Quantum Chemical calculations with Gaussian.
In this lab we will look at some of the widely used features of the Gaussian program. I
will illustrate the way to set up the calculations using the projected screen in the Friezen
lab. So these notes will be minimal.
We will do exclusively Hartree Fock 3-21G calculations (the default in Gaussian). These
calculations will be fast, and they illustrate the points I wish to make. More accurate
calculations are certainly possible, but they take significantly longer. We will use the old
version of Gaussview, (3.0). Version 5.0 has difficulties with visualizing orbitals in the
Friezen lab. The older 3.0 version of Gaussview pops up a window when the calculation
is done, which might be hidden under other pallets. Make sure you keep track of this
window, and hit the OK button. Otherwise you will sit there for ever, waiting for things
to happen.
A. Building molecular structures, optimizing geometries,
calculating and visualizing vibrational frequencies.
Let us build ethylene, C2H4, using the sp2 carbon from the atoms menu. After building,
click calculate and select jobtype = opt+freq, and under method set up a Hartree-Fock 321G calculation for a singlet state (all defaults). Click the submit button and save the file
in a suitable directory and with a good name. Next we can submit the calculation. When
it returns (hit the OK button in the returned window) we can investigate the bond angles
and bond lengths of the optimized geometry. Open the results file (it uses a .log
extension), which opens a new window. Now in this window we can investigate the
optimized structure. Moreover we can visualize the vibrational spectrum. Go to
results/Vibrations, and a new window pops up with the desired info. By clicking start and
selecting particular vibrations, you can see the associated normal mode motion. Only
vibrations/normal modes that have non-zero dipole derivatives are IR active. The
program also calculates Raman intensities.
Excersise: Build the CO2 molecule and investigate the four normal modes of the system.
Which modes are degenerate, which modes are IR active? We have discussed this in
class. Just checking Gaussian does it right! To create a new inputfile use file/new/create
molgroup.
B. Investigating thermochemistry.
Using the previous output (on ethylene) we also have all the information to extract
thermochemical data. If we open the output file (view file under results), and scroll to the
end and then move upwards, we find a thermo chemistry section. It lists rotational
constants (from the optimized geometry), and then has all the information to calculate the
partition function (statistical mechanics). You can see info on entropy, Gibbs free energy
(G), enthalpy (H), heat capacity (Cv).
Note: Hartree-Fock 3-21 G is useless for thermochemistry. One needs to do a much more
accurate calculation, for example B3LYP (DFT) with a cc-PVTZ basis set. This takes a
longer time to calculate. But in this way you could calculate the enthalpy of reaction of
for example the reaction
C2 H 2 ( g )  H 2 ( g )  C2 H 4 ( g )
All gas phase reactions can in principle be studied (given enough computer resources).
We have discussed all of the underlying theoretical principles in class: particle in the box:
translational energy; Rigid Rotor model, (using spherical harmonics): rotational energy
contributions; harmonic oscillator models for polyatomics: vibrational part of the energy.
The major component of the reaction enthalpy is the difference in the electronic energy at
the minimum of the potential (the optimized geometry), for each of the molecules
involved in the reaction. Here accurate calculations are critical, and in class we only
scratched the surface regarding electronic energy calculations.
C: Visualizing molecular orbitals.
Let us build the trans-butadiene molecule, and optimize the geometry. Once this is done,
we click on the orbital icon. This lists all the orbitals and their symmetries. We will be
looking at the  -orbitals in particular, and they are around the HOMO and LUMO levels
(if we use the 3-21G basis set): orbitals of a’’ symmetry, #12-17 or thereabouts. We need
to first generate the MO’s: click on New in the orbital window, and then click generate
where it ask for checkpoint file. Once this calculation is done (click OK on the (hidden)
Gaussian pallet that says it is done), we click on visualize, and we can select the orbitals
we wish to look at. Type for example 13-17 in the window where you can specify which
orbitals to look at. Then click update. If instead you click the very tempting OK button,
you can start over again! I like to look at orbitals using the mesh view (right click in the
orbital window, and select surfaces). Then you can see both the orbital and the molecular
framework.
Sometimes, I encountered a problem with this. In that case after generate you have to
upload the .chk file yourself, before you visualize. Also hit the OK button that is hidden
behind all your windows (and scream!). I hope it works …
Excersise: Identify the  -orbitals in trans-butadiene. You can increase the isosurface
value a bit (to 0.1 for example), to get a clearer view of the orbital coefficients
(regenerate the orbitals, using update). These coefficients are not all equal. See
McQuarrie for the precise values of the coefficients in Hückel theory (Chapter 11).
