Excited-State Charge Transfer Dynamics of p-Dimethylaminobenzonitrile in Quadrupolar Solvents

Simulating the Nonadiabatic Relaxation Dynamics of 4-(N,N-Dimethylamino)benzonitrile (DMABN) in Polar Solution

The compound 4-(N,N-dimethylamino)benzonitrile (DMABN) represents the archetypal system for dual fluorescence, a rare photophysical phenomenon in which a given fluorophore shows two distinct emission bands. Despite extensive studies, the underlying mechanism remains the subject of debate. In the present contribution, we address this issue by simulating the excited-state relaxation process of DMABN as it occurs in polar solution. The potential energy surfaces for the system are constructed with the use of the additive quantum mechanics/molecular mechanics (QM/MM) method, and the coupled dynamics of the electronic wave function and the nuclei is propagated with the semiclassical fewest switches surface hopping method. The DMABN molecule, which comprises the QM subsystem, is treated with the use of the second-order algebraic diagrammatic construction (ADC(2)) method with the imposition of spin-opposite scaling (SOS). It is verified that this level of theory achieves a realistic description of the excited-state potential energy surfaces of DMABN. The simulation results qualitatively reproduce the main features of the experimentally observed fluorescence spectrum, thus allowing the unambiguous assignment of the two fluorescence bands: the normal band is due to the near-planar locally excited (LE) structure of DMABN, while the so-called "anomalous" second band arises from the twisted intramolecular charge transfer (TICT) structure. The transformation of the LE structure into the TICT structure takes place directly via intramolecular rotation, and is not mediated by another excited-state structure. In particular, the oft-discussed rehybridized intramolecular charge transfer (RICT) structure, which is characterized by a bent nitrile group, does not play a role in the relaxation process.

Solvatochromic behavior of some α-styrylpyridinium dyes

The influences of solvent polarity and substituent on the electronic transition of six different N-butyl-α-styrylpyridinium dyes have been investigated in 21 solvents. Reichardt's E(T)(30) scale has been used to propose a quantitative approach towards the relative stability of the electronic ground and excited state species. The solvents have been classified into three types and the dyes have been classified into four groups based on the contribution of field and inductive effects of the substituents towards the change in their absorption maxima values. Instead of a steady solvatochromism, all the dyes except p-nitro substituted one, suffer reversals in solvatochromism at E(T)(30) values of ~37 and ~48. The extents of contribution of non-polar and polar protic solvents towards the solvation of the excited states of the dye molecules have been determined to be 30-40% more than that towards the stability of their ground states by the dipolar aprotic solvents. The ortho effect shown by this class of dyes in contrast to their corresponding γ-isomers might have been responsible for their better solvent polarity sensing capability.

SOLVENT REORGANIZATION ENERGY WITH DIELECTRIC GREEN FUNCTIONAL AND ITS APPLICATION TO RETURN ELECTRON TRANSFER IN TETRACYANOETHYLENE-HEXAMETHYLBENZENE SYSTEM

Based on classical electrodynamics, the proper integral formula for general cases is adopted to estimate the electrostatic free energy difference between two given states, e.g. equilibrium and non-equilibrium states in the charging process of solute molecule in solution. With adequate consideration of the change of dielectric property in establishing the non-equilibrium state, the electrostatic free energy for this state can be obtained in a form differing from the traditional theories. The general formula of the solvent reorganization energy is derived according to the definition of the free energy difference between the non-equilibrium and equilibrium states due to the same electronic state of the solute molecule. Applying it to the two-sphere model and single-sphere model, we obtain the new expressions of the solvent reorganization energy, which are convenient to be used in practice. In the investigation of the return electron transfer of tetracyanoethylene-hexmethylbenzene system, good results can be obtained by using our expression when they are compared with those from the experiment.

Molecular simulations of outersphere reorganization energies in polar and quadrupolar solvents. The case of intramolecular electron and hole transfer

Outersphere reorganization energies (lambda) for intramolecular electron and hole transfer are studied in anion- and cation-radical forms of complex organic substrates (p-phenylphenyl-spacer-naphthyl) in polar (water, 1,2-dichloroethane, tetrahydrofuran) and quadrupolar (supercritical CO2) solvents. Structure and charge distributions of solute molecules are obtained at the HF/6-31G(d,p) level. Standard Lennard-Jones parameters for solutes and the nonpolarizable simple site-based models of solvents are used in molecular dynamics (MD) simulations. Calculation of lambda is done by means of the original procedure, which treats electrostatic polarization of a solvent in terms of a usual nonpolarizable MD scheme supplemented by scaling of reorganization energies at the final stage. This approach provides a physically relevant background for separating inertial and inertialless polarization responses by means of a single parameter epsilon(infinity), optical dielectric permittivity of the solvent. Absolute lambda values for hole transfer in 1,2-dichloroethane agree with results of previous computations in terms of the different technique (MD/FRCM, Leontyev, I. V.; et al. Chem. Phys. 2005, 319, 4). Computed lambda values for electron transfer in tetrahydrofuran are larger than the experimental values by ca. 2.5 kcal/mol; for the case of hole transfer in 1,2-dichloroethane the discrepancy is of similar magnitude provided the experimental data are properly corrected. The MD approach gives nonzero lambda values for charge-transfer reaction in supercritical CO2, being able to provide a uniform treatment of nonequilibrium solvation phenomena in both quadrupolar and polar solvents.

