M. V. Basilevsky

An advanced continuum medium model for treating solvation effects: Nonlocal electrostatics with a cavity

The Born–Kirkwood–Onsager (BKO) model of solvation, where a solute molecule is positioned inside a cavity cut into a solvent, which is considered as a dielectric continuum, is studied within the bounds of nonlocal electrostatics. The nonlocal cavity model is explicitly formulated and the corresponding nonlocal Poisson equation is reduced to an integral equation describing the behavior of the charge density induced in the medium. It is found that the presence of a cavity does not create singularities in the total electrostatic potential and its normal derivatives. Such singularities appear only in the local limit and are completely dissipated by nonlocal effects. The Born case of a spherical cavity with a point charge at its centre is investigated in detail. The corresponding one‐dimensional integral Poisson equation is solved numerically and values for the solvation energy are determined. Several tests of this approach are presented: (a) We show that our integral equation reduces in the local limit to the chief equation of the local BKO theory. (b) We provide certain approximations which enable us to obtain the solution corresponding to the preceding nonlocal treatment of Dogonadze and Kornyshev (DK). (c) We make a comparison with the results of molecular solvation theory (mean spherical approximation), as applied to the calculation of solvation energies of spherical ions.

The 1:1 host-guest complexation between cucurbit[7]uril and styryl dye.

The photophysical properties of aqueous solution of styryl dye, 4-[(E)-2-(3,4-dimethoxyphenyl)ethenyl]-1-ethylpyridinium perchlorate (dye 1), in the presence of cucurbit[7]uril (CB[7]) was studied by means of fluorescence spectroscopy methods. The production of 1:1 host-guest complexes in the range of CB[7] concentrations up to 16 μM with K = 1.0 × 10(6) M(-1) has been observed, which corresponds to appearance of the isosbestic point at 396 nm in the absorption spectra and a 5-fold increase in fluorescence intensity. The decay of fluorescence was found to fit to double-exponential functions in all cases; the calculated average fluorescence lifetime increases from 145 to 352 ps upon the addition of CB[7]. Rotational relaxation times of dye 1 solutions 119 ± 14 ps without CB[7] and 277 ± 35 ps in the presence of CB[7] have been determined by anisotropy fluorescence method. The comparison of the results of quantum-chemical calculations and experimental data confirms that in the host cavity dye 1 rotates as a whole with CB[7].

Nonlocal continuum solvation model with exponential susceptibility kernels

An algorithm is developed for performing calculations for the nonlocal electrostatic solvation theory of an ion in a cavity, accounting for electrostatic boundary conditions. The latter implies an induced charge distribution on the cavity surface as well as an induced volume charge distribution in the medium. This approach is validated by a variational derivation which also provides a general expression for the solvation energy. The procedure, implemented for spherical ions, is tested by calculating the analytic solution for an exponential nonlocal dielectric kernel and determining the corresponding solvation energy. Parametrization is presented for a range of solvents, fitted to experimental solvation energies.

Computations of solvation free energies for polyatomic ions in water in terms of a combined molecular–continuum approach

The combined molecular–continuum approach developed in the preceding paper was applied for calculations of equilibrium solvation energies for a large number of polyatomic ions. The structure and charge distribution of the given ion were computed using the restricted Hartree–Fock level with the 6-31G** basis set. The standard Lennard-Jones (LJ) parameters, which were not specially calibrated to fit the solvation energies, were used in molecular dynamics simulations. Water (the SPC model) was considered as a solvent. The computations show that the new scheme works satisfactorily for nitrogen cations in the frame of a standard parametrization and can be further improved for oxygen ions by tuning solute–solvent LJ parameters. The calculated relative change of the energies in families of similar cations—i.e., ammonium-type or oxonium-type cations—fits the experimental trends. The present approach is specially addressed to separate the inertial contribution to solvation free energies, which is important in view...

An advanced dielectric continuum approach for treating solvation effects: Time correlation functions. I. Local treatment

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 e(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.

Computation of hydration free energies of organic solutes with an implicit water model.

A new approach for computing hydration free energies ΔGsolv of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component ΔGel of ΔGsolv and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (ΔGnel). The novel features include the following: (a) two different cavities are used for treating ΔGel and ΔGnel. For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of ΔGnel is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H‐bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.

