Frame inversion

A-frame complexes which have a bridging hydride ligand, or which are capable of rearranging rapidly to a complex with a bridging hydride, undergo A-frame inversion on the NMR time scale. This A-frame inversion occurs through an intermediate with a linear Pt—H—Pt group.1451... 

Although parity is defined by the even/odd-ness of the complete molecular wavefunction under inversion of laboratory-frame coordinates of all electrons and nuclei (denoted either as I or E ), Hougen (1970) shows that erv, applied to the complete electronic-vibration-rotation wavefunction, has the same effect as laboratory frame inversion. 

In the early amplitude selection, the number of scan lines was 2-4, and the frame frequency /p was 50-60 Hz. Because of a frame inversion for the AC drive, the minimum driving frequency of the drive voltage applied to the LCD was H /p, which means 30 Hz. The effective dielectric constant under such low frequencies fluctuated because the ionic conduction mainly fluctuated which led to malfunctions. More than lO Q. cm were required as the specific resistance of the bulk liquid crystal material. 

Figure 2. The space-fixed (XYZ) and body-fixed xyz) frames in a diatomic molecule AB. The nuclei are at A and B, and 1 represents the location of a typical electron. The results of inversions of their SF coordinates are A A, B B, and 1 1, respectively. After one executes only the reinversion of the electronic SF coordinates, one obtains 1 — 1. The net effect is then the exchange of the SF nuclear coordinates alone.

The Hubbard relation in the frames of the liquid cage model 257 existence of an inverse operator for the right f is sufficient to obtain... 

Flame shape images and traces extracted from the high-speed schlieren movie (5000 frames/s) of a stoichiometric methane/air flame going through a tulip inversion while propagating in a square cross-section (38.1 mm on the side) closed tube. 

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

The 13CO inversion pulse can be achieved by a PIP with the carrier placed at the centre of the 13C . This inversion PIP causes an additional procession of the 13C spins. The amount of the phase shift in the rotating frame of the 13CO, where the centre of the 13CO spins is on-resonance to the inversion PIP, can be calculated... 

In this section, three experiments are going to be discussed. Two of them, a broadband inversion and a Hahn spin echo, are well-known in the rotating frame. They need to meet the requirement of the phase coherence in PIPs in order to work properly in the Eigenframe. The third is a composite pulse with offset modulation. 

As shown in Fig. 21a, the simulated broadband inversion profile by the three PIPs resembles the profile by the composite pulse 90°180°90° except for a different excitation region. The inversion profile is severely distorted (Fig. 21b) if the three initial phases, phase relationship in the rotating frame is the wrong one in the Eigenframe. The phase coherence in PIPs needs to be considered even for PIPs with the same frequency shift, A/ = 50 kHz in this case. 

Temperature-dependent lineshape changes were observed in an early study of the fluo-renyllithium(TMEDA) complex. A detailed study by lineshape analysis, which was also applied to the TMEDA complex of 2,3-benzofluorenyllithium(TMEDA) (Figure 29f, yielded barriers AG (298) of 44.4 and 41.9 kJmoD for the 180° ring flip in these systems, respectively . A second dynamic process, which was detected via the temperature dependence of, the spin-lattice relaxation time in the rotating frame, is characterized by barriers of 35.1 and 37.6 kJmoD, respectively, and may be ascribed to the ring inversion process. For the fluorenyl complex, a barrier AG (298) of 15.9 kJmoD for the methyl rotation in the TMEDA hgand was determined from temperature-dependent NMR spectra of the deuteriated system. 

Polymer Dynamics. 13C spin-lattice relaxation times (Ti) were determined with either an inversion-recovery sequence (16) (for carbons observed by direct polarization) or with a modified cross-polarization experiment (17). 13C rotating-frame relaxation times (Tip(C)) were derived from measurements of the carbon signal that remained after a Tjp(C) hold time of... 

Fig. 3. Numerical simulations of four different selective inversion pulses. (Top) Pulse shapes. From left to right 180° rectangular, 180° Gaussian truncated at 2.5%, Quaternion cascade Q, and l-BURP-2. (Middle) Trajectories of Cartesian operators in the rotating frame during...

Another approach employed to establish the occurrence of a density nversion between the two solutions subsequent to boundary formation involves dialysis between the two solutions s0>. The dialysis membrane is impermeable to the polymer solutes but permeable to the micromolecular solvent, H20. Transfer of water across the membrane occurs until osmotic equilibrium involving equalization of water activity across the membrane is attained. Solutions equilibrated by dialysis would only undergo macroscopic density inversion at dextran concentrations above the critical concentration required for the rapid transport of PVP 36 0 50). The major difference between this type of experiment and that performed in free diffusion is that in the former only the effect of the specific solvent transport is seen which is equivalent to a density inversion occurring with respect to a membrane-fixed or solute-fixed frame of reference. Such restrictions are not imposed on free diffusion where equilibration involves transport of all components in a volume-fixed frame of reference. The solvent flow is governed specifically by the flow of the polymer solutes as described by Eq. (3) which, on rearrangement, gives... 

Figure 3. Log of the inverse of the spin lattice relaxation time (T 1), the spin-lattice relaxation time in the rotating frame (T lp 1), and the line shape as a function of time for the HP sample after the sample was heated to 460°K and brought back to room temperature.

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