Gennady N. Chuev

An accurate prediction of hydration free energies by combination of molecular integral equations theory with structural descriptors.

In this work, we report a novel method for the estimation of the hydration free energy of organic molecules, the structural descriptors correction (SDC) model. The method is based on a combination of the reference interaction site model (RISM) with several empirical corrections. The model requires only a small number of chemical descriptors associated with the main features of the chemical structure of solutes: excluded volume, branch, double bond, benzene ring, hydroxyl group, halogen atom, aldehyde group, ketone group, ether group, and phenol fragment. The optimum model was selected after testing of different RISM free energy expressions on a training set of 65 molecules. We show that the correction parameters of the SDC model are transferable between different chemical classes, which allows one to cover a wide range of organic solutes. The new model substantially increases the accuracy of calculated HFEs by RISM giving the standard deviation of the error for a test set of 120 organic molecules around 1.2 kcal/mol.

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.

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.

Hydration of ionic species studied by the reference interaction site model with a repulsive bridge correction.

We have tested the reference interaction site model (RISM) for the case of the hypernetted chain (HNC) and the partially linearized hypernetted chain (PLHNC) closures improved by a repulsive bridge correction (RBC) for ionic hydrated species. We have analyzed the efficiency of the RISM/HNC+RBC and RISM/PLHNC+RBC techniques for decomposition of the electrostatic and the nonpolar hydration energies on the energetic and the enthalpic parts for polyatomic ions when the repulsive bridge correction is treated as a thermodynamic perturbation, and investigate the repulsive bridge effect on the electrostatic potential induced by solvent on solute atoms. For a number of univalent and bivalent atomic ions, molecular cations, and anions, the method provides hydration energies deviating only by several percents from the experimental data. In most cases, the enthalpic contributions to the free energies are also close to the experimental results. The above models are able to satisfactory predict the hydration energies as well as the electrostatic potential around the ionic species. For univalent atomic ions, they also provide qualitative estimates of the Samoilov activation energies.

An Operational Haar Wavelet Method for Solving Fractional Volterra Integral Equations

An operational Haar wavelet method for solving fractional Volterra integral equations A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

Reference interaction site model study of self-aggregating cyanine dyes

Using the reference interaction site model and supramolecular approach, we modeled the aggregation of thea-monomethinecyanine dyes in water. Various modifications of the hypernetted-closure expression for the excess free energy have been studied. We found that the partial wave approximation with semiempirical corrections for excluded volume and hydrogen bonding effects provides estimations of the binding and dimerization energies of the aggregates, which are in agreement with available experimental data. The hydrated H-dimers are obtained to be more stable than the hydrated J-dimers. However, the complexes consisting from more than four monomers change their arrangement while self-assembling in water and form ladderlike structures. We propose a model explaining this structural transition.

A structured low-rank wavelet solver for the Ornstein-Zernike integral equation

In this article, we present a new structured wavelet algorithm to solve the Ornstein-Zernike integral equation for simple liquids. This algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank approximations of the obtained convolution matrices. The fundamental properties of wavelet bases such as the interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets and Newton-Raphson algorithm, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.

In silico screening of bioactive and biomimetic solutes using Integral Equation Theory

The Integral Equation Theory (IET) of Molecular Liquids is a theoretical framework for modelling solution phase behaviour that has recently found new applications in computational drug design. IET allows calculation of solvation thermodynamic parameters at significantly lower computational expense than explicit solvent simulations, but also provides information about the microscopic solvent structure that is not accessible by implicit continuum models. In this review we focus on recent advances in two fields of research using these methods: (i) calculation of the hydration free energies of bioactive molecules; (ii) modelling the aggregation of biomimetic molecules. In addition, we discuss sources of experimental solvation data for druglike molecules.

Integral Equation Theory of Molecular Solvation Coupled with Quantum Mechanical/Molecular Mechanics Method in NWChem Package.

We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and quantum mechanical/molecular mechanics (QM/MM) methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into consequent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce significantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through computation of the water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.

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.