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.

Nonequilibrium solvation energy by means of constrained equilibrium thermodynamics and its application to self-exchange electron transfer reactions.

This work presents a self-consistent thermodynamic approach to nonequilibrium solvation energy. By imposing an extra electric field onto the nonequilibrium solvation system, a constrained equilibrium state is prepared. New expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. The numerical algorithm combining the new formulation with the dielectric polarizable continuum model has been implemented. As an application, self-exchange electron transfer (ET) reactions between tetramethylhydrazine, tetraethylhydrazine, and tetrapropylhydrazine and their corresponding radical cations have been investigated. The inner and solvent reorganization energies are calculated by the "four-point" method and the new method for nonequilibrium solvation, respectively. Besides, we also calculated the electronic coupling matrix. The rate constants for the three self-exchange ET reactions correlate well with experimental results. We have shown that the inner reorganization energies of these self-exchange ET are not very sensitive to compound size while the compound size has some effect on the solvent reorganization energy in acetonitrile. The new method for nonequilibrium solvation energy based on continuum model provides a reasonable result for the solvent reorganization energy.

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.

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.

Single-sphere model for absorption spectrum of interfacial molecules with application to predictions of orientational angles.

In this work, a novel expression for nonequilibrium free energy is introduced within the framework of the continuum model. A simple and analytical model for the solvent effect of absorption spectrum of an interfacial molecule is deduced. This model overcomes some lacks existing in the previous theoretical treatments. Associated with the experimental data of N,N-diethyl-p-nitroaniline and 4-(2,4,6-triphenylpyridinium)-2,6-diphenylphenoxide, the present model gives reasonable predication of orientational angles for different interfaces.

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.

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.

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium.

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.