Adiabatic rotation

Carter S and Bowman J M 1998 The adiabatic rotation approximation of rovibrational energies of manymode systems description and tests of the method J. Chem. Phys. 108 4397... 

The total rotations of the molecule (as distinct from internal rotation) are sometimes described as the adiabatic rotations because formation of the transition state occurs without change of angular momentum. 

Theoretical calculations have been made on stilbene which are relevant to photoisomerization dynamics. MNDO calculations of stilbene potential energy properties shows no evidence of a doubly excited "phantom" state but a singly excited state with adiabatic rotation around the central ethylene bond has only a small barrier on this path23T Calculations of dipole moments, optical spectra, and second order hyperpolarizability coefficients of some mono- and disubstituted stilbene molecules allows the design of useful nonlinear optical molecules 38. 

Adiabatically rotating the mixing angles 6 from 0 to 7t/2 leads to a complete and reversible transfer of all photonic states to a collective atomic excitation if the maximum number of photons n + m is less than the number of atoms N. Let the initial quantum state of the light field be described by the density matrix... 

Previous fully quantum mechanical studies of predissociation phenomena in triatomic molecules do not, to our knowledge, use a Hamiltonian that has a non-zero total angular momentum. Tennyson et al[43, 44, 45, 46, 47, 48, 49, 50, 51] solve the same equations as we do but have not yet, to our knowledge, treated any predissociation problems. The adiabatic rotation approximation method of Carter and Bowman[52] plus a complex C2 modification have, on the other hand, been used to compute rovibrational energies and widths in the HCO[53, 54] and HOCl[55, 56, 57] molecules. This method is based upon the the Wilson and Howard[58], Darling and Dennison[59] and Watson[60] formalism. It is less transparent but the exact formalism in refs.[58, 59, 60] is equivalent to the one presented here and in ref [43]. While both we and Tennyson et al[43] include the exact Hamiltonian in our formalism the latter authors 152] use an approximate method which they have analysed and motivated. 

Mulder EAA, de Graaf RA, Kaptein R, Boelens R (1998) An off-resonance rotating frame relaxation experiment for the investigation of macromolecular dynamics using adiabatic rotations. J Magn Reson 131 351-357... 

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant Tip. On the other hand, the time constant T2p. characterizes the relaxation of magnetization that is perpendicular to the effective field. Michael et showed that T2p can be measured directly with Carr Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation T2p characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical... 

ARES Adiabatic rotation of effective spin orientations... 

Equation (5.3) is not valid when Ag is large [23, 24] and it has been shown in the literature how Eq.(5.3) can be understood in terms of the adiabatic rotation of effective spin orientations (ARES) [23, 24]. The authors show that the term (Ag Ag) in Eq. (5.3) should be replaced by the y tensor (which relates L -i- S to with representing the effective spin angular momentum, L and S are the vector operators of the orbital and spin angular momentum respectively). The y tensor therefore is a measure of how effectively S follows the molecular axis. Only in the weak spin-orbit coupling case (i.e. where the effective spin follows the rotation of the molecular axis weakly) does the traditional spin-rotation Hamiltonian follow the ARES Hamiltonian. (i.e. Eq.(5.3) is obtained.)... 

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