Why are the calculated NMR values on the DFT & GIAO level of cyclopentane-1,3-dione so far off?

Question

I'm trying to simulate the ¹³C NMR spectrum of cyclopentane-1,3-dione (PubChem CID: 77466; CAS 3859-41-4; ChemSpider ID: 69875; SDBS No: 15258; SMILES: C1CC(=O)CC1=O). There are three equivalence classes of carbons: The two directly attached to the oxygens (≈197 ppm, call this class 1), the one carbon between those two (≈105 ppm, call this class 2) and the "other two" (≈31.3 ppm, class 3).

I've been using Gaussian 16 via the guidance provided by Dean Tantillo's group at UC Davis, the chemical shift repository (CHESHIRE) in particular first performing molecular structure optimization at some level (e.g. B3LYP/6-31+G(d,p)) and then calculating shieldings (at mPW1PW91/6-311+G(2d,p) with solvent corrections, scrf=(solvent=chloroform, smd)). But I keep getting shielding values that are radically off.

In particular, regardless of the settings I arrive at isotropic shielding values for classes 1, 2, 3, of ≈-34, ≈136, ≈144. Now of course observed chemical shifts and shieldings are often related by a linear scaling, per the Tantillo group's work (and others), which means that it's very odd that classes 2 & 3 here (the non-Oxygen-attached carbons) have nearly identical shielding values.

I am new to chemistry and DFT methods, so I worry I might be something wrong, but it might also be the case that this is just a "hard" molecule for DFT methods to get right. I wanted to know:

1. Are there any higher levels of theory that I should try / better methods for shielding calculation that would be worth assessing?

2. Is there any way of analyzing the output from Gaussian16 to get a hint that things might be going awry?

3. Is there something that just makes this a "hard" molecule to calculate? I get the impression that the contributions in liquid state from various rotamers, etc. is relatively minor as it seems quite rigid (although I have not quantified this).

Answer 1

Brief Summary

The computational results given below indicate that there is something inherently problematic with this seemingly simple system.

Computational Methodology

Full optimizations and corresponding harmonic vibrational frequency computations of cyclopentane-1,3-dione was were at two levels of theory:

1. B3LYP/6-31+G(d,p)
2. MP2/aug-cc-pVTZ

Each optimized geometry was subjected to GIAO-NMR computations at the following levels of theory:

1. mPW1PW91/6-311+G(2d,p)
2. mPW1PW91/IGLO-II
3. PBE0/IGLO-II
4. mPW1PW91-SMD/6-311+G(2d,p)
5. mPW1PW91-SMD/IGLO-II
6. PBE0-SMD/IGLO-II

The NMR levels of theory were chosen specifically to look at basis set effects as well as implicit solvation (SMD) effects. The solvent chosen was chloroform.

All computations were carried out using the Gaussian 09 software package. All DFT computations employed an ultrafine integration grid. The frozen-core approximation was invoked for the MP2 computations.

Results

Table 1 presents the absolute isotropic shielding constants ($\sigma\ce{C}$) as well as the computed chemical shifts ($\delta\ce{C}$; determined using Equation 1 given by Martin in the comments) with all values given in ppm. The carbons are labeled in figure 1 for cyclopentane-1,3-dione. Despite the level of theory used for the optimization or NMR computation, the $\delta\mathrm{C}^2$ values are consistently off by ≈50 ppm with respect to the 'experimental' values obtained from equation 1.

Figure 1: Cyclopentane-1,3-dione with labeled carbons

Equation 1: $$\delta=\frac{\text{intersection}-\sigma}{-\text{slope}}= \frac{186.5242-\sigma}{1.0533}$$

I am actually quite surprised by these results as I did not expect this system to be difficult to characterize with straightforward NMR computations.