Which of the following diagrams correctly illustrates the phases and orientations of the atomic orbitals giving rise to a 𝜋 star orbital?
To answer this question, we should start by reviewing what we already know about molecular orbital theory. We know, for example, that when we combine atomic orbitals to create molecular orbitals, the overall number of orbitals that we have doesn’t change. So if we started with two atomic orbitals, we would create two molecular orbitals. We know that when we combine atomic orbitals, we can form different kinds of molecular orbital. For example, you could have a 𝜎 or 𝜎 star, orbital, or 𝜋 or 𝜋 star. In order to answer this question, we need to work out which types of atomic orbitals combine to create the various different types of molecular orbital. In this case, we’re particularly interested in the 𝜋 star antibonding molecular orbital.
Let’s begin by looking at the difference between 𝜎 and 𝜋 molecular orbitals. The atomic orbitals, used to form 𝜎 molecular orbitals, must be cylindrically symmetrical along the bond axis. S orbitals and Pz atomic orbitals both fit this description. So 𝜎 molecular orbitals are made up of S and Pz atomic orbitals, which have been linearly combined. For 𝜋 molecular orbitals, all of the constituent atomic orbitals need to be perpendicular to the bond axis. This means that we’re using Px and Py atomic orbitals to build these 𝜋 molecular orbitals. If we look back at our question, we are asked specifically about a 𝜋 star orbital. So when we look down our possible answers, we can exclude anything that’s not made up of atomic orbitals, which are perpendicular to the bond axis.
So let’s look at our potential answers now and see if there are any which we can already exclude. Answer B shows two Pz orbitals since these lie along the bond axis. Combining these would form a 𝜎 molecular orbital, not 𝜋. So we can rule this answer out. The same is true of answer E. So this can also be ruled out. If we look at answer C, we can see that one of the orbitals is a Pz orbital. And the other is Px. Combining these two atomic orbitals will not form a molecular orbital. Let’s revisit this answer in a minute.
Now let’s consider what we need to form an antibonding starred orbital. Whether a molecular orbital is bonding or antibonding depends on the phases of each lobe of the orbital. In order to form a bonding molecular orbital, we want phases of the constituent atomic orbitals to be the same. Because we know that we’re looking for a 𝜋 orbital for this question, we’ll only consider appropriate atomic orbitals. But the same is true for those orbitals which combine to form 𝜎 molecular orbitals. For our Px and Py orbitals, we have two lobes, each of which has an opposing phase. This is denoted by one of the lobes being shaded or colored in some way.
In order to create a bonding overlap between these two atomic orbitals, we need the approaching lobes to have the same phase as each other. In this diagram, we can see that this is the case. These will go on to form a bonding 𝜋 orbital like that shown. If, however, the approaching lobes have opposing phases, this is when we form an antibonding orbital. The resulting antibonding orbital looks a little like this. Notice it has a nodal plane down the center, an area where there is no probability of finding an electron.
So going back to the question, we’re looking for two atomic orbitals which are perpendicular to the bond axis, so a Px or Py orbital, but also which have opposing phases. We can see in answer A that we have the right shape atomic orbital. But the phases are matched. Therefore, this would create a bonding 𝜋 orbital. So we can rule this out as an answer. Answer D, on the other hand, with similarly shaped orbitals does have an opposing phase arrangement. This means that these two atomic orbitals would indeed combine to give a 𝜋 star antibonding orbital. So this is a correct answer.
Just for completeness, let’s quickly revisit answer C. The question remains, what happens when we combine these two atomic orbitals? The answer is that they actually don’t combine to form a molecular orbital. This is because the lobe of the Pz orbital, closest to the Px, actually only overlaps constructively with the top part of the Px orbital. While this sounds positive, we also have to consider how this lobe interacts with the bottom half of the Px orbital. Because we have a phase mismatch, this causes destructive interference. Due to their symmetry, this means that the two interactions cancel each other out. And we’re left without a resultant molecular orbital. So C is also an incorrect answer.
So the correct set of atomic orbitals which give rise to the 𝜋 star orbital are D.