We developed a technique to decrease memory requirements when solving the integral equations of three-dimensional (3D) molecular theory of solvation, a.k.a. 3D reference interaction site model (3D-RISM), using the modified direct inversion in the iterative subspace (MDIIS) numerical method of generalized minimal residual type. The latter provides robust convergence, in particular, for charged systems and electrolyte solutions with strong associative effects for which damped iterations do not converge. The MDIIS solver (typically, with 2 × 10 iterative vectors of argument and residual for fast convergence) treats the solute excluded volume (core), while handling the solvation shells in the 3D box with two vectors coupled with MDIIS iteratively and incorporating the electrostatic asymptotics outside the box analytically. For solvated systems from small to large macromolecules and solid-liquid interfaces, this results in 6- to 16-fold memory reduction and corresponding CPU load decrease in MDIIS. We illustrated the new technique on solvated systems of chemical and biomolecular relevance with different dimensionality, both in ambient water and aqueous electrolyte solution, by solving the 3D-RISM equations with the Kovalenko-Hirata (KH) closure, and the hypernetted chain (HNC) closure where convergent. This core-shell-asymptotics technique coupling MDIIS for the excluded volume core with iteration of the solvation shells converges as efficiently as MDIIS for the whole 3D box and yields the solvation structure and thermodynamics without loss of accuracy. Although being of benefit for solutes of any size, this memory reduction becomes critical in 3D-RISM calculations for large solvated systems, such as macromolecules in solution with ions, ligands, and other cofactors.
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