## High resolution nuclear magnetic resonance spectroscopy. 2 |

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Page 106

... defined by equation (3.216). To solve for A E from equation (3.216) would

involve the problem that we are trying to avoid, namely the evaluation of the

summation. In practice a value for AE is estimated. The application of the average

energy approximation to spin-spin coupling theory has been discussed by

McLachlan<61), Alexander'62' and Karplus(63), and other methods of evaluating

the summation have been discussed by the last two authors. 3.14.2

... defined by equation (3.216). To solve for A E from equation (3.216) would

involve the problem that we are trying to avoid, namely the evaluation of the

summation. In practice a value for AE is estimated. The application of the average

energy approximation to spin-spin coupling theory has been discussed by

McLachlan<61), Alexander'62' and Karplus(63), and other methods of evaluating

the summation have been discussed by the last two authors. 3.14.2

**Molecular****Orbital**Approach ...Page 123

the molecule ; Das and Bersohn( 1 7) have used a number of valence bond and

calculate <rH2. Their results, shown in Table 4. 1 , indicate that the best M.O. and

V.B. functions give almost identical results (compare the results from the

Hirschfelder-Linnet function with those from the Coulson shielded function). The

Hirschfelder-Linnet function is(18) ^ = a(l)6(2)[l + * Z2 (xA(l) AfB(2) + ;A(1) yB(2)}

+ ,5 Z2 ...

the molecule ; Das and Bersohn( 1 7) have used a number of valence bond and

**molecular orbital**functions with the variational function given by equation (4.2) tocalculate <rH2. Their results, shown in Table 4. 1 , indicate that the best M.O. and

V.B. functions give almost identical results (compare the results from the

Hirschfelder-Linnet function with those from the Coulson shielded function). The

Hirschfelder-Linnet function is(18) ^ = a(l)6(2)[l + * Z2 (xA(l) AfB(2) + ;A(1) yB(2)}

+ ,5 Z2 ...

Page 124

Zis again the effective nuclear charge, and the value of 1- 193 is the value

obtained by minimising the binding energy of the molecule. Both the valence

bond and the

agreement with that of Ramsey (2-68 x 10-5)<5). It is interesting to note the

success of Stephen's variational procedure when used with a simple

calculation of a for the ...

Zis again the effective nuclear charge, and the value of 1- 193 is the value

obtained by minimising the binding energy of the molecule. Both the valence

bond and the

**molecular orbital**function give a value of aH2 which is in goodagreement with that of Ramsey (2-68 x 10-5)<5). It is interesting to note the

success of Stephen's variational procedure when used with a simple

**molecular****orbital**function. The function is one suggested by Fixman<23) and applied in thecalculation of a for the ...

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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