Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients.

The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.

Simulations of electric field gradient fluctuations and dynamics around sodium ions in ionic liquids.

The T1 relaxation time measured in nuclear magnetic resonance experiments contains information about electric field gradient (EFG) fluctuations around a nucleus, but computer simulations are typically required to interpret the underlying dynamics. This study uses classical molecular dynamics (MD) simulations and quantum chemical calculations, to investigate EFG fluctuations around a Na+ ion dissolved in the ionic liquid 1-ethyl 3-methylimidazolium tetrafluoroborate, [Im21][BF4], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na+ in [Im21][BF4], and the anti-shielding coefficient is comparable to its value in water. EFG correlation functions, CEFG(t), calculated using quantum mechanical methods or from force field charges are roughly equivalent after 200 fs, supporting the use of classical MD for estimating T1 times of monatomic ions in this ionic liquid. The EFG dynamics are strongly bi-modal, with 75%-90% of the de-correlation attributable to inertial solvent motion and the remainder to a highly distributed diffusional processes. Integral relaxation times, ⟨τEFG⟩, were found to deviate from hydrodynamic predictions and were non-linearly coupled to solvent viscosity. Further investigation showed that Na+ is solvated by four tetrahedrally arranged [BF4]- anions and directly coordinated by ∼6 fluorine atoms. Exchange of [BF4]- anions is rare on the 25-50 ns timescale and suggests that motion of solvent-shell [BF4]- is the primary mechanism for the EFG fluctuations. Different couplings of [BF4]- translational and rotational diffusion to viscosity are shown to be the source of the non-hydrodynamic scaling of ⟨τEFG⟩.

Quantifying Fluctuations of Average Solvent Environments for Embedding Calculations.

The viability and effectiveness of replacing an ensemble of embedded solute calculations by a single calculation using an average description of the solvent environment are evaluated. This work explores the fluctuations of the average description of the system obtained in two ways: from calculations on an ensemble of geometries and from an average environment constructed from the same ensemble. To this end, classical molecular dynamics simulations of a rigid acetone solute in SPCE water are performed in order to generate an ensemble of solvent environments. From this ensemble of solvent configurations, a number of different approaches for constructing an average solvent environment are employed. We perform a thorough numerical analysis of the fluctuations of the electrostatic potential experienced by the solute, as well as the resulting fluctuations of the solute's electronic density, measured through its dipole moment and fitted atomic point charges. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed method for generating the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum confinement effects, which may be important in certain cases, the fluctuations in the shift due to the interaction with the solvent are evaluated using frozen-density-embedding theory. Our results demonstrate that, for normally distributed environments, the constructed average environment is a reasonably good representation of a fluctuating molecular solvent environment. We then provide guidance for future comparisons between these theoretical treatments of solute/solvent systems to experimental measurements.

Molecular Dynamics Simulations of Bimolecular Electron Transfer: the Distance-Dependent Electronic Coupling.

Understanding the distance dependence of the parameters underpinning Marcus theory is imperative when interpreting the results of experiments on electron transfer (ET). Unfortunately, most of these parameters are difficult or impossible to access directly with experiments, necessitating the use of computer simulations to model them. In this work, we use molecular dynamics simulations in conjunction with constrained density functional theory calculations to study the distance dependence of the electronic coupling matrix element, |HRP|, for bimolecular ET. Contrary to what is typically assumed for such intermolecular reactions, we find that the magnitude of |HRP| does not decay exponentially with the center-of-mass separation of the reactants, rCOM. The addition of other simple measures of donor/acceptor (D/A) orientation did not improve the correlation of |HRP| with rCOM. Using the minimum distance separation, rmin, of the reactants as the structural descriptor allowed the system to be partitioned into high-coupling/close-contact and low-coupling/non-contact regimes, but large fluctuations of |HRP| were still found for the close-contact reactant pairs. Despite the persistent large fluctuations of |HRP|, its mean value was found to decay piecewise exponentially with increasing rmin, which was attributed to significant changes in the average D/A pair structure. The results herein advise one to use caution when interpreting the experimental results derived from spherical reactant models of bimolecular ET.

