**7. Theoretical Calculations**

A theory for the calculation of isotope effects on chemical shifts was presented by Jameson [72,73]. In a simplified way, deuterium isotope effects can be calculated by assuming that the XH bond is shortened upon deuteration. This approach has been described in a number of papers [62,71,72,74]. The shortening can be determined by the calculation of the hydrogen bond potential, but this is time consuming [43,75]. A simpler approach is to assume a reasonable value and as all the isotope effects of the molecule depend on the same shortening, a plot vs. experimental values will determine whether an intrinsic isotope effect is at hand. An example is shown in Figure 29.

**Figure 29.** Plot of calculated vs. experimental deuterium isotope effects on 13C chemical shifts.

The investigated compounds are of type with R´ being methyl or phenyl and R being alkyl or aromatic. The calculations were of MP2/6-311+G(d2d,p) type. Reprinted with permission from Ref. [74]. Copyright 2018 Wiley.

An ab initio multi-component molecular orbital method on *o*-hydroxyacetophenones seems to overshoot the experimental values [76]. MC-MO calculations were also used for amino acid pairs [77]. A more recent example is a multicomponent hybrid density functional method combined with the polarizable continuum method [78]. This method was applied to picolinic N-oxide and led to decent predictions for the deuterium isotope effects on 13C chemical shifts, whereas the primary deuterium isotope effects were less well predicted. In the case of deuterium isotope effects, this was also the case for acetylacetone. Gräfenstein has developed a difference dedicated second-order vibrational perturbation theory to calculate isotope effects [79]. This was applied to a series of *o*-hydroxybenzaldehydes [80]. Ab initio path integral molecular dynamics (PIMD) calculations showed a barrier-less proton transfer and a C2V symmetry of the hydrogen bond. The calculated isotope effects were rather small [81]. An isocytosine dimer was studied at a low temperature. PIMD calculations were applied to the isocytosine base pair. For N3, the <sup>1</sup>ΔN(D) = 0.88 ppm [82]. The PIMD calculations gave somewhat too large values, but of the right order.

### **8. Conclusions**

Isotope effects on chemical shifts cover a very broad range of hydrogen bonds ranging from the very weak over dihydrogen bonds to the very strong hydrogen bonds found in, e.g., dicarboxylic acid anions. Isotope effects on chemical shifts in small molecules provide a basis and an understanding for use in larger, e.g., biological molecules. One-bond deuterium isotope effects on 15N chemical shifts and two-bond deuterium isotope effects on 1H chemical shifts can be used to monitor the distance to nearby hydrogen bond acceptors and/or charges.

Isotope effects on chemical shifts are a strong tool in the investigation of tautomeric systems and can lift degeneracies in symmetrical systems as seen in the monanions of dicarboxylic acids. 18O labelling of the latter is central in the discussion of single- vs. double-well potentials.

Two-bond deuterium isotope effects on 13C chemical shifts are related to hydrogen bond strength and to hydrogen bond energies.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.

## **References**

