When you have two atoms which can exchange electrons by hopping of them, then you have a molecule. Obtaining the states of this molecule you enable to the electrons and their eigenvalues, it is possible to see bonding and antibonding states. Thus when the molecule is in a bonding state the atoms are as if an external energy were joining them.
Generalizing that to a chain of atoms with certain translation symmetry, it is possible to translate levels of energy by bands. The difference in energy between the bonding and antibonding bands extreme energies cannot exceed four times the hopping energy for the exchanged electrons. This is known as the band wight.
Although that is not simple to go to three dimensions, in fact this is the form to understand the binding of the atoms in a solid.
One good reference is:
A.Sutton, Electronic Structure of Materials, Clarendon Press-Oxford(1993)
I hope that this can helps
I shall explain the relationship between stability and binding energy in a crystal. The stability of a complex like-wise should depend on the same principles.
When one begins to study solid state physics, the first question that comes to the mind is how the atoms come together to form a stable crystal structure. The electrostatic attraction between the positively charged nuclei and the negatively charged electrons is primarily responsible for binding. In order that the structure is stable, the positive nuclei should be kept apart; the negative electrons should also be kept apart; and the electrons should be closer to the nuclei. However, in doing so, care should be taken to see that this does not increase the kinetic energy unnecessarily causing instability. Depending on the structure and configurations, the mechanisms of attraction of different solids are different. These are Van der waal’s interaction in inert gas solids, where the attraction comes from electrostatic dipole-dipole type of interaction; Madelung energy responsible for the Coulomb attraction in ionic crystals; covalent bonds arising out of spin-dependent Coulomb interaction; metallic binding which is little more complex because of many body correlations among the conduction electrons and the Hydrogen bonds. However, whatever might be the type of attractive interaction, when the atoms come closer, collision and instability is prevented by a repulsive interaction arising out of Pauli exclusion principle and quantum mechanical uncertainty principle. Thus both attraction and repulsion are responsible for the stability of a crystal, and should be so also for molecular complexes with small variations.
For details, any Solid State Physics book at the introductory level is sufficient. My choice is Introduction to Solid State Physics, by C. Kittel ( any edition).
Lets try making this simple. "Binding energy" referss to the amount of energy it takes to break something in pieces. For an electron in a hydrogen atom (ground state) this energy is equivalent to its ionization energy: 13.6 eV. For comparison, it takes about 25 eV to remove an electron from a He atom. Since it takes more energy for charge separation, you may refer to He as being more stable. In these examples, the energies involved ar both pretty large, certainly so with respect to normal thermal energies.
This concept of binding energy can be transferred to formation of molecules complexes and solids, as others mentioned before. In the case of complexes, we might not really be interested in the total binding energy (i.e. the energy required to separate the complex into its elemental constituents) but the weakest bond might be most interesting. So one may define a bond-specific binding energy for this one specifically. But again, it should be obvious that the larger this energy, the higher the (thermal) stability.
Chemical stability may be related to thermal stability but here you also have the chemistry-specific aspects (binding energy/enthalpy differences between starting and end products, barrier height for the transition state...). Then it gets more intricate and the relation between binding energy and stability might not be totally obvious in all cases.
thanks to all of you.
but i want more clarity in the concept . suppose i have two different complexes with negative and positive values of binding energy. Then how can i predict which one is stable and other is less stable ?
Dear Amrish,
before making such a assumptions (about negative and positive binding energies), you would first have to concisely define what you want us to understand when you use this word. Depending on definition, either a positive or a negative binding energy may be defined as stable. You should first find out whether there is a standard definition in your context.
Whatever the definition, in a simple sense if you suppose you have two cases, one with positive and one with negative binding energy, then one will be stable, the other will not, because the total energy can be lowered by falling apart. (all this is neglecting the thermodynamic aspects of real chemistry...)
Dear Amrish,
The interaction is purely electromagnetic exchenging electrons (hopping) with a certain frequency which depends strongly of the able states to them (orbitals). You have two kind of energies: bonding and antibonding, and you need to see what is the one that you can have for your complex. But at the end all that you need to calculate is
= hopping energy for the electron
between state a and b. Obviously these kind of integrals are not simple and also the states are not simply defined, but you can use ab initio techniques based in DFT or Hartree-Fock methods.
Dear Amrish Sharma
Have a good time and all success
The stability of a complex is related to its binding energy. Simply, the greater the binding energy the greater the stability of the chemical composition.
There is a model known as chemical bond approach model, this model relates the stability and the electronic properties of the composition to what so called cohesive energy of that composition.
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