Non-equilibrium Solvation Effects Research Articles

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects.

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

State-specific solvation for restricted active space spin-flip (RAS-SF) wave functions based on the polarizable continuum formalism.

The restricted active space spin-flip (RAS-SF) formalism is a particular form of single-reference configuration interaction that can describe some forms of strong correlation at a relatively low cost and which has recently been formulated for the description of charge-transfer excited states. Here, we introduce both equilibrium and nonequilibrium versions of a state-specific solvation correction for vertical transition energies computed using RAS-SF wave functions, based on the framework of a polarizable continuum model (PCM). Ground-state polarization is described using the solvent's static dielectric constant and in the nonequilibrium solvation approach that polarization is modified upon vertical excitation using the solvent's optical dielectric constant. Benchmark calculations are reported for well-studied models of photo-induced charge transfer, including naphthalene dimer, C2H4⋯C2F4, pentacene dimer, and perylene diimide (PDI) dimer, several of which are important in organic photovoltaic applications. For the PDI dimer, we demonstrate that the charge-transfer character of the excited states is enhanced in the presence of a low-dielectric medium (static dielectric constant ɛ0 = 3) as compared to a gas-phase calculation (ɛ0 = 1). This stabilizes mechanistic traps for singlet fission and helps to explain experimental singlet fission rates. We also examine the effects of nonequilibrium solvation on charge-separated states in an intramolecular singlet fission chromophore, where we demonstrate that the energetic ordering of the states changes as a function of solvent polarity. The RAS-SF + PCM methodology that is reported here provides a framework to study charge-separated states in solution and in photovoltaic materials.

Nonequilibrium Solvent Effects during Photodissociation in Liquids: Dynamical Energy Surfaces, Caging, and Chemical Identity.

In the gas phase, potential energy surfaces can be used to provide insight into the details of photochemical reaction dynamics. In solution, however, it is unclear what potential energy surfaces, if any, can be used to describe even simple chemical reactions such as the photodissociation of a diatomic solute. In this paper, we use mixed quantum/classical (MQC) molecular dynamics (MD) to study the photodissociation of Na2+ in both liquid Ar and liquid tetrahydrofuran (THF). We examine both the gas-phase potential surfaces and potentials of mean force (PMF), which assume that the solvent remains at equilibrium with the solute throughout the photodissociation process and show that neither resemble a nonequilibrium dynamical energy surface that is generated by taking the time integral of work. For the photodissociation of Na2+ in liquid Ar, the dynamical energy surface shows clear signatures of solvent caging, and the degree of caging is directly related to the mass of the solvent atoms. For Na2+ in liquid THF, local specific interactions between the solute and solvent lead to changes in chemical identity that create a kinetic trap that effectively prevents the molecule from dissociating. The results show that nonequilibrium effects play an important role even in simple solution-phase reactions, requiring the use of dynamical energy surface to understand such chemical events.

Theoretical study of the photophysical processes of a styryl‐bodipy derivative eliciting an AND molecular logic gate response

AbstractWe study, via density functional theory and time dependent DFT calculations, the photophysical processes of a styryl‐bodipy derivative, which acts as a three metal‐cation‐receptor fluorophore in order to (a) gain information on the appropriate computational approach for successful prediction of molecular logic gate candidates, (b) rationalize the available experimental data and (c) understand how the given combination of three different receptors with the BODIPY fluorophore presents such interesting optoelectronic responses. The fluorophore (1), its monometallic complexes (1‐Ca 2+, 1‐Zn 2+, and 1‐Hg 2+), and its trimetallic complex (2) are studied. The calculated λmax values for absorption and emission are in excellent agreement with experimental data. It was found that the observed quenching of emission of 1 and of the monometallic complexes is attributed to the fact that their first excited state is a charge‐transfer state whereas this does not happen for the complex 2. It should be noted that for the correct ordering of the excited states, the inclusion of corrections to the excitation energies for nonequilibrium solvent effects is required; while in the case of 1‐Ca 2+, the additional explicit inclusion of the solvent is necessary for the quenching of the emission spectra.

Finding Order in the Disordered Hydration Shell of Rapidly Exchanging Water Molecules around the Heaviest Alkali Cs+ and Fr.

