Solvent Electronic Polarization Research Articles

Introducing the mean field approximation to CDFT/MMpol method: Statistically converged equilibrium and nonequilibrium free energy calculation for electron transfer reactions in condensed phases

A new theoretical method to study electron transfer reactions in condensed phases is proposed by introducing the mean-field approximation into the constrained density functional theory/molecular mechanical method with a polarizable force field (CDFT/MMpol). The method enables us to efficiently calculate the statistically converged equilibrium and nonequilibrium free energies for diabatic states in an electron transfer reaction by virtue of the mean field approximation that drastically reduces the number of CDFT calculations. We apply the method to the system of a formanilide-anthraquinone dyad in dimethylsulfoxide, in which charge recombination and cis-trans isomerization reactions can take place, previously studied by the CDFT/MMpol method. Quantitative agreement of the driving force and the reorganization energy between our results and those from the CDFT/MMpol calculation and the experimental estimates supports the utility of our method. The calculated nonequilibrium free energy is analyzed by its decomposition into several contributions such as those from the averaged solute-solvent electrostatic interactions and the explicit solvent electronic polarization. The former contribution is qualitatively well described by a model composed of a coarse-grained dyad in a solution in the linear response regime. The latter contribution reduces the reorganization energy by more than 10 kcal/mol.

Solvation dynamics and energetics of intramolecular hydride transfer reactions in biomass conversion.

Hydride transfer changes the charge structure of the reactant and thus, may induce reorientation/reorganization of solvent molecules. This solvent reorganization may in turn alter the energetics of the reaction. In the present work, we investigate the intramolecular hydride transfer by taking Lewis acid catalyzed glucose to fructose isomerization as an example. The C2-C1 hydride transfer is the rate limiting step in this reaction. Water and methanol are used as solvents and hydride transfer is simulated in the presence of explicit solvent molecules, treated quantum mechanically and at a finite temperature, using Car-Parrinello molecular dynamics (CPMD) and metadynamics. Activation free energy barrier for hydride transfer in methanol is found to be 50 kJ mol(-1) higher than that in water. In contrast, in density functional theory calculations, using an implicit solvent environment, the barriers are almost identical. Analysis of solvent dynamics and electronic polarization along the molecular dynamics trajectory and the results of CPMD-metadynamics simulation of the hydride transfer process in the absence of any solvent suggest that higher barrier in methanol is a result of non-equilibrium solvation. Methanol undergoes electronic polarization during the hydride transfer step. However, its molecular orientational relaxation is a much slower process that takes place after the hydride transfer, over an extended timescale. This results in non-equilibrium solvation. Water, on the other hand, does not undergo significant electronic polarization and thus, has to undergo minimal molecular reorientation to provide near equilibrium solvation to the transition state and an improved equilibrium solvation to the post hydride shift product state. Hence, the hydride transfer step is also observed to be exergonic in water and endergonic in methanol. The aforementioned explanation is juxtaposed to enzyme catalyzed charge transfer reactions, where the enhanced solvation of the transition and product states by enzymes, due to electrostatic interactions, reduces the activation free energy barrier and the free energy change of the reaction. Similarly, we suggest that, in the intramolecular hydride shift, improved solvation of the transition state and of the product state by water is achieved due to minimal polarization and reorientation, and (near) equilibrium solvation.

Effects of hydrogen bond and solvent polarity on the C=O stretching of bis(2-thienyl)ketone in solution

The optimized structural parameters, the absorption and the resonance Raman spectra have been investigated for the bis(2-thienyl)ketone in gas phase, in cyclohexane, methanol, and acetonitrile solvents by means of time dependent density functional theory calculations, the solvent electronic polarization effect on the solvation shift is examined and in well accordance with the calculation. The effect of increasing the polarity of the solvent is well represented by the polarizable continuum model, both for the absorption spectra and resonance Raman intensities. The Raman spectra of the C=O stretching mode, which is sensitive to the intermolecular interaction for bis(2-thienyl)ketone dissolved in solvents, were systematically studied. It was found that the hydrogen bond effect plays an important role in reducing the carbonyl stretching wavenumbers. The results of Raman shifts were interpreted through the dilution effect, solvation effects, and hydrogen bond-forming effects. Furthermore, the excitation profiles of several important Raman bands of bis(2-thienyl)ketone molecule in different solvents have been critically analyzed. The solvent effects on structural and symmetry properties of the molecule in S2 electronic state as well as the short-time photo relaxation dynamics have been discussed.

