Polar solvation dynamics of polyatomic solutes: Simulation studies in acetonitrile and methanol

Solvent effects on the intramolecular charge transfer excited state of 3CzClIPN: a broadband transient absorption study

The prediction of solvent properties using molecular probes often relies on correlating steady-state absorption and fluorescence measurements, as well as determining absorption maxima and/or Stokes shifts. In this study, we employ femtosecond broadband transient absorption (fs-bb-TA) spectroscopy to investigate the spectroscopic behaviour of the intramolecular charge transfer (ICT) excited state of 3CzClIPN (2,4,6-tri(9H-carbazol-9-yl)-5-chloroisophthalonitrile), a representative ICT organic molecule, in both aromatic and non-aromatic solvents. Unlike observations in non-aromatic media, fs-bb-TA spectra of 3CzClIPN in aromatic solvents exhibit enhanced spectral broadening that strongly correlates with the solvent's polarity. We hypothesise that this spectral broadening originates from a wider configurational energy landscape experienced by the positively charged carbazole Cz+ group, owing to the larger size and, consequently, reduced solvation effectiveness of aromatic solvent molecules.

Bond-Breaking Reactions Encounter Distinct Solvent Environments Causing Breakdown of Linear Response

Solvent effects are important for understanding solution-phase chemical reactions. Surprisingly, very few studies have explored how solvent dynamics change during the course of a reaction with solutes that encounter a wide range of configurations. Here, we use quantum simulation methods to explore the solvent dynamics during a solution-phase bond-breaking reaction: the photodissociation of Na₂⁺ in liquid Ar. We find that the solute experiences a small number of distinct solvent environments that change in a discrete fashion as the bond lengthens. In characterizing the solvent environments, we show also that linear response fails by all measures, even when nonstationarity of solvent dynamics is considered. This observation of distinct solvent response environments with a solvent that can undergo only translational motions highlights the complexity of solute-solvent interactions, but that there are only a few environments gives hope to the idea that solvation dynamics can be understood for solution-phase reactions that explore a wide configuration space.

Solvation dynamics: improved reproduction of the time-dependent Stokes shift with polarizable empirical force field chromophore models

The inclusion of explicit polarization in molecular dynamics simulation has gained increasing interest during the last several years. An understudied area is the role of polarizability in computer simulations of solvation dynamics around chromophores, particularly for the large solutes used in experimental studies. In this work, we present fully polarizable ground and excited state force fields for the common fluorophores N-methyl-6-oxyquinolium betaine and Coumarin 153. While analyzing the solvation responses in water, methanol, and the highly viscous ionic liquid 1-ethyl-3-methylimidazolium trifluoromethanesulfonate we found that the inclusion of solute polarizability considerably increases the agreement of the obtained Stokes shift relaxation functions with experimental data. Solute polarizability slows down the inertial solvation response in the femtosecond time regime and enables the chromophore to adapt its dipole moment to the environment. Furthermore, the developed chromophore force field reproduces the solute dipole moments in both the electronic ground and excited state in environments ranging from gas phase to highly polar media correctly. Based on these studies it is anticipated that polarizable models of chromophores will lead to an improved understanding of the relationship of their environment to their spectroscopic properties.

Fundamental limitations of the time-dependent Stokes shift for investigating protein hydration dynamics

In the TDSS measured in protein systems, large protein contributions fully obscure hydration dynamics.

Changes in protein hydration dynamics by encapsulation or crowding of ubiquitin: strong correlation between time-dependent Stokes shift and intermolecular nuclear Overhauser effect

The local changes in protein hydration dynamics upon encapsulation of the protein or macromolecular crowding are essential to understand protein function in cellular environments. We were able to obtain a spatially-resolved picture of the influence of confinement and crowding on the hydration dynamics of the protein ubiquitin by analyzing the time-dependent Stokes shift (TDSS), as well as the intermolecular Nuclear Overhauser Effect (NOE) at different sites of the protein by large-scale computer simulation of single and multiple proteins in water and confined in reverse micelles. Besides high advanced space resolved information on hydration dynamics we found a strong correlation of the change in NOE upon crowding or encapsulation and the change in the integral TDSS relaxation times in all investigated systems relative to the signals in a diluted protein solution.

Changes in local protein hydration dynamics caused by encapsulation or crowding are reflected in the TDSS and the intermolecular NOE alike.

