Understanding the Optical Band Shape: Coumarin-153 Steady-State Spectroscopy

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.

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.

Theory and Electrochemistry of Cytochrome c

Extensive simulations of cytochrome c in solution are performed to address the apparent contradiction between large reorganization energies of protein electron transfer typically reported by atomistic simulations and much smaller values produced by protein electrochemistry. The two sets of data are reconciled by deriving the activation barrier for electrochemical reaction in terms of an effective reorganization energy composed of half the Stokes shift (characterizing the medium polarization in response to electron transfer) and the variance reorganization energy (characterizing the breadth of electrostatic fluctuations). This effective reorganization energy is much smaller than each of the two components contributing to it and is fully consistent with electrochemical measurements. Calculations in the range of temperatures between 280 and 360 K combine long, classical molecular dynamics simulations with quantum calculations of the protein active site. The results agree with the Arrhenius plots for the reaction rates and with cyclic voltammetry of cytochrome c immobilized on self-assembled monolayers. Small effective reorganization energy, and the resulting small activation barrier, is a general phenomenology of protein electron transfer allowing fast electron transport within biological energy chains.

Probe dependence on polar solvation dynamics from fs broadband fluorescence

Solvation dynamics is remarkably independent of the probe as long as specific interactions remain similar.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.

Surface Polarity and Nanoscale Solvation

Linear solvation theories are well established to describe electrostatic hydration of small solutes when the hydration free energy is dominated by the electrostatic free energy of the solute multipole. In contrast, hydration of nanometer solutes is driven by surface hydration. We address the question of whether the linear-response thermodynamics established for small multipolar solutes applies to surface hydration. To this end, molecular dynamics simulations are carried out on a model C180 solute that carries no global multipole, but the surface of which is decorated with radially pointing dipoles. Linear response is dramatically violated in this case. Further, two crossovers in the solvation thermodynamics are discovered as the surface polarity is increased. Both transformations produce strongly nonlinear solvation response. The second, more collective, crossover leads to a dramatic slowing down of the interfacial dynamics, reaching the time-scales of nanoseconds. Our picture offers the possibility of flipping water domains at interfaces of nanoparticles and biomolecules.

Femtosecond broadband fluorescence upconversion spectroscopy: improved setup and photometric correction

A setup for fluorescence upconversion spectroscopy (FLUPS) is described which has 80 fs temporal response (fwhm) for emission in the spectral range 425-750 nm. Broadband phase matching is achieved with tilted gate pulses at 1340 nm. Background from harmonics of the gate pulse is removed and sensitivity increased compared to previous designs. Photometric calibration of the upconversion process is performed with a set of fluorescent dyes. For Coumarin 153 in methanol the peak position, bandwidth, and asymmetry depending on delay time are reported.

Dynamic polar solvation is reported by fluorescing 4-aminophthalimide faithfully despite H-bonding

Solvation dynamics of 4-aminophthalimide (4AP) in methanol is measured by broadband upconversion of the fluorescence band. The peak emission frequency nu(t) is determined from 100 fs onward with 85 fs time resolution. Polar solvation based on simple continuum theory, including solute polarizability, describes the temporal shape of nu(t) quantitatively. Extrapolation nu(t-->0) points to an initial emission frequency which agrees with the result from stationary spectroscopy in a nonpolar solvent. The extent (4300 cm(-1)) of the dynamic Stokes shift is largely due (50%) to H-bonding, however. The observations imply that H-bonds with 4AP adiabatically follow the dielectric relaxation of the methanol network. The stimulated emission band is also used to measure solvation dynamics. The evolving band is monitored by transient absorption spectroscopy of supercontinuum probe pulses. But the excited-state absorption spectrum, its relative amplitude, and its evolution are needed to extract nu(t) from such measurements. These key data are obtained by comparison with the upconversion results. Thus calibrated photometrically, 4AP transient absorption can be used to monitor solvation dynamics in any solvent. The excited-state absorption spectrum is assigned with the help of time-dependent density-functional calculations. Fluorescence excitation and double-resonance spectroscopy of isolated 4AP, cooled in a supersonic jet, is used to determine optically active modes. An intramolecular reorganization energy is inferred which is consistent with the value in 2-methylbutane (2025 cm(-1)). The crystal structure is also provided.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Contrasts in the 77 K Emission Spectra, Structures, and Dynamics of Metal-to-Metal and Metal-to-Ligand Charge-Transfer Excited States