Continuum Model for Electronic Polarization Based on a Novel Dielectric Response Function

A generalized response function based on the use of dielectric spectra for dielectric relaxation process is derived. We apply the general response function to the special case in order to examine how special dielectric relaxation functions developed by other authors for solvent relaxation can be derived based on our formulations. Three typical solvents, water, methanol, and acetonitrile are used to investigate the electronic polarization processes of polar solvents. The solvent electronic polarization process is shown after a linear variation with the external electric field imposed on the solvent. The results show a conclusion that the electronic polarization of the solvents will accompany the electronic transition synchronously, without time lag.

The conformational analysis of push–pull enaminoketones using Fourier transform IR and NMR spectroscopy, and quantum chemical calculations: II. β-Dimethylaminoacrolein

IR Fourier and 1H NMR spectra of β-dimethylaminoacrolein (DMAA) were investigated in various pure solvents. Quantum chemical calculations by the method AM1 also was carried out to evaluate relative energy and dipole moment of each conformer. On the basis of NMR and IR-spectra we showed that the (DMAA) presented in solutions as equilibrium of two conformers, ( E- s- Z) ⇌ ( E-s-E). Constant of this equilibrium, K eq = C( E- s- E)/ C( E- s- Z), depended strongly on the total (DMAA) concentration: ln K eq = ln K eq 0 + a ( 1 − e − b C total ) . Besides, ( E- s- Z) conformer of the (DMAA) was more polar and more stable than the ( E- s- E) conformer. Correlation of the out-of-phase ν ˜ ( C O ) and in-phase ν ˜ ( C C ) vibrations with solvatochromic parameters of Kamlet, Abbot, and Taft (KAT) revealed that the main contribution to the shift of the out-of-phase ν ˜ ( C O ) vibrations of the both conformers made solvent's hydrogen bond acceptor (HBA) ( β) term, whereas hydrogen bond donor (HBD) acidity ( α) term influenced predominantly on the shift of the in-phase ν ˜ ( C C ) vibrations of the conformers. Moreover, influence of these dominated terms was more pronounced for the ( E- s- Z) conformer in comparison with the ( E- s- E) conformer, hence the first conformer was more polarized than the last. Investigations of the enthalpies of the ( E- s- Z) ⇌ ( E- s- E) equilibrium in carbon tetrachloride, 1,4-dioxane and their mixtures showed that these enthalpies depended predominantly on the solvent's atomic and electronic polarization and dispersive interactions.

Electronic Energy Transfer in Condensed Phase Studied by a Polarizable QM/MM Model.

We present a combined quantum mechanics and molecular mechanics (QM/MM) method to study electronic energy transfer (EET) in condensed phases. The method introduces a quantum mechanically based linear response (LR) scheme to describe both chromophore electronic excitations and electronic couplings, while the environment is described through a classical polarizable force field. Explicit treatment of the solvent electronic polarization is a key aspect of the model, as this allows account of solvent screening effects in the coupling. The method is tested on a model perylene diimide (PDI) dimer in water solution. We find an excellent agreement between the QM/MM method and "exact" supermolecule calculations in which the complete solute-solvent system is described at the QM level. In addition, the estimation of the electronic coupling is shown to be very sensitive to the quality of the parameters used to describe solvent polarization. Finally, we compare ensemble-averaged QM/MM results to the predictions of the PCM-LR method, which is based on a continuum dielectric description of the solvent. We find that both continuum and atomistic solvent models behave similarly in homogeneous media such as water. Our findings demonstrate the potential of the method to investigate the role of complex heterogeneous environments, e.g. proteins or nanostructured host materials, on EET.

