Wave function propagation mechanisms

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

The autowave chemical conversion in a film was initiated by a local mechanical disturbance in the form of a puncture or scratch. Figure 14 presents the results of measuring the averaged value of the wave-front propagation velocity as a function of the irradiation dose. It is seen that for... 

Our wish to study how the quantum mechanical subsystem evolves in time requires that we select appropriate operators, that will provide time propagation of the wave functions. These unitary transformation operators are... 

Nuclear motion can be described by quantum mechanical propagation of the vibrational wave function or classical motion on the time-dependent adiabatic potentials. In our approach, the classical equations of motion are solved by the velocity Verlet algorithm. The typical time increment for integration. At, was 0.5 fs. 

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