Preferential solvation of spherical ions in binary DMSO/benzene mixtures.

We consider a new qualitative approach for treating theoretically the solvation of single-atomic ionic solutes in binary mixtures of polar and nonpolar aprotic solvents. It is based on the implicit continuum electrostatic model of the solvent mixture involving distance-dependent dielectric permittivity epsilon(R) (where R is the distance from the ion) and local concentrations C(1)(R) and C(2)(R) of the solvent ingredients. For a given R, the condition for local thermodynamic equilibrium provides the transcendental equation for explicitly establishing the permittivity and concentration profiles. Computations performed with real Cl(-) and model Cl(+) ions as solutes in benzene/DMSO mixtures are compared with the molecular dynamics simulations of the same systems. A significant discrepancy of molecular and continuum results is revealed for the concentration profiles in the close vicinity of the ion boundary, although the general trends are similar. The continuum methodology cannot account for the formation of rigid solvent structures around ions, which is most significant for the case of Cl(+). Such defect, however, proves to become of less importance in calculations of the solvation free energy, which are quite satisfactory for Cl(-) ion. Free energy calculations for Cl(+) are less successful in the range of low DMSO concentration.

Advanced dielectric continuum model of preferential solvation.

A continuum model for solvation effects in binary solvent mixtures is formulated in terms of the density functional theory. The presence of two variables, namely, the dimensionless solvent composition y and the dimensionless total solvent density z, is an essential feature of binary systems. Their coupling, hidden in the structure of the local dielectric permittivity function, is postulated at the phenomenological level. Local equilibrium conditions are derived by a variation in the free energy functional expressed in terms of the composition and density variables. They appear as a pair of coupled equations defining y and z as spatial distributions. We consider the simplest spherically symmetric case of the Born-type ion immersed in the benzene/dimethylsulfoxide (DMSO) solvent mixture. The profiles of y(R) and z(R) along the radius R, which measures the distance from the ion center, are found in molecular dynamics (MD) simulations. It is shown that for a given solute ion z(R) does not depend significantly on the composition variable y. A simplified solution is then obtained by inserting z(R), found in the MD simulation for the pure DMSO, in the single equation which defines y(R). In this way composition dependences of the main solvation effects are investigated. The local density augmentation appears as a peak of z(R) at the ion boundary. It is responsible for the fine solvation effects missing when the ordinary solvation theories, in which z=1, are applied. These phenomena, studied for negative ions, reproduce consistently the simulation results. For positive ions the simulation shows that z>>1 (z=5-6 at the maximum of the z peak), which means that an extremely dense solvation shell is formed. In such a situation the continuum description fails to be valid within a consistent parametrization.

Nonlocal continuum solvation model with oscillating susceptibility kernels: A nonrigid cavity model

A nonlocal continuum theory of solvation is applied using an oscillatingdielectric function with spatial dispersion. It is found that a convergent solution cannot be calculated using a model of a fixed solute cavity inside the solvent continuum. This is attributed to the fact that the dielectricoscillations appear as a result of coupling between polarization and density fluctuations, contradicting the concept of a fixed cavity. The theory is corrected by allowing the cavity size to vary. A cavitation energy and an interaction between the medium reaction field and the cavity size are added to the solvation free energy, and a new theory obtained by a variational treatment. The interaction term enables convergent solutions to become attainable, resulting in an oscillatingelectrostatic solvation energy as a function of cavity radius, the cavitation term enables these oscillations to be smoothed out, resulting in a regular, monotonic solvation free energy.

Inclusion complexes of β-cyclodextrine with organic ligands: molecular dynamics simulation of the thermodynamic stability in gas phase and in water solution

The double decoupling version of the thermodynamic integration procedure is applied to perform the molecular dynamical modelling of binding free energies of β-cyclodextrine (CD) with a number of organic ligands. Simulations for water solutions show a satisfactory agreement (within 1–2 kcal/mol) with the experimentally measured equilibrium binding constants. The values are also reported for the gas phase complexation of the same ligands, although no experimental data are available for such systems. These gas phase computations have revealed the large stabilisation effect for the CD complexes of ionic ligands. Only in this special case the attempt of a qualitative rationalising the obtained simulation data proved to be fairly successful. The problems specific for simulations for ionic ligands in water solution are discussed.