Square One: The Chemical Bond

Everything in this universe tries to attain stability one way or the other. Our idea of stability of atoms is mostly empirical. We have observed what makes atoms stable and have centered our theories around them. The most common one being the Lewis theory which states that all atoms are stable as long as they have $8$ electrons in their outermost shell, and $2$ for hydrogen and helium.

This one tallies out quite well with smaller atoms as well as noble gases. Atoms either come together to lose electrons or gain them in order to fulfill this "octet" configuration. For example, if we consider the compound: $\ce{NaCl}$, sodium has an electronic configuration: $2,8,1$ and chlorine, $2,8,7$. The reasonable way for both these atoms to gain an octet, by the Lewis theory, requires sodium to lose an electron and for chlorine to gain that electron. When this transfer of electron happens, the sodium atom becomes positively charged whereas the chlorine atom becomes negatively charged. Because of this charge separation, an electrostatic interaction is set up and this interaction is what keeps the ions together. This is called the ionic bond. 

Another way to attain the octet is by sharing of electrons. If we have two fluorine atoms, each with an electronic configuration of $2,7$ , we can see that gaining one electron for each atom will suffice to attain the octet. This electron can be gained by sharing an electron(in the valence shell). What this means is that an electron will now equally belong to both the atoms hence giving us a total of $8$ valence electrons in each atom, which contributes to a stable $\ce{F2}$ molecule. The single bond formed here is called a covalent bond and these bonds are essentially the backbone of organic chemistry. 

What makes carbon so special, is that it can bond with many other carbon atoms, forming long chains. This property is called catenation. Two carbon atoms can also bond with each other multiple times over forming either double or triple bonds which give certain organic compounds their characteristic properties. 

In recent developments over the period of time (since 1926) , we have come to recognize the electron more like a probability distribution function(quantum theory). We can only predict to some certainty where the electron will lie, radially away from the nucleus. The region in space where we can find an electron with maximum certainty (more than 95%)  are called orbitals. According to the quantum theory, a bond is formed when two orbitals, each coming from a different atom overlap. The bond strength is then determined by the effectiveness of the overlap. When two atoms of the same kind, e.g. $2$ carbon atoms, $2$ fluorine atoms etc. form a single covalent bond, the bond turns out to be significantly strong, because of equal sizes of orbitals. 

Another significant aspect of bonding is the nuclear charge. Imagine two atoms(of the same kind) coming together. By principle, the closer they get, the stronger the bond. Now, how close they come is dependent on both attractions and repulsions. The valence electrons of one atom will be attracted by the nucleus of the second, and the other way round. But the nuclei of both the atoms will repel and so will the valence electrons. To have a significant bond strength(significant overlap of the orbitals of both the atoms) the attractive forces should dominate the repulsive ones. This is one major reason why carbon can form long chains, but fluorine cannot. Let's look at this in a little more detail. 

As the number of protons in the nucleus increases, the nucleus can pull the valence electrons to a greater extent towards itself. As a result, the atom overall becomes smaller. The smaller the atom becomes, the closer two of the same kind must come together for an effective bond. The closer both the atoms come, more the repulsive forces will dominate. According to this logic, fluorine atoms when brought together, face more repulsion than carbon atoms brought together. Hence, formation of long chains of fluorine is not feasible. The same goes for almost all other elements. Either the attraction is too weak or the repulsion is too strong. Carbon happens to be in the Goldilocks' zone between these two extremes, allowing it to form as very long chains

Why is this "long chain formation" important, you ask ? For starters, organic life wouldn't exist otherwise. Your very DNA is made of such long chains of carbon atoms, that when stretched completely, spans the diameter of the solar system. 

In conclusion, chemical bonds not only make up the entirety of organic chemistry, but also the universe as it is today.