Pascal type triangles for nuclei with I &gt; 1/2

Koster, David F.; Jones, W.P.

doi:10.1021/ed059p289

Cited by 4 publications

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“…5. 85,86 This stick diagram was calculated using a value of 2 J iso ( 51 V, 31 P) = 48(5) Hz for the indirect spin-spin coupling constant. Convolution of this multiplet by a Gaussian peak of 70 Hz full-width at half-maximum results in a better representation of the experimental line shape than a mere Gaussian peak (Fig.…”

Section: Magnetic Field Dependencementioning

confidence: 99%

Phosphorus-31 and vanadium-51 solid-state nuclear magnetic resonance spectroscopy of β-vanadyl phosphate — Effects of homo- and heteronuclear spin-spin, electrostatic, and paramagnetic interactions

Eichele

GrimmerArnd-Rüdiger

2011

Can. J. Chem.

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Field-dependent 31 P solid-state NMR studies demonstrate that the line shape in spectra of b-VOPO4 depends on 51 V-31 P direct and indirect spin-spin interactions (M 2 ( 51 V, 31 P) = 101(23) × 10 6 rad 2 s -2 , 2 J iso ( 51 V, 31 P) = 48(5) Hz) and, to a lesser extent, on 31 P chemical shift anisotropy (d iso = -10.4(2), U = d 11 -d 33 = 22(2) ppm) and 31 P-31 P interactions (M 2 ( 31 P, 31 P) = 6.7(1) × 10 6 rad 2 s -2 ). In contrast, homonuclear dipolar interactions play an important role for the field and spinning rate dependent 31 P spin-lattice relaxation via paramagnetic impurities (T 1 = 20-60 s). Vanadium-51 magic-angle spinning NMR spectra indicate a sizeable chemical shift anisotropy (d iso = -754(1), d 11 = -336(10), d 22 = -344(6), d 33 = -1581(8) ppm) and nuclear quadrupole interaction (c = 1.5(1) MHz, h = 0.35 (5)); the principal axis systems of both interactions are clearly not coincident, with an angle of 35(5)°between the greatest component of the electric field gradient tensor and d 33 .Résumé : Des études RMN du 31 P à l'état solide et dépendant du champ démontrent que la forme des raies dans les spectres du b-VOPO 4 dépend des interactions spin-spin directes et indirectes (M 2 ( 51 V, 31 P) = 101(23) × 10 6 rad 2 s -2 , 2 J iso ( 51 V, 31 P) = 48(5) Hz) et, à un degré moindre, sur l'anisotropie du déplacement chimique du 31 P (d iso = -10,4(2); U = d 11 -d 23 = 22(2) ppm) et aux interactions 31 P-31 P (M 2 ( 31 P, 31 P) = 6,7(1) × 10 6 rad 2 s -2 ). Par ailleurs, les interactions dipolaires homonucléaires jouent un rôle important pour la relaxation spin-réseau du 31 P qui varie avec le champ et la vitesse de rotation par le biais d'impuretés paramagnétiques (T 1 = 20-60 s). Les spectres RMN du vanadium à l'angle magique de rotation indiquent qu'il existe une anisotropie importante du déplacement chimique (d iso = -754(1), d 11 = -336(10), d 22 = -344(6), d 33 = -1581(8) ppm) et une interaction quadripolaire nucléaire (c = 1,5(1) MHz, h = 0,35(5)); il est clair que les axes principaux des systèmes des deux interactions ne coïncident pas, avec un angle de 35(5)°entre la composante principale du tenseur du gradient de champ électrique et d 33 .Mots-clés : spectroscopie RMN à l'état solide, RMN du 31 P, RMN du 51 V, relaxation spin-réseau, couplage spin-spin nucléaire indirect, anisotropie du déplacement chimique, tenseur du gradient de champ électrique, phosphate de vanadyle.[Traduit par la Rédaction]

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Section: Magnetic Field Dependencementioning

confidence: 99%

Phosphorus-31 and vanadium-51 solid-state nuclear magnetic resonance spectroscopy of β-vanadyl phosphate — Effects of homo- and heteronuclear spin-spin, electrostatic, and paramagnetic interactions

Eichele

GrimmerArnd-Rüdiger

2011

Can. J. Chem.

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“…nitrogen, but there is a severe price to pay for the benefit of trapping the undetectable R-in that most of the structural information in R-is lost. In adducts of structure 13 only the y hyperfine constant shows any dependence on the structure of R-, while adducts 14 show only the indicated (17). Fortunately the magnitude of this hyperfine does vary somewhat from one spin adduct to another, and can be used to help identify a radical Rprovided that the experimentalist can obtain a spectrum of the authentic Rspin adduct.…”

Section: Spin Trappingmentioning

confidence: 99%

Introduction to the interpretation of electron spin resonance spectra of organic radicals

Bunce¹

1987

J. Chem. Educ.

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Interpretation of spectroscopic data is now established as an important part of the undergraduate curriculum. These interpretive skills may be acquired as part of courses in organic chemistry, since full-year organic texts now all include chapters on the major spectroscopic methods (IR, NMR, and mass spectrometry). Alternatively, a separate course in spectroscopic interpretation may be offered, allowing the introduction of topics that are not usually covered in standard organic tests. One of these is electron spin resonance (ESR).Historically, ESR was discovered before NMR, but, since most undergraduates are much more familiar with the latter technique, this article assumes some knowledge of proton NMR, and treats ESR comparatively. This article is written in a style that is intended to be addressed directly to undergraduates, rather than to their instructors. Principles of ESRElectron spin resonance (ESR), also known as electron paramagnetic resonance (EPR), is an important spectroscopic technique for the study of molecules and ions containing unpaired electrons. It can only be applied to systems in

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“…The polynomial coefficients are conveniently obtained from generalizations of Pascal's triangle, where each coefficient is the sum of the 2 I + 1 coefficients above it. Thus, for I = 1, each coefficient is the sum of the three coefficients above it, according to Equation and as illustrated in Figure .…”

Section: Polynomial Coefficientsmentioning

confidence: 99%

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

Perrin

2018

Magnetic Reson in Chemistry

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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.

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Pascal type triangles for nuclei with I > 1/2

Abstract: Relating the number and relative intensity of the lines in an NMR or EPR spectrum to Pascal's triangle.

Cited by 4 publications

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Phosphorus-31 and vanadium-51 solid-state nuclear magnetic resonance spectroscopy of β-vanadyl phosphate — Effects of homo- and heteronuclear spin-spin, electrostatic, and paramagnetic interactions

Phosphorus-31 and vanadium-51 solid-state nuclear magnetic resonance spectroscopy of β-vanadyl phosphate — Effects of homo- and heteronuclear spin-spin, electrostatic, and paramagnetic interactions

Introduction to the interpretation of electron spin resonance spectra of organic radicals

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

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