Forces between atoms
Attractive forces between atoms are characterised as van der Waals, covalent, ionic and metallic. There is also a repulsive force between the atoms which dominates the attractive force at close range. There is an eqilibrium distance where the two forces are equal, or where the energy is minimised.
The bonding force is the result of electrostatic attraction between opposite charges, due to quantum wave-mechanics effects the chemical bonding can seen very different from simple electrostatics.
Van der Waals force
The van der Waals force is often referred to as the weak attractive force, it is the only appreciable force between well seperated atoms and molecules. It is responsible for the condensation of noble gases and chemically saturated molecules as temperature is decreased. The van der Waals force results from fluctuations and surges of electronic charge in the atom, when two atoms approach fairly close these fluctuations can occur in unison.
Ionic Bonding
An ionic bond is formed when electrons pass from one atom to a more electonegative one, the positive and negative ions which are formead are electostatically attracted to each other. The repulsive force that balances this attraction is due to overlap of completely filled electron shells. Overlap forces can be thought of as short-range forces. The force results from the promotion of electrons into higher energy levels because of the Pauli exclusion principle, when two shells overlap the electron no longer belongs to one atom but to the molecule as a whole. When completley filled electron shells begin to overlap, the single group of atoms formed is too large for all the electons to go into the low energy quantum states, the incease in energy gives rise to the repulsive overlap force.
Covalent Bonding
When partly empty electon shells overlap the result leads to very strong bonds of covalent or metallic type. These bonds can occur between atoms of the same type, for example H2, diamond, copper. The interatomic forces are brought about by sharing the electons in the partly-filled/partly-empty electon outer electron shells. These electrons are often referred to as the valency electons. Again the repulsive force comes when the inner filled shells of electrons start to impinge.
The simplest covalant bond occurs in Hydrogen. In the region between H nuclei the electron is electrostatically attracted to both nuclei, this attraction is stronger than the repulsion between the nuclei because of the shorter distance. Wavve mechanics can be used to calculate the kinetic energy of the electron and how much time it spends in the region between the nuclei. For molecules more complicated than H2 [most everything then] it is usually too difficult to solve the wave equation.
The next element Helium cannot bond covalantly because there are no unpaired electons, the 1s shell is full. Lithium has an additional electron, usually occupying the 2s shell, which can access 4 energy levels (one 2s and three 2p states), remember each state or energy level can be occupied by 2 electons of opposite spin. This means there are always far more energy levels accessible than electrons to fill them, and they cannot be saturated however many Li atoms we bring together. This means we can form an indefinitely large molecule, a huge aggregate of atoms bonded together by unsaturated covalent bonds, these aggregates we regard being metal.