Now for electrons in molecules. Just as the behavior of electrons in atoms is dictated by the atomic orbitals they reside in, so electrons in molecules behave in ways dictated by the molecular orbitals which contain them. We think of molecules as being built from atoms (even if that is not actually how you would usually make them), and likewise we can think of molecular orbitals as being built up from a combination of atomic orbitals. As atomic orbitals are wavefunctions, they can be combined in the same way that waves combine. You may be already familiar with the ideas of combining waves either constructively (in phase) or destructively (out of phase):

Atomic orbitals can combine in the same ways—in phase or out of phase. Using two 1s orbitals drawn as circles (representing spheres) with dots to mark the nuclei and shading to repre sent phase, we can combine them in phase (that is, we add them together), resulting in an orbital spread over both atoms, or out of phase (by subtracting one from the other). In this case we get a molecular orbital with a nodal plane down the centre between the two nuclei, where the wavefunctions of the two atomic orbitals exactly cancel one another out and with two regions of opposite phase.

The resulting orbitals belong to both atoms—they are molecular rather than atomic orbitals. Now, imagine putting electrons into the first of these orbitals (the bonding orbital). Remember, you can put zero, one, or two electrons into an orbital, but no more. The diagram of the orbital shows that the electrons would spend most of their time in between the two atomic nuclei. Being negatively charged, the electrons will exert an attractive force on each of the nuclei, and would hold them together. We have a chemical bond! For this reason, the in-phase molecular orbital is called a bonding orbital.

The out-of-phase molecular orbital offers no such attractive possibility—in fact putting electrons into the out-of-phase molecular orbital works against bonding. These electrons are mainly to be found anywhere but between the two nuclei, where there is a node. The exposed positively charged nuclei repel each other, and that is why this orbital is known as an anti-bonding molecular orbital. The combination of the atomic 1s orbitals to give the two new molecular orbitals can also be shown on a molecular orbital energy level diagram. The two atomic orbitals are shown on the left and the right, and the molecular orbitals which result from combining them in and out of phase are shown in the middle. The diagram as a whole is a sort of ‘before and after’ diagram—the situation before the interaction between the orbitals is shown on the left and the right, and after the interaction is shown in the middle. Notice that the bonding orbital is lower in energy than the constituent 1s orbitals, and the antibonding orbital is higher.

Now we can actually put the electrons into the orbitals, just as we did on p. 84 when we were building up the picture of atomic orbitals. Each hydrogen atom has one electron and so the resulting hydrogen molecule (shown in the middle) contains two electrons. Always fill up orbitals from the lowest energy fi rst, putting a maximum of two electrons into each orbital, so both of these electrons go into the bonding orbital. The antibonding orbital remains empty. The electrons therefore spend most of their time in between the nuclei, and we have a plausible explanation for the existence of a chemical bond in the H₂ molecule.

Diagrams such as these are central to the way we can use molecular orbital theory (MO theory) to explain structure and reactivity, and you will in future meet many more of them. So, before we go on it is worth clarifying several points about this one:

• Two atomic orbitals (AOs) combine to give two molecular orbitals (MOs). You always get the same number of MOs out as you put AOs in.

 • Adding the wavefunctions (combining them in phase) of the two AOs makes the bonding orbital; subtracting them (combining them out of phase) makes the antibonding orbital.

• Since the two atoms are the same (both H), each AO contributes the same amount to the MOs (this will not always be the case).

 • The bonding MO is lower in energy than the AOs. • The antibonding MO is higher in energy than the AOs.

 • Each hydrogen atom initially had one electron. The spin of these electrons is unimportant.

• The two electrons end up in the MO lowest in energy—the bonding MO.

 • Just as with AOs, each MO can hold two electrons as long as the electrons are spin paired (shown by opposing arrows). You do not need to be concerned with the details of spin-pairing at this stage, just with the result that any orbital may contain no more than two electrons.

• The two electrons between the two nuclei in the bonding MO hold the molecule together—they are the chemical bond.

• Since these two electrons are lower in energy in the MO than they were in the AOs, the molecule is more stable than its constituent atoms; energy is given out when the atoms combine.

• Or, if you prefer, we must put in energy to separate the two atoms again and to break the bond. From now on, we will always represent molecular orbitals in energy order—the highest energy MO at the top (usually an antibonding MO) and the lowest in energy (usually a bond ing MO and the one in which the electrons are most stable) at the bottom. Before you leave this section, let’s recap how we got to the MO diagram of H2. It’s worth working through these steps to check you can draw your own MO diagram before you leave this section.

1. Draw two H atoms along with the 1s atomic orbitals which contain the electron, one on either side of the page.

2. Sketch the result of adding and of subtracting the wavefunctions of these two 1s orbitals to show the bonding and antibonding MOs. These go one above the other (high energy antibonding orbital on top) in between the AOs.

3. Count up the total number of electrons in the atoms going in to the molecule, and put that number of electrons into the MOs, starting at the bottom and building upwards, two in each orbital.

مواضيع ذات صلة

Forming bonds using 2s and 2p atomic orbitals: σ and π orbitals

Bond order

Why hydrogen is diatomic but helium is not

Breaking bonds

Four short clarifications about orbitals before we go on

The phase of an orbital

s and p orbitals have different shapes

Electrons occupy atomic orbitals

Electrons have quantized energy levels

Atomic emission spectra

Introduction

Looking forward to Chapters 13 and 18