Evaluating excited state atomic polarizabilities of chromophores

Ground and excited state atomic polarizabilities of the chromophores N-methyl-6-oxyquinolinium betaine and coumarin 153 have been evaluated via quantum mechanics.

Ground and excited state dipoles and polarizabilities of the chromophores N-methyl-6-oxyquinolinium betaine (MQ) and coumarin 153 (C153) in solution have been evaluated using time-dependent density functional theory (TD-DFT). A method for determining the atomic polarizabilities has been developed; the molecular dipole has been decomposed into atomic charge transfer and polarizability terms, and variation in the presence of an electric field has been used to evaluate atomic polarizabilities. On excitation, MQ undergoes very site-specific changes in polarizability while C153 shows significantly less variation. We also conclude that MQ cannot be adequately described by standard atomic polarizabilities based on atomic number and hybridization state. Changes in the molecular polarizability of MQ (on excitation) are not representative of the local site-specific changes in atomic polarizability, thus the overall molecular polarizability ratio does not provide a good approximation for local atom-specific polarizability changes on excitation. Accurate excited state force fields are needed for computer simulation of solvation dynamics. The chromophores considered in this study are often used as molecular probes. The methods and data reported here can be used for the construction of polarizable ground and excited state force fields. Atomic and molecular polarizabilities (ground and excited states) have been evaluated over a range of functionals and basis sets. Different mechanisms for including solvation effects have been examined; using a polarizable continuum model, explicit solvation and via sampling of clusters extracted from a MD simulation. A range of different solvents have also been considered.

Picosecond Solvation Dynamics in Nanoconfinement: Role of Water and Host-Guest Complexation

The dynamics of solvation of an excited chromophore, 5-(4″-dimethylaminophenyl)-2-(4'-sulfophenyl)oxazole, sodium salt (DMO), has been explored in confined nanoscopic environments of β-cyclodextrin (βCD) and heptakis(2,6-di- O-methyl)-β-cyclodextrin (DIMEB). Solvation occurs on a distinctly slower time scale (τ_S³ ∼ 47 ps, τ_S⁴ ∼ 517 ps) in the host cavity of DIMEB than in that of βCD (τ_S³ ∼ 20 ps, τ_S⁴ ∼ 174 ps). The calculated equilibrium solvation response of DMO was characterized by four relaxation components (τ_S¹ ∼ 0.46-0.48 ps, τ_S² ∼ 3.2-3.4 ps, τ_S³ ∼ 32.3-37.7 ps, and τ_S⁴ ∼ 232-485 ps), of which the longer ones (τ_S³, τ_S⁴) are well-consistent with experiments, whereas the ultrafast components (τ_S¹, τ_S²) are unresolved. The observed time constant (τ_S³) within the ∼20-47 ps range arises from slow water molecules in the primary hydration layers of the host CDs and is slower for DIMEB than for βCD presumably due to longer-lived and stronger hydrogen bonds that water forms with the former host relative to the latter. Decomposition of the calculated solvation response of DMO has revealed that conformational fluctuations of the macrocyclic hosts give rise to the observed long-time relaxation component (τ_S⁴), which is much slower for the inclusion complexes with DIMEB than for those with βCD because of slower conformational dynamics of the former host than that of the latter.

Solvation dynamics in polar solvents and imidazolium ionic liquids: failure of linear response approximations

This study presents the large scale computer simulations of two common fluorophores, N-methyl-6-oxyquinolinium betaine and coumarin 153, in five polar or ionic solvents. The validity of linear response approximations to calculate the time-dependent Stokes shift is evaluated in each system. In most studied systems linear response theory fails. In ionic liquids the magnitude of the overall response is largely overestimated, and linear response theory is not able to capture the individual contributions of cations and anions. In polar liquids, the timescales of solvation dynamics are often not correctly reproduced. These observations are complemented by a detailed analysis of Gaussian statistics including higher order correlation functions, variance of the energy gap distribution and its time evolution. The analysis of higher order correlation functions was found to be not suitable to predict a failure of linear response theory. Further analysis of radial distribution functions and hydrogen bonds in the ground and excited state, as well as the time evolution of the number of hydrogen bonds after solute excitation reveal an influence of solvent structure in some of the studied systems.

