chemical bond

Chemical Bonding
Chemical compounds are formed by the joining of two or more atoms. A stable compound occurs when the total energy of the combination has lower energy than the separated atoms. The bound state implies a net attractive force between the atoms ... a chemical bond. The two extreme cases of chemical bonds are:
Covalent Bonds
Covalent chemical bonds involve the sharing of a pair of valence electrons by two atoms, in contrast to the transfer of electrons in ionic bonds. Such bonds lead to stable molecules if they share electrons in such a way as to create a noble gas configuration for each atom.
Hydrogen gas forms the simplest covalent bond in the diatomic hydrogen molecule. The halogens such as chlorine also exist as diatomic gases by forming covalent bonds. The nitrogen and oxygen which makes up the bulk of the atmosphere also exhibits covalent bonding in forming diatomic molecules.

Covalent bonding can be visualized with the aid of Lewis diagrams.
Comparison of Properties of Ionic and Covalent Compounds
Because of the nature of ionic and covalent bonds, the materials produced by those bonds tend to have quite different macroscopic properties. The atoms of covalent materials are bound tightly to each other in stable molecules, but those molecules are generally not very strongly attracted to other molecules in the material. On the other hand, the atoms (ions) in ionic materials show strong attractions to other ions in their vicinity. This generally leads to low melting points for covalent solids, and high melting points for ionic solids. For example, the molecule carbon tetrachloride is a non-polar covalent molecule, CCl4. It's melting point is -23°C. By contrast, the ionic solid NaCl has a melting point of 800°C.

Ionic Compounds

Crystalline solids (made of ions)
High melting and boiling points
Conduct electricity when melted
Many soluble in water but not in nonpolar liquid
Covalent Compounds

Gases, liquids, or solids (made of molecules)
Low melting and boiling points
Poor electrical conductors in all phases
Many soluble in nonpolar liquids but not in water
You can anticipate some things about bonds from the positions of the constituents in the periodic table. Elements from opposite ends of the periodic table will generally form ionic bonds. They will have large differences in electronegativity and will usually form positive and negative ions. The elements with the largest electronegativities are in the upper right of the periodic table, and the elements with the smallest electronegativities are on the bottom left. If these extremes are combined, such as in RbF, the dissociation energy is large. As can be seen from the illustration below, hydrogen is the exception to that rule, forming covalent bonds.
Elements which are close together in electronegativity tend to form covalent bonds and can exist as stable free molecules. Carbon dioxide is a common example.

Ionic Bonds
In chemical bonds, atoms can either transfer or share their valence electrons. In the extreme case where one or more atoms lose electrons and other atoms gain them in order to produce a noble gas electron configuration, the bond is called an ionic bond.
Typical of ionic bonds are those in the alkali halides such as sodium chloride, NaCl.

Ionic bonding can be visualized with the aid of Lewis diagrams.
Pauli Repulsion in Ionic Molecules
An ionic bond may be modeled in terms of the ionization energy to produce the positive ion, the electron affinity associated with the negative ion, the dissociation energy for the molecule, the coulomb potential between the ions, and the repulsive force which limits the closeness of approach of the ions. This repulsive force is typically called Pauli repulsion. The energy balance of all these terms can be written in the form

Measured data about ionic diatomic molecules allow us to imply the energy of the Pauli repulsive force at the equilibrium separation. It is modeled above with two parameters C and a which can be adjusted to fit the data. This repulsive force is more than just an electrostatic repulsion between the electron clouds of the two atoms. It has a quantum mechanical character rooted in the Pauli exclusion principle, and is often called just the "exclusion principle repulsion". When the ions are widely separated, the wavefunctions of their core electrons do not significantly overlap and they can have identical quantum numbers. As they get closer, the increasing overlap of the wavefunctions causes some to be forced into higher energy states. No two electrons can occupy the same state, so as a new set of energy states is formed for the composite, two-nucleus system, the lower energy states are filled and some of the electrons are pushed into higher states. This requires energy and is experienced as a repulsion, preventing the ions from coming any closer to each other. The nature of the Pauli repulsion term for sodium chloride is shown in the energy diagram below.

