We present a new integral equation formulation of the polarizable continuum model (PCM) which allows one to treat in a single approach dielectrics of different nature: standard isotropic liquids, intrinsically anisotropic medialike liquid crystals and solid matrices, or ionic solutions. The present work shows that integral equation methods may be used with success also for the latter cases, which are usually studied with three-dimensional methods, by far less competitive in terms of computational effort. We present the theoretical bases which underlie the method and some numerical tests which show both a complete equivalence with standard PCM versions for isotropic solvents, and a good efficiency for calculations with anisotropic dielectrics.

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A direct inversion iterative subspace version of the relaxed constrained algorithm is found to be a very powerful convergence acceleration technique for the solution of the self-consistent field equations found in the Hartree–Fock method and Kohn–Sham-based density functional theory (KS-DFT). The present algorithm, abbreviated EDIIS, is benchmarked against the direct inversion iterative subspace method based on the commutator of the density and Fock matrices developed by Pulay (DIIS). Our findings indicate that while EDIIS is able to rapidly bring the density matrix from any initial guess to a solution region, the DIIS method is faster when the density matrix is close to convergence. Consequently, we propose a combination of EDIIS and DIIS methods, which is both very robust and highly efficient. We also show how EDIIS can detect the presence and determine the value of fractional occupations in KS-DFT.

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In the past years it has become evident that stochastic effects in regulatory networks play an important role, leading to an increasing in stochastic modelling attempts. In contrast, metabolic networks involving large numbers of molecules are most often modelled deterministically. Going towards the integration of different model systems, gen-regulatory networks become part of a larger model system including signalling pathways and metabolic networks. Thus, the question arises of how to efficiently and accurately simulation such coupled or hybrid systems. We present an algorithmic approach for the simulation of hybrid stochastic and deterministic reaction models that allows for adaptive step-size integration of the deterministic equations while at the same time accurately tracing the stochastic reaction events. We present a mathematical derivation of the hybrid system on the stochastic process level, and present numerical examples that outline the power of hybrid simulations.Résumé. Au cours des dernières années, il est devenu clair que les effets aléatoires jouaient un rôle important dans les réseaux de régulation, et les modèles employés aujourd'hui pour décrire ces réseaux sont de nature stochastique. En revanche, les réseaux métaboliques, qui mettent en jeu un grand nombre de molécules, sont le plus souvent décrits par des modèles déterministes. Dans la modélisation de systèmes complexes, réseaux régulateurs de gènes, chemins de signaux et réseaux métaboliques sont intégrés dans un même modèle. Se pose alors la question de simuler efficacement et avec précision de tels modèles couplés (on parle aussi de modèles hybrides). Nous présentons ici une approche pour la simulation de modèles de réactions hybrides stochastiques/déterministes permettantà la fois d'avoir recoursà des pas de temps adaptatifs dans l'intégration deséquations déterministes et de simuler précisément les réactions décrites par des processus stochastiques. Des simulations numériques illustrent la puissance de ces simulations hybrides.

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.