Excersise: Calculate the molecular orbitals for water. What do you anticipate the orbitals
to look like? Two lone pairs on the oxygen atom, responsible for the hydrogen bonds in
liquid water?
Answer: Look and see for yourself. The truth is that molecular orbitals are not unique.
The only thing that matters is the Slater determinant they create. One can make linear
combinations of the canonical Hartree-Fock orbitals and make more localized orbitals, or
the familiar hybrid orbitals from VSEPR. You can play with the NBO option in Gaussian
to see this in action. I didn’t try it yet myself.
D. Singlet and triplet states, Jahn-Teller distortions for a Hückel type problem.
A case study.
The following problem is a bit extensive. Let’s see if we can get through it in class.
I want to create (CH2)3C, which is planar and has the maximum D3h symmetry. The first
hurdle is to create this structure. Pay attention! The central atom is like an aromatic
carbon. I started by making the structure (CH3)C(CH2)2, (using a center aromatic C, two
sp2 carbons and one sp3 carbon) then delete a H-atom (delete atom button). Next clean up
the structure (use the broom icon). Then select the dihedral angle tool to rotate the two
out of plane hydrogens in the plane of the molecule (select HCCC dihedral angle). This
should look more or less right. Then go under edit and select point group. If you use the
loose or very loose criterion, you will see the molecule is recognized as having D3h
symmetry. Click the symmetrize button on the right. Finally, you can click the reconnect
button, which draws aromatic bonds for visual pleasures. Pooh! We have our molecule.
There might be easier ways to get there!
Actually there is: If you get stuck creating this structure (or even before that for the sake
of time) go to the chem356 website and copy the input file I created for this molecule.
Right click on the Gaussian input file C_CH2_3_triplet.gjf and use save target as to save
this file as a Gaussian input file in your directory. Do not open the file directly (it will
launch the newer bad version of gaussview), but just save it. The open the file from the
Gaussview that is already open. You can visualize the input file, and do the rest of the
calculations starting from this starting point. It has the desired D3h symmetry.
Now: use the symmetric D3h structure and do a geometry and frequency calculation for
the triplet state. This has to be selected under the method button in calculate. You will see
that the triplet has D3h symmetry, as predicted by Hückel theory. Let us look at the  orbitals for the optimized structure, using the orbital viewer. You can see that they nicely
match the orbitals predicted by Hückel. Look at both the occupied and virtual orbitals.
Notice that the HOMO is degenerate, and both are occupied by a single alpha spin
electron. This is the hallmark of the triplet state. Also notice that the alpha and beta
orbitals have different energies (and occupation patterns).
Now we will calculate the singlet state. The molecule will distort. By enlarging one of the
CCC bond angles to say 130 degrees (use the angle button to do this), we will create a
structure in which the ‘anti-bonding’  -orbital is doubly occupied. Optimize this
structure, and investigate the changes in structure (use the measuring tool). Next, starting
again from the triplet D3h geometry, we can make one of the CCC angles sharper (e.g.
105 degrees). This disfavors the ‘anti-bonding’  -orbital, which will now become
empty. Instead the other orbital, which was degenerate in the triplet will become doubly
occupied. Again we can optimize the structure and find a distorted geometry, now with
one sharp (acute) and two obtuse angles (> 120 degrees). These are stable structures for
the singlet state. There are really two (or even three) singlet states involved, which are all
very close together in energy. This kind of molecule is called a biradical. While we get
qualitatively correct structures, the energetics at the Hartree-Fock level is probably very
poor. These states are hard to calculate as there is strong mixing of configurations. You
can anticipate this by looking at the orbital energies. Also, by slight geometrical changes
the occupation pattern of the orbitals changes completely. This is a complicated system!
How complicated? Imagine that for the molecule you can distort either one of the three
equivalent angles to become less than or greater than 120 degrees. Each of these would
yield a different minimum (observable experimentally if you would replace some of the
hydrogens by deuteriums, such that the triplet structure is no longer D3h symmetry,
although the electrons are oblivious to this. In summary the potential energy surface for
the singlet state has a bunch of local minima (6), and the occupied HF orbitals rapidly
change with geometry.
In general the same is true for low spin transition metal compounds that show
Jahn-Teller distortion. There are always very low lying excited states, and many
structures related by symmetry. The low spin surfaces are complicated.
Cute stuff, nice to ask about on the final exam in a Hückel context!