Improvements of DRISM calculations: symmetry reduction and hybrid algorithms

Abstract

We present a symmetry-reduced version of the dielectrically-consistent reference interaction site model (DRISM) equation and an adaptation of the Labík-Malijevský-Vonka hybrid algorithm for its numerical solution. This approach is used for the calculation of site-site correlation functions of water, acetone and a water-acetone mixture. Compared to the traditional Picard iteration of non-reduced DRISM theories, savings of more than 90% in computational time are obtained. The resulting site-site pair-correlation functions are in reasonable agreement with computer simulations.

Biomolecular electrostatics and solvation: a computational perspective

“…The 1D-RISM (Reference Interaction Site Model) theory provides site-site radial distribution functions coming from an angular average over the orientation of both solute and solvent molecules (see Figure 3). This approach has been successfully applied to small molecules in general (Chuev & Fedorov, 2004; Du et al, 2008; Du et al,2000; Freedman & Truong, 2004; Frolov et al, 2011; Imai et al, 2007; Imai et al, 2000; Kiyota et al, 2009; Kiyota et al, 2011; Kovalenko & Hirata, 1998; Kovalenko & Hirata, 1999; Kovalenko & Hirata 2000a; Kovalenko & Hirata, 2000c; Kovalenko & Hirata, 2000b; Maruyama et al, 2010; Miyata & Hirata, 2008; Nishiyama et al, 2009; Stumpe et al, 2011; Woelki et al, 2008; Yoshida et al, 2006). Unlike the 1D model, 3D-RISM keeps the orientational dependence of solute molecules, which is necessary to properly describe solvation properties of large molecular solutes.…”

Solvation Thermodynamics of Organic Molecules by the Molecular Integral Equation Theory: Approaching Chemical Accuracy

“…We note that the Newton-Raphson (NR) method itself is not typically an efficient way to solve IET equations because it requires the calculation and inversion of a large Jacobian matrix. In this hybrid methods, the dimensionality of the Newton-Raphson part is reduced by expansions of the IET equations in basis sets of roof functions, 244 plane waves [245][246][247] or wavelets. 221,248,249 In the third category are procedures for solving the OZ equation using matrix-free iterative Krylov or Newton-GMRES solvers.…”

In Silico Screening of Bioactive and Biomimetic Solutes Using Molecular Integral Equation Theory

“…In the first category there are methods based on Picard iterations with techniques like vector extrapolation or iterative subspace extrapolation used to improve the convergence [42,[48][49][50]. In the second category there are hybrid Newton-Raphson/Picard iteration methods [51][52][53][54][55][56][57][58][59][60], which have been combined with expansions of the RISM equations in basis sets of roof functions [51], plane waves [52,55,60] or wavelets [57][58][59]. We note that the Newton-Raphson (NR) method cannot typically be applied directly to solve the RISM equations because it would require the calculation and inversion of a Jacobian matrix of a size > 10 4 .…”