A stable fluctuating-charge polarizable model for molecular dynamics simulations: Application to aqueous electron transfers

A stable and efficient variant of the dynamical fluctuating charge (fluc-q) model for electronically polarizable molecular dynamics (MD) simulation is developed and applied to electron transfer (ET) reactions in water. The energy divergence problem often encountered with the original form of the fluc-q model is essentially removed by introducing an alternative functional form for the electronic self-energy term of hydrogen atoms without any additional parameters. In the application to the aqueous ET problem we find the following: For the present donor–acceptor (DA) model of moderate size, the induced dipole is slightly smaller in the first solvation shell than in the outer region even under the electrostatic field from the ion pair state of the DA, which suggests that the induced dipole is enhanced more in the solvent–solvent hydrogen-bonding structure. The structural aspects are also examined via radial distribution functions. The solvent reorganization energy is demonstrated to be renormalized, both in the magnitude and in the slope along the inverse DA distance, due to coupling with electronic polarization. In the time correlation and spectral density functions of the solvent reaction coordinate, the frequency of the librational coupling motion is slightly blue-shifted and its intensity is suppressed due to inclusion of the solvent electronic polarization. The impact of the electronic polarization on the scaled quantum energy gap law of the ET rate is found to be modest.

Solvent electronic polarization effect on the electronic transitions in solution: Charge polarizable reference interaction site model self-consistent field approach

Effect of the electronic polarization in solvent on the solvatochromic shift for the excitation energy of solute molecule is studied by the reference interaction site model self-consistent field (RISM-SCF) method. The electronic polarization in solvent molecule is represented by the charge response kernel (CRK) obtained by ab initio calculations. Employing the CRK, a charge polarizable RISM-SCF method is proposed for describing the electronic structure of solute molecules in solution and estimating the excitation energies. The excitation energy for nπ* transition of acetone is calculated in CH3CN, CHCl3, CCl4, and CS2 solvents and the solvent electronic polarization effect on the solvation shift is examined. As a result, a blue shifts of 1225, 675, 166, and 92 cm−1 is obtained in those solvents. Furthermore, the solvation shifts in the transitions to the 11B1, 11B2, and 21A1 states of pyridine are evaluated in the same solvents. A blue shift is observed for the 11B1 ← 11A1 transition in all the solvent, while the 21A1 ← 11A1 one shows a red shift.

A Theory for the Rate Constant of a Dissociative Proton-Coupled Electron-Transfer Reaction

A theory that predicts the rate of a dissociative proton-coupled electron-transfer reaction is presented. The electron and proton transfer is treated as one quantum event that is driven by the coupling of the respective charges to the solvent's orientational polarization. The final state, where both electron and proton have transferred, corresponds to a repulsive surface for the proton motion. Consequently, the reaction products include a dissociated proton-transferred species. The origin of the repulsive surface is attributed to a combination of the hydrogen bond's relative weakness and the role of the solvent's electronic polarization in aiding the dissociation. The rate constant depends on the reaction free energy and reorganization energy, the bound state energies and wave functions in the initial proton surface, and the parameters of the proton final state repulsive surface. The rate constant can be quite large and should provide a reaction pathway competitive with consecutive electron and proton transfer.

Self-Consistent Reaction Field Calculations of Nonequilibrium Solvent Effects on Proton Transfer Processes through Low-Barrier Hydrogen Bonds

We investigate dynamic solvent effects on proton transfer reactions in the strongly hydrogen-bonded hydroxyl−water model system by using a self-consistent nonequilibrium reaction field method. The initial motivation for the present work lies in the results of a recently reported molecular dynamics simulation for the same system in aqueous solution, carried out through combined density functional and molecular mechanics potentials. Such a study has confirmed that proton transfer occurs in an essentially frozen environment and that solvent fluctuations may play a crucial role in the reaction dynamics. Nevertheless, owing to the use of effective charge water models in molecular dynamics simulations, the effect of solvent electronic polarization, which can be assumed to respond instantaneously to solute charge modifications, cannot be accounted for explicitly. Our main goal in the present study is to analyze such an effect in the effective energy profile instantaneously experienced by the proton, using for th...

A frequency-resolved cavity model (FRCM) for treating equilibrium and non-equilibrium solvation energies

A refined continuum medium model, denoted as the `frequency-resolved cavity model' (FRCM), for describing solvation effects of electrically charged solutes in polar solvents is considered. The principal distinction between the commonly accepted Born–Kirkwood–Onsager model and the FRCM treatment is that in the latter case the medium polarization field induced by the solute charge distribution is subdivided into inertial and inertialess components associated with different cavities. The inertialess field, arising from solvent electronic polarization modes, involves an inner cavity confined inside a larger one, which establishes the boundary for inertial polarization modes corresponding to collective orientational and translational motions of solvent molecules outside both cavities. The model is formulated so as to be applicable to complicated chemical solutes, with no symmetry limitations imposed on the shape of their cavities and charge distributions. In introducing two cavities, we find that a single extra parameter in the refined model, chosen to control the distinct sizes of the cavities, is capable of providing the necessary additional flexibility to the FRCM parametrization scheme. By this means one can redistribute inertial and inertialess contributions to equilibrium solvation energies in a way which is consistent with existing experimental data for both equilibrium solvation energy solvent reorganization energy.

