Molecular motion, vibration-rotation

The motions of a molecular system, for example a solution, occur on many time scales. There are very fast electronic motions, the basic mechanism in chemical reactions. Then, there are the nuclear motions—vibrations, rotations, and translations (diffusion). 

These values of S ° are measures of the energy that a substance requires at 25.0°C in order to maintain its characteristic variety of internal atomic and molecular motions (vibrations and rotations), and its random movement in... 

A related method is derived from the description of molecular motions in rotational and vibrational spectroscopy. The basic idea is to relate a distorted structure with coordinates to a reference structure with coordinates s). The conditions imposed for superposition are ... 

The scattering from a molecule will be more complicated than for a single atom because the other molecular motions of rotation and vibration come into play. If there are no inelastic features in the measured energy transfer range studied, the vibrational term will only affect the measured intensities in the QENS domain through a Debye-Waller factor. On the other hand, the influence of the rotation on the observed profiles has to be treated in more detail. Sears has derived analytical expressions for the total differential cross-section of a molecular system, where the rotational motion is isotropic [12]. From his work, a simplified expression (Eq. 22) for the double-differential cross-section can be obtained it is spht into three terms ... 

The time-scale for these recurrences will reflect the time-scale of the corresponding molecular motion. Thus, rotational recurrences will be much longer (picoseconds) than vibrational recurrences ( 100-200 fs). Further details can be found, for example, in Levine (2005). 

A difference between molecules and atoms is that only molecules can store energy in vibrational and rotational motion (vibrational-rotational quantum states). Thus, a molecular gas necessarily has heat capacities different from those of a monatomic gas. An ideal molecular... 

We find it convenient to reverse the historical ordering and to stait with (neatly) exact nonrelativistic vibration-rotation Hamiltonians for triatomic molecules. From the point of view of molecular spectroscopy, the optimal Hamiltonian is that which maximally decouples from each other vibrational and rotational motions (as well different vibrational modes from one another). It is obtained by employing a molecule-bound frame that takes over the rotations of the complete molecule as much as possible. Ideally, the only remaining motion observable in this system would be displacements of the nuclei with respect to one another, that is, molecular vibrations. It is well known, however, that such a program can be realized only approximately by introducing the Eckart conditions [38]. 

The treatment of electronic motion is treated in detail in Sections 2, 3, and 6 where molecular orbitals and configurations and their computer evaluation is covered. The vibration/rotation motion of molecules on BO surfaces is introduced above, but should be treated in more detail in a subsequent course in molecular spectroscopy. 

This completes our introduction to the subject of rotational and vibrational motions of molecules (which applies equally well to ions and radicals). The information contained in this Section is used again in Section 5 where photon-induced transitions between pairs of molecular electronic, vibrational, and rotational eigenstates are examined. More advanced treatments of the subject matter of this Section can be found in the text by Wilson, Decius, and Cross, as well as in Zare s text on angular momentum. 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

There exist a series of beautiful spectroscopy experiments that have been carried out over a number of years in the Lineberger (1), Brauman (2), and Beauchamp (3) laboratories in which electronically stable negative molecular ions prepared in excited vibrational-rotational states are observed to eject their extra electron. For the anions considered in those experiments, it is unlikely that the anion and neutral-molecule potential energy surfaces undergo crossings at geometries accessed by their vibrational motions in these experiments, so it is believed that the mechanism of electron ejection must involve vibration-rotation... 

We describe as rigid-body rotation any molecular motion that leaves the centre of mass at rest, leaves the internal coordinates unaltered, but otherwise changes the positions of the atomic nuclei with respect to a reference frame. Whereas in a simple molecule, such as carbon monoxide, it is easy to visualize the two atoms vibrating about a mean position, i.e. with the bond length changing periodically, we may sometimes find it easier to see the vibration in our mind s eye if we think of one atom being stationary while the other atom moves relative to it. 

Many elements of chemists pictures of molecular structure hinge on the point of view that separates the electronic motions from the vibrational/rotational motions and treats couplings between these (approximately) separated motions as perturbations. It is essential to understand the origins and limitations of this separated-motions picture. 

---