Solvent effects on excitation energies obtained using the state-specific TD-DFT method with a polarizable continuum model based on constrained equilibrium thermodynamics

Nonequilibrium solvation effects need to be treated properly in the study of electronic absorption processes of solutes since solvent polarization is not in equilibrium with the excited-state charge density of the solute. In this work, we developed a state specific (SS) method based on the novel nonequilibrium solvation model with constrained equilibrium manipulation to account for solvation effects in electronic absorption processes. Time-dependent density functional theory (TD-DFT) is adopted to calculate electronic excitation energies and a polarizable continuum model is employed in the treatment of bulk solvent effects on both the ground and excited electronic states. The equations based on this novel nonequilibrium solvation model in the framework of TDDFT to calculate vertical excitation energy are presented and implemented in the Q-Chem package. The implementation is validated by comparing reorganization energies for charge transfer excitations between two atoms obtained from Q-Chem and those obtained using a two-sphere model. Solvent effects on electronic transitions of coumarin 153 (C153), acetone, pyridine, (2E)-3-(3,4-dimethoxyphenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (DMHP), and uracil in different solvents are investigated using the newly developed code. Our results show that the obtained vertical excitation energies as well as spectral shifts generally agree better with the available experimental values than those obtained using the traditional nonequlibrium solvation model. This new model is thus appropriate to study nonequilibrium excitation processes in solution.

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.

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.

Electron Transfer in a Radical Ion Pair: Quantum Calculations of the Solvent Reorganization Energy

Results are presented for an investigation of intermolecular electron transfer (ET) in solution by means of quantum calculations. The two molecules that are involved in the ET reaction form a solvent-separated radical ion pair. The solvent plays an important role in the ET between the two molecules. In particular, it can give rise to specific solute-solvent interactions with the solutes. An example of specific interactions is the formation of a hydrogen bond between a protic solvent and one of the molecules involved in the ET. We address the study of this system by means of quantum calculations on the solutes immersed in a continuum solvent. However, when the solvent can give rise to hydrogen bond formation with the negatively charged ion after ET, we explicitly consider solvent molecules in the solute cavity, determining the hydrogen bond energetic contribution to the overall interaction energy. Solute-solvent pair distribution functions, showing the different arrangement of solvent molecules before and after ET in the first solvation shell, are reported. We provide results of the solvent reorganization energy from quantum calculations for both the two isolated fragments and the ion pair in solution. Results are in agreement with available experimental data.

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.