Free Energy and Dynamics of Electron-Transfer Reactions in a Room Temperature Ionic Liquid

Reaction free energetics and dynamics of unimolecular electron-transfer processes in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PF6-) are investigated via molecular dynamics computer simulations employing a model diatomic solute and compared with those in aprotic acetonitrile. Using the free energy perturbation method, diabatic free energy curves relevant to charge separation and recombination processes are studied over a wide range of the reaction coordinate. The diabatic curves are found to vary with the solute charge distribution, especially in EMI+PF6-. Nevertheless, if the free energy of reaction is not that substantial, the Marcus free energy relationship holds reasonably well, provided that the reorganization free energy averaged between the reactant and product states is employed. The effective polarity, measured as solvation-induced stabilization of dipolar solutes, is higher for EMI+PF6- than for acetonitrile, consonant with many solvatochromic measurements. Thus, in the normal regime, activation barriers for charge separation and recombination reactions are, respectively, lower and higher in EMI+PF6- than in acetonitrile. The influence of solvent dynamics on reaction kinetics through modulations of activation, deactivation, and barrier crossing is analyzed. Even though overall solvent relaxation dynamics in EMI+PF6- are considerably slower than those in acetonitrile, the deviation of the rate constant from the transition state theory predictions is found to be small for both solvents. Implications of this finding for other reactions in ionic liquids are briefly discussed.

Solubility of Water in a Benzene−Cyclohexane Mixture†

The solubility of a water molecule in a binary mixture of nonpolar cyclohexane and quadrupolar benzene is studied with the ab initio method. A novel self-consistent reaction field theory that properly accounts for benzene quadrupole moments in the continuum solvent framework is used to describe the solvation effects of the solvent mixture. The free energy of transfer from pure cyclohexane to the mixture solvent is obtained with the neglect of nonelectrostatic contributions. A reasonable agreement with experiments indicates that the theoretical method presented here provides a promising approach to electronic structure calculations in quadrupolar solvents and their mixtures with nonpolar solvents.

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.

On the temperature and pressure dependences of cavities in the dielectric continuum picture

Cavity size at equilibrium and its variations with thermodynamic conditions are studied in the dielectric continuum framework of solvents. By employing Gibbs' theory of dividing surfaces, the fluctuating cavity description of Kim [H.J. Kim, J. Chem. Phys. 105, 6818 (1996)] is extended to include effects related to the local solvent density inhomogeneity near the cavity. The resulting theory is applied to study cavity size variations with temperature and pressure in dipolar and nondipolar solvents. Model calculations show that the cavity size tends to increase with temperature along an isobar and decrease with pressure along an isotherm.

Solvent Dependence of the Spectra and Kinetics of Excited-State Charge Transfer in Three (Alkylamino)benzonitriles

Steady-state absorption and emission spectra and emission decay kinetics are reported for 4-aminobenzonitrile (ABN), 4-(1-azetidinyl)benzonitrile (P4C), 4-(1-pyrrolidinyl)benzonitrile (P5C), and 4-(1-piperidinyl)benzonitrile (P6C) in 24 room temperature solvents. In solvents of modest to high polarity, P4C, P5C, and P6C exhibit dual fluorescence and emission decays characteristic of the transformation from an initially prepared (LE) state to a more polar charge transfer (CT) state, whereas ABN does not undergo this reaction. The frequencies of the steady-state absorption and emission spectra of all of these solutes can be rationalized using a dielectric continuum description of the solvent and considering only the minima on the reactive surfaces, which are assumed to involve both an intramolecular (twisting) and a solvation coordinate. Characteristics of the gas-phase solutes deduced from this analysis are in good agreement with electronic structure calculations and indicate that differences in their spectra mainly reflect differences in the relative energies of the gas-phase LE and CT states. The relative yields of LE and CT emission are not described as satisfactorily by this model, and reasons for this failure are discussed. The kinetics of the LE --> CT reaction vary considerably with solute and solvent. In many solvents, the emission decays of P4C are reasonably described by a simple two-state kinetic scheme with time-independent rate constants. In P5C and P6C multiexponential decays are observed that reflect time-dependent shifts of the component spectra as well as time-dependent reaction rates. A simplified analysis of these complex dynamics provides estimates for both the free energy change Delta(r)G and (average) LE --> CT rate constant k(f) for a wide range of solute and solvent combinations. The driving force for reaction (-Delta(r)G) follows the order P6C > P5C > P4C and increases with increasing solvent polarity. The reaction rates are correlated to Delta(r)G and follow the opposite trend. The relationships observed between k(f) and Delta(r)G suggest that static solvent effects, i.e., barrier height changes, are the primary determinants of the solvent dependence in P4C. Correlations between barrier-corrected rates and solvation times suggest that dynamical solvent effects contribute substantially to the solvent dependence of the rates in P5C, and especially P6C.

The effects of solute–solvent electrostatic interactions on solvatochromic shifts in supercritical CO2

Solvent clustering around attractive solutes is an important feature of supercritical solvation. We examine here the effects of the local density enhancement on solvatochromic shifts in electronic absorption and emission spectra in supercritical CO2. We use molecular dynamics (MD) simulation to study the spectral line shifts for model diatomic solutes that become more polar upon electronic excitation. The electronic transition is modeled as either a change from a quadrupolar to a dipolar solute charge distribution or as an increase in the magnitude of the solute dipole. Our main focus is on the density dependence of the line shifts at 320 K, which corresponds to about 1.05 times the solvent critical temperature, Tc, but results for higher temperatures are also obtained in order to determine the behavior of the line shifts in the absence of local density enhancement. We find that the extent of local density enhancement at 1.05Tc is strongly correlated with solute-solvent electrostatic attraction and that the density dependence of the emission line shifts resembles the behavior of the effective local densities, rho(eff), obtained from the first-shell coordination numbers. The differences that are seen are shown to be due to solute-solvent orientational correlations which provide an additional source of enhancement for electrostatic solvation energies and spectral line shifts.

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.