In this paper a simple phenomenological description of the effects of coherent quantum and incoherent mutual exchange of two deuteron nuclei in solid state transition metal complexes on their 2 H NMR spectra is given. This description is based on the quantum-mechanical density matrix formalism developed by Alexander and Binsch. Only the nuclear spin system is treated quantum mechanically. The quantum exchange interaction in NMR is included in the nuclear spin Hamiltonian, and the interaction with the surrounding bath and incoherent exchange processes are treated as phenomenological rate processes described by rate constants. The incoherent exchange corresponds formally to 180°rotations or jumps of the D-D vector around an axis perpendicular to this vector and averages the different quadrupole splitting of the two deuterons. In principle the dideuteron pair will exist in several rovibrational states. However, if the interconversion among these states is fast, the dideuteron exchange can be described by an average exchange coupling or tunnel frequency X 12 and a single average rate constant k 12 of the incoherent exchange. It is shown that the incoherent exchange gives rise to a relaxation of rate -2k 12 between coherences created between states of different symmetry. The 2 H NMR line shape of a dideuteron pair in the solid state as a function of tunnel and incoherent exchange rate is studied numerically. For single crystals, the effects of coherent and incoherent exchange are strongly different, in particular if the rate constants are on the order of the quadrupole splitting. The spectra of nonoriented powder samples are more similar to each other. Nevertheless, our calculations show that there are still pronounced differences, which should allow the distinction between coherent and incoherent exchange even in nonoriented samples.

The 2H solid state NMR spectra and relaxation data of a transition metal g2-dideuterium complex, namely T 1 have been measured in the temperature regime from 5.4 to 320 K. trans-[Ru(D 2)Cl(PPh 2 CH 2 CH 2 PPh 2) 2 ]PF 6 , In the sample, coherent and incoherent exchange processes on the time scale of the quadrupolar RuÈD 2 interaction have been found, leading at low temperatures to a tunnel splitting of the 2H NMR spectrum. With increasing temperature a slight increase of the tunnel splitting is observed, in conjunction with a strong increase of the incoherent exchange process, which Ðnally, at temperatures above 20 K, destroys the tunnel splitting and determines the spectral line shape. For the description of the experimental spectra a Liouville formulation of the AlexanderÈBinsch NMR line shape theory, adapted for exchanging deuterons, is employed. It is shown that the whole evaluation of the 2H magnetization takes place in four 2D and two 4D subspaces of the 81D Liouville space, leading to a drastic simpliÐcation of the numerical e †orts in the simulation of the spectral line shapes. The height of the tunnel barrier calculated from the value of the tunnel splitting is 270 meV (6.22 kcal mol~1). The incoherent exchange rates extracted from the spectra and from relaxation data T 1 are analyzed in terms of a Bell tunneling model, with a temperature dependent e †ective potential.

A selectively η2-D2 labeled isotopomer of the complex W(PCy3)2 (CO)3) (η2-D2) has been synthesized and the 2H NMR spectra and spin lattice relaxation rates of this complex have been measured in the temperature regime of 50 K to 300 K. The spectra have been analyzed employing a model of a combination of homonuclear dipolar D−D interaction and deuterium quadrupolar interaction and a D−D distance of 0.89 ± 0.1 Å. The line width of the spectra exhibits a weak temperature dependence at temperatures above 150 K. This temperature dependence is interpreted as a slight decrease of the quadrupolar coupling with increasing temperature, which is an indication of a change of the M−D2 distance with changing temperatures. The spin lattice relaxation data of the complex exhibit pronounced deviations from a simple Arrhenius behavior at lower temperatures, indicating the presence of a quantum mechanical tunneling process. This process is analyzed in terms of a simple one-dimensional Bell tunnel model. A comparison with INS data from the H2 complex reveals a strong isotope effect of 2 × 103 for the exchange rates of the deuterons.

The solid-state 'H MAS (magic-angle spinning), 2 H static, 15 N CP (cross polarization)-MAS and 15 N-'H dipolar CSA (chemical shielding anisotropy) NMR (nuclear magnetic resonance) spectra of two different modifications of Ca deuterated 15 N-polyglycine, namely PG I and PG II (-CO-CD 2 -15 NH-), are measured. The data from these spectra are compared to previous NMR, infrared, Raman and inelastic neutron scattering work. The deuteration of Ca eliminates the largest intramolecular 'H-'H dipolar coupling. The effect of the remaining (N)H-(N)H interaction (-5 kHz) is not negligible compared to the 15 N-'H coupling (about 10 kHz). Its effect on the dipolar CSA spectra, described as a two-spin system, is analyzed analytically and numerically and it is shown that those parts of the powder spectrum, which correspond to orientations with a strong dipolar 15 N-'H interaction, can be described as an effective two-spin system, permitting the measurement of the strength of the 15 N-'H dipolar interaction and the orientation of the dipolar vector with respect to the ' I N CSA frame. While in the PG 11 system the ' 5 N CSA tensor is collinear with the amide plane, in the PG I system the CSA tensor is tilted ca. 16° with respect to the (15,,15 22 ) CSA plane.