Hydrophilic Versus Hydrophobic Coupling in the Pressure Dependence of the Chemical Potential of Alkali Metal and Halide Ions in Water.

We computed the chemical potential for some alkali metal ions (K+, Rb+, and Cs+) and two halide ions (Br- and I-) in aqueous solution at ambient T and various pressures in the range 1-8000 atm. Results were obtained from classic Monte Carlo simulations in the NPT ensemble by means of the free energy perturbation method. Here, the chemical potential is computed as the sum of a term relative to a Lennard-Jones solute and a term relative to the process in which this solute is transformed into the ion. Hydrophobic and hydrophilic features of these two components of the chemical potential show opposite behaviors under isothermal compression. The increase in pressure determines an increase in the hydrophobic component, which becomes more positive with a stronger effect for larger ions. Correspondingly, the values of the hydrophilic component become more negative for alkali ions, whereas they are only slightly affected by compression for halide ions. Hydrophobic-hydrophilic quasi-compensation in the slopes is observed for Rb+. For a smaller ion, such as K+, the dependence on pressure of the hydrophilic component is slightly dominant. For a larger ion, as observed in the cases of Cs+, Br-, and I-, the hydrophobic component assumes the determinant role. Pressure dependence of the chemical potential is little affected by corrections introduced for molecular potential truncation. This view can change for possible boundary artifacts that could have affected the static electrostatic potential. Some inference is obtained from comparison with experimental data at 1 atm on the free energy of hydration. Discrepancies show the characteristic asymmetry between cations and anions. The further addition of a correction based on the static potential significantly reduces these discrepancies with important error cancellation on the sum of chemical potentials of ions of opposite charge. The correction is applied also at higher pressures, and results are compared with those obtained by adding an alternative correction that is based on the water number density. Regardless of the ion, changes of the chemical potential induced by an increase in pressure appear to be dominated by the hydrophobic component, in particular when using the alternative correction. For bromide and iodide electrolytes, the two corrections give chemical potentials in good agreement.

Method to Compute the Solute-Solvent Dispersion Contribution to the Electronic Excitation Energy in Solution.

A method formulated within the polarizable continuum model of the solvent and a quantum Monte Carlo treatment of the electronic states of the solute molecule is presented for the calculation of the solute-solvent dispersion contribution to the electronic excitation energy in solution. Variational quantum Monte Carlo is exploited to measure the fluctuations of the electronic electric field of the solute molecule to compute the London's dispersion forces with the solvent. The method previously applied to the ground state of the solute is here extended to excited states. To perform the Casimir-Polder integration, we introduce a positive parameter Ω whose value is properly chosen for this purpose. We derive a general expression that for Ω = 0 reduces to that already proposed for the ground state. For an excited state, Ω must be less than the first transition electronic energy of the solvent molecule but greater than the transition energy from the ground to excited electronic state of the solute molecule. Benchmark calculations were performed on the n → π* transition for formaldehyde, acrolein, and acetone in six solvents, including water, ethanol, cyclohexane, chloroform, carbon tetrachloride, and toluene, and the π → π* transition of acrolein in cyclohexane. Solvents are characterized by their ionization potential and the refractive index at frequency Ω. In all cases, we found that the dispersion solute-solvent interaction stabilizes the excited state of the solutes leading to red (negative) solvatochromic shifts.

Excess Volumes from the Pressure Derivative of the Excess Chemical Potential: Testing Simple Models for Cavity Formation in Water.

Excess volumes and excess compressibilities for hard spheres in water were computed by pressure derivatives of the excess chemical potential, which is equivalent to the work of cavity formation. This is relevant to the application of continuum solvation methods at various pressures. The excess chemical potential was modeled within phenomenological expressions for curved surfaces plus a pressure-volume term, for which two approaches were adopted, differing for the radius of the spherical volume. This implies a different dependence on pressure of parameters. In all cases, in the surface term, for the pressure derivative of parameters of the curvature function, use was made of the previously proposed expressions for the first two moments obtained from the density and radial distribution of oxygens in liquid water. Only for the parameter which has the dimension of surface tension (γ̃) was explicit dependence on pressure considered and results are affected by the specific polynomial used. In agreement with what inferred from simulation results obtained for cavities in TIP4P water, negative and positive adsorptions at the contact radius were extrapolated for a very large cavity at 1 and 8000 atm, respectively. The expressions here employed for the excess chemical potential predict the zero value of asymptotic adsorption to be at a pressure between 500 and 800 atm, which can be compared to results from the revised scaled particle theory. In the same range, for a nanometer-sized cavity, a change of behavior occurs regarding the ratio between the excess Helmholtz free energy and the product between pressure and excess volume.

Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States.

We present for the first time a quantum mechanics/molecular mechanics scheme which combines quantum Monte Carlo with the reaction field of classical polarizable dipoles (QMC/MMpol). In our approach, the optimal dipoles are self-consistently generated at the variational Monte Carlo level and then used to include environmental effects in diffusion Monte Carlo. We investigate the performance of this hybrid model in describing the vertical excitation energies of prototypical small molecules solvated in water, namely, methylenecyclopropene and s-trans acrolein. Two polarization regimes are explored where either the dipoles are optimized with respect to the ground-state solute density (polGS) or different sets of dipoles are separately brought to equilibrium with the states involved in the electronic transition (polSS). By comparing with reference supermolecular calculations where both solute and solvent are treated quantum mechanically, we find that the inclusion of the response of the environment to the excitation of the solute leads to superior results than the use of a frozen environment (point charges or polGS), in particular, when the solute-solvent coupling is dominated by electrostatic effects which are well recovered in the polSS condition. QMC/MMpol represents therefore a robust scheme to treat important environmental effects beyond static point charges, combining the accuracy of QMC with the simplicity of a classical approach.

Study of dispersion forces with quantum Monte Carlo: toward a continuum model for solvation.

We present a general method to compute dispersion interaction energy that, starting from London's interpretation, is based on the measure of the electronic electric field fluctuations, evaluated on electronic sampled configurations generated by quantum Monte Carlo. A damped electric field was considered in order to avoid divergence in the variance. Dispersion atom-atom C6 van der Waals coefficients were computed by coupling electric field fluctuations with static dipole polarizabilities. The dipole polarizability was evaluated at the diffusion Monte Carlo level by studying the response of the system to a constant external electric field. We extended the method to the calculation of the dispersion contribution to the free energy of solvation in the framework of the polarizable continuum model. We performed test calculations on pairs of some atomic systems. We considered He in ground and low lying excited states and Ne in the ground state and obtained a good agreement with literature data. We also made calculations on He, Ne, and F(-) in water as the solvent. Resulting dispersion contribution to the free energy of solvation shows the reliability of the method illustrated here.

Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: acrolein in water.

We investigate here the vertical n → π(*) and π → π(*) transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π(*) case and also improve considerably the shift for the π → π(*) transition.

Solvent Effects on Excited-State Structures: A Quantum Monte Carlo and Density Functional Study.

We present the first application of quantum Monte Carlo (QMC) in its variational flavor combined with the polarizable continuum model (PCM) to perform excited-state geometry optimization in solution. Our implementation of the PCM model is based on a reaction field that includes both volume and surface polarization charges and is determined self-consistently with the molecular wave function during the QMC optimization of the solute geometry. For acrolein, acetone, methylenecyclopropene, and the propenoic acid anion, we compute the optimal exited-state geometries in water and compare our results with the structures obtained with second-order perturbation theory (CASPT2) and other correlated methods, and with time-dependent density functional theory (TDDFT). We find that QMC predicts a structural response to solvation in good agreement with CASPT2 with the only exception of the π → π* state of acrolein where the robustness of the QMC geometry must be contrasted to the sensitivity of the perturbation result to the details of the calculation. As regards TDDFT, we show that all investigated functionals systematically overestimate the geometrical changes from the gas phase to solution, sometimes giving bond variations opposite in trend to QMC.

A density functional and quantum Monte Carlo study of glutamic acid in vacuo and in a dielectric continuum medium.

