Instantaneous interaction energy

Figure 6.5 Dynamics of a classical electric dipole induced and driven on resonance by a sequence of two phase-locked ultrashort laser pulses, The driving laser field is shown as gray solid lines in all frames, In addition, the top frames show the induced dipole oscillation as a black dashed line. The instantaneous interaction energy V(t) of the induced dipole in the external driving field is shown in the bottom frames as a black dotted line. Bold black lines display the time average of the interaction energy In Figure 6,5a, the phase relation between both pulses is designed such that the second pulse couples in antiphase to...

The focus of the bonding analysis is the instantaneous interaction energy, of the bond, which is the calculated energy difference between the molecule and the fragments in the frozen geometry of the compound. The interaction energy is divided into three main components ... 

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

Dispersion Interactions. Last but not least in the range of solute-solvent electrostatic interactions come the dispersion forces which depend on the polarizabilities of the molecules. Any atom or molecule—non-polar or polar—has a small fluctuating dipole moment as the electrons move around the nuclei. These instantaneous dipoles induce dipole moments in all other polarizable molecules, so that the interaction energy is proportional to the product of the average polarizabilities aM and as of the solute and solvent molecules... 

The dispersion or London forces [43] between adsorbed nonpolar molecules and any adsorbent emerges when the transient dipoles, become correlated. As a result, the instantaneous dipole of the adsorbed nonpolar molecule induces a dipole in the adsorbent atoms, and, subsequently, both interact to lower the energy of the adsorbate-adsorbent system. Due to the correlation, the attraction between the instantaneous dipoles, developed in the entire system, does not vanish, and produces an induced-dipole-induced-dipole interaction energy, described by the following equation ... 

The previous components of the interaction energy can be derived in the independent particle approximation and so appear within the context of Hartree-Fock level calculations. Nevertheless, inclusion of instantaneous correlation will affect these properties. Taking the electrostatic interaction as an example, the magnimde of this term, when computed at the SCF level, will of course be dependent on the SCF electron distributions. The correlated density will be different in certain respects, accounting for a different correlated electrostatic energy. The difference between the latter two quantities can be denoted by the correlation correction to the electrostatic energy. 

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