We report the structural and dynamical characterization of the intrinsically disordered hydration shells of the heaviest alkali ions, Cs+ and Fr+, obtained in ab initio molecular dynamics simulations. The knowledge of solvation and complexation properties of short-lived Fr+ is very limited and mostly based on extrapolations from the smaller alkali metal ions. To this end, we provide a critical insight into Fr+ solvation, demonstrating an extreme example of disordered solvation with no distinction between the ion-bound and solvent-bound states of water based on the ion-water distance. However, these two states are distinguished through distance-solvent rearrangement correlation, where either coordination number or electric field is employed to treat solvent rearrangement. Utilizing reaction rate theory, we find that the water exchange time scale for Fr+ (2.1-2.3 ps) is unexpectedly slower than for Cs+ (0.5-1.2 ps), because Fr+ experiences stronger nonequilibrium solvent effects. This study provides a new perspective on weak and hydrophobic solvation.

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.

Nonequilibrium solvent effects in Born-Oppenheimer molecular dynamics for ground and excited electronic states.

The effects of solvent on molecular processes such as excited state relaxation and photochemical reaction often occurs in a nonequilibrium regime. Dynamic processes such as these can be simulated using excited statemolecular dynamics. In this work, we describe methods of simulating nonequilibrium solvent effects in excited statemolecular dynamics using linear-response time-dependent density functional theory and apparent surface charge methods. These developments include a propagation method for solvent degrees of freedom and analytical energy gradients for the calculation of forces. Molecular dynamics of acetaldehyde in water or acetonitrile are demonstrated where the solute-solvent system is out of equilibrium due to photoexcitation and emission.

Valence-bond non-equilibrium solvation model for a twisting monomethine cyanine.

We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localizations, there are two possible twisting pathways with different charge localizations in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface, which leads to a manifold of TICT states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

AbstractA coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Nonequilibrium solvent effects in reaction kinetics — Steady-state solutions for the Agmon–Hopfield two-dimensional stochastic model

We propose an approximate localized-sink approach to the solution of the Agmon–Hopfield two-dimensional stochastic model for reactions in viscous media. The approach yields simple expressions for the sink location and the reaction rate constant, easy to use in the analysis of experimental data, and allows an intuitive phenomenological interpretation of the overall process in terms of a two-step kinetic scheme.

Symmetry breaking in cationic polymethine dyes, part 1: Ground state potential energy surfaces and solvent effects on electronic spectra of streptocyanines

AbstractCharge localization and dynamics in conjugated organic molecules, as well as their spectral signatures are of great importance for photonic and photovoltaic applications. Intramolecular charge delocalization in polymethine dyes occurs through π‐conjugated bridges and contributes to the appearance of low‐energy excited states that strongly influence their linear and nonlinear optical (NLO) properties. When the chain length in symmetrical cations exceeds the characteristic size of the soliton, the positive charge may localize at one of the terminal groups of the molecule and induce symmetry breaking of both the electron density distribution and molecular geometry. This charge localization is coupled with molecular vibrations and solvent effects. We investigated the mechanism of symmetry breaking in a series of cationic streptocyanines with different conjugated chain length and qualitatively predicted their electronic absorption spectra. This class of organic molecules is chosen as a model system to develop methodology which can subsequently be used to evaluate more complicated compounds for NLO applications. Our calculations show that the minimum number of vinylene groups in the conjugated chain necessary to break the symmetry of streptocyanines is eight in the gas phase and six in cyclohexane. We constructed the ground state potential energy surface (PES) in two dimensions using symmetry breaking and symmetry adapted coordinates. These were defined as the difference and the sum of the two central carbon–carbon bonds, respectively. This PES was found to have two equivalent minima for systems with symmetry breaking. The energy barrier between these two minima was estimated in the gas phase and in solution, which was taken into account by the polarizable continuum model. Charge localization in each minimum was found to be asymmetric. It is additionally stabilized by the solvent reaction field, which increases the energy barrier. The electronic absorption spectrum in solution is red shifted as compared to the gas phase. As the symmetry breaks, additional excited states with large oscillator strengths appear in the electronic spectrum. Geometry optimization and spectral predictions were also performed in a uniform external electric field in order to simulate nonequilibrium solvation effects due to the finite relaxation time of solvent molecules. Two asymmetric minima with different depths appear on the resulting PES. The lower minimum has charge localized at one of the two molecular terminal groups which is additionally stabilized by the solvent field, while the higher one has charge localized on another terminal group. This finding demonstrates the possibility that two forms with different charge distributions coexist in polar solvents. Our results suggest that nonequilibrium solvation may be a cause of absorption band broadening and splitting. This work is a first step in a larger study aimed at the analysis of the linear and nonlinear properties of long π‐conjugated systems of interest for NLO applications and plastic photovoltaics. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