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for obtaining spectroscopic observables and understanding complex, time-dependent properties. Currently, performing RT-TDDFT calculations on large, fully quantum mechanical systems is not computationally feasible. Previously, polarizable mixed quantum mechanical and molecular mechanical (QM/MMPol) models have been successful in providing accurate, yet efficient, approximations to a fully quantum mechanical system. Here we develop a coupling scheme between induced dipole based QM/MMPol and RT-TDDFT. Our approach is validated by comparing calculated spectra with both real-time and linear-response TDDFT calculations. The model developed within provides an accurate method for performing RT-TDDFT calculations on extended systems while accounting for mutual polarization between the quantum mechanical and molecular mechanical regions.

Effect of a Tertiary Butyl Group on Polar Solvation Dynamics in Aqueous Solution: A Computational Approach

The current computational study investigates the changes in solvation dynamics of water when introducing hydrophobic side chains to the molecular probe N-methyl-6-oxyquinolinium betaine. High-precision transient fluorescence and absorption measurements published in the companion article (10.1021/acs.jpcb.7b05031) revealed an influence of hydrophobic side chain alterations on the observed solvation dynamics of a chromophore in water. As the influence of shape, size, and structure of chromophores on the time-dependent Stokes shift was so far thought to play a role only in slowly rotating solvents compared to the solute or if the hydrogen bonding ability of the solute changes, this finding is quite unexpected. Analysis of the time-dependent Stokes shift obtained from nonequilibrium simulations corroborates experimental retardation factors and activation energies, and indicates that solute motion, namely vibration, is mainly responsible for the observed retardation of solvation dynamics. The faster dynamics around the smaller chromophore is in fact achieved by some normal modes located at the pyridinium part of the chromophore. Rotation also contributes to a very small extent to hydration dynamics, but for small and large derivatives alike. Local residence times furthermore reveal slight retardations in the first solvent shell around the chromophores. The current picture of the solute acting as a passive molecular probe therefore needs to be revised even for solvents like water.

Ultrafast Solvation Dynamics and Vibrational Coherences of Halogenated Boron-Dipyrromethene Derivatives Revealed through Two-Dimensional Electronic Spectroscopy

Boron-dipyrromethene (BODIPY) chromophores have a wide range of applications, spanning areas from biological imaging to solar energy conversion. Understanding the ultrafast dynamics of electronically excited BODIPY chromophores could lead to further advances in these areas. In this work, we characterize and compare the ultrafast dynamics of halogenated BODIPY chromophores through applying two-dimensional electronic spectroscopy (2DES). Through our studies, we demonstrate a new data analysis procedure for extracting the dynamic Stokes shift from 2DES spectra revealing an ultrafast solvent relaxation. In addition, we extract the frequency of the vibrational modes that are strongly coupled to the electronic excitation, and compare the results of structurally different BODIPY chromophores. We interpret our results with the aid of DFT calculations, finding that structural modifications lead to changes in the frequency, identity, and magnitude of Franck-Condon active vibrational modes. We attribute these changes to differences in the electron density of the electronic states of the structurally different BODIPY chromophores.

Time-resolved signatures across the intramolecular response in substituted cyanine dyes

The optically populated excited state wave packet propagates along multidimensional intramolecular coordinates soon after photoexcitation. This action occurs alongside an intermolecular response from the surrounding solvent. Disentangling the multidimensional convoluted signal enables the possibility to separate and understand the initial intramolecular relaxation pathways over the excited state potential energy surface. Here we track the initial excited state dynamics by measuring the fluorescence yield from the first excited state as a function of time delay between two color femtosecond pulses for several cyanine dyes having different substituents. We find that when the high frequency pulse precedes the low frequency one and for timescales up to 200 fs, the excited state population can be depleted through stimulated emission with efficiency that is dependent on the molecular electronic structure. A similar observation at even shorter times was made by scanning the chirp (frequencies ordering) of a femtosecond pulse. The changes in depletion reflect the rate at which the nuclear coordinates of the excited state leave the Franck-Condon (FC) region and progress towards achieving equilibrium. Through functional group substitution, we explore these dynamic changes as a function of dipolar change following photoexcitation. Density functional theory calculations were performed to provide greater insight into the experimental spectroscopic observations. Complete active space (CAS) self-consistent field and CAS second order perturbation theory calculated potential energy surfaces tracking twisting and pyramidalization confirm that the steeper potential at the FC region leads to the observation of faster wave packet dynamics.

