Oscillations of molecules

The identification of t0 with the time of an oscillation of adsorbed molecules leads to the assumption that t0 will be about 10 13 sec., the latter being the time of oscillation of bound atoms (191). In many cases of adsorption t0, indeed, proves to be about 10 12 sec., although this has nothing to do with a time of oscillation of molecules. 

Cruickshank DWJ (1956) Errors in bond lengths due to rotational oscillations of molecules. Acta Cryst 9 757-758... 

In the mid 1950s Durwaxd W. J. Cruickshank " noted that atoms in, for example, a rotating molecule, are displaced towards the rotation axis. Rotational oscillations of molecules, such as found in crystalline benzene near its melting point, will cause an apparent displacement of atomic positions from their true positions because the best fit to the electron density should be curvilinear but, with the limitations of present-day techniques, is generally linear (Figure 13.15). If the root-mean-square amplitude of libration about an axis is o> (in radians), then the apparent (but not real) shortening of the bond, d, is ... 

Now we have a driving force E(t) = Eq exp(—iu t) so that the molecule a oscillates with this laser field frequency u>l and due to the Fermi resonance interaction across the interface this leads to oscillations of molecules b with frequency 2ujl. As a result, we obtain an algebraic system of equations for the amplitudes A, B, Bu... ... 

If phase transitions occur in condensed phases, a nucleus is in contact with a large number of molecules in the initial metastable phase. In this case the lifetime of the critical nucleus is determined by the number of molecules present on its surface, Scr / b2 (b is the intermolecular distance), their oscillation frequency, vM, and the height of the potential energy barrier, U, that a molecule has to overcome in order to become attached to the nucleus surface. The frequency of thermal oscillations of molecules can be obtained from the expression vM = kT / h, where h is Planck s constant. The latter allows one to write the pre-exponential factor, J0, as... 

In an ideal molecular gas, each molecule typically has translational, rotational and vibrational degrees of freedom. The example of one free particle in a box is appropriate for the translational motion. The next example of oscillators can be used for the vibrational motion of molecules. 

The model of non-mteracting hannonic oscillators has a broad range of applicability. Besides vibrational motion of molecules, it is appropriate for phonons in hannonic crystals and photons in a cavity (black-body radiation). 

With the assumption of hannonic oscillators, the molecule s quantum energy levels are... 

As it stands, the picture of dynamics from Eq. (29) is derived from the interaction of molecules with a continuous light source, that is, the system is at equilibrium with the oscillating light field. It is also valid if the light source is an infinitely short laser pulse, as here all frequencies are instantaneously excited. 

The hamionic oscillator of two masses is a model of a vibrating diatomic molecule. We ask the question, What would the vibrational frequency be for H2 if it were a hamionic oscillator The reduced mass of the hydrogen molecule is... 

The vibration of molecules is best described using a quantum mechanical approach. A harmonic oscillator does not exactly describe molecular vibra-... 

In order for these molecules to jump from liquid positions to solid positions they must be moving in the correct direction. The number of times each liquid molecule oscillates towards the solid is v/6 per second (there are six possible directions in which a molecule can move in three dimensions, only one of which is from liquid to solid). Thus the number of molecules that jump from liquid to solid per second is... 

The application of these methods to unsaturated hydrocarbons involves certain complications. Unsaturated hydrocarbons show an additional polarizability19 of 0.58 x 10 24 cm3 per double bond and 0.86 x 10 24 cm3 per triple bond in the molecule. Similarly the polarizability of a molecule containing a benzene ring exceeds that computed for the atoms present by about 1.28 x 10 24 cm3. These results are most readily explained on the basis that oscillations of charge from atom to atom are significant when double bonds are present. 

This energy increase can take different forms. It can be added as translational kinetic energy to speed up the movement to and fro of the molecules it can be added to the rotations of the molecules to get them to spin faster it can be added to increase the amplitude of the vibrational oscillations of the molecules and it can be added to excite electrons to higher energy states in the atoms or molecules. Other forms of internal energy are also possible, but the above are the most common. 

Let us consider a diatomic molecule in such a crystal. As a first approximation we may neglect the translational oscillations of the molecule under consideration and both the translational and rotational motion of the other molecules in the crystal. The wave equation then may be written... 

In general photochemical reactions only occur when the affected substance absorbs radiation, i. e. when ti or n electrons are raised to an excited rt state. Interaction of the electric light vector with the electronic shell of the molecule brings about a change in the structure of the electronic shell. This change takes place during one period of oscillation of the light (ca. 10 s). The altered structure of the electronic shell cor-... 

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