The effects of solute–solvent electrostatic interactions on solvatochromic shifts in supercritical CO2

Modeling Solvation in Supercritical CO2

In recent decades, a microscopic understanding of solute-solvent intermolecular interactions has been key to advances in technologies based on supercritical carbon dioxide. In many cases, computational work has provided the impetus for new discoveries, shedding new light on important concepts such as the local structure around the solute in the supercritical medium, the influence of the peculiar properties of the latter on the molecular behavior of dissolved substances and, importantly, CO₂ -philicity. In this Review, the theoretical work that has been relevant to these developments is surveyed and, by presenting some crucial open questions, the possible routes to achieving further progress based on the interplay between theory and experiments is discussed.

Probing Lewis Acid-Base Interactions with Born-Oppenheimer Molecular Dynamics: The Electronic Absorption Spectrum of p-Nitroaniline in Supercritical CO2

The structure and dynamics of p-nitroaniline (PNA) in supercritical CO2 (scCO2) at T = 315 K and ρ = 0.81 g cm(-3) are investigated by carrying out Born-Oppenheimer molecular dynamics, and the electronic absorption spectrum in scCO2 is determined by time dependent density functional theory. The structure of the PNA-scCO2 solution illustrates the role played by Lewis acid-base (LA-LB) interactions. In comparison with isolated PNA, the ν(N-O) symmetric and asymmetric stretching modes of PNA in scCO2 are red-shifted by -17 and -29 cm(-1), respectively. The maximum of the charge transfer (CT) absorption band of PNA in scSCO2 is at 3.9 eV, and the predicted red-shift of the π → π* electronic transition relative to the isolated gas-phase PNA molecule reproduces the experimental value of -0.35 eV. An analysis of the relationship between geometry distortions and excitation energies of PNA in scCO2 shows that the π → π* CT transition is very sensitive to changes of the N-O bond distance, strongly indicating a correlation between vibrational and electronic solvatochromism driven by LA-LB interactions. Despite the importance of LA-LB interactions to explain the solvation of PNA in scCO2, the red-shift of the CT band is mainly determined by electrostatic interactions.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: Application to solvatochromic shift calculations

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Local density augmentation and dynamic properties of hydrogen-and non-hydrogen-bonded supercritical fluids: A molecular dynamics study

The local density inhomogeneities in neat supercritical fluids were investigated via canonical molecular dynamics simulations. The selected systems under investigation were the polar and hydrogen-bonded fluid methanol as well as the quadrupolar non-hydrogen-bonded carbon dioxide one. Effective local densities, local density augmentation, and enhancement factors were calculated at state points along an isotherm close to the critical temperature of each system (T(r)=1.03). The results obtained reveal strong influence of the polarity and hydrogen bonding upon the intensity of the local density augmentation. It is found that this effect is sufficiently larger in the case of the polar and associated methanol in comparison to those predicted for carbon dioxide. For both fluids the local density augmentation values are maximized in the bulk density region near 0.7rho(c), a result that is in agreement with experiment. In addition, the local density dynamics of each fluid were investigated in terms of the appropriate time correlation functions. The behavior of these functions reveals that the bulk density dependence of the local density reorganization times is very sensitive to the specific intermolecular interactions and to the size of the local region. Also, the estimated local density reorganization time as a function of bulk density of each fluid was further analyzed and successfully related to two different time-scale relaxation mechanisms. Finally, the results obtained indicate a possible relationship between the single-molecule reorientational dynamics and the local density reorganization ones.

Solvation Dynamics by Computer Simulation: Coumarin C153 in 1,4-Dioxane

Computer simulation results are presented for an atomistic pair potential model of 1,4-dioxane which takes into account molecular flexibility. The model has been conceived to be applied to the study of solvatochromism and solvation dynamics in the presence of the polar probe coumarin C153. Computer simulations on the pure liquid have produced thermodynamical, structural, and dynamical data in good agreement with available experimental measures. This constitutes a valuable test of the 1,4-dioxane all-atom model employed. The study of solute-solvent interactions for C153 in 1,4-dioxane has been motivated by the aim of casting light, through simulations, on the interesting experimental findings according to which such a solvent behaves as a "polar" solvent with respect to dynamic solvation properties. Molecular dynamics is particularly suitable to model the process and provides an interpretation of the so-called "dioxane anomaly". An investigation of the structure of the solvation shell and of the dynamics of solvation is presented and discussed. In particular, the satisfactory accordance between simulated and experimental solvation response implies that the simulations give a reliable description of both solute and solvent at a molecular level and reinforces the idea that the explicit inclusion of discrete solvent molecules is needed for a realistic treatment of solvation phenomena in which the local structure of the liquid plays a key role.

