Pseudorotation defined

Similar to the case without consideration of the GP effect, the nuclear probability densities of Ai and A2 symmetries have threefold symmetry, while each component of E symmetry has twofold symmetry with respect to the line defined by (3 = 0. However, the nuclear probability density for the lowest E state has a higher symmetry, being cylindrical with an empty core. This is easyly understand since there is no potential barrier for pseudorotation in the upper sheet. Thus, the nuclear wave function can move freely all the way around the conical intersection. Note that the nuclear probability density vanishes at the conical intersection in the single-surface calculations as first noted by Mead [76] and generally proved by Varandas and Xu [77]. The nuclear probability density of the lowest state of Aj (A2) locates at regions where the lower sheet of the potential energy surface has A2 (Ai) symmetry in 5s. Note also that the Ai levels are raised up, and the A2 levels lowered down, while the order of the E levels has been altered by consideration of the GP effect. Such behavior is similar to that encountered for the trough states [11]. 

Ultrafast electron diffraction was used to define the structure of the cyclopenta-dienyl radical formed through photodissociation of CpCo(CO)2. The structure obtained reflected the Jahn-Teller distortion from D h symmetry, a dynamic structure thanks to pseudorotations converting dienylic and elongated conformations. ... 

Ring inversion (when strictly defined) of achiral conformations is nothing more than a pseudorotation. Ring inversion in the cyclohexane chair, for example, leaves the molecule apparently rotated by 60° along the C3 axis. Nevertheless, in order to conform with common usage, we will exclude ring inversion from the definition of ring pseudorotation. 

A particular ring conformer can be described by two parameters, the puckering amplitude (Xm) and the pseudorotational phase angle (P), which can be illustrated by the pseudorotational wheel shown in Figure 21 for a D-aldofuranose [106]. The radius of the circle is and P, which defines the part of the ring that is most puckered. 

In the case of furanosides, especially nucleosides, Altona and Sundara-lingam s original symbols for the pseudorotational angle P and pucker (or sometimes (p are used P = is defined as the T2 conformation. Figure 2.4 shows the pseudorotational itinerary, with a nucleoside (sugar D-ribose) as an example. Nucleoside chemists refer to conformations with 0 < P < 36° as N ... 

The dipolar structure (rdipolar interactions without correction for vibrations, but in which slower motions, if present (e.g., the rotation of methyl groups and the interconversion of conformers such as ring inversion or pseudorotation), have been accounted for. 

Because the rearrangement of a trigonal bipyramid is so widely important, it is useful to have a graphical representation of how the various permutations of vertex atoms are interrelated by the relevant pathway for rearrangement, which is assumed to be the Berry mechanism or pseudorotation just discussed. Necessary but not sufficient criteria for defining such a graph are ... 

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