Remember that an orbital is a mathematical function which describes the wave-like behavior of one electron, and review how we combined two 1s atomic functions to obtain two sigma orbitals, one 'bonding' and the other 'antibonding'. Recall also how the effects of electronegativities are manifested by changes in the values of coefficients in the atomic orbitals.

We'll now use GausView to visualize the MO's of H2 and HHe+.
!!!(Remember to telnet to hpc and not to use the local hpclab computer [or fish SUN] that you logged onto.)
1-type gv;
2-click on the -H button then in the middle of the screen to obtain the H2 molecule;
3-click on calculate, G98;
4-write %chk=hh.chk in the Link0 Commands box; choose opt+freq;
5-in the basis set box, choose STO-3G, in Additional Keywords type in pop=reg, and then submit;
6-click on the save box that appears and then give a name such as hh.com in the select a file box that appears; then OK.
7- When you get the message Gaus calc complete, open the resulting log file, hh.log.
8-Look at the vibrational mode and record its frequency.
9-Measure the H-H bond length by clicking on the Bond box, then bring the cursor and click on the first atom then the other. Record the answer (in Angstroms) and click cancel.
10-To get a picture of the MOs, we'll need another type of output file. Click on file then open. (You don't need to save any files.)
11-At the top of the 'open file' box, choose chk from the file type menu, then outline your file hh.chk, and click on open. The picture looks like the original one of the molecule.
12-From the Results menu, choose surfaces and in the new box 'generate' (in the upper right).
13-Click on okay and then on the warning box OK, then Apply.
14-Click on the generate button again in the surfaces box. In the options, orbital= box replace 1 by 2, hit okay, then apply.
15-Rotate the molecule in several directions. The red areas show where the value of the MO = +0.02, while the green is for -0.02

<X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X>
The resulting figure gives a surface of points where the value of the MO = 0.02. Remember when you plotted the wavefunction psi against distance x for H2 and HeH+? You arbitrarily plotted psi between x=-5 and x=5. Now we are finding a 3D surface where the value of psi is exactly 0.02. We could have done that before but that would mean plotting a point at x>0 and x<0 where psi = 0.02
<X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X> <X|X>

Now repeat for HHe+. You might call the file hhe.com.
16-Choose File, then Open, then the -H box, then click on the screen to get an H2 molecule;
17-From the Element button choose He, then click on the He button (changing the number of bonds to one) and choose "He Atom";
18-bring the cursor to one of the H atoms, click on it. This changes the H to He (faint blue color).
19-From calculate, G94 setup box, fill in %chk=hhe.chk, opt+freq, STO-3G, and in the upper right corner, change to Charge = 1.
20-Submit the calculation and repeat steps 6 to 15. Compare all the results to H2. To get a better view, click on View on the main menu and then 'Show symbols'; again in View, choose "Display format' and then from the Display format menu choose translucent (or mesh).

To find out the values of the coeffidients of the AOs that make up the two MOs, edit the hh.log or hhe.log files. Near the bottom you will find "Population analysis using the SCF density.", then a little further 'eigenvalues'. The eigenvalues are the orbital energies. The energy of the highest occupied MO is approximately equal to the negative of the ionization potential (IP), which is the energy needed to eject an electron. Which has a higher IP, H2 or HHe+? and why? The coefficients of the AOs that make up the bonding sigma MO are in the first column under the orbital energies and those of the antibonding MO are in column 2. You might want to use these values if you go over the exercices in the introductory section on Quantum Chemistry. Another comparison between the two molecules is the vibrational frequencies. Which two factors should come immediately to mind when judging differences of vibrational frequencies?

If you do this exercise for the molecule BH, you will be able to 'see' some common types of orbitals: a core, sigma bonding and antibonding, and a lone pair.

"Core" 1s orbital on B. Notice the large value of the AO coefficient of the B 1s AO that contributes to this MO.

Second MO, a bonding combination of an sp hybrid orbital [Look at the coefs for 2s and 2px] and the H 1s orbital.

Third MO, the lone pair, another combination of an sp hybrid orbital [Look at the coefs for 2s and 2px] and the H 1s orbital. There is still a significant participation of the H 1s orbital [0.376 coef compared to 0.789 and 0.58].

The fourth and fifth MO's, which are the two unused 2p AO's on Boron, one in the z direction, the other in the y.

The sixth MO, an antibonding combination of an sp hybrid orbital [Look at the coefs for 2s and 2px] and the H 1s orbital.