Theoretical calculation of reorganization energy for electron self-exchange reaction by constrained density functional theory and constrained equilibrium thermodynamics.

Within the framework of constrained density functional theory (CDFT), the diabatic or charge localized states of electron transfer (ET) have been constructed. Based on the diabatic states, inner reorganization energy λin has been directly calculated. For solvent reorganization energy λs, a novel and reasonable nonequilibrium solvation model is established by introducing a constrained equilibrium manipulation, and a new expression of λs has been formulated. It is found that λs is actually the cost of maintaining the residual polarization, which equilibrates with the extra electric field. On the basis of diabatic states constructed by CDFT, a numerical algorithm using the new formulations with the dielectric polarizable continuum model (D-PCM) has been implemented. As typical test cases, self-exchange ET reactions between tetracyanoethylene (TCNE) and tetrathiafulvalene (TTF) and their corresponding ionic radicals in acetonitrile are investigated. The calculated reorganization energies λ are 7293 cm(-1) for TCNE/TCNE(-) and 5939 cm(-1) for TTF/TTF(+) reactions, agreeing well with available experimental results of 7250 cm(-1) and 5810 cm(-1), respectively.

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.

Polarizable continuum model associated with the self-consistent-reaction field for molecular adsorbates at the interface.

In this work, a new procedure has been developed in order to realize the self-consistent-reaction field computation for interfacial molecules. Based on the extension of the dielectric polarizable continuum model, the quantum-continuum calculations for interfacial molecules have been carried out. This work presents an investigation into how the molecular structure influences the adsorbate-solvent interaction and consequently alters the orientation angle at the air/water interface. Taking both electrostatic and non-electrostatic energies into account, we investigate the orientation behavior of three interfacial molecules, 2,6-dimethyl-4-hydroxy-benzonitrile, 3,5-dimethyl-4-hydroxy-benzonitrile and p-cyanophenol, at the air/water interface. The results show that the hydrophilic hydroxyl groups in 2,6-dimethyl-4-hydroxy-benzonitrile and in p-cyanophenol point from the air to the water side, but the hydroxyl group in 3,5-dimethyl-4-hydroxy-benzonitrile takes the opposite direction. Our detailed analysis reveals that the opposite orientation of 3,5-dimethyl-4-hydroxy-benzonitrile results mainly from the cavitation energy. The different orientations of the hydrophilic hydroxyl group indicate the competition of electrostatic and cavitation energies. The theoretical prediction gives a satisfied explanation of the most recent sum frequency generation measurement for these molecules at the interface.

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.

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.