The 77 K emission spectrum of trans-[(ms-Me6[14]aneN4)Cr(CNRu(NH3)5)2]5+ has components characteristic of ligand field (LF) and metal-to-metal charge transfer (MMCT) excited states (ms-Me6[14]aneN4=5,12-meso-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane). The LF component of the emission is best resolved for irradiations at appreciably higher energies than the MMCT absorption band, while only the MMCT emission is observed for irradiations on the low-energy side of the MMCT absorption band. The LF emission component from this complex has vibronic structure that is very similar to that of the trans-[(ms-Me6[14]aneN4)Cr(CN)2]+ parent, but it is red-shifted by 560 cm-1 and the bandwidths are much larger. The red shift and the larger bandwidths of the ruthenated complex are attributed to configurational mixing between the LF and MMCT excited states, and the inferred mixing parameters are shown to be consistent with the known electron-transfer properties of the Ru(NH3)5 moieties. The MMCT excited-state lifetime is about 1 micros at 77 K and am(m)ine perdeuteration of this complex leads to an isotope effect of kNH/kND approximately 15-20. However, the contribution of the N-H stretching vibration to the emission sideband is too weak for a single vibrational mode model to be consistent with the observed lifetimes or the isotope effect. These features are very similar to those reported previously (J. Phys. Chem. A 2004, 108, 5041) for the MMCT emission of trans-[([14]aneN4)Cr{CNRu(NH3)5}2]5+ ([14]aneN4=1,4,8,11-tetraazacyclotetradecane), with the exception that the higher energy LF emission was not well resolved in the earlier work. The energies of the charge transfer absorption and emission maxima of both of these Cr(CN)Ru complexes are very similar to those of [Ru(NH3)4bpy]2+, but the latter has a 50-fold shorter 77 K excited-state lifetime, a 10-fold smaller NH/ND isotope effect, and a very different structure of its vibronic sidebands. Thus, the vibronic sidebands imply that the dominant excited-state distortions are in the metal-ligand vibrational modes for the Cr(CN)Ru complexes and in the bipyridine vibrational modes for the [Ru(NH3)4bpy]2+ complex. While an "equivalent" single vibrational mode model based on the frequencies and amplitudes of the dominant distortion modes is not consistent the observed lifetimes, such models do appear to be a good basis for qualitatively distinguishing different classes of excited-state dynamic behavior. A multimode, multichannel model may be necessary to adequately describe the excited-state dynamics of these simple electron-transfer systems.

Fluorescence Probing of Temperature-Dependent Dynamics and Friction in Ionic Liquid Local Environments

