On Macroscopic Quantum Phenomena in Biomolecules and Cells: From Levinthal to Hopfield
Figure 1
The (semi)classical problem of many-electron hypersurface as a potential energy for adiabatically decoupled vibrational and conformational system (with local minima as (semi)classical “positions”, i.e., many-atomic isomer configurations on many-electronic hypersurface (broken line in the figure))—not adiabatically well-defined when traversing between two adjacent local minima—is replaced in the framework of theory of nonradiative resonant transitions [30, 31] by better defined problem of two (virtually intersecting) isomeric many-electronic hypersurfaces (hyperparaboloids) serving as potential hypersurfaces for two vibrational (isomeric) problems (full line in the figure). In this approach, by time-dependent external perturbation of the isomer, at this very intersection, the conditions for electronic-vibrational nonradiative resonant transitions between the two isomers are achieved: in the first approximation, the matrix element of dipole transition from th to th isomer is given by . It is obvious that allowed transitions between isomeric states are possible only for close states with nonvanishing electronic and vibrational dipole moments, and and nonvanishing electronic and vibrational overlap integrals and or in cascade resonant transitions between close intermediate participating isomeric states, which might be related to nondissipative polaron/soliton-like transport [32, 33]. Also, during these resonant transitions the perturbed biomolecular system is shortly described by quantum-coherent superposition , before its quantum decoherence into final electronic state or into initial electronic state (with subsequent deexcitations into lower vibrational states).
