# Why do NMR coupling constants change with temperature?

Why do coupling constants change with temperature in NMR?

• Could we have some additional background information? For example, how do coupling constants respond to temperature? Many folks (myself included) may have only passing knowledge of this phenomenon. I know that they are temperature dependent (and I can probably posit why they are temperature dependent). However, I do not know if the coupling constants get larger or smaller as temperature increases (or maybe both depending on structural elements). – Ben Norris Feb 21 '15 at 13:52
• As it stands, your question is hard to answer without this information. Do you want to know why coupling constants change with temperature? Do you want to be able to predict the change given the structure of a molecule? Do you want to use the temperature-dependent change to learn something about structure? – Ben Norris Feb 21 '15 at 13:54
• Alright. May we change it to "Why do coupling constants in NMR spectroscopy change with temperature?" – Crystal Lettuce Feb 21 '15 at 20:12

Let’s use vicinal 3-bond $\ce{H-C-C-H}$ proton coupling constants as an example. Coupling is a through bond phenomenon and as such the coupling constant will change depending if we have better (the coupling constant will increase) or worse (the coupling constant will decrease) overlap between the two $\ce{C-H}$ bonds involved. Overlap is maximized when the two, vicinal $\ce{C-H}$ bonds are aligned in an eclipsed conformation ($\ce{H-C-C-H }$ dihedral angle =0°) or anti ($\ce{H-C-C-H }$ dihedral angle =180°) conformation. When the dihedral angle is ~90° the overlap of the two vicinal $\ce{C-H}$ bonds is minimized. This thinking is embodied in the Karplus equation which relates vicinal coupling constants to dihedral angle. The following graph illustrates this dependence of the vicinal coupling constant on the dihedral angle. image source

All of this tells us that an experimentally observed vicinal coupling constant will be dependent upon the relative populations of the eclipsed, staggered and anti conformations. Said differently, the vicinal coupling constant will be an average of each of the individual coupling constants for each conformation, weighted by the relative population of that conformation. Since the relative conformer populations change with temperature, the coupling constant will also change with temperature.

One reason that coupling constants vary with temperature is because the alignment of the coupled atoms changes with temperature.

For example, in 1H NMR, proton-proton coupling between vicinal protons (HCCH) can be estimated by the Karplus equation, in which the coupling is mainly a function of dihedral angle between the two separate C-H bonds. However, the degree to which the molecule can rotate freely around the C-C bond is a strong function of temperature. Thus at high temperatures the observed coupling should be an average of all possible dihedral angles, while at lower temperatures where particular conformations are stable on NMR time scales, the Karplus equation can predict coupling directly.

This is just one reason for the T sensitivity. I hope other chem.se users with more experience in NMR can provide better, more detailed answers.