Formation of Molecular Orbitals

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle to start. Two hydrogen atoms come close, and each one brings just one orbital. Those two orbitals combine. So, how many orbitals come out? And here is the strange part. They can combine in two ways. One way holds the atoms together, and the other way works against the bond. Same two orbitals, opposite results? Strange, right? Hold that thought; by the end of this video it will make complete sense. Molecular orbital theory comes up often in JEE, and all of it starts from this one idea. So, let's begin.

0:41LCAO: how molecular orbitals form

So, the idea has a name: LCAO, short for linear combination of atomic orbitals. In simple words, the atomic orbitals of two atoms combine. Okay? And they form new orbitals, called molecular orbitals; M O for short, and the small s just makes it plural. Now notice this: the molecular orbital does not belong to one atom. It spreads over the whole molecule. Right? Now, back to our puzzle. Two hydrogen atoms, one orbital each, so two atomic orbitals go in. How many molecular orbitals come out? Two, exactly! Not one big orbital, but two. The rule: n atomic orbitals give n molecular orbitals, where n is just a number. The double arrow on screen means, gives. The count of orbitals stays the same. Clear?

1:38Add or subtract: bonding and antibonding

Now look at the figure. On the left, H one s is the one s orbital of each hydrogen atom, and the small up arrow is its one electron. Energy goes up along the arrow on the far left. Each atomic orbital is described by a wave function, written with the Greek letter psi, the one that looks like a trident. Psi A is for atom A, and psi B is for atom B; the small letters below psi are just labels, okay? So, in how many ways can two wave functions combine? Look at the right side of the figure for a clue. Two ways, yes! Add them, or subtract them. First, we add them: psi A plus psi B gives the bonding molecular orbital, lower in energy. In the figure, it is the bottom level, sigma one s, marked bonding. Sigma is the Greek letter like a small o with a tail. With me? Now see the grey oval at the bottom right. The two dots are the two nuclei. When we add, the electron density piles up between the nuclei, and that density holds the two nuclei together. That is why we call it bonding. Got it? Now the second way: subtract. Psi A minus psi B gives the antibonding molecular orbital, higher in energy. We mark it with a little star, the asterisk on screen. In the figure, it is the top level: sigma star one s. Okay? Now look at the middle, between the two nuclei. When we subtract the two waves, what happens to the electron density there? It cancels, correct! There is a node between the nuclei, a place with zero electron density. See the dashed line between the two pink lobes, at the top right? That is the node. So this orbital works against the bond. That was the strange part of our puzzle: add the waves, and you get bonding; subtract them, and you get antibonding. Right? Last point. Electrons fill molecular orbitals by the rules you already know: the aufbau principle, lowest energy first; the Pauli principle, at most two electrons, with opposite spins; and Hund's rule. So in hydrogen, both electrons go into sigma one s, the bonding orbital. See the two arrows, one up and one down? And the line at the bottom, the bond order, we work out later in this chapter. Clear?

4:00When can two atomic orbitals combine?

Alright, next question. Each atom has many orbitals. Can any orbital of one atom combine with any orbital of the other? No, not at all! There are three conditions. First, the two orbitals must have similar energies. Okay? Second, the same symmetry about the molecular axis. The molecular axis is simply the line joining the two nuclei. Right? And third, appreciable overlap, which means a good amount of overlap. All three must hold together. Got it? Now, the allowed pairs. We take the molecular axis along z. Two s with two s; and two p z with two p z, where the small z below the p means it points along the axis. These meet head-on and give sigma molecular orbitals. The dash between them just means, with. Clear? Next, two p x with two p x, and two p y with two p y. These stand parallel, side by side, so they overlap sideways and give pi molecular orbitals. Pi is the Greek letter like a little table with two legs. With me? Now, here is a JEE trap. Two s and two p x are both in the second shell. So they should combine, right? No, no, careful! Never two s with two p x, when the axis is along z. The two p x orbital has two lobes of opposite sign, one on each side of the axis. The s orbital overlaps both lobes equally, so the two parts cancel: zero net overlap. Different symmetry, so no combination. Remember this one, okay?

5:37Example 1: how many MOs from 2s and 2p of two atoms

Alright, example one. How many molecular orbitals are formed from the two s and two p orbitals of two atoms? Pause the video, and try it first. Done? Okay, let's check. Two s and two p, so two orbitals per atom. Two atoms, so four atomic orbitals, and four molecular orbitals, right? Oh no, careful! Two p is not one orbital. It is a set of three: two p x, two p y and two p z. So each atom brings two s plus three two p orbitals: four in all. Clear? Two atoms: four plus four, that is eight atomic orbitals. Right? And n atomic orbitals give n molecular orbitals. So, eight molecular orbitals. That's the answer! Got it? And a quick check with the four pairs we listed. Two s with two s, two p z with two p z, two p x with two p x, and two p y with two p y: four pairs. Each pair gives one bonding and one antibonding orbital. Four times two, eight. It matches! Nice, isn't it?

6:49Example 2: which atomic orbital pairs can combine

Now a harder one, example two. The molecular axis is z. Which of these combinations are allowed? Two p z with two p z; two s with two p x; two p x with two p x; and two p x with two p y. Pause the video, and try it. Done? Okay, let's check them one by one. Two p z with two p z: both point along the axis and meet head-on. Allowed, and it gives sigma. Okay? Two s with two p x: the trap we just saw. Different symmetry, zero net overlap, so not allowed. Clear? Two p x with two p x: parallel, side by side, so they overlap sideways. Allowed, and it gives pi. With me? Now the last one: two p x with two p y. Both are two p orbitals, same shell, same type. So this one is allowed, right? No, no, wait! Two p x points along x, and two p y points along y; they are at right angles. So zero net overlap, and not allowed. Got it? So, the answer: only two p z with two p z, and two p x with two p x. Two out of four. See, the symmetry decides, not just the shell. Perfect!

8:09Quick revision: LCAO, bonding vs antibonding, conditions

So, quick revision. By LCAO, n atomic orbitals combine into n molecular orbitals. Adding the wave functions gives the bonding orbital, lower in energy; subtracting gives the antibonding orbital, starred and higher. And orbitals combine only with similar energy, the same symmetry, and good overlap. Now go and try the practice problems on this page. You will find them easy. All the best!