Perturbation theory for the energy of an atom

A rather more justified theoretical basis exists for the estimates of the corrections for the incompleteness of the angular parts of the orbital basis. It has been shown in [19,20] that the correction to the energy of an atom in the second order perturbation theory is... 

In the homogeneous metal, there are no real" charge fluctuations, just as in the Helium atom there is no real" dipole moment. Van der Waals attraction between two Helium atoms comes about as the result of the correlated quantum fluctuations of a virtual dipole moment induced in each atom by the other. Similarly, an attractive force comes about from correlated, virtual, charge fluctuations In the two planes. I eliminate H from the Hamiltonian to leading order in W. using the operator generalization of second-order perturbation theory for the energy levels. This yields ... 

Turning to molecular physics, we note first papers by Ya.B. which are close to the problem of phase transition. We begin with the theory of interaction of an atom with a metal (11). By applying quantum-mechanical perturbation theory to the interaction of the virtual dipole moment of an atom with conducting electrons of the metal, the dependence on distance of the attractive force of the atom to the surface is obtained. The calculation led to a slow, r2, law for the potential energy decay with distance. This paper was published in 1935, and for many years remained essentially the only one devoted to the subject. 

An example will show the application of some of the ideas introduced above. Let us start with the simple two-ccntcr-two-orbital problem described exhaustively in Chapter 2. In the language of perturbation theory these two orbitals experience a degenerate interaction for the case of H2 where the energies of each atomic orbital are the same. The result is an in-phase (bonding) combination and an out-of-phase (antibonding) combination, between the centers A and B. A more complicated example arises when there are two orbitals on A and one on B as when the orbitals of linear H3 are constructed from those of II2 + H (3.10). This is shown in Figure 3.1, where the relative phases of the orbitals have been chosen so that Sij and are positive. 

A most interesting recent development is the work of Augustin and Rabitz, who obtained a transition between statistical and perturbation theories for any type of collision, not only complex-forming ones. More general stochastic aspects of unimolecular reactions have been discussed by Sole and Widom. An application of a phase-space model to electronic transitions in atomic collisions has been reported, as well as a simple RRKM model for electronic to vibrational energy transfer in 0( Z)) -I- Nj collisions. ... 

The physical properties of atoms and molecules embedded in polar liquids have usually been described in the frame of the effective medium approximation. Within this model, the solute-solvent interactions are accounted for by means of the RF theory [1-3], The basic quantity of this formalism is the RF potential. It is usually variationally derived from a model energy functional describing the effective energy of the solute in the field of an external electrostatic perturbation. For instance, if a singly negative or positive charged atomic system is considered, the RF potential is simply given by... 

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