When using Gaussian to calculate NMR, what's the default solvent and frequency?

Question

If I choose GIAO HF/STO-3G, is the default solvent $\ce{CD3Cl}$? Is the default frequency for $\ce{^1H-NMR}$ 500 MHz? What about the frequency for $\ce{^13C-NMR}$?

Answer 1

While Greg's answer describes sufficiently what the program does, I would like to extend a little on his remark. (This should have been a comment, but it was too long.)

The HF/STO-3G level of theory is what you call the minimised ab initio approach. It is unreliable in many ways, but it is fast. However, even geometries of well known and/or calculated molecules may be wrong. In short, it fails more often than it is correct. The problems start with HF, since it does not describe correlation sufficiently. (It only describes Pauli correlation, but this is exact.) The next problem is the basis set: It substantially lacks basis functions. It is called the minimal basis for a reason. Using this setup for NMR calculations is worse than guessing.

The first thing to do would be to increase the basis set. Maybe move away from Pople basis all together. A few basis set families come to mind: Dunning's augmented family, aug-cc-pVDZ and larger, Ahlrichs and Weigend's def2 family, def2-SVP and larger, and many others, see EMSL.

Calculating NMR tensors is always an accuracy versus time tradeoff. And it might be complicated to find the best (in the sense of most efficient) setup. The best way is to start a geometry optimisation on quite a low level. For reasonably large molecules a semi-empirical model like pm6 can be used to scan for configurational space.

Increase the level of theory to pure DFT. You can use density fitting here to speed up your calculation: e.g. #P BP86/Def2SVP/W06 DenFit.

Validate your geometries with a higher basis set, e.g. #P BP86/Def2TZVPP/W06 DenFit and different functionals, e.g. TPSS, PBE1PBE, M06, etc.

Validate your geometries with the dispersion correction of Grimme, e.g. BP86 EmpiricalDispersion=GD3BJ, PBE1PBE EmpiricalDispersion=GD3BJ, B2PLYPD3, etc.

Apply solvent corrections for your system, e.g. SCRF=(Solvent=Chloroform). Make sure to run single point calculations first and try optimisations later.

If you have fully converged geometries at DFT level, you might want to check basic properties with ab initio techniques. Most appropriate would be perturbation theory, e.g. MP2.

After you have done all the above you can go ahead and calculate NMR tensors. It may be combined with solvent approximations. It requires a very well converged structure, a local minimum on the potential energy hyper surface. (Check that with a frequency calculation, e.g. FREQ.) You can set it up like this sample input:

%oldchk=filenameOfPreviousOptimization.chk
%chk=newCheckpoitfile.chk
#P MP2/def2TZVPP
SCRF(solvent=chloroform)
NMR(GIAO)
geom=AllCheck guess=read

Be advised that that computing NMR data with only one method can lead to many misinterpretations. It is very important to verify your structures and tensor on a variety of methods. If you cannot afford MP2 with a large basis, then you should at least check 4 or 5 DFT methods. It is also important to know, that including solvent effects is still something where the theory is not exact. If you have a system that changes a lot with the solvent, then you should consider explicit treatment. Then you might want to dive into molecular modelling, molecular dynamics, MM/QM, ONIOM, etc. pp.

Answer 2

Performing calculations with the "NMR" keyword in Gaussian gives the magnetic shielding tensor in ppm and the spin-spin coupling in Hz. These numbers are independent of instrumental parameters like the frequency of the H-NMR. It doesn't contain any correction for any kind of solvent effect.

One remark: HF/STO-3G is a terrible, terrible low level of theory for ANY kind of calculations.

Answer 3

If I choose GIAO HF/STO-3G, is the default solvent $\ce{CD3Cl}$?

No, the default is gas phase as usual. But you can choose whatever solvent is programmed through the scrf=(solvent=...) command. The available solvents are listed at the bottom of the related Gaussian keyword site.

Is the default frequency for $^1$H−NMR $500~\mathrm{MHz}$? What about the frequency for $^{13}$C−NMR?

There is no default frequency as there is no frequency at all. The program calculates the absolute nuclear shielding tensors that you afterwards need to relate to some other substance's nuclear shielding tensor. As In experimental spectra one chooses TMS or the solvent signal, this must be done also by calculating the shielding tensors for TMS on your chosen combination of method and basis set.