The solvation dynamics and local orientational friction for a series of four ionic liquids have been probed using coumarin 153 (C153) as a function of temperature. These ionic liquids are comprised of nonaromatic organic cations paired with a common anion, bis(trifluoromethylsulfonyl)imide (NTf(2)-). The specific liquids are as follows: N-methyl-tri-N-butylammonium NTf(2)- (N(1444)+/NTf(2)-), N-hexyl-tri-N-butylammonium NTf(2)- (N(6444)+/NTf(2)-), N-methyl-N-butylpyrrolidinium NTf(2)- (Pyrr(14)+/NTf(2)-), and N-methyl-N-ethoxyethylpyrrolidinium NTf(2)- (Pyrr(1(2O2))+/NTf(2)-). The observed solvation dynamics and fluorescence depolarization dynamics occur over a broad range of time scales that can only be adequately fit by functions including three or more exponential components. Stretched exponential distributions cannot adequately fit our data. The solvation and reorientational dynamics of the C153 probe are studied over a range of temperatures from 278.2 to 353.2 K. For both the solvation dynamics and the probe reorientational dynamics, the observed temperature dependence is well fit by a Vogel-Tammann-Fulcher law. To correlate the observed microscopic dynamics with macroscopic physical properties, temperature-dependent viscosities are also measured. Differential scanning calorimetry is used to study the thermodynamics of the phase transitions from the liquid to supercooled liquid to glassy states. For the two tetraalkylammonium liquids, the observed melting transitions occur near 300 K, so we are able to study the dynamics in a clearly supercooled regime. Very long time scale orientational relaxation time constants dynamics on the order of 100 ns are observed in the C153 fluorescence anisotropy. These are interpreted to arise from long-lived local structures in the environment surrounding the C153 probe.

Energetics of electron-transfer reactions in soft condensed media

The coupling of electronic transitions within molecules to condensed-phase media involves a complex hierarchy of spatial and dynamical scales. Thermodynamics of activation is related to the length scale of microscopic interactions reflected in the non-Arrhenius reaction kinetics. Solvent dynamics make a particularly strong impact on the activation barrier when the time scale of the reaction is comparable to the relaxation time of the solvent, and the reaction barrier becomes nonergodic. Finally, molecular polarizability is responsible for complex nonparabolic free energy surfaces for electron transfer. We discuss the application of these ideas to soft condensed solvents such as supercooled liquids, liquid crystals, and photosynthetic reaction centers.

Molecular Simulation of Solvent-Induced Stokes Shift in Absorption/Emission Spectra of Organic Chromophores

The values of steady-state solvatochromic Stokes shifts (SS) in absorption/emission electronic spectra of organic chromophores are studied theoretically in the framework of the Hush-Marcus model. Charge distributions for chromophore solutes in their S0 and S1 states are found by means of conventional quantum-chemical methods combined with the continuum PCM approach for treating solvation effects. The solvent reorganization energies, which are expected to correlate with the solvent-induced part of 1/2 SS, are found in a molecular dynamics (MD) simulation which invokes a novel method for separation of the inertial piece of the electrostatic response (Vener, et al. J. Phys. Chem. B 2006, 110, 14950). Computations, performed in two solvents (acetonitrile and benzene), consider three organic dyes: coumarin 153 as a benchmark system and two other chromophores, for which experimental spectra are also reported. The results are found to be in reasonable agreement with the experiment. A consistent treatment of nonlinear effect in the solvent response, promoted by the polarizability of solutes and contributing to the solvent reorganization energies (Ingrosso, et al. J. Phys. Chem. B 2005, 109, 3553), improves the results of computations.

Solvation and Solvatochromism in CO2-Expanded Liquids. 2. Experiment−Simulation Comparisons of Preferential Solvation in Three Prototypical Mixtures

Electronic absorption and emission spectra of 10-bis(phenylethynyl)anthracene (PEA) and coumarin 153 (C153) are measured as functions of composition along the bubble-point curve at 25 degrees C in CO2-expanded cyclohexane (c-C6H12), acetonitrile (CH3CN), and methanol (CH3OH). The nonlinear dependence of the spectral frequencies on composition suggests substantial preferential solvation of both solutes by the liquid components of these mixtures. Estimates of enrichment factors (local mole fraction of a component divided by its bulk value) based on the assumption that spectral shifts are linearly related to local composition are quite large (approximately 10) in the cases of the C153/CH3CN + CO2 and C153/CH3OH + CO2 systems at high xCO2. Computer simulations of anthracene, the chromophore of PEA, and C153 in these three CO2-expanded liquids are used to clarify the relationship between local composition and spectral shift. A semiempirical model consisting of additive electrostatic and dispersive interactions is able to capture the main features observed experimentally in all six solute/solvent combinations. The simulations show that the commonly used assumption of a linear relation between spectral shifts and local compositions grossly exaggerates the extent of preferential solvation in these mixtures. The collective nature of electrostatic solvation and the composition dependence of the solute's coordination number are shown to be responsible for the breakdown of this assumption.

