## The Use Of 1h1 H Coupling Constants To Determine Stereochemistry And Conformation

Clearly we can extract important information from coupling patterns about the number and equivalence groupings of other protons that are nearby (generally two or three bonds away) in the bonding network. But we can also get valuable information from the magnitude of the coupling constants, which tells us about the geometric relationship of the bonds connecting the two protons. Three-bond (vicinal) relationships are the most useful because the coupling constant is related in a predictable way to the dihedral angle between the bonds attached to the protons. For example, for two protons attached to neighboring saturated (sp3 hybridized) carbons (H-C-C-H), rotation of the C-C bond leads to different relationships of the two C-H bonds: anti if they are opposite each other (180° dihedral angle) and gauche if they are next to each other in a staggered conformation (60° dihedral angle). If you look directly down the C-C bond, with one carbon right behind the other, the angle described by the two C-H bonds is the dihedral angle. Because J coupling is transmitted through bonds, and more specifically through electrons in bonding orbitals, the magnitude of the coupling constant depends on orbital overlap. The largest coupling constant actually corresponds to the anti conformation (180° dihedral angle), which is counterintuitive in terms of a through-space interaction but makes sense in terms of oribtal overlap. The minimum J coupling is observed when the two C-H bonds are exactly perpendicular (90° dihedral angle) because the orbital overlap is at a minimum for perpendicular molecular orbitals. This relationship between dihedral angle and coupling constant has been formalized into a mathematical relationship

20 40 60 80 Calculated dihedral angle (degrees)

### Figure 2.11

called the Karplus relation or the Karplus curve. This is really an empirical relationship that has been "parameterized" into many different equations for different specific situations. A general equation used for organic molecules with two saturated carbons (H-C-C-H) can be written as follows:

where O is the dihedral angle. This equation is plotted in Figure 2.11, with experimental J values for nine different steroid metabolites plotted against calculated dihedral angles obtained from energy-minimized structures. The clustering of experimental points around 60o and 180° reflects the preference for staggered conformations (in this case cyclohexane chair conformations) with either gauche (60°) or anti (180°) relationships. The eclipsed conformation (0° dihedral angle), though rare, gives a second maximum in coupling constant that is a bit smaller than the maximum at 180°. The minimum J values are observed for dihedral angles near 90°, also a rare occurrence. More specific subsets of vicinal relationships can be fit more accurately to yield specific Karplus equations. For example, in NMR of peptides and proteins, the H-N-Ca-H dihedral angle (related to the O angle that, along with the & angle, defines the backbone conformation of the polypeptide) can be related quite accurately to the H^-Ha J value by comparing dihedral angles measured in X-ray crystal structures of proteins to J values measured by NMR. There is another Karplus equation for three-bond couplings between 1H and 13C, relating to the dihedral angle H-C-C-C, so that long-range heteronuclear couplings, 3JCH, can be used to obtain stereochemical and conformational information. J couplings are also sensitive to electronegative substituents, so we must be careful not to overinterpret the general Karpus relation in specific situations.

Steroids are rigid molecules, particularly in the locked six-membered A, B, and C rings. More flexible molecules give rise to conformational averaging, whereby NMR measurables such as J values are really weighted averages of the values expected for each of the multiple conformations available, weighted by the percent of time spent in each conformation. Usually, these conformational changes are rapid on the timescale of the NMR experiment (1/J), so we see only the average values. For example, a vicinal *H-XH coupling across a C-C bond with free rotation will average to about 7 Hz, which is the average of the J values expected for the three staggered conformations: 4 Hz (60°), 4 Hz (-60°), and 13 Hz (180°). If the conformational change happens on a scale comparable to 1/J, we will see broadening of the NMR lines due to the uncertainty in the J value.

If dihedral angles are measured from energy-minimized structures, it is important to consider whether the structure is rigid (a steep potential well) or flexible (a broad minimum) or if there are multiple steep minima (multiple interconverting conformations). Most energy minimization programs simply search from the starting conformation for an energy minimum and then stop—this may be a broad minimum signifying little about the actual structure, or it may be one of several minima. Solvents also affect conformation, and most structure calculations do not specifically include solvent.

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