Ring puckering Rotation

The microwave spectmm of 3,6-dihydro-1,2-dioxin 2 was measured in the frequency range of 10-26 GHz at dry ice temperature <1994JST(323)79> the structures on the basis of the rotational constants are half-chair conformers which readily interconvert at ambient temperature by ring puckering. This interconversion process could be frozen out spectroscopically and its free energy of activation determined (AG = 9.82 kcal moF ) by low-temperature NMR. 

RGURE 8-18 Structural variation in DNA. (a) The conformation of a nucleotide in DNA is affected by rotation about seven different bonds. Sx of the bonds rotate freely. The limited rotation about bond 4 gives rise to ring pucker, in which one of the atoms in the five-membered furanose ring is out of the plane described by the other four. This conformation is endo or exo, depending on whether the atom is displaced to the same side of the plane as C-5 or to the opposite side (see Fig. 8-3b). (b) For purine bases in nucleotides, only two conformations with respect to the attached ribose units are sterically permitted, anti or syn. Fyrimidines generally occur in the anti conformation. 

Usually there are many possible interconversion movonents between these isomers, which can change one degenerate configuration into another one of same energy. These interconversion movements are internal rotations, inversions, ring puckerings, etc...They can be described by some operators, M,-, acting on X, which will leave the nuclear Hamiltonian operator (7) invariant. 

Let X be the ring-puckering coordinate and y the PH inversion coordinate in 3-phospholene (see Fig. 33). The dynamics of isomerization in this molecule is assumed to be adequately described by these coupled two DOF s without need for consideration of other DOFs. Under this assumption, the Harthcock-Laane potential energy surface consists of a fourth-order polynomial in x, a fourth-order polynomial in y, and a sixth-order polynomial coupling x and y. With molecular rotation neglected, the model Hamiltonian for 3-phospholene is given by... 

Cyclopentane adopts an envelope, or puckered, conformation the puckering rotates rapidly around the ring in a process called pseudorotation. 

The analysis of the microwave rotational spectra of small ring compounds can provide valuable information about the nature of large-amplitude ring-puckering potential functions. The type of information obtained may vary, depending on the potential function. 

Fig. 2.5. Variation of the B rotational constant (in MHz) with ring-puckering vibrational state for oxetanone-3. Similar variations are found for the A and C rotational constants. [Reproduced from Gibson, J. S., Harris, D. O. J. Chem. Phys. 57, 2318 (1972).]...

The variation of rotational constants with ring-puckering vibrational state is very sensitive to the presence of a barrier at the planar conformation. This is shown for cyclobutanone16 and methylenecyclobutane17) in Fig. 2.6. The presence of a very small barrier, ca. 7.6 cm-1 in the case of cyclobutanone, causes deviation from a smooth variation for the lower levels. In the case of methylenecyclobutane, a very pronounced zig-zag of the rotational constants is observed due to the presence of a 140 cm-1 barrier. The dependence of the rotational constants on vibrational state may be used quantitatively to determine the shape of the potential function as discussed in subsequent sections. 

Fig. 2.6. Variation of the A rotational constants (in MHz) with ring-puckering vibrational state for cyclobutanone and methylene-cyclobutane.

The rotational constants, expressed by power series through quartic terms, are averaged over the ring-puckering vibrational states ... 

In the case of oxetanone-3, the coefficients in the rotational constant expansions [Eq. (4.2)] were treated as empirical parameters and the potential function was taken from a previous vibrational study10). Figure 2.5 shows the smooth variation, with a definite curvature, of the B rotational constant with ring-puckering vibrational state. Table 4.2 lists the observed and calculated values of the rotational constants. The smooth variation indicates a single-minimum potential with a definite curvature due to the quartic potential term and the quartic terms in the expansion [Eq. (4.3)]. 

Since even functions are more affected than odd functions, the variation of rotational constants with ring-puckering quantum states is expected to deviate from the regular dependence shown by planar molecules (e. g. Fig. 2.5 for oxetanone-3). From Eq. (4.2) we see that alteration of the wave functions of the even levels will affect the expectation values of Z2 and Z4 in this equation, primarily Z2, and lead to an irregular pattern for the lowest few levels. 

The effect of the ring-puckering vibration, particularly in the v = 0 and v = 1 states, on the rotational spectrum of trimethylene sulfide is striking18 . in Eq. 

If we restrict the Hamiltonian given by Eq. (3.10) to one vibrational coordinate, a ring-puckering coordinate with a constant effective mass, the following vibration-rotation Hamiltonian results... 

The two types of vibration-rotation interaction terms are the PaPc + PcPa term and the Pb term (the b axis is perpendicular to the symmetry plane which is maintained throughout the ring-puckering.). Their coefficients are functions of the vibrational coordinate or the vibrational momentum or both. It is possible to choose the coordinate system so that the PaPc + PcPa term is zero and all of the coupling between rotational angular momentum and vibrational momentum is manifested by the Pb term. The matrix elements for the Hamiltonian in the basis of the solutions to the pure vibrational (J = 0) problem, are... 

---