Dihydrogen, rotational states

The even values of J correspond to antisymmetric wavefiinctions and must be combined with symmetric spin wavefunctions. The only allowed rotational states of spin paired, or antiparallel, (t4 ) dihydrogen are thus those with, J = 0, 2, 4... This defines para-hydrogen. There are 27+1 possible spin states for each acceptable J value and it follows from Eq. (6.7) that there is only one spin state for the para-hydrogen ground state, J=0. 

The angular probability density function, P B, provides the basis for a pictorial description of the rotational states of dihydrogen. The function is a surface represented in polar coordinates. Any point on the surface can be joined to the origin by a line. The 0, (f) coordinates of the line correspond to the orientation of the dihydrogen molecular axis and the probability of any particular orientation occurring is given by the... 

Fig. 6.4 The energies of the rotational states of dihydrogen in the field of Eq. (6.20), relative to the J = 0, ground state. Given as a function of the parameter a/B. A nominal value ofb = 0.2 B is used to remove the degeneracy in M.

The complexes provide a bridge between physisorbed and dissociated states of dihydrogen. As such they can be viewed from two directions as an example of dihydrogen rotating in a strong potential or as a conventional complex. Since both viewpoints are describing the same phenomenon they should be equivalent. However, we shall see that both viewpoints are incomplete. 

Fig. 6.13 The energies of the rotational states of dihydrogen as a perturbed planar rotor in a deep attractive field, the 2-DP type. The dashed vertical line shows the transitions expected for [W(CO)3(H2) P(cyclohexyI)3 2] with a tunnel splitting of 0.89 cm (inset).

The ions being stored in the trap for very long periods, they are usually radiatively deexdted on their ground state (electronic and vibrational). This is a great advantage of the technique. In dihydrogen, due to the very slow ortho-para conversion, both rotational states J=1 and are present in this experiment. However it is unclear if they are in the normal 3 1 ortho-para ratb or if some conversion does occur on the apparatus walls. 

In Ch. 21 Buntkowsky and Limbach review recent NMR work on the dynamics of dihydrogen and dideuterium in the coordination sphere of transition metals. In addition to inelastic neutron scattering and liquid state NMR, the effects of coherent (exchange couplings) and incoherent rotational tunneling of D2 pairs in transi-... 

The origins of symmetry induced nuclear polarization can be summarized as follows as mentioned above molecular dihydrogen is composed of two species, para-H2, which is characterized by the product of a symmetric rotational wave-function and an antisymmetric nuclear spin wave function and ortho-H2, which is characterized by an antisymmetric rotational and one of the symmetric nuclear spin wavefunctions. In thermal equilibrium at room temperature each of the three ortho-states and the single para-state have practically all equal probability. In contrast, at temperatures below liquid nitrogen mainly the energetically lower para-state is populated. Therefore, an enrichment of the para-state and even the separation of the two species can be easily achieved at low temperatures as their interconversion is a rather slow process. Pure para-H2 is stable even in liquid solutions and para-H2 enriched hydrogen can be stored and used subsequently for hydrogenation reactions [54]. 

Related studies have made use of 2H NMR spectroscopy in the solid state. The theoretical foundation for the study of dynamics in dihydrogen complexes was developed by Buntkowsky and coworkers.124 Solid-state 2H NMR spectroscopy has been used to study the dynamics of bound D2 in tntns- Ru( D2)CI(dppe)2 PI>, where evidence was found for coherent rotational tunneling, with a barrier of 6.2kcal/ mol.125 In more recent work, solid-state 2H NMR spectroscopy has been used to determine the structure and dynamics of several dihydrogen Ru complexes.126... 

Solution and solid state studies of non-classical transition metal hydride systems have revealed fast intramolecular motions of the dihydrogen ligands [7, 8]. These motions represent a rotational diffusion around the axis perpendicular to the H-H (or D-D) vector (Scheme 1), a libration (Scheme 2) or 180° - jumps (Scheme 3) around the same axis [43]. It has been shown that the type of motion, its frequency and the orientation of eq z (angle a in Scheme I) affect strongly on the 2H NMR parameters, causing an elongation of the H T, time in solution [25] or a decrease of the quadrupole splitting in the solid -state H NMR spectra [22]. This influence creates additional problems for DQCC determinations from experimental relaxation measurements or solid state NMR data, particularly when the orientation of the eqzz vector is unknown. 

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