A VB/MM View of the Identity SN2 Valence-Bond State Correlation Diagram in Aqueous Solution

The valence-bond state correlation diagram (VBSCD), which was developed by Shaik and co-workers is an excellent tool to understand reactivity patterns in chemical reactions. The strength of the model is in its ability to describe the whole spectrum of reaction types and unify them under a single general paradigm. Moreover, it allows one to understand, conceptualize, and predict chemical reactivity in a general as well as specific manner. As such, VBSCD is a valuable model. The model has been largely tested on various systems in the gas phase both qualitatively and quantitatively. However, its application to reactions in solution was given less attention because of the difficulties to represent solvent reorganization and estimate non-equilibrium solvation effects, which, on the basis of the model, are expected to be fundamental. The recently developed valence-bond molecular mechanics (VB/MM) method overcomes these difficulties because it involves explicit solvent molecules and thus allows quantitative examination of these solvent effects. This work presents a study of the identity S(N)2 reaction X(-) + H(3)CX --> XCH(3) + X(-); (X = F, Cl, Br, I) in aqueous solution. The various parameters that form the VBSCD model are calculated and compared with the corresponding model's estimated values. A relatively good agreement between the calculated and estimated values is found. It is shown that when facing quantitative considerations, the picture may not be as simplistic as in the qualitative study; yet, the fundamental nature of the description is unaffected. This indicates that combined together, the VB/MM approach and the VBSCD model offer a very powerful tool to study reactions in complex systems and understand their reactivity patterns.

Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach

A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescence spectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.

Dynamic effects of nonequilibrium solvation: Potential and free energy surfaces for Z/E isomerization in solvent-solute coordinates

A novel definition of a solvent coordinate associated with a given reaction is formulated in terms of molecular-dynamic trajectories of the solvent and is applied to discuss the topography of potential energy and free energy surfaces of model liquid phase Z/E isomerization reactions in solvent-solute coordinates. It is shown that the arrangement of the reactant and product valleys on these surfaces can vary from consecutive to parallel, depending on the strength of the solvent-solute interactions.

Challenge of the discharge of a hydronium ion at a mercury electrode: Beyond the Tafel plots

Abstract The mechanism of discharge of a hydronium ion at a mercury electrode is explored using a combined microscopic approach. The quantum mechanical aspects of the proton and electron tunneling are addressed in the framework of Dogonadze–Kuznetsov–Levich theory. The cluster model is employed to describe the electrode surface; quantum chemical calculations are performed at the density functional theory level. The classical molecular dynamics simulations are performed for a hydronium ion at the mercury/water molecules interface, in order to judge about the distance dependent work term. The results of simulations indicate that the hydronium ion does not specifically adsorb at the uncharged electrode surface. The proton energy surfaces are built at several values of the H3O+-electrode distances using a quantum chemical approach, which allows for non-equilibrium solvent effects. The electron transfer is found to be adiabatic; the proton tunneling probability is estimated by means of an effective computational scheme. The Tafel plots are constructed in a wide range of the electrode potentials; their origin is ascribed mostly to the complex interplay between the partial contributions to the resulting current. An attempt is also made to model the kinetic isotope effect.

A priori evaluation of the solvent contribution to the reorganization energy accompanying intramolecular electron transfer: Predicting the nature of the Creutz–Taube ion

The solvent contribution to the reorganization energy is one of the key physical properties controlling electron-transfer processes. A priori computational schemes have been developed that can predict realistic values for all other properties controlling charge transfer such as electronic couplings, vibronic couplings for intramolecular modes, the effects of asymmetry, and the effects of symmetric modes, but robust schemes for treating solvation remain elusive. In recent years, excited-state quantum chemical electronic-structure packages have gained the ability to calculate non-equilibrium solvation effects without the need to treat solvent explicitly, establishing the core of the required technology. While quantum chemical schemes involving excited-states represented as perturbed ground states can readily be applied in such calculations, they in general fail to include sufficient inactive-electron correlation to properly describe the excited-state manifold of charge transfer states, states for which only multi-reference procedures may robustly be applied. We develop computational procedures by which complete-active-space self-consistent-field (CASSCF) and related multi-reference calculations may be applied to electron-transfer systems whose energetics are controlled by the solvent–solute interaction. This is tested through the evaluation of the reorganization energy for electron-transfer in the bis-pentaammineruthenium complexes of α,ω-dipyridyl trans-polyenes in aqueous solution. Predictions are then made for the Creutz–Taube ion that place it clearly in the region of maximum breakdown of the Born–Oppenheimer approximation for which both the localized and delocalized diabatic descriptions of its electronic structure become inappropriate. This result is in qualitative agreement with conclusions drawn over the last four years based on a number of sources.

