Details

Autor(en) / Beteiligte

• Perrin, Charles L.

Titel

Polynomial coefficients. Application to spin–spin splitting by N equivalent nuclei of spin I > 1/2

Ist Teil von

• Magnetic resonance in chemistry, 2018-09, Vol.56 (9), p.799-802

Ort / Verlag

England: Wiley Subscription Services, Inc

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These are conveniently obtained from Pascal's triangle, equivalent to the chemist's branching diagram. Much less well‐known is the pattern from splitting by N identical nuclei of spin I > 1/2. This was originally presented in terms of multinomial coefficients, but polynomial coefficients are more convenient. These describe the number of ways that N objects can be distributed to 2I + 1 numbered boxes. They arise in the polynomial expansion and are conveniently obtained from generalizations of Pascal's triangle. Examples and predictions are given. The intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These can be obtained from Pascal's Triangle, equivalent to the chemist's branching diagram. Less well known are polynomial coefficients, which give the pattern from splitting by N nuclei of spin >1/2. These arise in the polynomial expansion and are conveniently obtained from generalizations of Pascal's Triangle or from a branching diagram. Examples and predictions are given.