The Internal Motions of Molecules

It has been emphasized in Section A that the nuclear framework of molecules must not be conceived as a rigid structure formed of fixed immobile particles. Rather, the individual atoms execute various motions under the influence of the forces holding the whole molecule together and under the influence of temperature knowledge of these motions is just as important to an understanding of the molecular structure as is knowledge of the nuclear framework itself. For the study of these internal motions throws light on the field of force to which the molecule owes its existence and by which its physical and chemical properties are determined. 

The internal motions of a molecule may be divided conveniently and easily into two distinct types into oscillations and rotations  

In precise investigation of atomic oscillations in the molecule, it appears that two different types are again distinguishable valence oscillations and deformations or break oscillations. The former consist of the periodic motion of the atoms in the direction of the main valences linking them the oscillation therefore causes an intermittent variable extension and contraction of any bond distance, a few data for which are shown in Table 2. In the break oscillations, however, the deformations of the atom are executed perpendicular to the bond direction and effect a periodic increase and diminution of the valence angle numerical data are also given for these in Table 4. 

Both oscillations suggest that the rigid nuclear framework of the molecule can actually be regarded only as a temporary mean position. At any particular instant it is distorted according to the magnitude and direction of the existing elongations of the atoms. 

The rotation of individual parts of the molecule plays a role which is especially prominent in larger molecules. This is particularly true in organic molecules, where, in consequence of the possibility of free rotatory power around the simple primary valence bonds, the components of a molecule may be moved toward one another without causing appreciable 

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As we shall see, in molecules as well as atoms, the interplay between the quantum description of the internal motions and the corresponding classical analogue is a constant theme. However, when referring to the internal motions of molecules, we will be speaking, loosely, of the motion of the atoms in the molecule, rather than of the fiindamental constituents, the electrons and nuclei. This is an extremely fundamental point to which we now turn. 

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

The Gibbs formulation of an equilibrium statistics is in error when applied to the internal motions of molecules and also to the external motions of light molecules such as helium or hydrogen at low temperatures. 

The internal motion of molecules in crystals is, however, not always confined to rigid-body motion or uncorrelated motion of segments of the structure. Often the overall motion is the result of a combination of... 

For real fluids the hard-sphere model gives a reasonable approximation to long-time phenomena, such as particle diffusion, but it is not realistic for short-time phenomena, such as collisional excitation of the internal motions of molecules, because of the impulsive nature of hard-sphere impacts. In the next two sections the more realistic case will be studied in which the test particle-bath particle interaction occurs through a continuous central potential. 

BD simulation is similar to MD simulations [26]. However it introduees a few new approximations that allow one to perform simulations on the mieroseeond timescale whereas MD simulation is known up to a few nanoseeonds. In BD the explicit description of solvent molecules used in MD is replaced with an implicit continuum solvent description. Besides, the internal motions of molecules are typically ignored, allowing a much larger time step than that of MD. Therefore, BD is particularly useful for systems where there is a large gap of time scale governing the motion of different components. For example, in polymer-solvent mixture, a short time-step is required to resolve the fast motion of the solvent molecules, whereas the evolution of the slower modes of the system requires a larger time-step. However, if the detailed motion of the solvent molecules is concerned, they may be removed from the simulation and their effects on the polymer are represented by dissipative (-yP) and random (o C (0) force... 

Figure 13 shows an example of a pump-probe experiment. The upper part depicts the vibrational motion of Na2 in an excited electronic state as a function of time. The oscillations of the wave packet between the inner and the outer turning points are reflected in the ionization signal as a function of the delay time in the lower panel of Figure 13. In this way it is possible to make the internal motion of molecules visible in real time. The pump-probe signals are quite reminiscent of the autocorrelation functions depicted in Figure 7.

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