Red-Emitting Fluorophores as Local Water-Sensing Probes.

Fluorescent probes are known for their ability to sense changes in their direct environment. We introduce here the idea that common red-emitting fluorophores recommended for biological labeling and typically used for simple visualization of biomolecules can also act as reporters of the water content in their first solvent sphere by a simple measurement of their fluorescence lifetime. Using fluorescence spectroscopy, we investigated the excited-state dynamics of seven commercially available fluorophores emitting between 650 and 800 nm that are efficiently quenched by H2O. The amount of H2O in their direct surrounding was modulated in homogeneous H2O-D2O mixtures or, in heterogeneous systems, by confining them into reverse micelles, by encapsulating them into host-guest complexes with cyclodextrins, or by attaching them to peptides and proteins. We found that their fluorescence properties can be rationalized in terms of the amount of H2O in their direct surroundings, which provides a general mechanism for protein-induced fluorescence enhancements of red-emitting dyes and opens perspectives for directly counting water molecules in key biological environments or in polymers.

Molecular Dynamics Simulations of Bimolecular Electron Transfer: Testing the Coulomb Term in the Weller Equation.

Reliable estimation of the driving force for photoinduced electron transfer between neutral reactants is of utmost importance for most practical applications of these reactions. The driving force is usually calculated from the Weller equation, which contains a Coulomb term, C, whose magnitude in polar solvents is debated. We have performed umbrella sampling molecular dynamics simulations to determine C from the potentials of mean force between neutral and ionic donor/acceptor pairs of different sizes in solvents of varying polarity. According to the simulations, C in polar solvents is a factor of 2 more negative than typically calculated according to the Weller equation. Use of the π-stack contact distance in the Weller equation instead of the van der Waals radius recovers the correct value of C, but this is mostly fortuitous due to the compensating effects of overestimating the dielectric screening at contact and neglecting both charge dilution and desolvation.

Characterization of a New Electron Donor-Acceptor Dyad in Conventional Solvents and Ionic Liquids.

Ionic liquids are being tested as potential replacements for current electrolytes in energy-related applications. Electron transfer (ET) plays a central role in these applications, making it essential to understand how ET in ionic liquids differs from ET in conventional organic solvents and how these differences affect reaction kinetics. A new intramolecular electron donor-acceptor probe was synthesized by covalently linking the popular photoacceptor coumarin 152 with the donor dimethylaniline to create the dyad "C152-DMA" for potential use in probing dynamical solvent effects in ionic liquids. Molecular dynamics simulations of this dyad show the considerable conformational flexibility of the linker group but over a range of geometries in which the ET rate parameters vary little and should have minimal effect on reaction times >100 ps. Steady-state and time-resolved fluorescence methods show the spectra of C152-DMA to be highly responsive to solvent polarity, with ET rates varying over the range of 108 to 1012 s-1 between nonpolar and high-polarity conventional solvents. The sensitivity to hydrolysis in the presence of acidic impurities limits the dyad's use to ionic liquids of high purity. The results in the few ionic liquids examined here suggest that in addition to solvent polarity, electron transfer in C152-DMA also depends on solvent fluidity or solvation times.

Structural dynamics of an excited donor-acceptor complex from ultrafast polarized infrared spectroscopy, molecular dynamics simulations, and quantum chemical calculations.

