) would have sphere containing eighteen electrons (the chloride ion) next to a sphere with a net positive charge (the sodium ion). The electrons in the chloride ion would tend to be attracted towards the sodium ion: they would spend more of their time on the same side of the chlorine nucleus as the sodium ion and less of their time on the opposite side. The chloride ion would be distorted from being a perfect sphere into more of an egg shape. In the solid sodium chloride, the chloride ions would be pulled from spheres into (very) rounded octahedra: at the same time, the ten electrons of the sodium ion would tend to be pushed away into the spaces between the negatively-charged chloride ions. The interlocking polyhedra of Plato find a modern (and softer) reflection!
This distortion is to referred to as polarisation, and the tendency for an ion to be polarised is known as its polarisability: polarisability is measurable by experiment, and ionic polarisabilities are known and tabulated. The distortion of the spherical ion so that there is more electron density between the nuclei is exactly equivalent to the addition of a certain covalent character to the ionic bond. Unfortunately it is impossible to determine the "polarising power" of cations, in particular because the phenomenon of polarisation is mutual, although it is generally accepted to vary as q/r2, i.e. small and highly charged cations have the greatest polarising power. Hence the effect of polarisation on individual ionic bonds cannot be determined with certitude, although measurements by nuclear quadrupole resonance (which is sensitive to distortions in the symmetry of the electron cloud) suggest that the most ionic of ionic bonds have a little less than 10% covalent character.
Ionic bonds form between atoms of widely differing electronegativity, and there is no doubt that the effects of polarisation become more marked (i.e. the bonds become more covalent in nature) as this difference in electronegativity decreases. Silver chloride has the same structure as sodium chloride, but is insoluble in water and has an experimental lattice energy much larger than would be expected from purely electrostatic considerations. A series of empirical rules for predicting the stability of an ionic bond was proposed by Fajans in 1928: for an ionic bond to be stable,
- the two ions must be electronically stable, e.g. the should conform to the octet rule;
- the charges on the ions must be small;
- the anion should be small and the cation should be large (to minimise the effects of polarisation).
Another indication of increasing covalent character in the bonding is the appearance of structures which would not be predicted by the radius ratio rule, such as the layer structure of molybdenum disulfide. The significance of this last example was not lost on the doctoral student who first determined its structure, a certain Linus Pauling...
[edit] Coordinate bonds
The description of bonding in metal complexes has historically followed different routes from that of other compounds. Although Pauling proposed a valence bond description in On the Nature of the Chemical Bond, this never gained wide acceptance. Crystal field theory was developed at about the same time, originally (as the name suggests) to explain the optical properties of certain crystals: it also proved successful at explaing the optical and magnetic properties of many transition metal complexes, particularly those of the first row metals. Crystal field theory is a pure ionic model of metal–ligand bonding, with the ligands being treated as point charges and with no polarisation. It developed into ligand field theory, in which polarisation is considered as a perturbation of the pure ionic bonding. This proved even more successful, but suffered from its semi-empirical nature: many of its parameters were taken directly from experimental results and so, while it could predict the properties of new compounds, it was unable to provide an independent explanation for them. Attempts to apply molecular orbital theory to transition metal complexes were for long disappointing, as the available approximations were unable to accurately model d-orbitals within the limits of the available computing power. The increase in computing power and the development of density functional theory have largely overcome these problems, although many chemists still view the bonds in metal complexes as "a bit different" from those in better known compounds and the subject remains poorly treated (if treated at all) in university-level textbooks.
Coordinate bonds can be described as spanning the middle ground (if such a middle ground exists) between polar covalent bonds and polarised ionic bonds. The essential element of a ligand is the presence of a pair of electrons which it can "donate" to the metal ion. Ligands are classified as "weak field" or "strong field" according to the photochemical series depending on their effect on the relative energies of the metal d-orbitals. The photochemical series is roughly the opposite order to ligand electronegativity: fluoride is a weak-field ligand while ligands such as cyanide which bind through carbon atoms are strong-field.
The bonding between metals and weak-field ligands can be considered to be mostly ionic in nature, although with more ligand polarisation than in the alkali metal halides. In terms of molecular orbital theory, the ligand orbitals are much lower in energy than the metal d-orbitals, so that there is little overlap. It could be said that if the bonding in, say, solid iron(III) chloride is described in ionic terms, it should be expected that the bonding in chloride complexes of iron(III) be described similarly. The partial covalent character of the bonds gives them a (relative) stability in aqueous solution, while the polarisation of the ligands discourages the formation of a solid lattice.
The covalent character of the metal–ligand bond increases with the ligand field strength, and the organometallic compounds of the transition metals are probably best described as having polar covalent bonds. Such compounds often show an interaction between the filled metal d-orbitals and empty antibonding orbitals on the ligand, a property known as back-bonding. This has the effect of strengthening the metal–ligand bond while weakening bonds within the ligand.
[edit] Metallic bonding
| Strengths of metallic bonds |
|
|---|---|
| Na–Na | 27 kJ/mol 6.5 kcal/mol |
| Fe–Fe | 87 kJ/mol 20.9 kcal/mol |
| W–W | 137 kJ/mol 32.9 kcal/mol |
| Calculated per bond for dissociation to neutral atoms. | |
Metals are characterised by the close proximity of large numbers of atoms and by their relatively low ionisation energies. The interaction of so many metal orbitals leads to "bands" of energy which are available to the electrons, and metallic bonding is usually described using band theory. Within the bands the available energies are effectively continuous, while the bands are separated by ranges of energies which are forbidden to the electrons. Any solid with an infinite lattice structure may be described using band theory: metals are characterised by the fact that the highest energy band, known as the conduction band, is only partially filled. Electrons in the conduction band can be set in motion with only a minimal input of energy, which leads to metallic conductivity.
