Ke-Xiang Fu

SOLVATION ENERGY OF NONEQUILIBRIUM POLARIZATION: OLD QUESTION, NEW ANSWER

Although an old question, the electrostatic free energy of nonequilibrium solvation in a continuous dielectric has recently been disputed. Here we show that the nonequilibrium solvation energy can be obtained without any ambiguity by imposing a suitable external electric field with its source localized in the ambient so as to bring the nonequilibrium into an equilibrium state but constrain its charge distribution, polarization, and entropy unchanged. As an application, a two-sphere cavity model is proposed for estimating the solvent reorganization energy, which solves the longstanding issue that it tends to be overestimated by a factor of two by the popular continuum models.

Continuous Medium Theory for Nonequilibrium Solvation: II. Interaction Energy between Solute Charge and Reaction Field and Single-Sphere Model for Spectral Shift

On the basis of continuous medium theory, a model for evaluation of spectral shifts in solution has been developed in this work. The interaction energy between solute dipole and reaction field and the self‐energy of the reaction field have been formulated through derivations. Applying the interaction energy expression together with the point dipole approximation to the case of spherical cavity produces new formulations of spectral shifts. The same expression of electrostatic free energy of the nonequilibrium state is achieved by integrating the change of the electrostatic free energy for a charging process. Moreover, generalized formulations evaluating spectral shifts have been established in the charge‐potential notation, and the reduction of them to the point dipole case consistently leads to the same formulations of spectral shifts as those by interaction energy approach. Mutual supports provide convincing evidences for the reliability of the present results. In this work, attentions are particularly paid to the conclusion of zero self‐energy of the reaction field, which is different from the previous theory. Reasoning and arguments are given on this point. From the present derivations, it is concluded that the spectral shifts of light absorption and emission were theoretically exaggerated in the past, in particular, by a factor of 2 for the spectral shift sum.

Spectral shift of the n → π* transition for acetone and formic acid with an explicit solvent model.

In our recent work, a new form of the electrostatic solvation energy for the nonequilibrium polarization has been derived by introducing the method of constrained equilibrium state in the framework of continuous medium theory. Up until now, the idea of the constrained equilibrium state method has not been introduced into the explicit solvent model by others; therefore this nonequilibrium energy form was further equivalently extended to the explicit solvent model in this work based on the discrete representation of the solvent permanent charges and induced dipoles. Making use of this expression in explicit solvent model, we modified the nonequilibrium module in the averaged solvent electrostatic potential/molecular dynamics program to implement numerical calculations. Subsequently, the new codes were applied to study the solvatochromic shifts of the n → π* absorption spectra for acetone and trans-formic acid in aqueous solution. The calculation results show a good agreement with the experimental observations. When our results of spectral shift are compared with those achieved directly from the continuum model, it can be seen that both the explicit solvent model and continuum model derived based on the constrained equilibrium approach can give reasonable predictions. The hydrogen bond effect was also discussed and deemed to be a dominant contribution to the spectral shift by calculating the n → π* absorption spectra of acetone-water complexes.

Vertical detachment energy of hydrated electron based on a modified form of solvent reorganization energy.

In this work, the constrained equilibrium principle is introduced and applied to the derivations of the nonequilibrium solvation free energy and solvent reorganization energy in the process of removing the hydrated electron. Within the framework of the continuum model, a modified expression of the vertical detachment energy (VDE) of a hydrated electron in water is formulated. Making use of the approximation of spherical cavity and point charge, the variation tendency of VDE accompanying the size increase of the water cluster has been inspected. Discussions comparing the present form of the VDE and the traditional one and the influence of the cavity radius in either the fixed pattern or the varying pattern on the VDE have been made.

Continuous medium theory for nonequilibrium solvation: IV. Solvent reorganization energy of electron transfer based on conductor-like screening model.

In this work the authors present some evidences of defects in the popular continuous medium theories for nonequilibrium solvation. Particular attention has been paid to the incorrect reversible work approach. After convincing reasoning, the nonequilibrium free energy has been formulated to an expression different from the traditional ones. In a series of recent works by the authors, new formulations and some analytical application models for ultrafast processes were developed. Here, the authors extend the new theory to the cases of discrete bound charge distributions and present the correct form of the nonequilibrium solvation energy in such cases. A numerical solution method is applied to the evaluation of solvent reorganization energy of electron transfer. The test calculation for biphenyl–cyclohexane–naphthalene anion system achieves excellent agreement with the experimental fitting. The central importance presented in this work is the very simple and a consistent form of nonequilibrium free energy for both continuous and discrete charge distributions, based on which the new models can be established.