On the validity of linear response approximations regarding the solvation dynamics of polyatomic solutes

Gaussian statistics and linear response predictions of the nonequilibrium solvation dynamics are tested for numerous solute/solvent combinations.

Diabatic Population Matrix Formalism for Performing Molecular Mechanics Style Simulations with Multiple Electronic States

An accurate description of nonbonded interactions is important in investigating dynamics of molecular systems. In many situations, fixed point charge models are successfully applied to explaining various chemical phenomena. However, these models with conventional formulations will not be appropriate in elucidating the detailed dynamics during nonadiabatic events. This is mainly because the chemical properties of any molecule, especially its electronic populations, significantly change with respect to molecular distortions in the vicinity of the surface crossing. To overcome this issue in molecular simulations yet within the framework of the fixed point charge model, we define a diabatic electronic population matrix and substitute it for the conventional adiabatic partial charges. We show that this matrix can be readily utilized toward attaining more reliable descriptions of Coulombic interactions, in combination with the interpolation formalism for obtaining the intramolecular interaction potential. We demonstrate how the mixed formalism with the diabatic charges and the interpolation can be applied to molecular simulations by conducting adiabatic and nonadiabatic molecular dynamics trajectory calculations of the green fluorescent protein chromophore anion in aqueous environment.

Dielectric spectra of ionic liquids and their conversion to solvation dynamics: a detailed computational analysis of polarizable systems

For the three molecular ionic liquids 1-ethyl-3-methylimidazolium tetrafluoroborate, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate and 1-butyl-3-methylimidazolium tetrafluoroborate, dielectric spectra were calculated from molecular dynamics simulations based on polarizable force fields. Using the reaction field continuum model the dielectric spectra were converted to the solvation dynamics of coumarin 153. It is shown in detail that the inclusion of the static conductivity in this model is essential. When simplifying the dielectric spectrum to the static conductivity hyperbola, the solvation response function becomes mono-exponential. Taking into account the frequency dependence of the conductivity, the typical two time-regimes of the solvation response function in ionic liquids are already obtained. However, the mean relaxation time remains the same. When converting the complete dielectric spectrum, i.e. also including frequency-dependent dielectric permittivity, quantitative changes are observed, but the qualitative shape is conserved. In accordance with previous experimental studies, solvation dynamics in ionic liquids predicted by the reaction field continuum model is too fast for longer times. This correlates with the suppression of the fine structure of the dielectric spectrum at low frequencies by the static conductivity hyperbola. By scaling down the static conductivity this effect can be partially amended. In addition to the impact of the solvent dielectric spectrum on solvation dynamics, solute-specific effects, i.e. anisotropy in shape and charge distribution as well as polarizability, were also studied.

Two-photon voltmeter for measuring a molecular electric field

We present a new approach for determining the strength of the dipolar solute-induced reaction field, along with the ground- and excited-state electrostatic dipole moments and polarizability of a solvated chromophore, using exclusively one-photon and two-photon absorption measurements. We verify the approach on two benchmark chromophores N,N-dimethyl-6-propionyl-2-naphthylamine (prodan) and coumarin 153 (C153) in a series of toluene/dimethyl sulfoxide (DMSO) mixtures and find that the experimental values show good quantitative agreement with literature and our quantum-chemical calculations. Our results indicate that the reaction field varies in a surprisingly broad range, 0-10(7)  V cm(-1) , and that at close proximity, on the order of the chromophore radius, the effective dielectric constant of the solute-solvent system displays a unique functional dependence on the bulk dielectric constant, offering new insight into the close-range molecular interaction.

Fast photoinduced reactions in the condensed phase are nonexponential

Time-resolved measurements of photoinduced reactions reveal that many ultrafast reactions in the femto- to picosecond time scale are nonexponential. In this article we provide several examples of reactions that exhibit a nonexponential rate. We explain the wide range of the nonexponential reaction by the lack of time separation between τ(s), the characteristic fast equilibration time of the population in the reactant potential well, and the longer time τ(e), the characteristic time to cross the energy barrier between the reactant and the product.

