Polarizable continuum model numerical methods

In a previous contribution in this book, Cancfes has presented the formal background of the integral equation methods for continuum models and has shown how the corresponding equations can be solved using numerical methods. In this chapter the specific aspects of the implementation of such numerical algorithms within the framework of the Polarizable Continuum Model (PCM) [1] family of methods will be considered. 

Abstract The computational study of excited states of molecular systems in the condensed phase implies additional complications with respect to analogous studies on isolated molecules. Some of them can be faced by a computational modeling based on a continuum (i.e., implicit) description of the solvent. Among this class of methods, the polarizable continuum model (PCM) has widely been used in its basic formulation to study ground state properties of molecular solutes. The consideration of molecular properties of excited states has led to the elaboration of numerous additional features not present in the PCM basic version. Nonequilibrium effects, state-specific versus linear response quantum mechanical description, analytical gradients, and electronic coupling between solvated chromophores are reviewed in the present contribution. The presentation of some selected computational results shows the potentialities of the approach. 

An overview of the Polarizable Continuum Model (PCM) for the modelling of solvent effects on the state and the properties of quantum mechanical molecular systems is presented. The main theoretical and numerical aspects of this method are presented and discussed, together with its extension to the derivative theory. We present some selected applications concerning the evaluation of molecular response properties, and of the corresponding spectroscopic quantities, of different solvated systems. 

Methods based on an ASC have a long history in quantum-mechanical (QM) calculations with continuum solvent [60, 61, 77], where they are generally known as polarizable continuum models (PCMs). However, PCMs have seen little use in the area of biomolecular electrostatics, for reasons that are unclear to us. In the QM context, such methods are inherently approximate, even with respect to the model problem defined by Poisson s equation, owing to the volume polarization that results from the tail of the QM electron density that penetrates beyond the cavity and into the continuum [13, 14, 89], The effects of volume polarization can be treated only approximately within the ASC formalism [14, 15, 89], For a classical solute, however, there is no such tail and certain methods in the PCM family do afford a numerically exact solution of Poisson s equation, up to discretization errors that are systematically eliminable. Moreover, ASC methods have been generalized to... 

We have calculated the second- and fourth-order dipole susceptibilities of an excited helium atom. Numerical results have been obtained for the ls2p Pq-and ls2p f2-states of helium. For the accurate calculations of these quantities we have used the model potential method. The interaction of the helium atoms with the external electric held F is treated as a perturbation to the second- and to the fourth orders. The simple analytical expressions have been derived which can be used to estimate of the second- and higher-order matrix elements. The present set of numerical data, which is based on the Green function method, has smaller estimated uncertainties in ones than previous works. This method is developed to high-order of the perturbation theory and it is shown specihcally that the continuum contribution is surprisingly large and corresponds about 23% for the scalar part of polarizability. 

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