Since the ionization energies, electron affinities, and dissociation energies have been tabulated from experiment, and since the bond length is obtainable from independent experiments such as rotational spectroscopy, it is possible to estimate the energy of the Pauli repulsion by using the relationship above. Some examples are shown below, with the Pauli term calculated from the other data as the value which would balance the energy.
Molecule
Ionization Energy(eV)
Positive Ion

Electron affinity (eV)
Negative Ion

Dissociation Energy (eV)

Equilibrium Separation (nm)
(Bond length)

Coulomb Energy (eV) at Equilibrium

Pauli Repulsion (eV) for Energy Balance

NaCl
5.14

3.62

4.27

0.236

6.10

0.31

NaF
5.14

3.41

5.38

0.193

7.46

0.35

KCl
4.34

3.62

4.49

0.267

5.39

0.19

KBr
4.34

3.37

3.94

0.282

5.11

0.20

NaH
5.14

0.76

1.92

0.189

7.62

1.32

LiH
5.39

0.76

2.47

0.239

6.02

1.08

For the alkali halides, the Pauli term is a few tenths of an eV. The values for the Pauli term for the hydrides is enough different to suggest that something different is going on, but I lack the chemical insight to comment further on that. Any comments would be welcomed.
Metallic Bonds
The properties of metals suggest that their atoms possess strong bonds, yet the ease of conduction of heat and electricity suggest that electrons can move freely in all directions in a metal. The general observations give rise to a picture of "positive ions in a sea of electrons" to describe metallic bonding.
Hydrogen Bonding
Hydrogen bonding differs from other uses of the word "bond" since it is a force of attraction between a hydrogen atom in one molecule and a small atom of highelectronegativity in another molecule. That is, it is an intermolecular force, not an intramolecular force as in the common use of the word bond.
When hydrogen atoms are joined in a polar covalent bond with a small atom of high electronegativity such as O, F or N, the partial positive charge on the hydrogen is highly concentrated because of its small size. If the hydrogen is close to another oxygen, fluorine or nitrogen in another molecule, then there is a force of attraction termed a dipole-dipole interaction. This attraction or "hydrogen bond" can have about 5% to 10% of the strength of a covalent bond.
Hydrogen bonding has a very important effect on the properties of water and ice. Hydrogen bonding is also very important in proteins and nucleic acids and therefore in life processes. The "unzipping" of DNA is a breaking of hydrogen bonds which help hold the two strands of the double helix together. The attractive forces between molecules in a liquid can be characterized as van der Waals bonds. van der Waals Bonding
Water molecules in liquid water are attracted to each other by electrostatic forces, and these forces have been described as van der Waals forces or van der Waals bonds. Even though the water molecule as a whole is electrically neutral, the distribution of charge in the molecule is not symmetrical and leads to a dipole moment - a microscopic separation of the positive and negative charge centers. This leads to a net attraction between such polar molecules which finds expression in the cohesion of water molecules and contributes to viscosity and surface tension. Perhaps it is fair to say that van der Waals forces are what holds water in the liquid state until thermal agitation becomes violent enough to break those van der Waal bonds at 100°C. With cooling, residual electrostatic forces between molecules cause most substances to liquify and eventually solidfy (with the exception of helium, which never becomes a solid at atmospheric pressure).
Even nonpolar molecules experience some van der Waals bonding, which can be attributed to their being polarizable. Even though the molecules don't have permanent dipole moments, they can have instantaneous dipole moments which change or oscillate with time. These fluctuations of molecular dipole moments lead to a net attraction between molecules which allow nonpolar substances like carbon tetrachloride to form liquids. Examination of the dipole electric field shows that the electric field from one instantaneous dipole will tend to polarize a neighboring molecule such that it will be attracted - sort of the electrical analog to a bar magnet magnetizing a paper clip so that it will be attracted to the magnet. (This happens regardless of which pole of the magnet is brought close to the paper clip.) The weaker van der Waals forces in nonpolar liquids may be manifested in low surface tension and low boiling points.
Sodium Chloride, NaCl
The classic case of ionic bonding, the sodium chloride molecule forms by the ionization of sodium and chlorine atoms and the attraction of the resulting ions.
An atom of sodium has one 3s electron outside a closed shell, and it takes only 5.14 electron volts of energy to remove that electron. The chlorine lacks one electron to fill a shell, and releases 3.62 eV when it acquires that electron (it'selectron affinity is 3.62 eV). This means that it takes only 1.52 eV of energy to donate one of the sodium electrons to chlorine when they are far apart. When the resultant ions are brought closer together, their electric potential energy becomes more and more negative, reaching -1.52 eV at about 0.94 nm separation. This means that if neutral sodium and chlorine atoms found themselves closer than 0.94 nm, it would be energetically favorable to transfer an electron from Na to Cl and form the ionic bond.

