Principal axis of rotation

The rotation axis of highest order is called the principal axis of rotation it is usually placed in the vertical direction and designated the z-axis of the molecule. Planes of reflection which are perpendicular to the principal axis are called horizontal planes (h). Planes of reflection which contain the principal axis are called vertical planes (v), or dihedral planes (d) if they bisect 2 twofold axes. 

Due to the characteristics of the technique, comparisons of -parameters in microwave spectroscopy are not meaningful within 0.01 A6, particularly if one or several atoms are close to a principal axis of rotation. When restructures are determined from three rotational constants for a species with more than three degrees of freedom, no estimate is possible of the significance of the results. 

When the plane is perpendicular to the principal axis of rotation, it is called (y (horizontal). Other planes, which contain the principal axis of rotation, are labeled or o-rf. 

Figure 4.5 The nuclear configuration for H2O in the yz-plane. The x-axls is perpendicular to the paper, and passes through 0. One of the two mirror planes lies in the plane of the paper, whilst the second is perpendicular to the paper and contains the 0 atom. The principal axis of rotation is the z-axis...

As described in earlier discussions, the L parameter quantifies distortions in the axial direction, and is only strictly defined when the cluster is symmetric about the unique axis (for the cluster to be symmetric about the principal axis, the principal axis of rotation must be at least a 3-fold axis). The 5 electron species illustrate the effect of a distortion perpendicular to the principal axis. The electronic structure of these clusters is Is2 lpo lp > and consequently is orbitally degenerate. The Jahn-Teller theorem predicts that a distortion will occur to lift the degeneracy and lower the energy of the system. In order to lift the degener-... 

The framework of atoms in a linear, bent or planar molecule can always be drawn in a plane, but this plane can be labelled only if the molecule possesses a C axis perpendicular to the plane. If the plane contains the principal axis, it is labelled CTv- Consider the H2O molecule. This possesses a C2 axis (Figure 3.3) but it also contains two mirror planes, one containing the H2O framework, and one perpendicular to it. Each plane contains the principal axis of rotation and so may be denoted as a., but in order to distinguish between them, we use the notations and af. The label refers to... 

Table 3.3 shows the character table for the Cgv point group. The NH3 molecule possesses C3V symmetry, and worked example 3.2 illustrated the principal axis of rotation and planes of symmetry in NH3. In the character table, the presence of three cr planes in NH3 is represented by the notation 3ctv in the top line of the table. The notation 2C3 summarizes the two operations C3 and C3. The operation C3 is equivalent to the identity operator, E, and so is not specihed again. 

It is often convenient to choose the principal axis of rotation such that the rotation Hamiltonian takes the diagonal form ... 

For the target molecule T, we choose the molecular z axis to be along the r coordinate as in Figure 14.1. With this choice of the z axis, the Euler angles that specify the spatial orientation of molecule T are independent of the coordinate r. The (x, y) axes, on the other hand, can be chosen such that the element of moment of inertia tensor Ixy = Iyx vanishes. For the reactant molecule R, it is convenient to choose the principal axis of rotation such that the rotation Hamiltonian has the diagonal form as in eqn (14.16). 

The initial conditions for the vibrational modes of the (gly-FI)+ were chosen via the quasiclassical normal-mode method, with the energy for each normal mode of vibration selected from the mode s 300 K harmonic oscillator Boltzmann distribution. A 300 K rotational energy of RT/2 was added to each principal axis of rotation of the projectile. Initial conditions for the diamond surface were chosen by first equiHbrating the surface to a 300 K Boltzmann distribution with 2 ps of molecular dynamics and scaHng the atomic velocities. The structure and atomic velocities obtained from this equilibration process are then used as the initial conditions for an equilibration run at the beginning of each trajectory. 

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