I still remember my encounter with quantum mechanics. It was during my eleventh and twelfth-grade textbooks of chemistry. When the physics textbooks were busy describing the formative years of quantum mechanics using the Bohr model, the chemistry textbooks had already introduced us to the Schrodinger equation and wavefunction. Of course, they didn’t attempt us to solve the Schrodinger equation. The chemistry books had to deal with a lot of situations regarding how atoms join to form molecules. They wanted to equip us with some qualitative tools that will give us insight into how atoms undergo such interesting arrangements and form a stable configuration of molecules. The molecular structure was the first quantum mechanical application I learned.
How did these textbooks achieved to teach intricacies of quantum mechanics to kids that are in their final years in schools? By depicting a wave function as an electron cloud. When we were visualizing, for example, the wave function of the hydrogen molecule, we were instead creating a 3D picture of not the wavefunction of the molecule but some other function calculated out of the wavefunction – the probability density. The probability density is like taking the square of the wave function. Yet, it is a more workable quantity. You can easily start intuiting about it. This three-dimensional picture of the probability density function is like a cloud of electron and was called the orbital in our textbooks.
You will object, “how can two electrons of the hydrogen molecule make a cloud?” Yes, it is possible because of the miracle of quantum mechanics, our textbooks told us. If you take a snapshot of the electron at a given time, you will find it at a point near to protons of the hydrogen moment. Take a snapshot at the next moment and it is gone somewhere else. The successive snapshots, when developed on a single photographic plate, will give the final picture of how the electron is behaving. The picture will look like a cloud which is denser around the two protons and less dense in the middle – like a dumbbell.
The most intriguing aspect of this picture is that the electron is not moving from one point to another in a well-defined trajectory. If you quickly project the snapshots on the screen like an animation film instead of developing them on a single photographic plate, don’t expect a nice movie of an electron moving from one point to another in a continuous manner. You will see the electron far away from both the protons at one instant and at the next instant it will be in the middle of the two protons. You will be seeing a dot appearing and disappearing on the screen at random points – like a shooter shooting bullets on a screen. However, if you watch long enough, you will discover a pattern in the dots on the target screen. You will find that the shooter is aiming for two points – the two protons! So, most of his aims are distributed around those two points.
We were told that there are only a few standard shapes these clouds can acquire, each shape having its own energy. When two atoms come close enough, their electrons clouds rearrange into new shapes of lower energies. These new clouds were called molecular orbitals. A few qualitative rules about these molecular orbits enabled us to make sense of the complicated world of molecular structure.