Other Nuclear Constants

The most important relaxation processes in NMR involve interactions with other nuclear spins that are in the state of random thermal motion. This is called spin-lattice relaxation and results in a simple exponential recovery process after the spins are disturbed in an NMR experiment. The exponential recovery is characterised by a time constant Tj that can be measured for different types of nuclei. For organic liquids and samples in solution, Tj is typically of the order of several seconds. In the presence of paramagnetic impurities or in very viscous solvents, relaxation of the spins can be very efficient and NMR spectra obtained become broad. 

Magnetic equivalence chemically equivalent nuclei are magnetically equivalent if they display the same coupling constants with all other nuclear spins of the molecule 2,3. For example, the 2,2 -... 

In these equations S is the total electron spin of the paramagnetic ion, r is the electron-nuclear distance, co is the electron resonance frequency, and x i - and x 2 are the rate constants for the reorientation of the coupled magnetic moment vectors. They are related to other rate constants by the expressions ... 

Hwang et al.131 were the first to calculate the contribution of tunneling and other nuclear quantum effects to enzyme catalysis. Since then, and in particular in the past few years, there has been a significant increase in simulations of QM-nuclear effects in enzyme reactions. The approaches used range from the quantized classical path (QCP) (e.g., Refs. 4,57,136), the centroid path integral approach,137,138 and vibrational TS theory,139 to the molecular dynamics with quantum transition (MDQT) surface hopping method.140 Most studies did not yet examine the reference water reaction, and thus could only evaluate the QM contribution to the enzyme rate constant, rather than the corresponding catalytic effect. However, studies that explored the actual catalytic contributions (e.g., Refs. 4,57,136) concluded that the QM contributions are similar for the reaction in the enzyme and in solution, and thus, do not contribute to catalysis. 

Ruden et al calculated the indirect nuclear spin-spin coupling constants of allene, cyclopropane, and cyclopropene at different levels of electronic-structure theory and compared them with experimental equilibrium constants, which were obtained from experiment by subtracting evaluated vibrational contributions. It was found that, even in a relatively small basis set, the coupled-cluster singlesand-doubles (CCSD) method provides very good results. SOPPA consistently performed better than RASSCF. Hybrid DFT performed as well as SOPPA for the one-bond coupling constants, while, for the other coupling constants, it provided results of similar quality as CCSD. 

It is anticipated teat the exchange of similar information, and tee collaboration with other installatiinis, may lead to a better determination of nuclear constants and to an improvement in the general capability of quantitative nunierical predictions for problems in neutron transport. 

There are other important properties tliat can be measured from microwave and radiofrequency spectra of complexes. In particular, tire dipole moments and nuclear quadmpole coupling constants of complexes may contain useful infonnation on tire stmcture or potential energy surface. This is most easily seen in tire case of tire dipole moment. The dipole moment of tire complex is a vector, which may have components along all tire principal inertial axes. 

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

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