Vibronic angular momentum

In this connection, it is of interest to note that when nonadiabatic effects are small, as in strongly coupled systems at low energy or substantial vibronic angular momentum, a semi-classical quantization scheme beginning with the adiabatic nuclear Hamiltonian yields fairly... 

In the B state, the three sodium atoms perform a nearly free pseudorotational motion in the moat of a pseudo Jahn-Teller potential that is characterized by a vibronic angular momentum quantum number j. 

B = constant for methyl-group rotation / = vibronic angular momentum J = total angular momentum with a projection of K in the molecular frame m = rotational quantum number n = principal quantum number N = total angular momentum excluding spin a = torsional angle v = vibrational quantum number (o = corresponding vibrational constant. 

The potentials of equation (28), often referred to as Mexican hat , represent the prototype of a conical intersection. The azimuthal symmetry of the adiabatic potentials reflects the existence of a constant of motion of file linear Jahn-Teller problem, the so-called vibronic angular momentum "... 

Eigure a shows that the eigensurfaces form an interconnected double sheet, the lower member of which has a ring of equivalent minima at r = and IV = — k. As expected angular momentum is conserved, but with the complication that it is vibronic, rather than purely vibrational in character. 

In the limit of strong vibronic coupling, F4S = 0, c = 5 /3, s=, c2 - s2 =, and the dynamic Jahn-Teller effect thus renders nugatory the orbital contributions to the angular momentum, and reduces the splitting, A, by a factor of two. Note in addition that the c and s quantities used in the vibronic treatment do not correspond to those of the adiabatic case, although the expressions are formally similar, so that the static distortion, A, cannot accurately be calculated from the c and s values deduced from the and 4 data. 

Figure 1. Linewidlhs of different rotational transitions in the 14q1q vibronic band of benzene measured with Doppler-free two-photon absorption. The observed strong dependence on the quantum number J of the rotational angular momentum is evidence for a rotationally dependent intramolecular coupling process. (Taken from Ref. 3.)...

The vibronic matrices defined in a T2-basis can be expressed in terms of the matrices of the fictitious angular momentum operator as follows ... 

The diagonal elements of the density matrix contain the populations of each of the BO states, whereas off-diagonal elements contain the relative phases of the BO states. The components of the density matrix with a = a describe the vibrational and rotational dynamics in the electronic state a, while the rotational dynamics within a vibronic state are described by the density matrix elements with a = a and va = v ,. The density matrix components with na = n a, describe the angular momentum polarization of the state Ja, often referred to as angular momentum orientation and alignment [40, 87-89]. The density matrix may be expanded in terms of multipole moments as ... 

For molecules, the spectroscopic nomenclature for molecular energy levels and their vibronic and rotational sublevels is messy and very specialized. Already for homonuclear or heteronuclear diatomic molecules a new quantum number shows up, which quantifies the angular momentum along the internuclear axis, but the reader need not be burdened with the associated nomenclature. 

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