Probes of the Metal-to-Ligand Charge-Transfer Excited States in Ruthenium-Am(m)ine-Bipyridine Complexes: The Effects of NH/ND and CH/CD Isotopic Substitution on the 77 K Luminescence

The effects of ligand perdeuteration on the metal-to-ligand charge-transfer (MLCT) excited-state emission properties at 77 K are described for several [Ru(L)(4)bpy](2+) complexes in which the emission process is nominally [uIII,bpy-] --> [RuII,bpy]. The perdeuteration of the 2,2'-bipyridine (bpy) ligand is found to increase the zero-point energy differences between the ground states and MLCT excited states by amounts that vary from 0 +/- 10 to 70 +/- 10 cm(-1) depending on the ligands L. This indicates that there are some vibrational modes with smaller force constants in the excited states than in the ground states for most of these complexes. These blue shifts increase approximately as the energy difference between the excited and ground states decreases, but they are otherwise not strongly correlated with the number of bipyridine ligands in the complex. Careful comparisons of the [Ru(L)(4)(d(8)-bpy)](2+) and [Ru(L)(4)(h(8)-bpy](2+) emission spectra are used to resolve the very weak vibronic contributions of the C-H stretching modes as the composite contributions of the corresponding vibrational reorganizational energies. The largest of these, 25 +/- 10 cm(-1), is found for the complexes with L = py or bpy/2 and smaller when L = NH(3). Perdeuteration of the am(m)ine ligands (NH(3), en, or [14]aneN(4)) has no significant effect on the zero-point energy difference, and the contributions of the NH stretching vibrational modes to the emission band shape are too weak to resolve. Ligand perdeuteration does increase the excited-state lifetimes by a factor that is roughly proportional to the excited-state-ground-state energy difference, even though the CH and NH vibrational reorganizational energies are too small for nuclear tunneling involving these modes to dominate the relaxation process. It is proposed that metal-ligand skeletal vibrational modes and configurational mixing between metal-centered, bpy-ligand-centered, and MLCT excited states are important in determining the zero-point energy differences, while a large number of different combinations of relatively low-frequency vibrational modes must contribute to the nonradiative relaxation of the MLCT excited states.

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.

Photophysics of trans-4-(Dimethylamino)-4‘-cyanostilbene and Its Use as a Solvation Probe

Electronic structure calculations, steady-state electronic spectroscopy, and femtosecond time-resolved emission spectroscopy are used to examine the photophysics of trans-4-(dimethylamino)-4'-cyanostilbene (DCS) and its solvent dependence. Semiempirical AM1/CI calculations suggest that an anilino TICT state is a potential candidate for the emissive state of DCS in polar solvents. But observation of large and solvent-independent absorption and emission transition moments in a number of solvents (M(abs) = 6.7 +/- 0.4 D and M(em) = 7.6 +/- 0.8 D) rule out the involvement of any such state, which would have a vanishingly small transition moment. The absorption and steady-state emission spectra of DCS evolve in a systematic manner with solvent polarity, approximately as would be expected for a single, highly polar excited state. Attempts to fit the solvatochromism of DCS using standard dielectric continuum models are only partially successful when values of the solute dipole moments suggested by independent measurements are assumed. The shapes of the absorption and emission spectra of DCS change systematically with solvent polarity in a manner that is semiquantitatively reproduced using a coupled-state model of the spectroscopy. Kerr-gate emission measurements show that the emission dynamics of DCS down to subpicosecond times reflect only solvent relaxation, rather than any more complicated electronic state kinetics. The spectral response functions measured with DCS are well correlated to those previously reported for the solvation probe coumarin 153, indicating DCS to be a useful alternative probe of solvation dynamics.