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Angular Momentum CouplingThe orbital and spin angular momentum of bodies can interact in angular momentum coupling. These interactions in atoms are used in spectroscopy. Spin-orbit coupling In atomic physics, spin-orbit coupling describes the coupling of the particle spin and the orbital motion of this particle, e.g. the electron spin and its motion around an atomic nucleus. One of its effects is to degenerate the energy level for the parallel and anti parallel cases, of the spin and the Angular momentum. In astronomy, spin-orbit coupling is the ratio between the frequency with which a planet or other celestial body spins about its own axis to that with which it orbits another body. This is more commonly known as orbital resonance. LS coupling In monoelectronic or light atoms electron spins si interact among themselves so they combine to form a total spin angular momentum S. The same happens with orbital angular momenta li, forming a single orbital angular momentum L. This is called Russell-Saunders coupling or LS coupling. Then S and L add together and form a total angular momentum J: - where and
This situation is valid as long as extern magnetic fields are weak, so the coupling between orbital and spin angular momenta is stronger than with the external magnetic field. Strong magnetic fields cause these two momenta to decouple (Paschen-Back effect) which gives rise to a different splitting pattern in the energy levels. jj coupling In heavier atoms the situation is different. Having bigger nuclear charges, interactions spin-orbit become so prominent as spin-spin interactions or orbit-orbit interactions. In this situation, each orbital angular momentum li tends to combine with each individual spin angular momentum si, originating individual total angular momenta ji. These then add up to form the total angular momentum J -
This situation is known as jj coupling. Spin-spin coupling Spin-spin coupling or spin-spin splitting is the coupling of the spin angular momentum states of particles. H-NMR depends on the spin of the hydrogen nucleus. Multiple absorptions on the H-NMR spectrum are due to the interaction of nearby nuclei. The number of peaks in the spin-spin coupling are denoted as singlet, doublet, triplet, quartet, quintet etc. collectively called multiplets. The number of peaks in the multiplet is proportional to the number of equivalent adjacent protons (H+) on the carbon atom beside the atom that caused the peak. Protons that have x neighbouring protons have x + 1 peaks: this is called the x+1 rule. For example, if you have the molecule CH3-CH2-CH3, there would be two multiplet peaks on the H-NMR. One would be a triplet (3), because the methyl group (CH3), has two protons on the carbon next to it (x = 2, number of peaks = 2 + 1=3) and the other multiplet peak would be a septet (7), because the CH2 group has two CH3 groups beside it, each containing three protons, for a total of six (x = 6, number of peaks = 6 + 1 = 7). Also each multiplet has a ratio of intensities for its peaks, as follows: - Singlet 1
- Doublet 1:1
- Triplet 1:2:1
- Quartet 1:3:3:1
- Quintet 1:4:6:4:1
- Septet 1:6:15:20:15:6:1
This means that the peak in the middle of the multiplet will be the tallest peak, and its ratio depends on the number of peaks. There are also more complex spin spin splitting patterns. These signals do not follow the peak intensity ratios as shown above, because of overlapping signals from adjacent protons. These complex splitting signals mostly occur with cyclic and aromatic compounds. Term symbols Term symbols are used to represent the states and spectral transitions of atoms, they are found from coupling of angular momenta mentioned above. When the state of an atom has been specified with a term symbol, the allowed transitions can be found by applying selection rules found by considering which transitions that would conserve angular momentum. A photon has spin 1, and when there is a transition with emission or absorption of a photon the atom will need to change state to conserve angular momentum. The term symbol selection rules are. ΔS=0, ΔL=0,1, Δl=1, ΔJ=0,1 External links * term symbol
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