Simulation of Proton Transfer Reaction Rates: The Role of Solvent Electronic Polarization

A simulation method suitable for the prediction of the rate of a proton transfer reaction of the form A--H−B → A-−H--B+, where -- denotes a hydrogen bond, is presented. The method is based on a golden rule formulation, where the coupling between the two proton states is obtained by solution of Schrödinger's equation for the proton states in a double-well potential whose shape is determined, in part, by the solvent's electronic polarization. The reaction activation energy is determined by solvent fluctuations, as well as flanking group (A and B) vibrational motion. The surfaces for the AB vibrational motion with the proton in its initial and final states are also modified by the coupling to the solvent's electronic polarization. Consequently, the matrix elements of the proton coupling between the AB vibronic states with the proton in its initial and final state, as well as the reaction's activation energy, are dependent upon the coupling to the solvent's electronic polarization. The rate constant for proton transfer in a representative phenol−amine hydrogen-bonded solute immersed in a polar/polarizable model for dichloromethane is simulated. The rate constant can be quite large, in the ps-1 range, as the proton coupling can be large for smaller AB distances, and the AB vibration provides a number of channels for proton transfer.

Ultrafast spectroscopy of the aqueous chloride ion studied by quantum molecular dynamics simulations

The dynamics of the photodetachment of an electron from a chloride ion in water induced by excitation of the lowest charge-transfer-to-solvent state is explored by using quantum molecular dynamics simulations. The ejected electron is described in terms of floating Gaussian orbitals, and solvent electronic polarization effects are accounted for in a fully self-consistent way. The simulation results point to a two-step photodissociation mechanism: the formation of a metastable electron - atom pair on a subpicosecond time-scale followed on a picosecond time-scale by the competition between two different reaction channels, (i) a diffusive barrier-impeded dissociation of the pair, yielding a solvated halogen atom and a free electron, and (ii) a non-radiative quantum recombination, eventually leading to the chloride ion in its ground state. The computed transient absorption spectra are compatible with the experimental data either at early times during the formation of the electron - atom pair or at longer times when dissociation - recombination occurs.

Electronically adiabatic reaction field approach to solvation. II. Solvent effects on electronic spectra

The theoretical formulation developed in the preceding article [H. J. Kim, J. Chem. Phys. 105, 6818 (1996)] is analyzed via a second-order perturbation method and applied to the static electronic spectra of polarizable solutes in solution. In the Born–Oppenheimer (BO) framework of the solvent electronic polarization P⃗el, the solute electronic wave functions, together with their (free) energy levels and associated Franck–Condon (FC) energies, are examined in the presence of a spherical cavity of arbitrary size and a nonequilibrium solvent orientational polarization configuration P⃗or. It is found that the solute electronic structure and its free energetics vary strongly with both P⃗or and the cavity size. The solute dipole enhancement due to solvation decreases with increasing cavity size. Comparison with the self-consistent (SC) reaction field theory predictions shows that classical P⃗el is more effective in polarizing the solute than quantum P⃗el couched in the BO description. This is due to the dispersion stabilization mechanism present in the latter. The static electronic spectroscopy is studied to linear order in the solute polarizability and in the cavity size difference between the lower and upper electronic states involved in the FC transition. In the case of the vanishing cavity size difference, our analytic results for the solvent spectral and Stokes shifts are compared with various existing theories and the sources of the discrepancies are briefly discussed. The effects of the cavity size variation on the electronic spectra are illustrated by using a simple two-state model description for the solute. It is found that even in a nonpolar solvent, there can be a significant Stokes shift arising from the cavity size relaxation subsequent to the FC transition. Also the cavity size fluctuations can make a non-negligible contribution to the spectral line broadening.

