Spin-spin couplings between two nuclei will be dependent upon several factors: the nuclei involved, the distance between the two nuclei, the angle of interaction between the two nuclei, and the nuclear spin of the nuclei.
Coupling between two nuclei can be categorized as follows:
The number of interceding bonds between coupled nuclei will effect the absolute value of the coupling constant. The order of the strength of coupling is as follows:
| one-bond (1J) | > | two-bond (2J) | > | three-bond (3J) | > | long-range (4J - nJ) |
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| 110 - 270 Hz | 9 - 15 Hz | 6 - 8 Hz | 1 - 7 Hz |
Coupling occurs between nuclei because of the spin interaction of the nuclei with bonding electrons. Spin information between two nuclei is "transmitted" by the electrons in the bond(s). Because of this, the better the orbital overlap between the nuclei (through intervening bonds) the stronger the coupling will be. The bond angle between two interacting nuclei will have a direct affect on the coupling constant.
Two types of coupling are most affected by bond angles: geminal coupling (also called two-bond coupling or 2J) and vicinal coupling (also called three-bond coupling or 3J).
Geminal Coupling
Geminal coupling or 2J coupling is dependent upon the bond angle between the nuclei. Generally, the smaller the angle the bigger the coupling constant. Figure 24 indicates the dependence of the coupling constant on bond angle.
Figure 24. Dependence of the magnitude of the geminal coupling constant on the HCH angle.
Figure 25 contains examples of two-bond coupling systems and the corresponding coupling constants. Note that as the bond angle increases the coupling constant decreases.
Figure 25. Samples of 2J coupling constants.
Vicinal Coupling
Vicinal coupling or 3J coupling is dependent upon the dihedral angle between the nuclei. Generally, the more eclipsed or antiperiplanar the nuclei the greater the coupling constant.
The relationship between dihedral angle and coupling constant is known as the Karplus relationship and the following figure is known as the Karplus curve.
Figure 26. Dependence of the magnitude of the vicinal coupling constant on the dihedral angle.
Figure 27 contains examples of three-bond coupling systems and the corresponding coupling constants. Note that as the dihedral angle approaches the gauche orientation the coupling constant decreases.
Figure 27. Samples of 3J coupling constants.
When two nuclei spin-spin couple, the multiplicity of the peak for the observed nucleus will depend upon the nuclear spin quantum number (I) for those nuclei coupled to it. The multiplicity of the peak is determined by:
multiplicity = 2nI + 1
where:
n = number of nuclei splitting the observed signal
I = spin of the splitting nuclei
Coupling constants are denoted in many ways. The symbol for the coupling constant is J. The number of intervening bonds is usually denoted by prefix superscript to the J. Additionally, the types of atoms involved in coupling are denoted parenthetically after the J.
For example, one-bond coupling between carbon-13 and hydrogen-1 can be denoted as:
1J(13C-1H)
-or-
1JCH
and three-bond coupling between hydrogen-1 and hydrogen-1 can be denoted as:
3J(1H-C-1H)
-or-
3JHH
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