Rotational constants, vibration-rotation

When an electronic state is known only through its perturbations of a better known state, frequently only the energy and rotational constant of one or two vibrational levels of unknown absolute vibrational numbering can be determined. If the information available is insufficient to generate a realistic potential energy curve, then one has no choice but to adopt a model potential and exploit relationships between Dunham (l)m) and other derived constants (vibrational overlaps), which are rigorously valid for the model potential and approximately valid for general potentials. 

Although there had been some earlier attempts, the first practical ultrasonic motor was proposed by H. V. Barth of IBM in 1973 [55]. The rotor was pressed against two horns placed at different locations. By exciting one of the horns, the rotor was driven in one direction, and by exciting the other horn, the rotation direction was reversed. Various mechanisms based on virtually the same principle were proposed by Lavrinenko [56] and Vasiliev [57] in the former USSR. Because of difficulty in maintaining a constant vibration amplitude with temperature rise, wear and tear, the motors were not of much practical use at that time. 

Fortunately, not all regions of the potential energy surface are of equal interest or importance. For stable molecules the region around the equilibrium structure determines the rotational constants, vibrational frequencies, etc. For most molecules the energy in this region can be satisfactorily represented by a polynomial expansion in the internal coordinates. For an N atom molecule a quadratic (harmonic) representation of the surface requires only (3N-6)(3N-5) energy calculations (after the equilibrium structure has been determined). ... 

Midey A J and Viggiano A A 1998 Rate constants for the reaction of Ar" with O2 and CO as a function of temperature from 300 to 1400 K derivation of rotational and vibrational energy effects J. Chem. Phys. at press... 

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

If K is adiabatic, a molecule containing total vibrational-rotational energy E and, in a particular J, K level, has a vibrational density of states p[E - EjiJ,K). Similarly, the transition state s sum of states for the same E,J, and Kis [ -Eq-Ef(J,K)]. The RRKM rate constant for the Kadiabatic model is... 

Within physical chemistry, the long-lasting interest in IR spectroscopy lies in structural and dynamical characterization. Fligh resolution vibration-rotation spectroscopy in the gas phase reveals bond lengths, bond angles, molecular symmetry and force constants. Time-resolved IR spectroscopy characterizes reaction kinetics, vibrational lifetimes and relaxation processes. 

The only tenn in this expression that we have not already seen is a, the vibration-rotation coupling constant. It accounts for the fact that as the molecule vibrates, its bond length changes which in turn changes the moment of inertia. Equation B1.2.2 can be simplified by combming the vibration-rotation constant with the rotational constant, yielding a vibrational-level-dependent rotational constant. 

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

Microwave studies in molecular beams are usually limited to studying the ground vibrational state of the complex. For complexes made up of two molecules (as opposed to atoms), the intennolecular vibrations are usually of relatively low amplitude (though there are some notable exceptions to this, such as the ammonia dimer). Under these circumstances, the methods of classical microwave spectroscopy can be used to detennine the stmcture of the complex. The principal quantities obtained from a microwave spectmm are the rotational constants of the complex, which are conventionally designated A, B and C in decreasing order of magnitude there is one rotational constant 5 for a linear complex, two constants (A and B or B and C) for a complex that is a symmetric top and tliree constants (A, B and C) for an... 

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