Shielding polarizability

We apply this technique to study the effect of the spin-orbit coupling on an NMR shielding tensor and the shielding polarizability of the xenon atom. The shielding polarizabilities are defined as the second derivatives of nuclear shielding constants with respect to an electric field E... 

Table 5. The NMR shielding constant and shielding polarizabilities of the xenon atom calculated at the Hartree-Fock level using the Drrac-Coulomb Hamiltonian (SR + SO), its spin-free version (SR) as well as the non-relativistic Levy-Leblond Hamiltonian. The shielding constant is given in ppm and shielding polarizabilities in ppm/(au field2) (1 a.u. field = 5.14220642X 10" V...

I would like to dedicate this paper to Jens Oddershede on his 60th birthday. I would like to thank Magdalena Pecul for suggesting an additional s -exponent in the basis set used for the calculation of the shielding polarizability of the xenon atom. 

The intermolecular shielding surface and the effects of electric fields on shielding (shielding polarizabilities and hyperpolarizabilities) are useful in the interpretation of long-range intramolecular effects and in intermolecular effects on shielding. 

Effects of a Static Electric Field on Molecular Magnetic Properties Employing the CTOCD Method Shielding Polarizabilities of CO, H20, and CH4 Compounds... 

The third-rank tensors Zafir od a1 aft describe non linear response of the electron cloud to first order in E. These quantities are sometimes referred to as hypermagnetizabilities, which are related to Cotton-Motton effect (4-6), (CME- the birefringence of light in gases in a constant magnetic field) and as shielding polarizabilities (7-14). 

We shall briefly review some definitions to compute molecular magnetic properties in the presence of a static electric field, L e., hypermagnetizabilities and shielding polarizabilities, Zafr and a1. ... 

Advantage of the CTOCD Method Continuous Transformation of the Origin of the Current Density. The CTOCD method for theoretical determination of hypermagnetizabilities and shielding polarizabilities is reported in detail in ref. (28). In this section we make only a very brief description of the theory involved in the formulation of CrOCZ)-Z>Z r and a1/ -... 

In a change of coordinate system 21, the contributions to the shielding polarizabilities transform... 

The calculations reported in this work have been carried out by the SYSMO computer programs (44), modified by us to implement a new coupled Hartree-Fock (CHF) section to describe the CTOCD-DZ shielding polarizabilities. 

Only for basis set ZZZ, a a shielding polarizabilities are very close to the cr 7 values for both nuclei. The paramagnetic apIofly contributions, are approximately of the same quality for basis set JJand UJ. Our results are compared with those of Bishop and Cybulski (7,9), and with those of Coriani et al (18), both for the SCF level, and the agreement is very good, even if, those authors have used larger basis sets. 

Table IIH20 Proton nuclear shielding (In ppm) and CTOCD-DZ shielding polarizabilities (in ppm, an) for basis sets I-Ul,...

Our calculations do not include vibrational corrections. Bishop and Cybulski have computed them for nuclear magnetic shielding and shielding polarizabilities of CO (9). 

Nymand et al. ° performed molecular dynamics simulations on liquid water, and they used the electric field effect formalism [Eq. (6)] to explain the gas to liquid shifts of the and O nuclei. For the proton it turned out that the resulting gas to liquid shift of — 3.86 ppm at 300 K compared well with the experimental value of —4.70 ppm, whereas for O the method failed to reproduce the experiment. Even if electric field gradient terms are introduced, requiring additional quadrupolar shielding polarizabilities, no better results could be obtained for the O gas to liquid shifts. Isotropic proton chemical shifts are obviously a special case where many higher order terms cancel, hence it is justified to use the simple electric field equations in these chemical shift calculations. 

When evaluated, the summation in Eq. (11) is a rank-one polytensor that represents the potential experienced at molecule A in terms of field components, field gradient components, and so on. This can be used with response properties such as shielding polarizabilities to find property changes dues to electrical influence. The evaluation is analogous to Eq. (11). The incorporation of mutual or back polarization/hyperpolarization requires a self-consistent solution for the induced moments, and this can be done iteratively [170] or if there are no hyperpolarizabilities, it can be done by matrix inversion. 

Theoretical predictions have been presented for nuclear magnetic shielding polarizabilities in small size molecules, by which the change of shielding to first and second order in a spatially uniform electric field can be evaluated [4,7,23,24,26,28,37-45],... 

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