Electron-nuclear polarization

Finally, the application of optimal control theory to DNP studies needs to be discussed. Optimal control theory is a means to systematically design and optimize pulse sequences to maximize the efficiency of transfer between spin states. While this method was initially introduced to benefit high-resolution NMR studies, it has recently been adapted to improve the electron-nuclear polarization transfer in DNP applications by considering simple two- or three-spin systems. " While no experimental implementation of DNP pulse sequences designed by optimal control methods has been reported, these methods have the great potential to enhance DNP performance at X-band, due to the powerful pulsed ESR hardware that is commercially available at these frequencies. 

Fig. 3. Jablonski energy-level diagram typical for chromophores involved in ONP processes (specifically for pentacene in naphthalene, after Ref. [39]), showing the respective roles of optical excitation, ISC, OEP, electron-nuclear polarization transfer (here driven by mw radiation), and subsequent decay to the diamagnetic ground state. The relative populations of the triplet magnetic sublevels are given at the far right (assuming the crystal is oriented such that the long molecular axis of pentacene is parallel to the external magnetic field ).

Considerable efforts over the years have been directed towards enhancing the ONP process by driving the electron-nuclear polarization transfer via resonant or near-resonant (rf/mw) AC fields. This practice can not only improve the efficiency of the ONP process (particularly in systems or experimental regimes where LAC-ONP is not possible), but - with implementation of pulsed optical and AC fields - can permit time-resolved studies as well. 

One approach to improve the electron-nuclear polarization transfer rate in ONP experiments is to adapt time-tested Hartmann-Hahn-type approaches. Groups at Heidelberg and Leiden separately developed similar approaches (respectively dubbed Hartmann-Hahn ONP (HHONP) and nuclear orientation via electron spin locking (NOVEL) ) whereby a spin-lock mw pulse sequence is applied to the electrons such that their frequency in the rotating frame matches the Larmor frequency of the H nuclei in the lab frame. Thus, the formerly forbidden electron/nuclear flip-flop transitions effectively become thermodynamically allowed , improving the efficiency of the polarization transfer compared to MIONP experiments performed outside this Hartmann-Hahn condition. The polarization transfer typically occurs on the ps time scale, generally faster than both the electronic T and the triplet lifetime. ... 

Energies in kcal mol unrelaxed HF/6-31G(d) geometries the total contribution (TOT ) to the activation free enthalpy is due to the cavitation+solute/solvent dispersion+solvent structural rearrangement term (CDS ) and to the electronic+nuclear- polarization term (ENP ) in the AMSOL model in the Tomasi model CDR is the cavitation-rdispersion+repulsion term and ELEC is the electrostatic contribution ab initio calculations are standard HF/6-31G(d). 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

The first example of chemically induced multiplet polarization was observed on treatment of a solution of n-butyl bromide and n-butyl lithium in hexane with a little ether to initiate reaction by depolymerizing the organometallic compound (Ward and Lawler, 1967). Polarization (E/A) of the protons on carbon atoms 1 and 2 in the 1-butene produced was observed and taken as evidence of the correctness of an earlier suggestion (Bryce-Smith, 1956) that radical intermediates are involved in this elimination. Similar observations were made in the reaction of t-butyl lithium with n-butyl bromide when both 1-butene and isobutene were found to be polarized. The observations were particularly significant because multiplet polarization could not be explained by the electron-nuclear cross-relaxation theory of CIDNP then being advanced to explain net polarization (Lawler, 1967 Bargon and Fischer, 1967). 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

An ab initio MO calculation by Jorgensen revealed enhanced hydrogen bonding of a water molecule to the transition states for the Diels-Alder reactions of cyclopentadiene with methyl vinyl ketone and acrylonitrile, which indicates that the observed rate accelerations for Diels-Alder reactions in aqueous solution arise from the hydrogenbonding effect in addition to a relatively constant hydrophobic term.7,76 Ab initio calculation using a self-consistent reaction field continuum model shows that electronic and nuclear polarization effects in solution are crucial to explain the stereoselectivity of nonsymmetrical... 

Using the OPENCORE spectrometer, a research group led by M. Kitagawa in Osaka have developed an experimental setup for dynamic nuclear polarization (DNP) using electron spins in the photo-excited triplet state. This nuclear hyperpolarization technique, called hereafter triplet DNP,... 

A future optical device exploiting these two discoveries could write, read and operate on electron spins, while using patterned magnetic regions as memory elements. The region of large nuclear polarization rotates electron spins as they pass by- one necessary operation for quantum computing."... 

Finally, the use of DNP of shallow donors to enhance both 67Zn and surface ft nuclear polarizations has been demonstrated in ZnO nanoparticles by observation of EPR features rather than direct NMR observation [85, 87]. The electronic wavefunctions of these donors in ZnO have been probed by ENDOR experiments [36, 97], There is much potential for directly observing NMR with the sensitivity greatly enhanced by DNP not only in ZnO but in other nanoparticles as well. 

Further evidence for the formation of alkene radical cations derives from the work of Giese, Rist, and coworkers who observed a chemically induced dynamic nuclear polarization (CIDNP) effect on the dihydrofuran 6 arising from fragmentation of radical 5 and electron transfer from the benzoyl radical within the solvent cage (Scheme 6) [67]. 

Hence, provided that I g is known and that R has been determined by means of an independent experiment, provides the cross-relaxation rate ct. This enhancement is called nuclear Overhauser effect (nOe) (17,19) from Overhauser (20) who was the first to recognize that, by a related method, electron spin polarization could be transferred to nuclear spins (such a method can be worked out whenever EPR lines are relatively sharp it is presently known as DNP for Dynamic Nuclear Polarization). This effect is usually quantified by the so-called nOe factor p... 

Any CIDNP-based assignment of the sign and relative magnitude of hfcs is valid only if the radical pair mechanism (RPM) is operative they become invalid if an alternative process is the source of the observed effects. The triplet-Overhauser mechanism (TOM) is based on electron nuclear cross-relaxation. For effects induced via the TOM, the signal directions depend on the mechanism of cross-relaxation and the polarization intensities are proportional to the square of the hfc. Thus, they do not contain any information related to the signs of the hfcs. 

Whilst this demonstrates that calculations using the methods of this paper may prove very useful in studies of molecules containing only low-Z atoms, a major objective has been to study systems containing heavier atoms. So far, only a limited number of molecular calculations have been carried out with BERTHA at the DHF level, mainly in connection with studies of hyperfine and PT-odd effects in heavy polar molecules such as YbF [33] and TIF [13]. The reader is referred to the literature for an assessment of these calculations and for technical details on the construction of basis sets which must not only describe molecular bonding properly but also give a good representation of spinors close to the heavy nuclei to handle the short-range electron-nuclear electroweak interactions. 

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