Cavity fields total energy calculations

The total energy (161) of the field inside the cavity (above the initial Casimir level) can be obtained by integrating the density W(x) (166) over x. The contribution of the vacuum [function Fq in (167)] and diagonal terms (given by the partial sum in (167) over n = k) can be calculated with the aid of the formula... 

Figure 11.2 Comparison of total energies (on a logarithmic scale) for aqueous amino acids, where the solute is described using the amber99 force field and the solvent is a dielectric continuum. The continuum electrostatics problem is solved either by finite-difference solution of Poisson s equation using the APBS software [5], or else using two different forms of lEF-PCM (X = DAS orX = SAD as described in Section 11.2.2.1). What is plotted is the difference ief-pcm — E apbs between these two solutions. The APBS and lEF-PCM solute cavities are identical. APBS calculations used a 193 x 193 x 193 grid with a grid resolution of 0.1 A, whereas lEF-PCM calculations used 590 Lebedev points per atomic sphere with Gaussian blurring.

The data presented above demonstrate that the total solvation free energy of organic compounds in aqueous solution can be calculated with some confidence using a minimum number of parameters (the dielectric constant and the solute cavity size contibution for the solvent) and provided that appropriate quantum chemical and statistical physical models are used for the description of the reaction field and dispersion interactions, and the cavity formation in solution. 

Thus the cavity polariton dispersion has a simple interpretation. Let us calculate the electric fields from eqn (10.7) for the modes (10.16). Neglecting small terms of the order of q2 /n2, the fields Ei and Et are related in these modes by Ei = —Et cot (p. Then the y-component of the fields Eu,l is equal to zero. In other words, with accuracy up to small terms (of the order of q2 /k2) the total in-plane electric field in the polaritonic modes is parallel to the dipole moment Pi for any direction of the wavevector q, and the value of the Rabi splitting energy thus does not depend on the wavevector direction. 

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