A variational formulation of the polarizable continuum model

Abstract

Articles you may be interested inContinuum solvation models are widely used to accurately estimate solvent effects on energy, structural and spectroscopic properties of complex molecular systems. The polarizable continuum model ͑PCM͒ is one of the most versatile among the continuum models because of the variety of properties that can be computed and the diversity of methods that can be used to describe the solute from molecular mechanics ͑MM͒ to sophisticated quantum mechanical ͑QM͒ post-self-consistent field methods or even hybrid QM/MM methods. In this contribution, we present a new formulation of PCM in terms of a free energy functional whose variational parameters include the continuum polarization ͑represented by the apparent surface charges͒, the solute's atomic coordinates andpossibly-its electronic density. The problem of finding the optimized geometry of the ͑polarized͒ solute, with the corresponding self-consistent reaction field, is recast as the minimization of this free energy functional, simultaneously with respect to all its variables. The numerous potential applications of this variational formulation of PCM are discussed, including simultaneous optimization of solute's geometry and polarization charges and extended Lagrangian dynamics. In particular, we describe in details the simultaneous optimization procedure and we include several numerical examples.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method

“…A detail account of both formalisms can be found elsewhere, and only the final expressions are considered here. 15,[32][33][34][35] No detail about the various flavors of PCM 2,[5][6][7][8][9][10][11][12][13]36 and the solution of the corresponding equations is discussed here since the PCM terms that enter the CC equations take the same form for all of the versions. Although nonequilibrium solvation 2,15,[21][22][23]34 is essential to reproduce experimental transition energies and is used in the calculations reported in Sec.…”

“…In the computational practice, the surface charge is discretized in finite elements and the PCM integral operators are replaced by their matrix representation. Modern implementations of the various flavors of PCM are very efficient, [6][7][8][9][10][11][12][13] and typically only increase the computational cost of self-consistent field methods (SCF), like those developed in Kohn-Sham density functional theory (DFT), by less than 20%. More recently, the coupling of PCM with CC wave functions has been proposed by Cammi,14 although, a similar development was presented by Christiansen and co-workers [15][16][17] on a related solvation model named dielectric continuum (DC).…”

Domain decomposition for implicit solvation models

“…(2) has a simple variational formulation 5 , whose discretization can be solved by the preconditioned conjugated gradient method), and the error made in first principle calculations by assuming that the charge distribution ρ is entirely supported in Ω (which is not the case for the electronic charge density) is smaller 6 .…”

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

“…15,32 This is not the case, however, in the discretized form of the IEF equations as usually reported in the literature (i.e., the matrix U IEF is not symmetric 15 ). We avoided this problem by employing the symmetrized version of the IEF equations as suggested by Lipparini et al, 32 so that Eq. (19) also applies in the discretized form.…”