Solvation in supercritical water

Solvation in supercritical water under equilibrium and nonequilibrium conditions is studied via molecular dynamics simulations. The influence of solute charge distributions and solvent density on the solvation structures and dynamics is examined with a diatomic probe solute molecule. It is found that the solvation structure varies dramatically with the solute dipole moment, especially in low-density water, in accord with many previous studies on ion solvation. This electrostrictive effect has important consequences for solvation dynamics. In the case of a nonequilibrium solvent relaxation, if there are sufficiently many water molecules close to the solute at the outset of the relaxation, the solvent response measured as a dynamic Stokes shift is almost completely governed by inertial rotations of these water molecules. By contrast, in the opposite case of a low local solvent density near the solute, not only rotations but also translations of water molecules play an important role in solvent relaxation dynamics. The applicability of a linear response is found to be significantly restricted at low water densities.

Solvation Dynamics of C153 in Supercritical Fluoroform: A Simulation Study Based on Two-Site and Five-Site Models of the Solvent

Molecular dynamics (MD) simulations of a probe solute (coumarin C153) in supercritical fluoroform are used to study time-dependent solute-solvent interactions. We study the dynamics of solvent reorganization in response to electronic excitation of C153 at a temperature of 1.03 T(c) (the critical temperature) and a series of densities above and below the critical density. Simulations of a two-site and five-site models of fluoroform are presented and compared. The time-dependent solvation response after solute electronic excitation is studied in the two cases, and the five-site results present an earlier onset of exponential decay that is closer to what is expected to be the experimental response. This is confirmed by comparison to experiment. In addition to obtaining the solvation response from nonequilibrium MD trajectories, approximate solvation responses were obtained from equilibrium time correlations of the fluctuations in the solvation energy change in the presence of ground- and excited-state solutes. For the five-site model, the equilibrium excited-state response shows stronger density dependence than the ground-state one. The nonequilibrium response appears to have an intermediate decay rate between the two equilibrium functions. The solute-partial-charge-solvent-induced-dipole interaction was also taken into account by means of a perturbative approach, which improved the agreement with experimental measurements available at densities corresponding to 1.4-1.6 rho(c) (where rho(c) the critical density). From the comparison between the two models, it is possible to conclude that an atomistic description is necessary for correctly representing the portion of solvation dynamics that is related to reorientation. This consideration is supported by providing results for orientational time correlation functions and by comparing the correlation times with the experimental ones.

Solvation of Coumarin 153 in Supercritical Fluoroform

We present a study of local density augmentation around an attractive solute (i.e., giving rise to more attractive interaction with the solvent than solvent-solvent interactions) in supercritical fluoroform. This work is based on molecular dynamics simulations of coumarin 153 in supercritical fluoroform at densities both above and below the critical density, ranging from dilute gas-like to liquid-like, at a reduced temperature (T/T(c)) of 1.03. We focused on studying the structure of the solvation shell and the variation of the solute electronic absorption and emission shifts with density. Quantum calculations at the density functional theory (DFT) level were run on the solute in the ground state, and time-dependent DFT calculations were performed in the solute excited state in order to determine the solute-solvent potential parameters. The results obtained for the Stokes shift are in agreement with the experimental measurements. To evaluate local density augmentation from simulations, we used two different definitions, one based on the solvation number and the other derived from solvatochromic shifts. In the former case, the agreement with experimental results is good, while, in the latter case, better agreement is achieved by perturbatively including the induced-dipole contribution to the solvation energy.

