Excitation energy, average dependence

The excitation energy and dynamic properties are evaluated from the time-averaged derivatives of the corresponding time-dependent energy functionals [11, 23-25]. However, a more straightforward way to define dynamic properties is through an expectation value of the corresponding properties over a state / ... 

Macroscopic treatments of diffusion result in continuum equations for the fluxes of particles and the evolution of their concentration fields. The continuum models involve the diffusivity, D, which is a kinetic factor related to the diffusive motion of the particles. In this chapter, the microscopic physics of this motion is treated and atomistic models are developed. The displacement of a particular particle can be modeled as the result of a series of thermally activated discrete movements (or jumps) between neighboring positions of local minimum energy. The rate at which each jump occurs depends on the vibration rate of the particle in its minimum-energy position and the excitation energy required for the jump. The average of such displacements over many particles over a period of time is related to the macroscopic diffusivity. Analyses of random walks produce relationships between individual atomic displacements and macroscopic diffusivity. 

It is also possible to make ab initio calculations of the A s, however, and at the same time to improve the Uns51d scheme by assuming that the A s are dependent on the indices 1, labelling the multipole operators (2 -poles) associated with the excitations. Such a non-empirical Unsold scheme has been proposed by Mulder et The average excitation energy is defined as the ratio ... 

The paramagnetic term depends on the number of electrons in the 2p orbital and multiple bond contributions as well as the average excitation energy A . Therefore, this term will have a significant deshielding effect on n systems. For further discussion the reader is referred to Pople s reference [63]. 

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