Subsystems electronic charges

We consider a cluster of AT He atoms of mass m and radius ro, together with a single excess electron. The subsystem of the helium atoms will be treated by the density functional formalism [113, 247]. The excess electron will be treated quantum mechanically. The energetics and charge distribution of the electron were calculated within the framework of the adiabatic approximation for each fixed nuclear configuration. 

In other words, the two scaled subsystem external potentials are defined to give rise to the true ground state densities of interacting subsystems, irrespectively of the current value of the the scaled electronic charge, which we indicate by the following mapping relation ... 

Figure 2. Uniform (1) and nonuniform (2-6) scaling paths of electronic charges in the complementary subsystems of M = (i4 B). The subsystem external potentials of the scaled hamiltonians for the starting and end points of each path are also listed, with the upper (lower) entries corresponding to ti (B).

The above definition of the external potentials coupled to densities of the nonuniformly scaled electronic charges of subsystems in - (A, A g) again implies for the two extreme imiform scaling points [see Fig. 2 and Eq.(44)] ... 

Examples of a non-uniform scaling of the subsystem electronic charges ame represented by the paths 2-6 in Fig. 2 we have summarized in the figure Eqs. (44) and (53)-(55) identifying the subsystem scaled external potentials corresponding to the four points defining these scaling trajectories. 

Some of these ideas could be generalized to a classification scheme for substituents in terms of their donor (D) and acceptor (A) properties. Following the usual partition procedure, four groups were specified (1) o acceptor and 7t acceptor, (2) o donor and 71 acceptor, (3) o donor and ti donor, and (4) o acceptor and 7t donor. Substituted benzenes were considered, and each system was partitioned in two subsystems. Subsystem A consisted of the benzene ring and subsystem B of the substituents. The change of electronic charge in the carbon framework of the ring due to substitution was defined as... 

Here we introduced the operator of the total (nuclear and electronic) charge density of the L-th subsystem ... 

The QM/MM interactions (Eqm/mm) are taken to include bonded and non-bonded interactions. For the non-bonded interactions, the subsystems interact with each other through Lennard-Jones and point charge interaction potentials. When the electronic structure is determined for the QM subsystem, the charges in the MM subsystem are included as a collection of fixed point charges in an effective Hamiltonian, which describes the QM subsystem. That is, in the calculation of the QM subsystem we determine the contributions from the QM subsystem (Eqm) and the electrostatic contributions from the interaction between the QM and MM subsystems as explained by Zhang et al. [13],... 

The atom system is formed from oppositely charged masses of nucleus and electrons. In this system energy characteristics of subsystems are the orbital energy of electrons (W,) and effective energy of nucleus that takes into consideration the screening effects (by Clementi). 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

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