Symmetric mode coupling

The e-mv couplings play an important role in superconductivity in organic materials, which contributes to static dielectric susceptibility. It is necessary to notice that not only totally symmetric modes couple with the electrons some out-of-plane molecular modes and intermolecular modes can also couple with the electron excitations. 

Historically, the study of the Jahn-Teller (1937) effect was preceded (Renner, 1934) by that of the Renner-Teller effect in linear molecules. It arises if linear, or more generally odd-powered, terms in Q cannot contribute to the adiabatic coupling operator for synunetry reasons. We shall use the term (pseudo-) Renner-Teller coupling for all such couplings between states that are (almost) degenerate. The term thus applies to every nontotally symmetric mode coupling two electronic states of the same symmetry. The lowest order contribution to the adiabatic coupling operator is then of the form JQ. ... 

Now the physical picture of multidimensional tunneling obtained from the above analysis is explained by taking a symmetric mode coupling model potential [30]. The Hamiltonian is given by... 

FIGURE 3.2 Schematic picture of tunneling in the case of symmetric mode coupling [see Equation (3.24)]. SP is the saddle point and S is the symmetry line. Dashed lines are solutions of the Hamilton-Jacobi equations but not the optimal tunneling path, (a) Case of modest and... 

Then the scaled Hamiltonian with the symmetric mode coupling (SMC) potential is given by... 

FIGURE 4.1 Contours of the symmetric mode coupling potential [Equation (4.15)] for the parameters (Oy, a) = (0.5, 1.0). The interval of contour is 0.02 and the contours with the energy higher than 0.28 are omitted. (Taken from Reference [31] with permission.)... 

Tunnel Splitting in the Symmetric Mode Coupling Potential Equation (4.15) Calculated Quantum Mechanically Numerically for Several Vibrationally Excited States. Parameter g Is Taken to be 0.04... 

Tunnel Splitting in the Symmetric Mode Coupling Potential Equation (4.15). The Second (Third) Column Is the Result by Exact Quantum Mechanical (EQM) Calculation [by the Sudden Approximation Equation (4.12)]. Parameters (u)y, a, g) Are Equal to (0.2,0.25,0.04)... 

Finally, we touch upon the adiabatic and sudden approximations in the present model. In the same way as in the case of symmetric mode coupling model, the adiabatic approximation leads to the tunneling splitting independent of Hy. This does not exhibit any characteristic behavior discussed above and can never be reliable. If we apply the sudden approximation, we also encounter a problem since the potential curve in jc direction is not symmetric except when y is zero. Thus we cannot use Equation (4.12) directly anymore. 

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