Electronically adiabatic reaction field approach to solvation. I. Theoretical formulation via multipole expansion in a fluctuating cavity

A theoretical framework for the solute electronic structure description under nonequilibrium solvation is developed via multipole expansions of a quantum dielectric continuum solvent formulation of Kim and Hynes [J. Chem. Phys. 96, 5088 (1992)]. By employing a spherical cavity for the solute and invoking a Born–Oppenheimer description for the solvent electronic polarization P⃗el, the cavity boundary effects on the solute electric and solvent polarization fields are taken into account exactly. The solute–solvent electronic correlation effects are also included within the dielectric continuum context in the fast P⃗el limit. Another novel feature of the theory includes the cavity size variation with the solute electronic charge distribution and its thermal fluctuations. This effectively accounts for, e.g., electrostriction, largely ignored in many solution-phase quantum chemistry calculations based on the reaction field methods. By employing a coherent state description for P⃗el, we obtain electronically adiabatic free energies as a function of the cavity radius variable that measures the fluctuating cavity size and the solvent coordinates that gauge the nonequilibrium solvent orientational polarization P⃗or. These define multidimensional electronic free energy surfaces, upon which nuclear dynamics occur. Their local structure near equilibrium, along with the solute polarizability effects on the force constant matrix, is analyzed. With a polaron description for the P⃗or kinetic energy, it is found that the frequency relevant for ultrafast inertial solvation dynamics decreases as the Pvec;or multipole character increases. This is in qualitative agreement with recent molecular solvation theory predictions. As for the cavity, the frequency associated with its symmetric breathing mode is examined by analyzing our previous molecular dynamics simulation results via the equipartition principle. It is found that the cavity frequency is comparable to that of P⃗or. The variation of the equilibrium cavity size with the solute charge distribution and its influence on free energetics are also studied. Model calculations in water show that the cavity size decreases with the increasing solute dipole moment. This results in a significant reduction of equilibrium free energy, compared to that obtained with the neglect of the electrostriction effect.

Reaction pathways in the photodetachment of an electron from aqueous chloride: A quantum molecular dynamics study

Reaction and relaxation processes induced by photoexcitation of an aqueous chloride ion are studied with quantum molecular dynamics simulations. A predominant channel leading to a metastable hydrated electron-chlorine pair is found. By means of theoretical transient and stationary absorption spectra, the solvent reorganization involved in the charge repartitioning is discussed. The dissipation of excess electron kinetic energy by surrounding water molecules plays an essential role in the equilibration of an electron-atom pair. For this intermediate species, two competing reaction pathways are identified. One is the barrier-impeded dissociation yielding a hydrated electron. Shape and height of the free energy barrier determined by quantum umbrella sampling point to a diffusion controlled electron photodetachment. The other channel is the geminate recombination via a nonadiabatic transition for which a self-consistent and fully dynamical treatment of the solvent electronic polarization is found to be important. From the rate constants computed for the individual channels, a kinetic model is derived to explain time-dependent spectral signatures and electron escape yields recently observed in photodetachment experiments on aqueous halides.

Solvation energies and electronic spectra in polar, polarizable media: Simulation tests of dielectric continuum theory

A dielectric continuum theory for the solvation of a polar molecule in a polar, polarizable solvent is tested using computer simulations of formaldehyde in water. Many classes of experiments, for example those which measure solvent-shifted vertical transition energies or electron transfer rates, require an explicit consideration of the solvent electronic polarization. Due to the computational cost of simulating a polarizable solvent, many simulation models employ non-polarizable solute and solvent molecules and use dielectric continuum theory to relate the properties of the non-polarizable system to the properties of a more realistic polarizable system. We have performed simulations of ground and excited state formaldehyde in both polarizable and non-polarizable water, and the solvation energies and solvent-shifted electronic spectra we obtained are used to test dielectric continuum, linear response predictions. Dielectric continuum theory correctly predicts that free energy differences are the same in polarizable and non-polarizable water. The theory wrongly predicts that the reorganization energy in a polarizable solvent is 30% smaller than the reorganization energy in a polar, non-polarizable solvent; in the simulations, the reorganization energies differ by only 6%. We suggest that the dielectric continuum theory fails because it assumes that both solute electronic states exist in the same size cavity in the solvent, whereas in the simulation the cavity radius increases by 20% after the electronic transition. We account for the change in the cavity size by adding a non-linear solute–solvent coupling to the dielectric continuum theory, and find that the resulting predictions are just outside the error bounds from the simulation. The cavity size corrections have the undesired and incorrect side-effect of predicting fluctuations far smaller than seen in the simulations. This reveals the inherent difficulty in devising a simple, fully self-consistent dielectric continuum theory for solvation.

