DFT calculations do not explain enantiospecific NMR responses in cross polarization

arising from T. Georgiou et al. Nature Communications 10.1038/s41467-024-49966-8 (2024)

Molecular chirality is one of the most fascinating phenomena in chemistry, with important implications in pharmaceutical chemistry, materials science, and nanotechnology. Although chiral molecules that are related by mirror-symmetry, known as enantiomers, can in most cases be separated using chiral chromatography and distinguished through chiroptical spectroscopy methods, determining their absolute configuration remains a major challenge for many chiral compounds. NMR spectroscopy, one of the most widely used methods for elucidating the constitution and three-dimensional structure of organic molecules, was long believed to be incapable of distinguishing enantiomers unless the molecules are derivatized with chiral agents, such as in Mosher ester analysis¹, dissolved in chiral solvents, oriented in a chiral aligning phase², or placed in an NMR environment under the influence of a simultaneously applied external radio-frequency (RF) electric field³. However, recent experimental studies have reported enantiospecific effects in cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR experiments^4,5 and proposed that these effects are caused by the chirality-induced spin selectivity (CISS) effect. While it remains unclear whether the observed differences in CP intensity between enantiomers arise due to variations in longitudinal relaxation (T₁) times caused by factors such as sample purity, crystallinity, and particle size⁶, T. Georgiou et al.⁷ provided a theoretical framework, supported by density functional theory (DFT) calculations, suggesting that the experimentally observed differences in CP experiments result from chirality-dependent indirect spin-spin coupling constants (SSCC) between nuclei. Here, we question the validity of these calculations. Based on DFT calculations performed at various levels of theory, we demonstrate that DFT cannot account for the enantiospecific NMR responses observed in CP, as detailed below.

In the publication by T. Georgiou et al.⁷, it was concluded that the CISS effect arises from the spin-orbital coupling (SOC) interactions. To investigate whether SOC plays a significant role in the calculation of indirect SSCC, we performed DFT calculations for the two selected amino acids, l-cysteine and l-serine, using three different approximations: (i) a standard non-relativistic one-component Hamiltonian, (ii) a scalar-relativistic X2C Hamiltonian, and (iii) a two-component X2C Hamiltonian⁸. As shown in Fig. 1, both scalar relativistic effects and SOC have only a marginal impact on the total SSCCs. The only notable difference appears in the coupling between sulfur and hydrogen, where relativistic calculations (both scalar and two-component X2C) show slight deviations from the non-relativistic calculations. Furthermore, the close agreement between scalar-relativistic and two-component SSCCs indicates that SOC plays only a minor role in the calculation of indirect SSCCs in this case. To further validate the accuracy of the X2C approximation in describing scalar-relativistic and SOC effects, we conducted full four-component DFT calculations for a selection of coupling constants. By comparing these results to the non-relativistic limit and artificially removing SOC effects, we observed a very similar trend as the results obtained with the X2C approximation (Table S1 in Supporting Information).

Fig. 1. Influence of common relativistic corrections to spin-spin coupling constants (SSCC).

¹J_CC-SSCC, ¹J_CH-SSCC and ¹J_XH-SSCC (X = N,O,S) calculated using the non-relativistic and the X2C approach in the scalar and two-component approximation for the Hamiltonian for (a) l-cysteine and (c) l-serine at the PBE0/x2c-TZVPall-unc level of theory. The corresponding molecular structures and atom numbering are shown in (b, d), respectively. Atoms have been colored according to their element in white (hydrogen), beige (carbon), blue (nitrogen), red (oxygen), and yellow (sulfur). Source data are provided as a Source Data file.

Since the two-component X2C approximation reliably captures the relevant relativistic contributions for these molecules, as demonstrated above, we used this approach to investigate potential SOC effects by comparing the differences between the enantiomers of the 20 standard amino acids. As shown in Fig. 2, the differences between enantiomers are generally very small. The largest deviation, observed for l- and d-serine, occurs between oxygen 1 and hydrogen 13, with a difference of just 0.2 mHz for a coupling of approximately −61.9 Hz. This difference arises mainly from small numerical errors in the number of decimal places used inverting the l-amino acids to the d-amino acids. When all decimal places of the l-amino acids are used, the difference decreases further to 0.02 mHz (see Table S3). The remaining minor differences most likely result from numerical integration noise and the chosen convergence settings (scfconv: 10⁻⁹, denconv: 10⁻⁷ and rpaconv: 10⁻⁶). This interpretation is further supported by the fact that similar noise-related deviations were observed for the achiral glycine (see Figure S2). Similar trends are observed across all 20 amino acids (Fig. S1–S5 in Supporting Information). Even for the couplings involving the heaviest nuclei in any amino acid, sulfur in cysteine (Fig. S2), no significant deviations between the enantiomers were found, further supporting the conclusion that SOC does not have a noticeable influence on the difference between the enantiomers.