The structural dynamics of an electron donor/acceptor complex (DAC) consisting of benzene and tetracyanoethylene (Bz/TCNE) solvated in CH2Cl2 have been investigated using ultrafast spectroscopy and mixed quantum/classical computer simulations. Population dynamics from visible and infrared transient absorption (TRIR) spectroscopy point to complex sub-10 ps dynamics followed by charge recombination on a 55-60 ps timescale. Structural dynamics involving large-scale reorganization of Bz˙+/TCNE˙- radical ion pairs are revealed using TRIR anisotropy measurements. A computational study combining quantum chemical calculations and classical molecular dynamics simulations was able to reproduce the experimental electronic absorption lineshape and TRIR anisotropy dynamics, allowing for a detailed investigation of the pair conformational dynamics. Contrary to the static single structure typically assumed in descriptions of DACs, we find that neither the ground nor excited state can be described using a single, well-defined species. Instead, the pair undergoes a rearrangement from disordered π-stacks to edge-to-face T-shaped structures following excitation. Translational diffusion of the radical ion pairs following excitation was found to be heterogeneous and dependent on both pair separation and orientation coordinates. Given the sensitivity of charge-transfer reactions to the arrangement of donor/acceptor pairs, the structural heterogeneity and corresponding dynamics demonstrated herein must be taken into account in future modeling of charge recombination processes in DACs.

Solvent controlled intramolecular electron transfer in mixtures of 1-butyl-3-methylimidizolium tetrafluoroborate and acetonitrile.

Time-resolved emission techniques were used to study the excited-state intramolecular electron transfer of 9-(4-biphenyl)-10-methylacridinium (BPAc+) in mixtures of 1-butyl-3-methylimidizolium tetrafluoroborate ([Im41][BF4])+ acetonitrile (ACN), a mixture previously shown to be of nearly constant polarity and nearly ideal mixing behavior. Reaction times (τ rxn) track solvation times (τ solv) as a function of mixture composition over a range of more than 3 orders of magnitude in τ solv. This same correlation extends to a variety of neat dipolar solvents and ionic liquids. Reaction times are ∼2-fold larger than τ solv over most of the range studied but appear to reach a limiting value of ∼3 ps in the fastest solvents.

Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects.

Herein are reported temperature-dependent measurements and molecular dynamics simulations designed to investigate the effects of molecular size, shape, and electrostatics on rotational dynamics in ionic liquids. Experiments were performed in the representative ionic liquid 1-butyl-3-methylimadazolium tetrafluoroborate ([Im41][BF4]) and simulations in the generic ionic liquid model ILM2 as well as a more detailed representation of [Im41][BF4]. 2H longitudinal spin relaxation times (T1) were measured for deuterated versions of 1,4-dimethylbenzene, 1-cyano-4-methylbenzene, and 1,4-dimethylpyridinium between 296 and 337 K. Fluorescence anisotropy measurements were made on the larger solutes 9,10-dimethylanthracene, 9-cyano-10-methylanthracence, and 9,10-dimethylacridnium between 240 and 292 K. Both experiment and simulation showed the nonpolar solutes rotate ∼2-fold faster than their dipolar and charged counterparts. The rotational correlation functions measured in fluorescence experiments are significantly nonexponential and can be fit to stretched exponential functions having stretching exponents 0.4 ≤ ß ≤ 0.8, with ß decreasing with decreasing temperature. Rotational correlation times in both the NMR and fluorescence experiments conform approximately to the hydrodynamic expectation τrot ∝ (η/T)p with p ≅ 1, and observed times are reasonably close to slip hydrodynamic predictions. Simulations, even with the idealized ILM2 solvent model, are in semiquantitative agreement with experiment when compared on the basis of equal values of ηT-1. When rotational diffusion coefficients (Di) rather than correlation times were considered, much larger departures from hydrodynamic predictions are found in many cases (p ∼ 0.5 and Di ≫ slip predictions). Rotational van Hove functions and trajectory analyses reveal the importance of large-angle jumps about some axes, even in the larger solutes.

Solvation Dynamics and Proton Transfer in Diethylaminohydroxyflavone.