BUT as there are sure default values that are chosen if one chooses the "NMR" command, there is no such thing as a "default route" for NMR calculations. I mean, you can simply click "NMR" in GaussView which will turn on NMR=GIAO calculations but there is more to think of, as Martin already stated.

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NMR Shieldings

I very much like the approach by Lodewyk, Siebert, Tantillo, Rablen and Bally called CHESHIRE - Chemical Shift Repository, because there you can find many recommended procedures for either G03 or G09.

What they have done, was to calculate the shieldings for many known small substances with various DFT functionals, basis sets and solvents in many combinations to get for each of those combinations a set of scaling factors via linear regression.

For me, I chose to optimize my structures with B3LYP/6-31+G(d,p) and afterwards calculate the NMR shieldings with mPW1PW91/6-311+G(2d,p)/PCM and nmr=giao. Then one simply has to write out the calculated shieldings and modify them by $$\delta=\frac{\sigma-\text{intercept}}{\text{slope}}$$ according to their manual with the appropriate scaling factors.

But as you mentioned that you have 200 atoms, you might consider a smaller approach. Good for you, besides their recommended scaling factors there is also a manual on how to calculate your own scaling factors and a vast table for many solvents and methods with their respective scaling factors.

Another really imporant point for such large systems is that they don't exist as one single configuration! What you have to do is to generate and optimize an enormous amount of possible isomers, calculate the shieldings for all those isomers and Bolzmann-weight them using their energy deviation regarding the isomer with the lowest energy. $$\delta_i = \sum_j w_j~\delta_{i,j} = \sum_j \frac{\exp\left(\frac{-E_j}{RT}\right)}{\sum_k \exp\left(\frac{-E_k}{RT}\right)}~\delta_{i,j}$$

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$^1$H,$^1$H-Coupling Constants

As an $^1$H-NMR doesn't consist of straight peaks but mostly multiplets, there could also be the need to calculate the coupling constants. There have been a few approaches towards accurate J values but one of the easiest is also stated on the CHESHIRE website.

1. Optimize the geometry with B3LYP/6-31G(d)

2. Run an NMR single-point calculation with the following route section in GAUSSIAN

   #n B3LYP/6-31G(d,p) nmr=(fconly,readatoms) iop(3/10=1100000)

   At the end of the molecule specification (separated by a blank line) read in: atoms=H

   A sample input file for chloroethane could be like:

   \#n B3LYP/6-31G(d,p) nmr=(fconly,readatoms) iop(3/10=1100000)
   
   Chloroethylene CS
   
   0,1
   C,0,0.,0.,0.
   C,0,0.,0.,1.32727906
   Cl,0,1.462671003,0.,-0.9634208566
   H,0,-0.8964932057,0.,-0.6096342696
   H,0,-0.9458848703,0.,1.8609603221
   H,0,0.9144771425,0.,1.9110938644
   
   atoms=H
   

3. From the resulting log file, extract the desired Fermi contact J values, and scale them by a factor of 0.9117

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Example: Nitrobenzene

According to SDBS, AIST the $^1$H resp. $^{13}$C-NMR spectrum have the following peaks: $$\begin{array}{ccccccc} \hline \ce{Nuc.} & \ce{Calc}. & \ce{Exp}. & & \ce{Nuc}. & \ce{Calc}. & \ce{Exp}. \\ & \ce{ppm} & \ce{ppm} & & & \ce{ppm} & \ce{ppm} \\ \hline & & & & \ce{C_{N}} & 146.47 & 148.30 \\ \ce{H_{A,~A'}} & 8.18 & 8.25 & & \ce{C_{A,~A'}} & 123.25 & 123.46 \\ \ce{H_{B,~B'}} & 7.37 & 7.56 & & \ce{C_{B,~B'}} & 127.75 & 129.43 \\ \ce{H_{C}} & 7.59 & 7.71 & & \ce{C_{C}} & 135.03 & 134.71 \\ \hline & \ce{RMSD} & 0.23 & & & \ce{RMSD} & 2.52\\ \hline \end{array}$$ The differences are not very big. As the carbon nuclei span a much wider shielding range the average error is considerably smaller when compared to the RMSD of the proton shifts. To get an image out of this pure numbers, the overlay of the calculated versus the experimental $^1$H-NMR spectrum can be seen below. It fits quite good, even if it could be better. Maybe the WP04 functional could have done a better job.