Fig. 2. Evaluation of spin-spin coupling constants (SSCC) and their influence on cross-polarization.

a Difference in SSCCs calculated using the two-component X2C framework at the PBE0/x2c-TZVPall-unc level of theory between the l- and d-serine. b Root mean squared deviation (RMSD) between simulated ¹⁵N magnetization trajectories during cross-polarization from protons to nitrogen as a function of varying J-coupling constants. Numerical calculations were performed using SIMPSON⁹ in a five-spin system approximation using the parameters for serine. Source data are provided as a Source Data file.

Even though the predicted SSCC differences between the two enantiomers are negligible, we sought to determine how large the difference in SSCCs would need to be to generate a noticeable difference in the CP spectra. To investigate this, we simulated the cross-polarization effect in solid-state NMR using an accurate numerical simulation approach implemented in the program SIMPSON⁹. To assess the influence of the J-coupling on the ¹⁵N magnetization build-up curves during ¹H-¹⁵N cross-polarization transfer, we first used the DFT-calculated difference, acknowledging that these are most likely due to numerical noise, between the enantiomers of serine (see Fig. S6) and then artificially varied the J-coupling difference between the enantiomers over a range of values up to +/− 50 Hz in a spin system derived from l-serine. Two additional spin-systems derived from proline and the achiral glycine can be seen in Fig. S7 in the Supporting Information. The results clearly show that the differences in J-coupling predicted by DFT, which are most likely due to numerical noise, are insufficient to cause any noticeable variation in the simulated ¹⁵N magnetization CP build-up curves between the two enantiomers. Although increasing the J-coupling difference does lead to a larger root mean square deviation (RMSD) between the CP build-up curves, the required magnitude of variation would be so large that it can be easily detected in conventional solution NMR experiments.

Based on the calculations described above, performed using non-relativistic, scalar-relativistic, and two-component (2c) relativistic approximations, we observe only minimal differences in spin-spin coupling constants between the two enantiomers. These differences are incapable to cause any noticeable variation in CP spectra in standard solid-state NMR experiments. Our findings stand in stark contrast to the conclusion drawn by T. Georgiou et al.⁷. We questioned why our calculations did not show the large SSCC differences reported in their study. Upon examining the data provided in the Supporting Information⁷, we found that the structures used for the study of the enantiomers are not mirror-images of each other and depict different conformations for the l- and d-enantiomers respectively. For example, by mirroring the provided structure of d-cysteine, yielding the l-amino acid, and aligning this structure with the provided structure for l-cysteine gave an overall RMSD of around 1 Å. Furthermore, the dihedral angles between the H_α and the two NH hydrogens are in the case of l-cysteine around 59° and −55°, while in the case of d-cysteine they are 61° and 177°. It is known from the Karplus equation¹⁰ that dihedral angles have a large influence on the SSCC, making the validity of the calculations by Georgiou et al. questionable, as the differences most likely reflect the change in conformation and are not related to the stereochemistry. We would like to note, that furthermore, at least the structure provided for d-alanine contains an unbounded fluorine atom, which, if used in the calculations, would also give much larger errors. Moreover, we note in passing that the presented SSCCs data of Georgiou et al. are generally not reproducible using the published structures and DFT protocol with deviations of up to 124 Hz for the case of ¹J_C1C2 in l-cysteine, when attempting to replicate the published data (See Table S2 in Supporting Information for the differences in ¹J_CC and ¹J_CH couplings for l-cysteine). The presented SSCCs dramatically exceed experimental expected SSCC ranges, i.e., ¹J_CαCβ and ¹J_CαC’ SSCCs overshoot 100 Hz and more; whereas our own calculations using the provided structures and DFT protocol are significantly closer to the experimentally expected ranges.

