The Two-state Model of Long-range Interactions

The different components of the C6 dispersion coefficients in the LaTbM scheme for (i) two different linear molecules, and (ii) an atom and a linear molecule, are given in Table 11.2 of Magnasco and Ottonelli (1999) in terms of the symmetry-adapted combinations of the elementary dispersion constants (Equations (4.27). For identical molecules, C = B in (4.27), and the (020) and (200) coefficients are equal. 

Therefore, the determination of the elementary dispersion constants (the quantum mechanical relevant part of the calculation) allows for a detailed analysis of the angle-dependent dispersion coefficients between molecules. 

We turn now to the more recently proposed two-state model of long-range interactions (Magnasco, 2004b). It is of interest in so far as it avoids completely explicit calculation of the matrix elements (Equations 4.12-4.17) occurring in RS perturbation theory, being based only on the fundamental principles of variation theorem and on a classical electrostatic approach. 

For the sake of simplicity, we mix in just two normalized states, an initial state i/ o and a final (orthogonal) state /q, the coefficients in the resulting quantum state if  

Since now 0 Hoi -C Hu—Hoo, the Taylor expansion of A we did in Chapter 2 gives for the lowest root the approximate form  

As an example, explicit expressions of can be given in the case of the dipole polarizability of the H atom and for a few simple VdW interactions which depend on the electrical properties of the molecules such as electric dipole moments and polarizabilities (Stone, 1996). As we have already said, these dipole moments, and the higher ones known generally as multipole moments, can be permanent (when they persist in absence of any external field) or induced (when due, temporarily, to the action of an external field and disappear when the field is removed). 

An atom or molecule distorts under the action of an external field, the measure of distortion being expressed through a second-order electrical quantity called the (dipole) polarizability a, which we define in terms of a transition moment /z, from state ipQ to and an excitation energy Si as  

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Expanded Energy Corrections up to Second Order The Two-state Model of Long-range Interactions... 

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