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

Perrin, Charles L.

Magnetic resonance in chemistry, 2018-09, Vol.56 (9), p.799-802 [Periódico revisado por pares]

England: Wiley Subscription Services, Inc

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  • Título:
    Polynomial coefficients. Application to spin–spin splitting by N equivalent nuclei of spin I > 1/2
  • Autor: Perrin, Charles L.
  • Assuntos: 11B ; 14N ; 35Cl ; Binomial coefficients ; EPR ; Equivalence ; multiplet pattern ; NMR ; Nuclear magnetic resonance ; Nuclei ; Organic chemistry ; Polynomials ; spin–spin splitting ; Splitting
  • É parte de: Magnetic resonance in chemistry, 2018-09, Vol.56 (9), p.799-802
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: 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.
  • Editor: England: Wiley Subscription Services, Inc
  • Idioma: Inglês
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