## High resolution nuclear magnetic resonance spectroscopy. 2 |

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Page 74

Now, if Fx represents the summation in equation (3.40), then for a

we may write Fx - F, + Fn (3.41) where Fx and Fy represent the values of Fx when

the molecule has its internu- clear axis perpendicular and parallel to the ...

Now, if Fx represents the summation in equation (3.40), then for a

**linear**moleculewe may write Fx - F, + Fn (3.41) where Fx and Fy represent the values of Fx when

the molecule has its internu- clear axis perpendicular and parallel to the ...

Page 298

can be expressed as a

product spin functions form such a set, with the added advantage that they are

eigenfunctions of an Hermitian operator lz which commutes with . The matrix ...

can be expressed as a

**linear**combination of a closed set of functions <pw; theproduct spin functions form such a set, with the added advantage that they are

eigenfunctions of an Hermitian operator lz which commutes with . The matrix ...

Page 299

and it may be shown that a

trace unchanged (reference 10 p. 331), Trace R = £ = I (8.67) k * where Rjk is the

matrix formed from the elements, R'Jk=f<p'J*R<p'k dr. (8.68) The trace of a matrix

...

and it may be shown that a

**linear**transformation of a unitary matrix leaves thetrace unchanged (reference 10 p. 331), Trace R = £ = I (8.67) k * where Rjk is the

matrix formed from the elements, R'Jk=f<p'J*R<p'k dr. (8.68) The trace of a matrix

...

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### Contents

Introduction | 1 |

J Chem Phys 3 4 3 5 3 6 4 2 4 3 5 2 6 14 7 1 7 2 7 7 8 3 8 19 8 22 8 26 8 | 3 |

General Theory of Nuclear Magnetic Resonance | 10 |

Copyright | |

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### Common terms and phrases

AA'BB absorption bands applied atomic orbitals benzene calculated carbon Chem chemical shift chemical shift difference components compounds coupling constants cycles sec-1 diamagnetic dipole effect eigenfunctions eigenvalues electron energy levels exchange experimental fluorine given gives Gutowsky H resonance Hamiltonian hence hydrogen atoms hydrogen bonding hydrogen nuclei hydrogen resonance interaction line width linear liquid magnetic field magnetic nuclei magnetically equivalent magnitude matrix elements Mc sec-1 measured methane method methyl molecular orbital molecule multiplet non-equivalent nuclear magnetic resonance observed obtained oscillator paramagnetic parameters Phys Pople radiofrequency radiofrequency field receiver coil reference relative intensities relative signs relaxation resonance spectrum ring current rotation sample sec1 Section secular equation shielding coefficient shielding constant shown in Fig sideband signal solution solvent spectra spectrometer spin functions spin system spin-lattice relaxation substituted susceptibility symmetry Table temperature tion transition energies valence bond values vector wavefunctions zero