An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...