(Irony that my intro background picture is from GAMESS since I don’t have any cool Gaussian pictures to show at the moment.)

Okay, you’ve got an optimized structure for a chemical by an ab initio method. You just spent months learning Hartree-Fock, then Density Functional Theory and even dabbled a bit in the nether regions of computational hell with MP2 and CCSD only to take a breath of air to swallow some AM1, what in the world do you do with it now? What’s the point? You’ve got B3LYP dripping out of every orifice and are worried there isn’t enough B3PLYP. Where do you go now if not the proctologist to make certain you don’t have colon cancer?

The whole point in the end is to predict real physical parameters of some sort. You want the model so that you can turn around and apply it to reality. If what you simulated is only true *in silico*, then the entire experience isn’t worth more than months spent on *Fortnite Battle Royale*. And, you might ultimately have more fun on *Fortnite*.

The point of struggling with GAMESS and Gaussian is the little off chance that what you produced inside the machine matches something in reality. *Fortnite* struggles to fake real. With Gaussian, the point is to go further and take that last step across the gap to make a numerical prediction that you can then turn around and measure in the world around you. And this is at the extreme fringes of real where the measurement applies.

With my work in Gaussian and GAMESS, there was a real research objective at the end of the tunnel. One stop-over along the route was to try to figure out how good of a measurement it’s possible to make. This is not a subtle point; did all this hard work amount to something?

One clear, measurable molecular quantity that you might care about are the electrostatic features of some molecule of interest. The most major that you will hear people talking about is the permanent dipole moment. Within a molecule, it often turns out that the average position of the electrons does not necessarily match the average position of the nuclei. The separation of these tends to generate a small local electric field that falls off over distance as 1/r^3. You may remember me talking in another post about the magnetic dipole moment. Electric dipole moment is the second moment of electrostatic charge distribution, derived much the same way. Dipole moment can be a very important quantity because the generalized electrostatic charge distribution of a molecule has a strong impact on how it can directly interact with another molecule.

While one might consider the dipole moment to be the most simplistic aspect of molecular charge distribution, it actually turned out to be something of a learning experience to calculate it accurately. I took something of a detour to learn how it was done well on a simple historic system of interest.

The dipole moment of water is an old and important physical chemistry computational target. First, it actually turned out to be a non-trivial measurement and was not actually measured well until 1973. The value you can find cited on Google by typing “dipole moment of water” was measured by Shepherd Clough and company using the Stark Shift. Stark shift is the Hamiltonian perturbation of an electric field on the quantum mechanical levels of an atom or molecule, causing degenerate quantum levels to split in energy relative to their interaction with the external electric field. Water has a permanent dipole moment of 1.85 Debye and this value is known well to four decimal places in the Clough paper, which is pretty good.

This value makes a good target for ab initio quantitation since it is already well enough measured for comparison. The modeling values that tend to turn heads came from Thom Dunning’s group and the group of Kim some twenty years after the Stark shift measurement. I became a fan of Dunning’s cc-pVNZ gaussian basis sets as a result of doing these calculations…

For your (semi-) entertainment, here is a tabulation of water dipole moments using various ab initio methods.

Through this little piece of work, you can see how the various combinations of technique and mathematical basis set interact to produce better and better estimates of the water dipole moment. In the methods, “HF” means Hartree-Fock, “DFT” is of course density functional theory, “CCSD” means coupled-cluster with single and double excitations, which is an configuration interaction theory considered to be a post-Hartree-Fock technique, “MP2” means second order Moller-Plesset perturbation, which is also post-Hartree-Fock. For Hartree-Fock, the bigger and bigger basis sets hit the correlation energy limit when the strength of the water dipole moment is about 2.0 Debye. The Dunning basis cc-pVQT is basically sitting on the Hartree-Fock limit for water. The values get better for higher levels of theory, and really turn good when you start applying post-Hartree-Fock to basis sets that include diffuse augmentation to correct the fringes of the gaussian sets to look more like exponentials. The B3LYP functional in DFT produced ridiculously good values, but you can see that it undercuts the water dipole moment as you push to larger basis sets–this means that the faulty asymptotic behavior of functional is combining with the incompleteness of the basis to produce a spuriously accurate value. It also means that you can’t really trust it to produce correct values in an unrelated system. Switching to the long-range corrected functional CAM-B3LYP causes the value to deviate to slightly higher dipole strengths, but restores the behavior of the functional to mimic that of the post-Hartree-Fock methods, allowing the basis set density to be the main contributor to accuracy.

One thing hidden here is the computational resources necessary to run a given technique. As it turns out, the HF and DFT are both relatively cheap. CCSD and MP2 are not. I managed to crash my computer, literally crash it, trying to apply MP2 to a bigger molecule for purposes of measuring the dipole moment. The computer hard drive literally overflowed with computational scratch files and prevented the computer from booting until I started in safe mode and deleted the scratch files by hand. And, CCSD is reputedly more costly than MP2. For a molecule the size of water, CCSD with cc-pVQZ took nearly ten minutes where the other techniques clocked in at 14 seconds or less.

Some of these methods can be really good for predicting physical properties. Be sure to bring your supercomputer!

Edit 4-30-30:

Yeah, I’ll add one disposable picture from Gaussian;-)