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

Influence of a nearby substrate on the reorganization energy of hole exchange between dye molecules

A numerical method is presented to estimate the influence of a nearby substrate on the polarization energy and outer sphere reorganization energy (λo) for intermolecular hole transfer for a series of dye molecules. The calculation considers the net charge distribution of the oxidised molecule (determined from quantum chemical calculation of the highest occupied molecular orbital of the neutral molecule within the frozen orbital approximation) encapsulated within a conformal cavity, by the molecules total electron density. An analytical point charge approximation was used at longer range. The molecular cavity was either surrounded by a single polarizable continuum, or, to simulate a nearby substrate, embedded at different positions relative to the interface between two semi-infinite slabs with different dielectric constants. The calculated λo values in the single dielectric medium were linearly related to the outer-sphere reorganisation energy calculated from DFT with a polarizable continuum model, validating the approach. In the two phase system, variations in λo was sensitive to the position of the substrate relative to the molecule and differences in the Pekar factor (1/εo - 1/εr) for the media. For dye molecules in ACN positioned touching a TiO2 substrate λo was typically about 20% lower than in pure ACN depending on the molecular configuration. Our approach can be adapted to systems of more than two media.

Sequential palladium catalyzed coupling–cyclocondensation–coupling (C3) four-component synthesis of intensively blue luminescent biarylsubstituted pyrazoles

Highly blue-fluorescent 1-, 3-, and 5-biarylsubstituted pyrazoles can be efficiently prepared by a MW-assisted consecutive four-component synthesis based upon a sequential Pd-catalyzed Sonogashira coupling–condensation–Suzuki coupling (C³) process.

One-pot three-component synthesis and photophysical characteristics of novel triene merocyanines

Novel triene merocyanines, i.e. 1-styryleth-2-enylidene and 4-(1,3,3-trimethylindolin-2-ylidene)but-2-en-1-ylideneindolones are obtained in good to excellent yields in a consecutive three-component insertion Sonogashira coupling-addition sequence. The selectivity of either series is remarkable and has its origin in the stepwise character of the terminal addition step as shown by extensive computations on the DFT level. All merocyanines display intense absorption bands in solution and the film spectra indicate J-aggregation. While 1-styryleth-2-enylideneindolones show an intense deep red emission in films, 4-(1,3,3-trimethylindolin-2-ylidene)but-2-en-1-ylideneindolones are essentially nonemissive in films or in the solid state. TD-DFT computations rationalize the charge-transfer nature of the characteristic broad long-wavelength absorptions bands.

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.

VARIATIONAL ELECTROSTATICS FOR CHARGE SOLVATION

We show that the equations of continuum electrostatics can be obtained entirely and simply from a variational free energy comprising the Coulomb interactions among all charged species and a spring-like term for the polarization of the dielectric medium. In this formulation, the Poisson equation, the constitutive relationship between polarization and the electric field, as well as the boundary conditions across discontinuous dielectric boundaries, are all natural consequences of the extremization of the free energy functional. This formulation thus treats the electrostatic equations and the energetics within a single unified framework, avoiding some of the pitfalls in the study of electrostatic problems. Application of this formalism to the nonequilbrium solvation free energy in electron transfer is illustrated. Our calculation reaffirms the well-known result of Marcus. We address the recent criticisms by Li and coworkers who claim that the Marcus result is incorrect, and expose some key mistakes in their approach.

Solvent Effects on Electronic Structures and Chain Conformations of α-Oligothiophenes in Polar and Apolar Solutions

Solvent effects on electronic structures and chain conformations of alpha-oligothiophenes nTs (n = 1 to 10) are investigated in solvents of n-hexane, 1,4-dioxane, carbon tetrachloride, chloroform, and water by using density functional theory (DFT) and molecular dynamics (MD) simulations. Both implicit and explicit solvent models are employed. The polarized continuum model (PCM) calculations and MD simulations demonstrate the weak solvent effects on the electronic structures of alpha-oligothiophenes. The lowest dipole-allowed vertical excitation energies of nTs, obtained from time-dependent DFT/PCM calculations at the B3LYP/6-31G(d) level, exhibit a red shift as the solvent polarity increases, in agreement with experiments. The studied solvents have little impact on the state order of the low-lying excited states provided that the nTs are kept in C2h or C2v symmetry. The MD simulations demonstrate that the chain conformations are distorted to some extent in polar and nonpolar solvents. A qualitative picture of the distribution of solvent molecules around the solvated nTs is drawn by means of radial and spatial distribution functions. The S...H-O and pi...H-O solute-solvent interactions are insignificant in aqueous solution.

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: 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: 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.

Investigation of photoinduced electron transfer in model system of vitamin E-duroquinone by time-dependent density functional theory

Photoinduced electron transfer of the model system composed of vitamin E and duroquinone has been investigated using time-dependent density functional theory. Calculations for the excited states tell that the photoexcitation of the model system can directly yield the charge transfer states in which the vitamin E moiety is positively charged but the duroquinone moiety is negatively charged. Our theoretical investigations indicate that the second charge transfer state of the model system can also be produced through the decay of higher locally excited state S(4). Since S(4) state in the model system corresponds to S(1) state of the isolated duroquinone used as a model for peroxyl radical, and S(2) state has the character of electron transfer from the tertiary amine group of the vitamin E moiety to the duroquinone moiety, the decay from S(4) to S(2) corresponds to the dynamic process following the photoexcitation of the duroquinone moiety of the model system, i.e., the initial stage of antioxidant reaction of vitamin E. Calculations of the kinetic parameters for the electron transfer have been carried out in the framework of the Marcus-Jortner-Levich formalism. Our calculations confirm that the electron transfer from S(4) to S(2) possesses the character of the inverted regime and the barrier is negligibly small.

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.