## High resolution nuclear magnetic resonance spectroscopy. 2 |

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Page 298

In general the order of the sub-determinants is given by the nth binomial

coefficients. Even with the factorisation achieved by means of product spin

functions the secular equation will still involve equations of order ^ 3 for small

values of n. 8.8 Basic

discuss the environment of the interacting magnetic nuclei: it has been sufficient

that the nuclei have coupled together. But the existence of a finite coupling

constant between two ...

In general the order of the sub-determinants is given by the nth binomial

coefficients. Even with the factorisation achieved by means of product spin

functions the secular equation will still involve equations of order ^ 3 for small

values of n. 8.8 Basic

**Symmetry**Functions So far it has not been necessary todiscuss the environment of the interacting magnetic nuclei: it has been sufficient

that the nuclei have coupled together. But the existence of a finite coupling

constant between two ...

Page 299

(8.68) The trace of a matrix representing a

character x(R) of the operator in the <pk representation. After performing a linear

transformation on the base functions <pk it may be possible to divide the/

functions (p'k into sub-sets/, ,/2 , . . ./* such that the functions in each sub-set are

transformed only into combinations of themselves by the group operators; that is,

the functions fx ,f2 . . .fk themselves form a basis for representations of the group,

but of ...

(8.68) The trace of a matrix representing a

**symmetry**operator is known as thecharacter x(R) of the operator in the <pk representation. After performing a linear

transformation on the base functions <pk it may be possible to divide the/

functions (p'k into sub-sets/, ,/2 , . . ./* such that the functions in each sub-set are

transformed only into combinations of themselves by the group operators; that is,

the functions fx ,f2 . . .fk themselves form a basis for representations of the group,

but of ...

Page 322

An A B2 system has C2

represented as being situated at the corners of an isosceles triangle as shown

below. A A reflection about a plane bisecting the angle BAB and perpendicular to

the plane of the triangle will result in the two B nuclei interchanging their

positions. Certain of the basic product functions for this system already remain

invariant under this

be regarded as ...

An A B2 system has C2

**symmetry**since the three nuclei concerned can berepresented as being situated at the corners of an isosceles triangle as shown

below. A A reflection about a plane bisecting the angle BAB and perpendicular to

the plane of the triangle will result in the two B nuclei interchanging their

positions. Certain of the basic product functions for this system already remain

invariant under this

**symmetry**operation: thus otottx, /Sa<%, a/S/9, and /?/?/? canbe regarded as ...

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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