Molecular dynamics simulation of an excess charge in water using mobile Gaussian orbitals

For mixed quantum-classical molecular dynamics simulations of solvated excess charges a novel and efficient method to expand the solute electronic wave function in a distributed Gaussian basis with a shell structure is presented. The aggregate of Gaussian orbitals is capable of mimicking the shape fluctuation of the excess charge distribution and its diffusion through the solvent. This approach also offers an easy pathway to treat the solvent electronic polarization in an explicit and self-consistent fashion. As applications, the results of adiabatic molecular dynamics simulations for the hydrated electron and the aqueous chloride are reported. For e−/H2O the computed ground state absorption spectrum is discussed. Adiabatic relaxation as well as nonadiabatic transition rates are evaluated—the latter by means of an original Golden Rule formula—and compared to experimental results. In the case of Cl−/H2O the charge transfer to solvent spectra are analyzed. The ability of the mobile basis set method to describe the photodetachment dynamics of an electron from aqueous chloride is also demonstrated.

On the role of solvent electronic polarization in charge transfer reactions

The effect of a solvent’s electronic polarization on the rate of a charge transfer reaction is studied in both continuum and discrete solvent models. An effective system Hamiltonian that contains the equilibrium solvation from the solvent electronic polarization is obtained, and leads to an effective matrix element Veff coupling the charge transfer states that is smaller than the gas phase value. Both the effective Hamiltonian and Veff are dependent on the solvent’s instantaneous nuclear configuration, and liquid state theory is used to carry out the configuration average. The solvent electronic polarization reduces the transition rate for both adiabatic and nonadiabatic reactions. A standard relation between the equilibrium solvation energy of the reactants and the solvent reorganization energy is established that permits evaluation of the effect of a molecular solvent (using a Drude model for the electronic degrees of freedom) on the rate by evaluating a partition function. This permits use of a path integral formulation for the mixed quantum (electronic polarization) classical (slow nuclear configuration) solvent that leads to the information required for the rate constant. In a strong coupling regime, where the coupling between the charge-transfer species would be so large as to preclude reactant and product species, we show that a new mechanism for charge localization arising from the solvating effect of the electronic polarization may occur, and formulate a rate constant expression for this regime. It has the form of a quantum Kramers rate and shows that the solvent provides a friction effect that will reduce the rate relative to the no-friction rate.

VB resonance theory in solution. I. Multistate formulation

A theory for the description of electronic structure in solution for solution phase chemical reactions is formulated in the framework of a dielectric continuum solvent model which takes solute boundary effects into account. This latter feature represents a generalization of the Kim–Hynes theory, in which the solute boundary was treated in the dielectric image approximation. The electronic structure of the molecular solute, embedded in a cavity of the dielectric, is described by a manifold of orthogonalized diabatic—e.g., valence bond (VB)—states. The polarization of the dielectric solvent is partitioned into an electronic (fast) and an orientational (slow) component. The formulation encompasses both nonequilibrium and equilibrium regimes of the orientational polarization with respect to the solute charge distribution. The analysis is carried out in the general case of quantized solvent electronic polarization, but with reference to two limits in terms of which the general results can be most readily comprehended: with the electronic polarization much slower than the solute electronic motions and equilibrated to a delocalized solute charge distribution—the self-consistent limit; with the electronic polarization fast enough to equilibrate to components of the solute electronic distribution rather than to the average distribution—the Born–Oppenheimer limit. The general results depend on the relative time scales of the resonant interconversion between the VB states and the solvent electronic polarization. With the ansatz that the nonequilibrium orientational polarization is a linear combination of equilibrium terms with nonequilibrium coefficients, the solute–solvent system free energy is obtained together with a nonlinear Schrödinger equation for the solute electronic structure. A procedure is given for the natural definition of the set of solvent coordinates which describe the nonequilibrium regime necessary for the treatment of chemical reactions, and convenient matrix forms for the free energy and the Hamiltonian matrix elements are provided.