Outlying Charge, Stability, Efficiency, and Algorithmic Enhancements in the Quantum‐Mechanical Solvation Method, COSab‐GAMESS

Abstract

This and the companion paper are dedicated to Professor Duilio Arigoni on the occasion of his 75th birthday.His steadfast work focused on the structure and biosynthesis of natural products, and mechanisms and stereochemistry of related biochemical processes, foreshadows important insights in our own investigations presented here.In this work, we present algorithmic modifications and extensions to our quantum-mechanical approach for the inclusion of solvent effects by means of molecule-shaped cavities. The theory of conductor-like screening, modified and extended for quantum-mechanical techniques, serves as the basis for our solvation methodology. The modified method is being referred to as COSab-GAMESS and is available within the GAMESS package. Our previous work has emphasized the implementation of this model by way of a distributed multipole approach for handling the effects of outlying charge. The method has been enabled within the framework of open-and closed-shell RHF and MP2. In the present work, we present a) a second method to handle outlying charge effects, b) algorithmic extensions to open-and closed-shell density-functional theory, second-derivative analysis, and reaction-path following, and c) enhancements to improve performance, convergence, and predictability. The method is now surtable for large molecular systems. New features of the enhanced continuum model are highlighted by means of a set of neutral and charged species. Computations on a series of structures with roughly the same molecular shape and volume provides an evaluation of cavitation effects.Introduction. ± In the development and refinement of continuum-solvation models (CSMs), highly accurate continuum-dielectric models are a desirable endpoint [1 ± 6]. Noncoupled iterative solute-specific shell approaches, including those of higher-order quantum-mechanical methods, such as coupled cluster [7] [8], M˘llerÀPlesset [9 ± 11], and multiconfigurational theories [12 ± 14], are now applied in this pursuit. Nonetheless, it is instructive to focus on some fine details of continuum-model implementations relevant for accurate predictions of chemical and biochemical systems, as well as in the efficiency and extensibility of CSMs. Particularly pertinent to our −COSab× model, are details that include methods to incorporate outlying-charge effects (which are mostly lost in the evaluation of E diel ) [15], nonelectrostatic components of the total solvation energy (e.g., cavitation), and self-consistency and convergence properties. As well, we have now implemented the ability to carry out open-and closed-shell densityfunctional-theory (DFT) computations, second-derivative analysis, and reaction-pathfollowing studies, which provide substantial upgrades to our model capabilities.

Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions

“…NPE solvers that employ the continuous charge density (without approximating it by distributed point charges or multipoles) will be further called density-based solvation models. An example of such models is the polarizable continuum model (PCM). , Various PCM formulations include the integral-equation-formalism protocol (IEF-PCM), − the dielectric version of PCM (D-PCM), ,, and the conductor-like screening algorithm. − It has been shown that the IEF-PCM formalism is equivalent to the SS(V)PE method of Chipman . Other implicit solvation models solve the NPE using alternative representations of the continuous density, for example, single- or multicenter multipolar expansions. − An alternative continuum model, the generalized Born (GB) approximation, − does not start with the NPE, but instead employs a starting point based on Coulomb’s law and represents the solute as a collection of point charges (a distributed monopole approximation), located at the nuclear positions.…”

“…However, the SMD parameters may also be used with other algorithms for solving the NPE in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm called, in various implementations, which sometimes differ in details, COSMO, generalized COSMO (GCOSMO), COSab, conductor-like PCM (CPCM or C-PCM), or CD-COSMO. − Here we use C-PCM to label the implementations called C-PCM in Gaussian03 and GAMESS, − and we use COSMO to label the implementation called COSMO in NWChem . C-PCM and COSMO solve the nonhomogeneous Poisson equation for an infinite dielectric constant (corresponding to the solvent being a conductor rather than a dielectric) but with scaled dielectric boundary conditions in order to approximate the result for a finite dielectric constant; this is a better approximation at high dielectric constant (e.g., 80) than at low dielectric constant (e.g., below 10).…”

“…2,3 Various PCM formulations include the integral-equation-formalism protocol (IEF-PCM), [4][5][6][7] the dielectric version of PCM (D-PCM), 2,3,8 and the conductor-like screening algorithm. [9][10][11][12][13][14][15] It has been shown 16 that the IEF-PCM formalism is equivalent to the SS(V)PE method of Chipman. 17 Other implicit solvation models solve the NPE using alternative representations of the continuous density, for example, singleor multicenter multipolar expansions.…”

Defined-Sector Explicit Solvent in Continuum Cluster Model for Computational Prediction of pKa: Consideration of Secondary Functionality and Higher Degree of Solvation

“…All calculations were performed with the GAMESS electronic structure program . Full optimizations were carried out including effects of solvation via the DSES-CC model, using B97-D/6-311+G­(2d,p)/COSab, with our most recent implementation of COSab solvation model. − Parameter optimization for several combinations of DFT functional type and basis sets have been carried out within the solvation model in previous work . In our initial development of the DSES-CC model, investigation covering basis set, wave function type, thermodynamic cycle, reaction scheme, and solvent parameters were carried out .…”

“…Dielectric permittivity of water (ε = 78.4) was used, with cavity parameters of 1082 points for the basic grid, 92 segments on the complete sphere. Outlying charge error correction was taken into account via the double cavity approach . DSES-CC representations were depicted using MacMolPlt …”