Coupling kinetic energy

Explicit forms of the coefficients Tt and A depend on the coordinate system employed, the level of approximation applied, and so on. They can be chosen, for example, such that a part of the coupling with other degrees of freedom (typically stretching vibrations) is accounted for. In the space-fixed coordinate system at the infinitesimal bending vibrations, Tt + 7 reduces to the kinetic energy operator of a two-dimensional (2D) isotropic haiinonic oscillator. 

Figure 7-15. Healing and equilibration phase of a typical MD simulation, In the ideal case, the temperature should fluctuate around the desired value (here 298 K), and the potential energy should remain constant. Remember that the total energy is the sum of potential and kinetic energy, the latter being directly coupled to the temperature of the system,...

Here, ej f are the vibration-rotation energies of the initial (anion) and final (neutral) states, and E denotes the kinetic energy carried away by the ejected electron (e.g., the initial state corresponds to an anion and the final state to a neutral molecule plus an ejected electron). The density of translational energy states of the ejected electron is p(E) = 4 nneL (2meE) /h. We have used the short-hand notation involving P P/p to symbolize the multidimensional derivative operators that arise in the non BO couplings as discussed above ... 

By introducing the simplest semi-classical approximation to the propagators, in which the nuclear motion kinetic energy is assumed to commute with the anion and neutral potential energy functions and with the non BO coupling operators, one obtains... 

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