Continuous medium theory for nonequilibrium solvation: III. Solvation shift by monopole approximation and multipole expansion in spherical cavity

According to the classical electrodynamics, a new and reasonable method about electrostatic energy decomposition of the solute‐solvent system has been proposed in this work by introducing the concept of spring energy. This decomposition in equilibrium solvation gives the clear comprehension for different parts of total electrostatic free energy. Logically extending this cognition to nonequilibrium leads to the new formula of electrostatic free energy of nonequilibrium state. Furthermore, the general solvation shift for light absorption/emission has been reformulated and applied to the ideal sphere case with the monopole approximation and multipole expansion. Solvation shifts in vertical ionizations of atomic ions of some series of main group elements have been investigated with monopole approximation, and the variation tendency of the solvation shift versus atomic number has been discussed. Moreover, the solvation shift in photoionization of nitrate anion in glycol has been investigated by the multipole expansion method.

A study on orientation and absorption spectrum of interfacial molecules by using continuum model

In this work, a numerical procedure based on the continuum model is developed and applied to the solvation energy for ground state and the spectral shift against the position and the orientation of the interfacial molecule. The interface is described as a sharp boundary separating two bulk media. The polarizable continuum model (PCM) allows us to account for both electrostatic and nonelectrostatic solute–solvent interactions when we calculate the solvation energy. In this work we extend PCM to the interfacial system and the information about the position and orientation of the interfacial molecule can be obtained. Based on the developed expression of the electrostatic free energy of a nonequilibrium state, the numerical procedure has been implemented and used to deal with a series of test molecules. The time‐dependent density functional theory (TDDFT) associated with PCM is used for the electron structure and the spectroscopy calculations of the test molecules in homogeneous solvents. With the charge distribution of the ground and excited states, the position‐ and orientation‐dependencies of the solvation energy and the spectrum have been investigated for the interfacial systems, taking the electrostatic interaction, the cavitation energy, and the dispersion–repulsion interaction into account. The cavitation energy is paid particular attention, since the interface portion cut off by the occupation of the interfacial molecule contributes an extra part to the stabilization for the interfacial system. The embedding depth, the favorable orientational angle, and the spectral shift for the interfacial molecule have been investigated in detail. From the solvation energy calculations, an explanation has been given on why the interfacial molecule, even if symmetrical in structure, tends to take a tilting manner, rather than perpendicular to the interface.

NEW FORMULATION FOR NON-EQUILIBRIUM SOLVATION: SPECTRAL SHIFTS AND CAVITY RADII OF 6-PROPANOYL-2-(N,N-DIMETHYLAMINO) NAPHTHALENE AND 4-(N,N-DIMETHYLAMINO) BENZONITRILE

In the present work, the new formulations describing spectral shifts by the authors have been introduced and employed to investigate two dye molecules, 6-propanoyl-2-(N,N-dimethylamino) naphthalene and 4-(N,N-dimethylamino) benzonitrile. From the viewpoints of the authors, the cavity radii were overestimated owing to the errors existing in the traditional models. Slightly differing from the results by other authors in the past, this work fits the cavity radii to the values of ~4.5 A for 6-propanoyl-2-(N,N-dimethylamino) naphthalene and ~3.2 A for 4-(N,N-dimethylamino) benzonitrile. In the fittings, both point dipole approximation and multipole expansion methods are employed. The calculations of the excited states are performed by means of the time-dependent density functional theory. Comparing the fitted cavity radii from the experimental spectra with those estimated from the molecular volumes by some well-known procedures such as COSMO and PCM, we find that the new formulations give fairly satisfactory results. By taking an atomic ion as an example, the authors argue that the Onsager radii recommended by some popular procedures are greatly exaggerated. The cavity radius derived simply from the volume encompassed by the solvent-accessible surface, without any addition of other parts, is suggested for application.

Nonequilibrium solvation theory: Comparison, modification and application

Faults existing in the current theories of nonequilibrium solvation have been clarified in this report. Based on a novel expression of solvation free energy for nonequilibrium, generalized formulations of solvent reorganization energy for electron transfer and of solvation shift for spectrum have been established. Furthermore, a new form of solvent reorganization energy for electron transfer in two-sphere case, which greatly differs from the one by Marcus, has been deduced. A single-sphere model for solvation shift of spectrum has been put forward both by deducing the generalized formulations and by showing the correct forms of self-energy of reaction field. It has been concluded that the current theories overestimate the solvent reorganization energy and the solvation shift by a factor of about 2. By applying the models established, the discrepancies between the theory and experiments before have been perfectly explained.

One approach to calculating the solvent reorganization energy of intramolecular electron transfer

On the basis of the electromagnetic field theory and the spherical cavity approximation, the expressions of Gibbs free energies under equilibrium and non-equilibrium solvation conditions are obtained by solving the electrostatic potential equations with boundary conditions. The surface charges produced by the orientational polarization of equilibrium solvation are taken fixed in the case of non-equilibrium situation, for the slow-response of the orientational polarization to electron transfer of the solvent molecules. A new expression of solvent reorganization energy has been obtained and this method is applied to the electron transfer systems, NO+/NO, NO2+/NO2, and NO2+/NO. The solvent reorganization energies have been evaluated.