4'-N,N-Diethylamino-3-hydroxyflavone (DEAHF) exhibits dual fluorescence in most solvents as a result of a rapid excited-state intramolecular proton transfer reaction. The high sensitivity of its dual emission to solvent polarity and hydrogen bonding make DEAHF of interest as a ratiometric fluorescence sensor. In addition, prior work has suggested that the rate of this proton transfer should depend on solvent relaxation in an unusual manner. It has been proposed that rapid solvation of the initially excited reactant should retard reaction. The present work tests this idea by using femtosecond Kerr-gated emission spectroscopy to measure the reaction kinetics of DEAHF in mixtures of propylene carbonate (PC) + acetonitrile (ACN). This mixture was chosen to maintain constant solvent polarity and thereby constant reaction energies while varying solvation times ∼10-fold with composition. The reaction kinetics observed in these mixtures are multiexponential, consisting of resolvable components of ∼2 and ∼30 ps and a small fraction of reaction faster than detectable by the 400 fs resolution of the experiment. Average reaction times increase by approximately a factor of 2 as a function of ACN mole fraction, primarily as a result of changes to the slower kinetic component. This trend is opposite to the composition dependence of solvation times, thereby supporting the unusual role of polar solvation dynamics in this proton transfer. In n-alkane solvents, where electrostatic coupling is minimized, frictional properties of the solvent do not influence reaction rates.

Rotational Dynamics in Ionic Liquids from NMR Relaxation Experiments and Simulations: Benzene and 1-Ethyl-3-Methylimidazolium.

Temperature-dependent (2)H longitudinal spin relaxation times (T1) of dilute benzene-d6 in 1-butyl-3-methylimidazolium tetrafluoroborate ([Im41][BF4]) and two deuterated variants of the 1-ethyl-3-methylimidazolium cation (Im21(+)-d1 and Im21(+)-d6) in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Im21][Tf2N]), measured at multiple Larmor frequencies, were used to probe rotational dynamics in ionic liquids. Rotational correlation times significantly faster than predicted by slip hydrodynamic calculations were observed for both solutes. Molecular dynamics simulations of these systems enabled extraction of more information about the rotational dynamics from the NMR data than rotation times alone. The multifrequency (2)H T1(T) data could be fit to within uncertainties over a broad region about the T1 minimum using models of the relevant rotational time correlation functions and their viscosity/temperature dependence derived from simulation. Such simulation-guided fitting provided confidence in the semiquantitative accuracy of the simulation models and enabled interpretation of NMR measurements to higher viscosities than previously possible. Simulations of the benzene system were therefore used to explore the nature of solute rotation in ionic liquids and how it might differ from rotation in conventional solvents. Whereas "spinning" about the C6 axis of benzene senses similarly weak solvent friction in both types of solvents, "tumbling" (rotations about in-plane axes) differs significantly in conventional solvents and ionic liquids. In the sluggish environment provided by ionic liquids, orientational caging and the presence of rare but influential large-amplitude (180°) jumps about in-plane axes lead to rotations being markedly nondiffusive, especially below room temperature.

Steady-State and Time-Resolved Studies into the Origin of the Intrinsic Fluorescence of G-Quadruplexes.

Stretches of guanines in DNA and RNA can fold into guanine quadruplex structures (GQSs). These structures protect telomeres in DNA and regulate gene expression in RNA. GQSs have an intrinsic fluorescence that is sensitive to different parameters, including loop sequence and length. However, the dependence of GQS fluorescence on solution and sequence parameters and the origin of this fluorescence are poorly understood. Herein we examine effects of dangling nucleotides and cosolute conditions on GQS fluorescence using both steady-state and time-resolved fluorescence spectroscopy. The quantum yield of dGGGTGGGTGGGTGGG, termed "dG3T", is found to be modest at ∼2 × 10(-3). Nevertheless, dG3T and its variants are significantly brighter than the common nucleic acid fluorophore 2-aminopurine (2AP) largely due to their sizable extinction coefficients. Dangling 5'-end nucleotides generally reduce emission and blue-shift the resultant spectrum, whereas dangling 3'-end nucleotides slightly enhance fluorescence, particularly on the red side of the emission band. Time-resolved fluorescence decays are broadly distributed in time and require three exponential components for accurate fits. Time-resolved emission spectra suggest the presence of two emitting populations centered at ∼330 and ∼390 nm, with the redder component being a well-defined long-lived (∼1 ns) entity. Insights into GQS fluorescence obtained here should be useful in designing brighter intrinsic RNA and DNA quadruplexes for use in label-free biotechnological applications.