Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

Theoretical studies of 31P NMR spectral properties of phosphanes and related compounds in solution

Selected theoretical methods, basis sets and solvation models have been tested in their ability to predict 31P NMR chemical shifts of large phosphorous-containing molecular systems in solution. The most efficient strategy was found to involve NMR shift calculations at the GIAO-MPW1K/6-311++G(2d,2p)//MPW1K/6-31G(d) level in combination with a dual solvation model including the explicit consideration of single solvent molecules and a continuum (PCM) solvation model. For larger systems it has also been established that reliable 31P shift predictions require Boltzmann averaging over all accessible conformations in solution

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multi-grid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation (SCCS) model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the PCM model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond forming compounds.Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at http://link.aip.org/link/?jcp

A Combined Discrete/Continuum Solvation Model: Application to Glycine

A new solvation model that combines discrete and continuum descriptions of the solvent has been developed. The discrete solvent molecules are represented by effective fragment potentials (EFP), while the continuum is represented by the Onsager model. This (EFP+Onsager) model has been applied to the relative stabilities of the neutral and zwitterionic forms of glycine. Other supermolecule-continuum calculations were also performed, using quantum mechanical discrete waters and the isodensity polarizable continuum model (IPCM) or solvation model 5.42R (SM5.42R) for the continuum. It is shown that the Onsager model provides a poor description of the solvent in the supermolecule-continuum calculations. On the other hand, more sophisticated models can predict the correct energy order of the glycine isomers. Thus, the development of mixed methods that combine sophisticated continuum models with the discrete EFP model appear to be promising

Erratum: “An advanced dielectric continuum approach for treating solvation effects: Time correlation functions. I. Local treatment” [J. Chem. Phys. 108, 1103 (1998)]

A local continuum solvation theory, exactly treating electrostatic matching conditions on the boundary of a cavity occupied by a solute particle, is extended to cover time-dependent solvation phenomena. The corresponding integral equation is solved with a complex-valued frequency-dependent dielectric function ε(ω), resulting in a complex-valued ω-dependent reaction field. The inverse Fourier transform then produces the real-valued solvation energy, presented in the form of a time correlation function (TCF). We applied this technique to describe the solvation TCF for a benzophenone anion in Debye (acetonitrile) and two-mode Debye (dimethylformamide) solvents. For the Debye solvent the TCF is described by two exponential components, for the two-mode Debye solvent, by three. The overall dynamics in each case is longer than that given by the simple continuum model. We also consider a steady-state kinetic regime and the corresponding rate constant for adiabatic electron-transferreactions. Here the boundary effect introduced within a frequency-dependent theory generates only a small effect in comparison with calculations made within the static continuum model