Molecular Orbital Theory Notes I

I took intermediate and advanced Inorganic Chemistry courses last year. Since then, I have been asked several questions by my friends who are just taking these courses and I tried to answer them as much as I could. So, I decided to write some posts about the MO Theory and how to construct simple molecular orbital diagrams for students like me. Another reason for me to write these is that writing (or teaching someone else) helps me too (win-win). I will try not to go into anything deep, so obviously you will need to read your textbook to get more information or a quantitative approach. Please correct me if there is anything wrong with my explanations.

First of all, to understand ANY discussion about orbitals, one HAS TO know the "shapes" of the d orbitals. You can see them below. The role of symmetry is also very important in understanding the electronic structure of a complex and in drawing a molecular orbital diagram. Because, the overlap integral (you can read more about it in a book) should be non zero in order to have an interaction. This means that orbitals must have some kind of symmetry to interact. 

image: http://upload.wikimedia.org/wikipedia/commons/5/58/D_orbitals.png

Let me give some very general information about d-orbitals here. 

Both dxz, dxy, dyz orbitals have two nodal planes (xy, yz; xz, yz; xz, xy respectively). Some people are confused with the signs of the lobes of these and other orbitals. If you imagine a coordinate system and give + and - signs for each coordinates, then you will notice that the sign of each lobe changes as you move along the quadrants. For example, for dxz orbital, when both x and z coordinates are +, the sign will be + too. But, when you assign - to x and + to z, the sign will be negative. You can try this on your own.

Now it's time to think about dx2-y2 orbital. This orbital as you can see above, lies along the x and y axes. Just like the other ones, this one also has two nodal planes. You can imagine them bisecting between x and y axes. The sign of each lobe will again change as you move from one lobe to another. Just by basic math skills, you can assign + to x and 0 to y and you can see how they will change. 

dz2 has an interesting shape. In fact this orbital is represented as "2z^2-x^2-y^2"for some mathematical reasons which I do not fully understand. But, for an undergraduate student, it is OK not to know it. At least, this has been my experience. Anyway, 2z^2 tells us that no matter the sign of z is, the sign of the lobe will be + along the z axis. But, when z is zero, the sign has to be -. It is that simple.