*2.2. Coupling Constants*

Two types of couplings are immediately useful, <sup>1</sup>*J*(N,H) and for derivatives of aldehydes, <sup>3</sup>*J*(NH,CH). <sup>1</sup>*J*(N,H), one-bond hydrogen nitrogen couplings show often a numerical value of around 90 Hz. This coupling is of course negative. Dudek and Dudek showed a small difference between hydrogen bonded and non-hydrogen bonded cases [61]. <sup>1</sup>*J*(N,H) couplings have also been calculated by DFT methods. A recent study optimized for secundary amines the functional and basis set as follows: B3LYP/6-311++G\*\* for structure optimization in chloroform (PCM approach) and APFD/6-311++G\*\*(mixed) for calculation of <sup>1</sup>*J*(15N,H) coupling constants. A very good agreemen<sup>t</sup> with experimental values was found. The shorter the bond the larger the coupling constant [62]. A number of useful trends were found to complement the not so many experimental data. Using a simpler basis set, B3LYP-6-31G, it was found that one has to distinguish between primary and secondary amines. For the primary amine cases dissolved in a hydrogen bonding solvent like dimethylsulfoxide, a sulfoxide molecule has to be hydrogen bonded to the "free" NH in order to obtain good results [3].

The <sup>3</sup>*J*(NH,CH) coupling is for a non-tautomeric case close to 12 Hz [61]. The observation of a coupling of this magnitude or <sup>1</sup>*J*(N,H) of around 90 Hz is a clear indication that one is actually dealing with a NH ... X hydrogen bond and not with an OH ... X one or a tautomeric system. The access to reliable calculations of <sup>1</sup>*J*(N,H) enables one to calculate values for tautomeric systems, but also to estimate the influence of substituents.

#### *2.3. Non-RAHB Cases. Couplings across Hydrogen Bonds*

The NH ... X bond is central both to proteins, DNA and RNA. A breakthrough was the observation of couplings across hydrogen bonds in RNA [63]. The presence of large *J* couplings (6–7 Hz) between the hydrogen bond (H-bond) donating and accepting 15 N nuclei in Watson–Crick base pairs in double-stranded RNA was found [64]. For proteins, both in α-helices and in β-sheets they are ubiquitous. These hydrogen bonds are generally not very strong. However, in the stronger cases very interesting coupling constants across hydrogen bonds between 15N and 13C=O (also referred to as C) have been observed [65,66] enabling pairing of hydrogen bond donors and acceptors. Correlations with bond lengths 3h*J*NC = −59000 exp( −4*R*NO) ± 0.09 Hz, or *R*NO = 2.75 − 0.25 ln( − 3h*J*NC) ± 0.06 Å have been established [67]. Normally such coupling can only be observed in proteins below 10 kD. However, with perdeutration 3h*J*NC scalar couplings across hydrogen bonds could be observed in the uniformly 2H/13C/15N-enriched 30 kDa ribosome inactivating protein MAP30 [68].

A study of lysine interactions in ubiquitine with carbonyl backbone revealed that the NH3 + groups of Lys29 and Lys33 exhibit measurable h3*J*NζC couplings arising from hydrogen bonds with backbone carbonyl groups of Glu16 and Thr14, respectively. For an example see Figure 16. <sup>3</sup>*J*NζCγ-coupling constants could also be measured, these together with relaxation studies showed that the NH3 + groups are involved in a transient and highly dynamic interaction [69].

**Figure 16.** Coupling from at carbonyl carbon to a side-chain lysine N via the hydrogen bond. Taken from [69] with permission from The American Chemical Society.

A plot of <sup>1</sup>*J*(N,H) vs. dN*H* for DNA and RNA demonstrated that the N1 ... N3 hydrogen bonds are stronger in dsRNA A:U than in dsDNA A:T bases pairs [70]. Both two-bond 1H-31P and three bond 15N-31P couplings have also been seen from a histidine to the phosphate group of DNA in a zink finger (see Figure 17) [71].

**Figure 17.** Hydrogen bond scalar coupling involving a phosphate and a histidine. Taken from [71] with permission from the American Chemical Society.

A very large N ... N coupling of 40 Hz through a hydrogen bond is seen in the compound in Figure 15E. The N..N distance is calculated as 2.54 Å. The coupling is the largest of this kind so far reported in a symmetric system [56].

Couplings across hydrogen bonds have also been calculated and summarized by Del Bene [72]. The couplings are dominated by the Fermi contribution and depends on the distance between the heavy atoms. Relationships are noted between hydrogen bond type, X–Y distances, NMR spin–spin coupling constants, and infrared proton-stretching frequencies. This also nicely reflects the experimental findings.

#### *2.4. Isotope Effects on Chemical Shifts*

Three different types of deuterium isotope effects on chemical shift are useful, nΔC(ND), <sup>1</sup>ΔN(D), nΔH(ND) and in principle nΔ17O(ND) in the study of intramolecular hydrogen bonds [73]. Isotope effects is in the present review defined as: nΔ = δX(H) − δX(D).

2.4.1. RAHB Cases (a "Double Bond" Connecting Cα and Cβ)

nΔC(ND) were early on studied in enaminones [74]. Later this study was extended 12,18,32,75,76]. An advantage of studying enaminones is that a number of these may exist both in an *E*- and a *Z*-form. The former without an intramolecular hydrogen bond, the latter with and thus giving a genuine reference compound. This kind of study clearly showed that the two-bond deuterium isotope effect on 13C chemical shifts, <sup>2</sup>ΔC(ND), are larger in the intramolecular hydrogen bonded case (Figure 18). This was ascribed to resonance assistance. Having e.g., a substituent at the C-β carbon can introduce steric strain. This will lead to a larger two-bond deuterium isotope effect as seen by comparing number from Figures 14 and 16 (see later) and to a stronger hydrogen bond. An interesting feature in such systems is also the observation of isotope effects at the carbon involved in the intramolecular hydrogen bond and even the carbon attached to the carbonyl group and beyond (see Figure 14) making this a tool for establishing pairs of hydrogen bonds in systems with several possibilities.

**Figure 18.** Deuterium isotope effects on 13C chemical shifts in ppm. Taken from Ref. [12].

Isotope effects have often been plotted vs. XH chemical shifts. [75] In the present case, two-bond deuterium isotope effects (TBDIE) are plotted vs. NH chemical shifts (Figure 19). It is clear that *E*- and *Z*-derivatives can be distinguished. The correlation covers enaminones, nitro- and sulphinyl derivatives [32].

**Figure 19.** Plot of two-bond deuterium isotope effects on 13C chemical shifts vs. NH chemical shifts for enamines. Open squares (*Z*)-enaminones, closed squares (*E*)-enaminones, + enamino esters, \* (*Z*)- nitroenamines, crosses (*Z*)-sulphinylenamines and diamonds (*E*)-sulphinylenamines, ϕ indicates N-phenyl groups. Taken from [32] with permission from Wiley.

One-bond deuterium isotope effects, <sup>1</sup>ΔN(D), depend strongly on hydrogen bonding (the geometry) and related to that RAHB (see Figure 20). [32]

**Figure 20.** One-bond deuterium isotope effects on 15N chemical shifts and two-bond deuterium isotope effects at carbon in ppm. From [76].
