Polarization of the nuclei

The total polarization of a gas may be due to polarization of the electrons in the gas molecules (for fixed nuclear positions), polarization of the nuclei (with change in the relative positions of the nuclei in the molecules), and orientation of molecules with permanent electric dipole moments. We are here discussing only the first of these mechanisms the second is usually unimportant, and the third is treated briefly in Section 49/. 

To measure NMR spectra, the molecules of interest are placed in a magnetic field generated by a cryo-magnet. In this way, the polarization of the nuclei is... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

CIDNP studies of the decomposition have centred mainly on thermal decompositions photochemical decomposition has generally been less intensively investigated. While most reports of polarization refer to n.m.r. spectra, a number of papers have described polarization of other nuclei, (Kaptein, 1971b Kaptein et al., 1972), (Lippmaa el al., 1970a, b, 1971 Kaptem, 1971b Kaptein et al., 1972 Kessenikh et al., 1971), and F (Kobrina et al., 1972) contained in the peroxide reactant. Additionally, polarization of P has been reported in the products of decomposition of benzoyl peroxide in phosphorus-containing solvents (Levin et al., 1970). 

Inclusion of part of the electronic polarization into the inertial polarization is due to strong interaction between the nuclei and electrons of the medium. The (slow) change in the nuclei positions inevitably produces polarization of the electron shells of the solvent molecules. Therefore, the latter also contribute to the slow polarization. 

The use of synchrotron radiation overcomes some of the limitations of the conventional technique. The high brilliance of up to 10 ° photons s mm mrad /0.1% bandwidth of energy, and the extremely collimated synchrotron beam lead to a large flux of photons through a very small cross section (0.1-1 mm ). This allows measurements with samples of small volume if isotopi-cally enriched (with the relevant Mossbauer isotope, e.g., Fe). Measurements that were described earlier [4] and that require a polarized Mossbauer source now become experimentally more feasible by making use of the polarization of the synchrotron radiation. Additionally, the energy can be tuned over a wide range. This facilitates measurements with those Mossbauer nuclei for which conventional sources are available but with life times that are too short for most experimental purposes, e.g., 99 min for Co —> Ni and 78 h for Ga —> Zn. 

The limitation of the above analysis to the case of homonuclear diatomic molecules was made by imposing the relation Haa = Hbb> as in this case the two nuclei are identical. More generally, Haa and for heteronuclear diatomic molecules Eq. (134) cannot be simplified (see problem 25). However, the polarity of the bond can be estimated in this case. The reader is referred to specialized texts on molecular orbital theory for a development of this application. 

Partially adiabatic transitions, in which the electrons follow adiabatically the motion of the nuclei but the state of the proton cannot adiabatically follow the change in the state of the medium polarization. 

The fact that dynamic 13C polarization is only possible through the indirect way via tire 1H spins suggests the mechanism of polarization transfer. Since the polarization transfer between the electrons and nuclei are driven by the dipolar interactions between them, and the fraction of the guest triplet molecules was small, it would be natural to assume that the polarization of the electron spins in the photo-excited triplet state is given to those H spins which happen to be close to the electron spins, and then the 1H polarization would be transported away over the whole volume of the sample by spin diffusion among the 1H spins. 

Pj and p2 represent the displacement vectors of the nuclei A and D (the corresponding polar coordinates are p1 cji, and p2, < )2, respectively) p, and pc are the displacement vectors and pT, r and pc, <[)f the corresponding polar coordinates of the terminal nuclei at the (collective) trans-bending and cis-bending vibrations, respectively. As a consequence of the use of these symmetry coordinates the nuclear kinetic energy operator for small-amplitude bending vibrations represents the kinetic energy of two uncoupled 2D harmonic oscillators ... 

The majority of double-resonance solid-state NMR experiments involving spin-1/2 nuclei use transfer of nuclear polarization via dipolar cross polarization (CP) to enhance polarization of the diluted spins S with small gyromagnetic ratio ys and significant longitudinal relaxation time T at the expense of abundant spins I with large y, and short 7 [215]. Typically, CP is used in combination with MAS, to eliminate the line broadening due to CS A, as well as with heteronuclear decoupling. To achieve the / S CP transfer, a (n/2)y pulse is applied at the I spin frequency,... 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

The concept of transition moment is of major importance for all experiments carried out with polarized light (in particular for fluorescence polarization experiments, see Chapter 5). In most cases, the transition moment can be drawn as a vector in the coordinate system defined by the location of the nuclei of the atoms4 therefore, the molecules whose absorption transition moments are parallel to the electric vector of a linearly polarized incident light are preferentially excited. The probability of excitation is proportional to the square of the scalar product of the transition moment and the electric vector. This probability is thus maximum when the two vectors are parallel and zero when they are perpendicular. 

Such treatment of CIDNP results produced serious objections. Lippmaa et al. (1973), investigating the same reaction, revealed a strong N, C, and CIDNP effect. The C nuclei in the phenoxyl part of the azo dye were not polarized. At the same time, polarization of N nuclei of the azo bond and C nuclei at positions 1 and 2 of the free-of-hydroxyl phenyl ring connected with... 

A third source of misassignment has its roots in the existence of nuclear-nuclear cross- relaxation." Again, depending on the mechanism of cross-relaxation and on the polarization of the originally polarized nucleus, this may result in enhanced absorption or emission. This process induces nuclear spin polarization in nuclei without hfc, or alters the nuclear spin polarization of nuclei with weak hfcs. On the other hand, the magnitude of these effects may be quite small and fall below the threshold of chemical significance. 

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