Wavelet treatment of radial distribution functions of solutes

Hydration structure of salt solutions from ab initio molecular dynamics

The solvation structures of Na(+), K(+), and Cl(-) ions in aqueous solution have been investigated using density functional theory (DFT) based Car-Parrinello (CP) molecular dynamics (MD) simulations. CPMD trajectories were collected for systems containing three NaCl or KCl ion pairs solvated by 122 water molecules using three different but commonly employed density functionals (BLYP, HCTH, and PBE) with electron correlation treated at the level of the generalized gradient approximation (GGA). The effect of including dispersion forces was analyzed through the use of an empirical correction to the DFT-GGA scheme. Special attention was paid to the hydration characteristics, especially the structural properties of the first solvation shell of the ions, which was investigated through ion-water radial distribution functions, coordination numbers, and angular distribution functions. There are significant differences between the present results obtained from CPMD simulations and those provided by classical MD based on either the CHARMM force field or a polarizable model. Overall, the computed structural properties are in fair agreement with the available experimental results. In particular, the observed coordination numbers 5.0-5.5, 6.0-6.4, and 6.0-6.5 for Na(+), K(+), and Cl(-), respectively, are consistent with X-ray and neutron scattering studies but differ somewhat from some of the many other recent computational studies of these important systems. Possible reasons for the differences are discussed.

3D WAVELET TREATMENT OF SOLVATED BIPOLARON AND POLARON

Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.

Absolute hydration free energy scale for alkali and halide ions established from simulations with a polarizable force field

A polarizable potential function for the hydration of alkali and halide ions is developed on the basis of the recent SWM4-DP water model [Lamoureux, G.; MacKerell, A. D., Jr.; Roux, B. J. Chem. Phys. 2003, 119, 5185]. Induced polarization is incorporated using classical Drude oscillators that are treated as auxiliary dynamical degrees of freedom. The ions are represented as polarizable Lennard-Jones centers, whose parameters are optimized to reproduce the binding energies of gas-phase monohydrates and the hydration free energies in the bulk liquid. Systematic exploration of the parameters shows that the monohydrate binding energies can be consistent with a unique hydration free energy scale if the computed hydration free energies incorporate the contribution from the air/water interfacial electrostatic potential (-540 mV for SWM4-DP). The final model, which can satisfyingly reproduce both gas and bulk-phase properties, corresponds to an absolute scale in which the intrinsic hydration free energy of the proton is -247 kcal/mol.

Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions

Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.

Wavelet treatment of structure and thermodynamics of simple liquids

A new algorithm is developed to solve integral equations for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions. The Coifman 2 basis set is employed for the wavelet treatment. To solve integral equations we have applied the combined scheme in which the coarse part of the solution is calculated by wavelets, while the fine part by the direct iterations. Tests on the PY and HNC approximations have indicated that the proposed procedure is more effective than the conventional method based on the hybrid algorithm. Possibilities for application of the method to molecular liquids and mixed quantum-classical systems are discussed.

Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.