Observations of probe dependence of the solvation dynamics in ionic liquids

Solvation and rotational dynamics of 4-aminophthalimide (4AP) in four ionic liquids (ILs) are measured using a combination of fluorescence upconversion spectroscopy and time-correlated single photon counting.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Hydrogen bond flexibility correlates with Stokes shift in mPlum variants

Fluorescent proteins have revolutionized molecular biology research and provide a means of tracking subcellular processes with extraordinary spatial and temporal precision. Species with emission beyond 650 nm offer the potential for deeper tissue penetration and lengthened imaging times; however, the origin of their extended Stokes shift is not fully understood. We employed spectrally resolved transient grating spectroscopy and molecular dynamics simulations to investigate the relationship between the flexibility of the chromophore environment and Stokes shift in mPlum. We examined excited state solvation dynamics in a panel of strategic point mutants of residues E16 and I65 proposed to participate in a hydrogen-bonding interaction thought responsible for its red-shifted emission. We observed two characteristic relaxation constants of a few picoseconds and tens of picoseconds that were assigned to survival times of direct and water-mediated hydrogen bonds at the 16-65 position. Moreover, variants of the largest Stokes shift (mPlum, I65V) exhibited significant decay on both time scales, indicating the bathochromic shift correlates with a facile switching between a direct and water-mediated hydrogen bond. This dynamic model underscores the role of environmental flexibility in the mechanism of excited state solvation and provides a template for engineering next-generation red fluorescent proteins.

Solvation of Coumarin 480 within nano-confining environments: structure and dynamics

Equilibrium and dynamical characteristics pertaining to the solvation of the fluorescent probe Coumarin 480 within different confining environments are investigated using molecular dynamics simulations. Three kinds of confining systems are examined: (i) the cetyltrimethylammonium bromide (CTAB)/isooctane/1-hexanol/water; cationic inverse micelle (IM) (ii) a CTAB/water direct micelle (DM), and (iii) a silica-surfactant nanocomposite, comprising a cylindrical silica pore (SP) containing small amounts of water and CTAB species adsorbed at the pore walls. The solvation structures in the three environments differ at a qualitative level: an exchange between bulk- and interface-like solvation states was found in the IM, whereas in the DM, the solvation states of the probe are characterized by its embedding at the interface, trapped among the surfactant heads and tails. Within the SP structure, the coumarin exhibits alternations between internal and interfacial solvation states that occur on a ∼20 ns time scale and operate via 90° rotations of its molecular plane. The solvation responses of the environment following a vertical excitation of the probe are also investigated. Solvation times resulted between 2 and 1000 times longer than those found in bulk water, with a fast-to-slow trend IM→DM→SP, which can be interpreted in terms of the solvation structures that prevail in each case.

Conductivity and Solvation Dynamics in Ionic Liquids

It was shown recently that a simple dielectric continuum model predicts the integral solvation time of a dipolar solute ⟨τsolv⟩ to be inversely proportional to the electrical conductivity σ0 of an ionic solvent or solution. In this Letter, we provide a more general derivation of this connection and show that available data on coumarin 153 (C153) in ionic liquids generally support this prediction. The relationship between solvation time and conductivity can be expressed by ln(⟨τsolv⟩/ps) = 4.37 - 0.92 ln (σ0/S m(-1)) in 34 common ionic liquids.

Experimental and database-transferred electron-density analysis and evaluation of electrostatic forces in coumarin-102 dye

The electron-density distribution of a new crystal form of coumarin-102, a laser dye, has been investigated using the Hansen-Coppens multipolar atom model. The charge density was refined versus high-resolution X-ray diffraction data collected at 100 K and was also constructed by transferring the charge density from the Experimental Library of Multipolar Atom Model (ELMAM2). The topology of the refined charge density has been analysed within the Bader `Atoms In Molecules' theory framework. Deformation electron-density peak heights and topological features indicate that the chromen-2-one ring system has a delocalized π-electron cloud in resonance with the N (amino) atom. The molecular electrostatic potential was estimated from both experimental and transferred multipolar models; it reveals an asymmetric character of the charge distribution across the molecule. This polarization effect is due to a substantial charge delocalization within the molecule. The molecular dipole moments derived from the experimental and transferred multipolar models are also compared with the liquid and gas-phase dipole moments. The substantial molecular dipole moment enhancements observed in the crystal environment originate from the crystal field and from intermolecular charge transfer induced and controlled by C-H···O and C-H···N intermolecular hydrogen bonds. The atomic forces were integrated over the atomic basins and compared for the two electron-density models.