Demonstrates an exceptional level of knowledge and understanding of the material. Answers are complete, scientifically accurate and based upon accepted understanding. Briefly describe what is the relevance of each of the following with respect to NMR spectroscopy, including a sketch to illustrate each answer. (i) A HMQC spectrum (ii) Karplus rule for three-bond couplings between hydrogen atoms.

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∻Solution∻ ‖ 1 ⋮ **A HMQC spectrum**: Heteronuclear Multiple Quantum Coherence (HMQC) spectroscopy is a two-dimensional NMR technique used to correlate hydrogen atoms ($^1H$) with directly bonded heteroatoms, typically carbon ($^{13}C$). This method is particularly useful for identifying which hydrogen atoms are attached to which carbon atoms in a molecule. The HMQC spectrum displays cross-peaks that indicate these direct $^1H$-$^{13}C$ couplings. Below is a sketch illustrating a typical HMQC spectrum: $$ \begin{array}{c|c} \text{Chemical Shift of } ^{13}C & \text{Cross-peaks} \ \hline \text{Chemical Shift of } ^1H & \text{Cross-peaks} \end{array} $$ The cross-peaks appear at the intersection of the chemical shifts of the $^1H$ and $^{13}C$ nuclei that are directly bonded. ‖ ‖ 2 ⋮ **Karplus rule for three-bond couplings between hydrogen atoms**: The Karplus rule describes the relationship between the dihedral angle ($\phi$) between two hydrogen atoms and the magnitude of the three-bond coupling constant ($J$). The rule is given by the equation: $$ J = A + B \cos(\phi) + C \cos(2\phi) $$ where $A$, $B$, and $C$ are empirical constants. This rule helps predict the coupling constants based on the dihedral angle, which is useful for determining the conformation of molecules. Below is a sketch illustrating the Karplus curve: $$ \begin{array}{c|c} \text{Dihedral Angle } (\phi) & \text{Coupling Constant } (J) \ \hline 0^\circ & \text{Maximum} \ 90^\circ & \text{Minimum} \ 180^\circ & \text{Maximum} \end{array} $$ The curve shows that the coupling constant is highest when the dihedral angle is 0° or 180° and lowest when it is 90°. ‖ ∻Answer∻ ⚹ The relevance of HMQC spectrum and Karplus rule in NMR spectroscopy ⚹ ∻Key Concept∻ ⚹ HMQC spectrum correlates $^1H$ and $^{13}C$ nuclei, while the Karplus rule relates dihedral angles to coupling constants ⚹ ∻Explanation∻ ⚹ HMQC helps identify which hydrogens are attached to which carbons, and the Karplus rule helps determine molecular conformation based on coupling constants ⚹◊What is the principle behind three-bond couplings between hydrogen atoms in NMR spectroscopy, as described by the Karplus rule?⍭ Generate me a similar question◊

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