Rotationally adiabatic

Simons J 1989 Modified rotationally adiabatic model for rotational auto ionization of dipole-bound molecular anion J. Chem. Phys. 91 6858-68... 

Fortunately most molecules, except H2 and D2, are non-adiabatically broadened. Only small corrections for rotational adiabaticity are required for such molecules as N2, but in the first approximation even these may be neglected. In this extreme, which is valid at A diffusion model. The non-adiabatic impact operator... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 91-92 Multiple independent spawning (MIS), direct molecular dynamics, non-adiabatic coupling, 402... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Time-dependent ground state (TDGS), molecular systems, component amplitude analysis, near-adiabatic limit, 220-224... 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Treating bound modes quantum mechanically, the adiabatic separation between s and u is equivalent to assuming that quantum states in bound modes orthogonal to s do not change throughout the reaction (as s progresses from reactants to products). The reaction dynamics is then described by motion on a one-mathematical-dimensional vibrationally and rotationally adiabatic potential... 

Recent calculations /16/ for some simple gas reactions show that T is shorter than the periods of vibrations and rotations of the activated complex, therefore, it cannot be considered as a stationary state configuration with a well-defined discrete energy spectrum. This is contrary to the assumption of vibrational-rotational adiabaticity which is related to the equilibrium hypothesis of activated complex theory. 

Under certain conditions to be discussed with more details in Sec.4 1 III, the one-dimensional treatment is shown to be a good approximation also for a dynamically non-separable reaction coordinate. These are namely the extreme conditions of a very slow and a very fast motion along the reaction coordinate in comparison with the non-reac-tive vibration and rotation motions. In the first case the inequality (6.II)must be satisfied, which means that the reaction must be vib-rationally or rotationally adiabatic. In the second case the inverse inequality (12.11) holds as a criterion for vibrational-rotational non-adiabaticity. 

Considering the high temperature limits of (67.Ill) or (79.Ill) in Sec.4.2, we assumed the validity of the condition (82.Ill) for vibrational-rotational adiabaticity from reactants to transition region of configuration space, which is equivalent to the condition (87.Ill) for the transition region. No restriction concerning the products region has been introduced in this way, however. 

It is of particular interest to consider the situation in which the condition (82,111) of vibrational-rotational adiabaticity is really fulfilled throughout the reaction. Then, the reaction probabilities obey the conditions... 

Let us now consider the other extreme situation of a very slow motion along the raction coordinate at which the condition (82.Ill) for a vibrational-rotational adiabaticity is valid. The factor... 

III). In conditions of vibration-rotational adiabaticity, will represent an apparent tunneling correction which is necessary only to obtain the correct values of the rate constant when using the collision theory expression (51.Ill), instead of Eyring s equation (67.Ill) (corrected by the real tunneling factor ). 

The advantage of the statistical theory appears for fully (electronically and vibration-rotationally) adiabatic reactions, involving activation energy, at sufficiently high temperatures at which a solution of the dynamical problem may be avoided, since the correction factor to any of the statistical formulations comes close to unity. In this situation the less restricted and most useful of these formulations is certanly the Eyring rate equation, which follows from the exact expression (67.Ill) if the condition (82.Ill) is valid only from reactants to transition region of configuration space. Since... 

SO that the separation of the angular momentum (p = const) means rotational adiabaticity, at least from the initial state (large values of X = r) to the transition state (the maximum of the potential Veff(x)).Therefore, the condition (82.Ill) written as... 

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