The potential energy curve shows that there is a minimum at 0.236 nm separation and then a steep rise in potential which represents a repulsive force. This repulsive force is more than just an electrostatic repulsion between the electron clouds of the two atoms. It has a quantum mechanical character rooted in the Pauli exclusion principle, and is often called just the "exclusion principle repulsion". When the ions are widely separated, the wavefunctions of their core electrons do not significantly overlap and they can have identical quantum numbers. As they get closer, the increasing overlap of the wavefunctions causes some to be forced into higher energy states. No two electrons can occupy the same state, so as a new set of energy states is formed for the composite, two-nucleus system, the lower energy states are filled and some of the electrons are pushed into higher states. This requires energy and is experienced as a repulsion, preventing the ions from coming any closer to each other.
The potential diagram above is for gaseous NaCl, and the environment is different in the normal solid state where sodium chloride (common table salt) forms cubical crystals. The ion separation is 0.28 nm, somewhat larger than that in the gaseous state.
A major part of the study of molecular structure is the description of the chemical bonds which are formed between atoms. The classic studies are the extremes of ionic bonding in sodium chloride and covalent bonding in the hydrogen molecule.
Hydrogen Molecule
The classic case of covalent bonding, the hydrogen molecule forms by the overlap of the wavefunctions of the electrons of the respective hydrogen atoms in an interaction which is characterized as an exchange interaction. The character of this bond is entirely different from the ionic bond which forms with sodium chloride, NaCl. If you measure then energy balance when you form H+ and H- ions and examine the attractive force between them, the energy required is positive for any value of ion separation. That is, there is no distance at which there is a net attractive interaction, so the bond cannot be ionic.
The electron distribution around the protons of the hydrogen is described by a quantum mechanical wavefuntion, and the wavefunction which describes the two electrons for a pair of atoms can be symmetric or antisymmetric with respect to exchange of the identical electrons. From the Pauli exclusion principle, we know that the wavefunctions for two identical fermions must be antisymmetric. Theelectron spin part of the wavefunction can be symmetric (parallel spins) or antisymmetric (opposite spins), but then the space part of the wavefunction must be the opposite. That gaurantees that the entire wavefunction (the product of the spin and space wavefunctions) is antisymmetric. The two possibilities for the spatial wavefunctions for distant hydrogens are shown below.

As shown below, when the hydrogen atoms are brought close together the symmetric spatial wavefunction leads to a bonding configuration of electrons and the antisymmetric one does not. The actual electron charge density is given by the square of the magnitude of the wavefunction, and it can be seen that the symmetric wavefunction gives a high electron density between the nuclei, leading to a net attractive force between the atoms (a bond).

The exchange interaction (an entirely quantum mechanical effect) leads to a strong bond for the hydrogen molecule with dissociation energy 4.52 eV at a separation of 0.074 nm. The potential energy of the anti-bonding orbital shown gives some insight into why a third hydrogen atom cannot bond to the two atoms of the hydrogen molecule. It would be in an anti-bonding situation with one of the other hydrogen atoms and would therefore be repelled. We say that the bond in the hydrogen molecule is "saturated" because it cannot accept another bond.

reference:
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html