Sign Change of Hyperpolarizabilities of Solvated Water, Revised: Effects of Equilibrium and Nonequilibrium Solvation

The second harmonic and electro-optical responses for the water molecule in its liquid state are theoretically revised. The continuum, semicontinuum, and supermolecular solvation models are employed using quadratic response theory at the Hartree-Fock level, either in the equilibrium or nonequilibrium implementation. The experimentally observed sign change of the second harmonic response of water on liquefaction is reproduced using the supermolecular and semicontinuum model for both equilibrium and nonequilibrium solvation. The conclusions of a previous study, which rested upon linear response theory in an equilibrium implementation, are confirmed. Also, the assumption of Kleinman symmetry and dispersion is addressed.

Kinetics and Mechanism of Monomolecular Heterolysis of Cage-Like Compounds: XVIII. Solvent Effect on the Rate of Heterolysis of 3-Bromocyclohexene. Correlation Analysis of Solvation Effects

The kinetics of E1 dehydrobromination of 3-bromocyclohexene in 23 aprotic and 9 protic solvents were studied by the verdazyl technique. The reaction rate is described by the polarity, electrophilicity, and ionizing power parameters of the solvent. Nucleophilicity, polarizability, and cohesion parameters of the solvent do not affect the reaction rate. The effects of equilibrium and nonequilibrium solvation of the transition state are discussed.

Continuum level treatment of electronic polarization in the framework of molecular simulations of solvation effects

The hybrid molecular–continuum model for polar solvation considered in this paper combines the dielectric continuum approximation for treating fast electronic (inertialess) polarization effects and a molecular dynamics (MD) simulation for the slow (inertial) polarization component, including orientational and translational solvent modes. The inertial polarization is generated by average charge distributions of solvent particles, composed of permanent and induced (electronic) components. MD simulations are performed in a manner consistent with the choice of solvent and solute charges such that all electrostatic interactions are scaled by the factor 1/ε∞, where ε∞ is the optical dielectric permittivity. This approach yields an ensemble of equilibrium solvent configurations adjusted to the electric field created by a charged or strongly polar solute. The electrostatic solvent response field is found as the solution of the Poisson equation including both solute and explicit solvent charges, with accurate account of electrostatic boundary conditions at the surfaces separating spatial regions with different dielectric permittivities. Both equilibrium and nonequilibrium solvation effects can be studied by means of this model, and their inertial and inertialess contributions are naturally separated. The methodology for computation of charge transfer reorganization energies is developed and applied to a model two-site dipolar system in the SPC water solvent. Three types of charge transfer reactions are considered. The standard linear-response approach yields high accuracy for each particular reaction, but proves to be significantly in error when reorganization energies of different reactions were compared. This result has a purely molecular origin and is absent within a conventional continuum solvent model.

Dynamics of biochemical and biophysical reactions: insight from computer simulations.

1. Introduction 5632. Obtaining rate constants from molecular-dynamics simulations 5642.1 General relationships between quantum electronic structures and reaction rates 5642.2 The transition-state theory (TST) 5692.3 The transmission coefficient 5723. Simulating biological electron-transfer reactions 5753.1 Semi-classical surface-hopping and the Marcus equation 5753.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 5803.3 Density-matrix treatments 5833.4 Charge separation in photosynthetic bacterial reaction centers 5844. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 5965. Energetics and dynamics of enzyme reactions 6145.1 The empirical-valence-bond treatment and free-energy perturbation methods 6145.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 6205.3 Entropic effects in enzyme catalysis 6275.4 What is meant by dynamical contributions to catalysis? 6345.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 6365.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δg[Dagger], not the transmission coefficient 6415.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 6485.8 Diffusive processes in enzyme reactions and transmembrane channels 6516. Concluding remarks 6587. Acknowledgements 6588. References 658Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 1034 accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.