# Gaussian Recipes for Rotational Spectroscopy

Recently I've had to do a few calculations using Gaussian where I had to keep going back and waste time to find out how to do something again. I basically got fed up with this, and I'm organizing this post to more or less create a cheatsheet that tells you how, and which keywords to use for calculations using Gaussian '09/'16 to do with spectroscopy, and where to look for the outputs.

## Which method to use

This is entirely a shameless plug, but this question depends on what you want. If you need to do a lot of calculations quickly, I've benchmarked a bunch of low-cost electronic structure methods, and used Bayesian statistics to tease out scaling factors. While these aren't more accurate than state-of-the-art coupled cluster, they are fast and on many occasions the scaling factors give better estimates of rotational constants than VPT2 (which can take a long time). Here is a table of scaling factors:

MethodBasis SetMeanLower boundUpper bound
PW6B95-D3cc-pVQZ0.98160.95111.0159
PW6B95-D36-31+G(d)0.99290.96031.0296
ωB97X-Dcc-pVQZ0.98660.95601.0208
M06-2Xcc-pVTZ0.98780.95701.0226
M05-2Xcc-pVQZ0.98480.95171.0218
cc-pVQZ0.98670.95581.0219
6-31+G(d)0.99650.96501.0323
ωB97X-Dcc-pVTZ0.98720.95461.0238
ωB97X-D6-31+G(d)0.99710.96421.0340

Simply take one of the method/basis above, and multiply your equilibrium rotational constants by these factors to obtain an effective scaled value to base predictions on:

$A(BC)'_0 = A(BC)_e \times \mathrm{scaling}$

. The mean scaling factor basically says statistically, on average your equilibrium value is this much off the experimental constant. The lower and upper bounds set a 95% credible interval, meaning that your result is contained within this boundary 95% of the time. For more details about the methodology, check out my paper. There are similar scaling parameters for dipole moments.

My recommendation is to use ωB97X-D/6-31+G(d), as it gives the best compromise between speed and uncertainty. If you have time to kill, ωB97X-D/cc-pVQZ is better, although of course if you have enough computing power and time you should run ae-CCSD(T)/cc-pWCVQZ. The bump in computational method here acts mainly to decrease the uncertainty, and in the case of the coupled-cluster approach, improve the accuracy.

## Default keywords

These are not nominally default, but for all spectroscopic calculations you should include these:

Int=Ultrafine specifies an ultrafine integration grid: this changes the result of every calculation, and so when you're making comparisons you need to make sure you're operating with the same integration grid settings.

SCF=VeryTight ensures that the SCF convergence is sufficiently good.

Opt=VeryTight ensures your geometry converges enough: since all spectroscopic calculations depend on geometry, you need this.

Say you are chaining a bunch of serial geometry optimizations, and you're simply modifying the basis set used. You don't have to constantly copy-paste the coordinates each time by specifying Geom=AllCheck or Geom=Check; the former reads the charge and multiplicity as well, while the latter only takes the geometry and still expects a charge/multiplicity line.

Keep in mind that this can be dangerous if the checkpoint file is corrupted, as you'll lose the geometry! I would suggest making a copy of the .chk file between runs.

## From Gaussian to SPFIT/SPCAT

There's actually an extremely useful keyword that you should have in every calculation; Output=Pickett. This creates a summary of spectroscopic parameters to higher precision at the end of the output file, and in the format of a .var file in the SPFIT format. Additionally, codings for significant hyperfine nuclei and quartic centrifugal distortion terms are added if you have nuclei with significant quadrupole couplings in the former, and if you're doing a harmonic frequency calculation for the latter. To get the whole shebang:

%chk=calc.chk
%nprocshared=4
%mem=4GB
# wB97XD/6-31+G* SCF=VeryTight Int=Ultrafine Output=Pickett Freq=VibRot
...

This will perform vibration-rotation analysis (to get harmonic $\alpha$ values)

## Changing the representation for parameters

While centrifugal distortion terms are given in both A and S reductions, the representation is actaully inferred by the calculation and often not the one you want. This will make a significant difference in the sign—and to a lesser extent magnitude—of your distortion terms (e.g.

$d_1$

and

$d_2$

are flipped in sign).

The procedure to change this is carried out after you've done an anharmonic calculation, i.e. Freq=Anharm. You can subsequently provide a ITop keyword that then lets you specify

$\mathrm{I_{r/l}-III_{r/l}}$

representations, and have the calculation read in all of the force constants. This should not require any significant re-calculation.

%chk=calc.chk
%nprocshared=4
%mem=4GB
SCF=VeryTight Int=Ultrafine Geom=Check
Changing representations of CD terms
0 1
Print=ITop=Ir

Where you have a calc.chk file containing the previous anharmonic calculation and structure. The calculation will read in the geometry from the checkpoint file, and the Print=Itop=Ir changes the representation explicitly to

$\mathrm{I_r}$

. Note the blank lines!

## Rare isotopic calculations

Some properties are automatically calculated for isotopologues

## Extracting hyperfine parameters

Although the Output=Pickett keyword formats the result nicely, there are cases where the output electric properties are not in the right orientation. Whatever you do, check the dipole moment values to make sure they are what you expect. Here's an example of a goofy result on the PhC<sub>3</sub>N molecule, which is a near-prolate top with only one permanent dipole moment along the

$a$

axis. Normally, you would put the dipole axis ordering to be

$x=a, y=b, z=c$

, however as seen in the following calculation the axes are swapped:

Rotational constants (MHZ):
5733.6904049    574.7286787    522.3680080
Nuclear quadrupole coupling constants [Chi] (MHz):
15  N(14)
aa=     2.5734   ba=     0.0094   ca=    -0.0000
ab=     0.0094   bb=     2.3852   cb=    -0.0000
ac=    -0.0000   bc=    -0.0000   cc=    -4.9586
Dipole moment (Debye):
-0.0000000     -0.0000000      5.8910287  Tot=      5.8910287
Atoms with significant hyperfine tensors:  N15-14

The consequence is that the quadrupole coupling is also messed up.

$\chi_{aa}$

should be the projection of the nitrogen quadrupole moment along the

$a$

-axis, and for cyanide groups this value is typically around -4.5 MHz, which actually turns out to be labelled

$\chi_{cc}$

. So this is a case of Gaussian messing up the labels, and calling the

$c$

-axis properties

$a$

. Chemical unintuition!

If you feel like I've left something out, or you have suggestions, feel free to let me know through an email or tweet!