New PDF release: A Primer of NMR Theory with Calculations in Mathematica

By Alan J. Benesi

ISBN-10: 1118588991

ISBN-13: 9781118588994

Offers the idea of NMR superior with Mathematica© notebooks

  • Provides brief, targeted chapters with short causes of well-defined subject matters with an emphasis on a mathematical description
  • Presents crucial effects from quantum mechanics concisely and for simple use in predicting and simulating the result of NMR experiments
  • Includes Mathematica notebooks that enforce the idea within the kind of textual content, portraits, sound, and calculations
  • Based on category proven tools constructed by means of the writer over his 25 yr educating profession. those notebooks express precisely how the speculation works and supply beneficial calculation templates for NMR researchers

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Additional resources for A Primer of NMR Theory with Calculations in Mathematica

Sample text

The relaxation matrix is diagonal1 and has as components the transverse or spin–spin relaxation rate 1/T2 and the longitudinal or spin lattice relaxation rate 1/T1. The next cells define the Bloch equation. The rate of change of the magnetization vector dMdt is given by the Bloch equation. Note that the Bloch equation contains a cross product of M and B and the relaxation rate matrix. The resulting dMdt vector contains x, y, and z components, respectively. These can be easily extracted as shown in the following cells.

In this reference frame, the x and y components of a magnetization vector at the observe frequency are fixed. The precession induced by the superconducting magnetic field thus vanishes for an on‐resonance magnetization vector in the rotating frame, as if there was no magnetic field, that is, Brot = {0,0,0}. Magnetization vectors that are slightly “off resonance,” that is, not at the exact Larmor frequency, precess at their difference frequencies, that is, ±δ kHz. The effective magnetic field for an off‐resonance magnetization vector is defined by its difference frequency δ, with Brot = {0,0,−δ/γ}, where γ is the gyromagnetic ratio of the nucleus.

The dipolar Hamiltonian is large, internuclear distance–dependent, and orientation‐dependent. It is a very useful source of information in solid‐state NMR where experiments ­utilize the dipolar Hamiltonian for coherence transfer between nuclei. Nevertheless, it averages to zero in liquid samples, that is, Ĥ Dij_liquid = 0. The Knight shift Hamiltonian Ĥ K is observed in conductive samples such as metals and conducting polymers. It arises from circulation of the electron density in open shell (metallic) orbitals.

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A Primer of NMR Theory with Calculations in Mathematica by Alan J. Benesi

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