Furthermore, standard perturbation theoretical SSCC calculations, as reported by Georgiou et al., are parity conserving^11,12, i.e., the energy and resulting molecular properties are degenerate, if enantiomeric (“mirror image”) structures are investigated. Parity-violation (see e.g., ref. ¹³) has been discussed and investigated in various contexts, including NMR chemical shifts and SSCCs (examples are found in refs. ^11,12,14,15). However, contributions of these electroweak interactions are not part of the standard (DFT) Hamiltonian as provided by ORCA¹⁶ or similar quantum chemical calculation packages. While a rigorous derivation and discussion of the quantum chemical principles underlying a potential enantiodiscriminating effect of the J-coupling tensor is beyond the scope of this work, we noted that enantiodiscriminating effects have been attributed by P. Garbacz and J. Vaara to the antisymmetric part of the tensor¹⁷, which has been experimentally observed only in the presence of a permanent electric polarization³.

As conclusion, we have demonstrated that the findings by T. Georgiou et al.⁷, which suggested that differences in indirect spin-spin coupling constants between enantiomers cause variations in CP spectra in solid-state NMR, are questionable. Instead, the CP intensity differences observed experimentally^4,5 are most likely due to variations in sample conditions. Caution should be exercised when interpreting enantiospecific NMR responses, as misinterpretations may lead to misunderstandings and unrealistic expectations regarding the feasibility of assigning absolute configuration using conventional NMR experiments.

Methods

DFT calculations

The initial structures of the l-amino acids have been geometry optimized at the PW6B95-D4/def2-TZVP(SMD(water)) level of theory in ORCA 5.0.4. The resulting structures have been mirrored by an inversion symmetry operation using a Python script, to yield the d-amino acids in the exact same conformation (more details in section 6 in the SI).

Both enantiomers of each amino acid have been used in spin-spin coupling calculations in TURBOMOLE 7.8 using the PBE0/x2c-TZVPall-unc level of theory. Non-relativistic, scalar-relativistic X2C and two-component X2C approximations (including the SNSO approximation) for the Hamiltonian have been used. Example TURBOMOLE control file for each method with all applied settings can been seen in section 5 in Supporting Information. For the analysis, couplings to and from methyl-protons have been used as average. Additionally, chemical shielding tensors have been calculated in TURBOMOLE as input for the SIMPSON 4.1.1 calculations.

Additionally, in the Supporting Information, ReSpect 5.3.0 has been used to calculate four-component spin-spin coupling constants, and CREST 2.12 and CENSO 1.2.0 have been used for initial conformational samplings. (See details in the Supporting Information) All input and log files for each DFT, CREST, and CENSO calculations are deposited on Zenodo¹⁸. Full references for all programs employed in this work are listed in the Supporting Information.

SIMPSON calculations

Using a five-spin system derived from serine (and glycine and proline in section 3 in SI), we examined differences in ¹⁵N magnetization dynamics during ¹H-¹⁵N cross-polarization transfer by calculating the root-mean-square deviation (RMSD) between the two simulated magnetization trajectories. The five-spin system was determined by the nitrogen spin of interest and four protons with the strongest dipolar couplings to that nitrogen. All dipolar and scalar couplings, as well as aniso- and iso-tropic interactions, were determined by the DFT calculations described above. Cross-polarization was calculated for 2 ms contact time at constant amplitude ¹H and ¹⁵N radio-frequency field. The input and output files from each of these simulations are deposited on Zenodo¹⁸.

Data analyses

The raw data from the DFT calculations and the SIMPSON simulations have been analyzed using Python 3.10.14 in Jupyter notebook (7.4.1) with the following additional packages: Pandas 2.2.1, Matplotlib 3.10.3, Seaborn 0.13.2, and NumPy 2.1.1. Plotting of the serine build-up curve (SI) has been done in Matlab R2015a. Molecules have been visualized using USCF ChimeraX version 1.9. All script used for data analysis and plotting are deposited on Zenodo¹⁸.

Author contributions

Conceptualization: H.S.; Methodology: A.F.K., V.S. Investigation: A.F.K., V.S., C.J.S. Visualization: A.F.K.; Writing, original draft: A.F.K., H.S.; Writing, review and editing: A.F.K., V.S., C.J.S., H.S., A.L.; Supervision: H.S., A.L. Funding acquisition: H.S., A.L.

Peer review

Peer review information

Nature Communications thanks Gustavo Aucar, Stanislav Komorovsky, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Data availability

Data supporting the finding of this manuscript are available either in the Supplementary Information or deposited on Zenodo¹⁸, under the accession code: 10.5281/zenodo.17276943. The Supplementary Information contains detailed description of the calculations and additional figures and tables supporting the arguments made in the manuscript, whereas the Zenodo deposit contains all data necessary for reproducing the presented data. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-66246-1.