Instantaneous, population

That is, the classical DoF propagate according to a mean-field potential, the value of which is weighted by the instantaneous populations of the different quantum states. A MFT calculation thus consists of the self-consistent solution of the time-dependent Schrodinger equation (28) for the quantum DoF and Newton s equation (32) for the classical DoF. To represent the initial state (15) of the molecular system, the electronic DoF dk Q) as well as the nuclear DoF xj Q) and Pj 0) are sampled from a quasi-classical phase-space distribution [23, 24, 26]. 

Computed fits of experimental signals probed at different wavelengths allow for the careful investigation of ultrafast electronic pathways (Fig.2). The transient signal at 400 nm is assigned to a very short-lived CTTS state of aqueous hydroxyl ions (OH), . This excited state is instantaneously populated, typically in less than 50 fs and follows a pseudo first order dynamics with a frequency rate of 5 x 1012 s. Semi-quantum MD simulations emphasize that transient excited CTTS states play a crucial role in photoinduced electron transfers [4-6]. 

Fig. 31. Diminution of differential heat of adsorption through addition of molecules to weakly held substates. Heat is estimated for instantaneous population at 298°K as determined by flash desorption. Contribution of individual states a, f lt f t, jSj based on constant energy of 20, 53, 75 and 100 keal/mole respectively.

It should be emphasized that eqn [61] is an instantaneous distribution, that is, the distribution of the chains generated during the time interval from t to t+At. The parameters z and p as defined in eqns [56] and [57] change during polymerization. The final produrt is thus the sum of all instantaneous populations accumulated inside a reactor... 

The formulations of the population balance equation based on the continuum mechanical approach can be split into two categories, the macroscopic- and the local instantaneous population balance equation formulations. The macroscopic approach consists in describing the evolution of a number density in time and space of several groups or classes of the dispersed phase properties. 

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