The bonding in metals is often compared to a lattice of positive ions bathed in a "sea of electrons": whilst evocative, this image is subject to caution. Metals vary greatly in the mobility of their electrons and in the directionality of their bonding. Only about half of the metals in the periodic table have close-packed structures, and only about half of metallic structures can be predicted from the electronic properties of the metal atoms. Metallic bonding is certainly less directional than "localised" covalent bonding, and this leads to the malleability and ductility of metals. However the bonding manganese is much more directional that that in sodium, and the reduced mobility of its electrons is reflected in its low electrical conductivity.
[edit] Intermolecular interactions
The term "chemical bond" is usually restricted to those interatomic forces which occur within molecules or giant lattices. However forces can also occur between atoms in different molecules: these are usually (but not always) weaker that the forces within molecules, and are generally referred to as "interactions". The distinction is one of convention, as there is no fundamental difference in the origins of the different bonds and interactions, nor is it always simple and unequivocal to define the difference between a single molecule and an interacting group of molecules: should the hydrogen-bonded dimers of acetic acid be classed as one molecule or two? There is no generally accepted criterion on the basis of bond strength, although the figure of 25 kJ/mol (6 kcal/mol) is sometimes suggested as the weakest bond which is chemically important: for comparison, the thermal energy available to molecules at room temperature is about 2.5 kJ/mol (0.6 kcal/mol), and it requires about 5.6 kJ/mol (1.3 kcal/mol) to heat water from room temperature to its boiling point.
[edit] Hydrogen bonds
A hydrogen ion (H+) is uniquely polarising given its small size, so polarising that it is never observed on its own in solids or liquids. Hydrogen atoms attached to electronegative atoms (F, O, N and, to a lesser extent, S) have a partial positive charge and can polarise nearby electron clouds. A hydrogen bond occurs when such a hydrogen atom interacts with the lone pair on another atom.
A hydrogen bond can be viewed either as a particularly strong dipole-dipole interaction (see below) or as a polarised version of a three centre-two electron bond (see above). The hydrogen atom can usually be described as remaining covalently bonded to one or other of the electronegative atoms: however, in the exceptional case of HF2−, the hydrogen atom is equidistant between the two fluorine atoms and the ion has no overall dipole moment.
Hydrogen bonds can occur both between molecules and within molecules (e.g. salicylic acid). Many of the unusual properties of water can be traced to the extensive network of hydrogen bonds which exists in the solid and the liquid (and which persists to a certain extent above 100 °C, 212 °F), notably the fact that ice is less dense than liquid water and so floats. They are also very important in determining protein structures.
[edit] Dipole-dipole interactions
Molecules with dipole moments tend to align themselves so that the the δ+ end of one molecule is closest to the δ− end of another, by Coulomb's Law. Such interactions are particularly important in polar lquid which do not have any hydrogens which can participate in hydrogen bonding (hydrogen bonds are usually stronger than other dipole-dipole interactions), such as acetone and dimethyl sulfoxide (DMSO). They are also important in stabilising the secondary structure of proteins: α helices and β pleated sheets.
[edit] London-Van der Waals forces
These forces are the most ubiquitous of chemical bonds, occurring between all atoms and molecules, but also among the weakest. The are known either as London dispersion forces after Fritz London, who first provided the mathematical description and explanation in 1930 ("dispersion" because they are related to polarisability, which can be measured by the dispersion of light), or Van der Waals forces after Van der Waals, as they provide and explanation for the attractive term in the Van der Waals equation of state: the two terms are equivalent for all practical purposes.
London-Van der Waals forces arise from an instanteous asymmetry in the electron distribution around an atom, creating an atomic electric dipole: this induces a dipole in a neighbouring atom, which is always oriented so that the two dipoles are attracted. London showed that the sum of these instanteous attractions is not zero as has previously been assumed, but an attractive force between the two atoms which depends on their polarisabilities and on the sixth power of the distance between them. Such forces are therefore very short range: for comparison, electrostatic interactions between point charges depends on the square of the distance between them. They are also strongest between heavy atoms, which contain the most electrons and which have the highest polarisabilities.
An alternative and equivalent description of these forces is to say that the movement of the electrons around the nuclei of the two atoms is correlated so that the average distance between the two electrons is maximised. This reduces the electrostatic repulsion between the two electrons and hence the energy of the system. Methods have been developed to model electron correlation in calculations, notably the Möller-Plesset series.
Although these forces are weak (25–30 kJ/mol, 6–7.5 kcal/mol at most), the sum of many such forces can become important, for example in receptor substrate recognition. The recognition of the hormone thyroxine depends on the interaction of the four iodine atoms with its receptor protein by Van der Waals forces. They find practical use in protein crystallography, where atoms of xenon are sometimes grafted onto proteins held by Van der Waals forces in order to resolve the phase problem by the heavy atom method. Strong Van der Waals forces also occur in some compounds of gold, where they have been called "aurophilic interactions".
[edit] Charge transfer complexes
The formation of coordinate bonds is not restricted to transition metal compounds. Where similar bonds form between two molecules, these are usually termed charge transfer complexes: an example is the deep blue complex formed between molecules of iodine and starch. The cation-π interaction between a positively-charged species and a π-bond is a similar example.
[edit] Bibliography
- Enciclopedia temática ciesa (tome 7), Barcelona:Compaña Internacional Editora, 1976. ISBN 84-85004-13-2.
