Continuous and smooth potential energy surface for conductorlike screening solvation model using fixed points with variable areas

Abstract

Rigorously continuous and smooth potential energy surfaces, as well as exact analytic gradients, are obtained for a conductorlike screening solvation model ͑CPCM, a variant of the general COSMO͒ with Hartree-Fock ͑RHF, ROHF, UHF, and MCSCF͒ and density functional theory ͑R-DFT, RO-DFT, and U-DFT͒ methods using a new tessellation scheme, fixed points with variable areas ͑FIXPVA͒. In FIXPVA, spheres centered at atoms are used to define the molecular cavity and surface. The surface of each sphere is divided into 60, 240, or 960 tesserae, which have positions fixed relative to the sphere center and areas scaled by switching functions of their distances to neighboring spheres. Analytic derivatives of the positions and areas of the surface tesserae with respect to atomic coordinates can be obtained and used to evaluate the solvation energy gradients. Due to the accurate analytic gradients and smooth potential energy surface, geometry optimization processes using these methods are stable and convergent.

Comment on “A smooth, nonsingular, and faithful discretization scheme for polarizable continuum models: The switching/Gaussian approach” [J. Chem. Phys. 133, 244111 (2010)]

“…They compare such discretization scheme with a few others previously published in the literature. [3][4][5] In particular, they implemented elements of the scheme described by us within the context of the continuous surface charge (CSC) formalism 5,6 for PCM in order to assess its quality and performance against the SWIG scheme. They refer to this modified CSC scheme as "subSWIG" and, at times, as "CSC/subSWIG."…”

New methods for computational drug design

“…For the FMO calculations, we used the recent completely analytical RHF/C-PCM gradient [44]. All PCM calculations were done using the FIXPVA [45] tesselation scheme with 60 tesserae per sphere. All geometry optimizations used a convergence criterion of 5.0 × 10 −4 Hartree/Bohr, unless noted otherwise.…”

Smooth potential energy surface for cavitation, dispersion, and repulsion free energies in polarizable continuum model

“…For example, compared with GEPOL, FIXPVA produces solvation energy that is 1.1 kcal/mol smaller in magnitude for acetate anion, which has a solvation free energy around Ϫ80 kcal/mol. 1 However, the G cav , G dis , and G rep in Eqs. ͑1͒-͑3͒ are sensitive to the surface areas.…”

“…For the calculation of G ele , values of 0.02, 0.3, 1.0, and 1.5 Å, respectively, were selected for the four parameters m 1 , m 2 , n 1 , and n 2 in the FIXPVA switching functions. 1 Using these parameters, FIXPVA produces solute surface roughly 10% less than the surface area computed from GEPOL. Fortunately, the G ele is insensitive to the modifications of the tessera areas.…”

“…Using the FIXPVA tessellation scheme, smooth potential energy surfaces and analytic gradients for the electrostatic solvation free energy ͑G ele ͒ in both conductorlike screening model and conductorlike ͑PCM͒, have been obtained. 1,11 In FIXPVA, the area of a tessera is scaled by switching functions of its distances to neighboring spheres. For the calculation of G ele , values of 0.02, 0.3, 1.0, and 1.5 Å, respectively, were selected for the four parameters m 1 , m 2 , n 1 , and n 2 in the FIXPVA switching functions.…”