We present density functional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in QMC, we use a PCM scheme we have developed to include both surface and volume polarization. We investigate the gas-phase protonation thermochemistry of the glutamic acid using a large set of structural conformations, and find that QMC is in excellent agreement with the best available theoretical and experimental results. For the solvated glutamic acid and glutamate ion, we perform DFT calculations for dielectric constants, ε, between 4 and 78. We find that the glutamate ion in the zwitterionic form is more stable than the non-zwitterionic form over the whole range of dielectric constants, while the glutamic acid is more stable in its non-zwitterionic form at ε = 4. The dielectric constant at which the two glutamic acid species have the same energy depends on the cavity size and lies between 5 and 12.5. We validate these results with QMC for the two limiting values of the dielectric constant, and find qualitative agreement with DFT even though the solvent polarization is less pronounced at the QMC level.

Quantum Monte Carlo formulation of volume polarization in dielectric continuum theory.

We present a novel formulation based on quantum Monte Carlo techniques for the treatment of volume polarization due to quantum mechanical penetration of the solute charge density in the solvent domain. The method allows to accurately solve Poisson's equation of the solvation model coupled with the Schrodinger equation for the solute. We demonstrate the performance of the approach on a representative set of solutes in water solvent and give a detailed analysis of the dependence of the volume polarization on the solute cavity and the treatment of electron correlation.

Excess densities and equimolar surfaces for spherical cavities in water.

For hard spheres with a radius up to 10 A in TIP4P water under ambient conditions, the author studies how the excess number of molecules at the accessible surface depends on the radius of the cavity. Simulation results derived from excess volumes are discussed in terms of radial distribution functions (rdfs), which compare well with extended simple point charge and theoretical rdfs from the literature. The excess number of molecules at the accessible surface inserted in the expression which refers to an arbitrary dividing surface enables one to find the position of the equimolar surface. The surface tension corresponding to this dividing surface was obtained from values of the free energy of cavity formation. For radii in the range of the simulation data, its behavior with curvature is quite different from that usually shown in the literature. A model, which describes how the excess number of molecules at the accessible surface changes with the radius, is discussed in the large length limit by examining consistent rdfs described by a simple analytical form. The inclusion in the model of a logarithmic term has also been considered. Comparison with theoretical results from the literature shows a good agreement for a cavity with a radius of 20 A. For a radius of 100 A and beyond, the model predicts instead sharper density profiles. Such differences have a poor effect on the surface tension at the equimolar surface.

Coupling quantum Monte Carlo to a nonlinear polarizable continuum model for spherical solutes.

Starting from the nonlinear dielectric response model of Sandberg and Edholm, we derive an analytical expression of the polarization contribution to the solvation free energy in terms of the electronic density of the solute and the dielectric properties of the solvent. The solvent inhomogeneity is taken into account with the use of a smooth switching function whose spacial variation is established on the basis of how the solvent is arranged around the solute. An explicit form of a local potential representing the solvent effect on the solute is thus obtained by functional analysis. This effective potential can be combined with density functional or quantum chemical methods for the quantum mechanical treatment of the solute. Here, we use quantum Monte Carlo techniques for the solute and apply the method to the hydration of atomic ions finding very good agreement with experimental data.

Modeling the cavitation free energy.

A new expression to compute the cavitation free energy has been derived by integrating a new model to fit its derivative with respect to the cavity radius. The derivatives were obtained from Monte Carlo simulations data of the contact values of distribution functions for hard-sphere solutes in TIP4P water at 298 K and 1 atm. The new expression, formulated in the framework of the thermodynamics of surfaces and unlike the classical simple models, gives good results also for very small cavities with a radius of approximately 1 A. The contribution to the free energy of a term, which depends on the excess number of molecules at the dividing surface, has been taken into account and discussed for the assumed dependence on r of the surface tension. The asymptotic behavior of the derivative has thus been considered, and a function t(r), which is 0 at r = 0 and 1 at infinity, has been introduced to describe the transition from small to large length regimes. The value of the surface tension obtained by fitting is in very good agreement with that obtained from a simulation of the liquid/vapor interface by using the TIP4P model.