The effects of solute-solvent electrostatic interactions on solvation dynamics in supercritical CO2

We present here the results of molecular-dynamics simulation of solvation dynamics in supercritical CO(2) at a temperature of about 1.05T(c), where T(c) is the critical temperature, and at a series of densities ranging from 0.4 to 2.0 of the critical density rho(c). We focus on electrostatic solvation dynamics, representing the electronic excitation of the chromophore as a change in its charge distribution from a quadrupolar-symmetry ground state to a dipolar excited state. Two perturbations are considered, corresponding to different magnitudes of solute excited-state dipoles, denoted as d5 and d8. The d8 solute is more attractive, leading to a larger enhancement in CO(2) clustering upon solute electronic excitation. This has a large impact on solvation dynamics, especially at densities below rho(c). At these densities, solvation dynamics is much slower for the d8 than for the d5 solute. For both solutes, solvation dynamics becomes faster at densities above rho(c) at which solvent clustering diminishes. We show that the slowest solvation time scale is associated with solvent clustering and we relate it to solute-solvent mutual translational diffusion and the extent of change in effective local density resulting from solute electronic excitation.

Estimation of Local Density Augmentation and Hydrogen Bonding between Pyridazine and Water under Sub- and Supercritical Conditions Using UV-Vis Spectroscopy

The local density around pyridazine was evaluated by examining the UV-vis spectral shift of pyridazine in a high-pressure liquid state and supercritical water from 25 to 450 degrees C and from 20 to 45 MPa. Augmentation of the local density was observed from 380 to 420 degrees C, and showed the maximum at a lower density than the critical density of water. The degree of hydrogen bonding was estimated in consideration of the local density augmentation. The estimated degree of hydrogen bonding under subcritical conditions without any difference between the local density and the bulk density corresponded to the previously reported results with a UV-vis absorbance spectral shift of quinoline and an NMR proton chemical shift. However, the degree of hydrogen bonding near the critical point of water was larger than that in the case that the local density augmentation was not taken into account. At 380 degrees C and 0.2 g cm(-3) of the bulk density there are 30% as many hydrogen bonds as those under the ambient condition, and it was around 1.5-times that without considering local-density augmentation.

Determination of Kamlet–Taft solvent parameters π* of high pressure and supercritical water by the UV-Vis absorption spectral shift of 4-nitroanisole

Kamlet-Taft solvent parameters, pi*, of high pressure and supercritical water were determined from 16-420 degrees C based on solvatochromic measurements of 4-nitroanisole. For the measurements, an optical cell that could be used at high temperatures and pressures was developed with the specification of minimal dead space. The low dead space cell allowed us to measure the absorption spectra of 4-nitroanisole at high temperature conditions before appreciable decomposition occurred. The behavior of pi* in terms of water density (pi* = 1.77rho- 0.71) was found to be linear, except in the near critical region, in which deviations were observed that could be attributed to local density augmentation. Excess density, which was defined as the difference between local density and bulk density, showed a maximum near the critical density of water. The frequencies of UV-Vis spectra of 4-(dimethylamino)benzonitrile and N,N-dimethyl-4-nitroaniline were correlated with pi* based on a linear solvation energy relationship (LSER) theory. Local density augmentation around 4-nitroanisole and that around 4-(dimethylamino)benzonitrile were similar but the augmentation observed around N,N-dimethyl-4-nitroaniline was larger.

Electron Donor−Acceptor Interactions in Ethanol−CO2 Mixtures: An Ab Initio Molecular Dynamics Study of Supercritical Carbon Dioxide

The nature of interactions between ethanol and carbon dioxide has been characterized using simulations via the Car-Parrinello molecular dynamics (CPMD) method. Optimized geometries and energetics of free-standing ethanol-CO2 clusters exhibit evidence for a relatively more stable electron donor-acceptor (EDA) complex between these two species rather than a hydrogen-bonded configuration. This fact has also been confirmed by the higher formation rate of the EDA complex in supercritical carbon dioxide-ethanol mixtures. The probability density distribution of CO2 molecules around ethanol in the supercritical state shows two high probability regions along the direction of the lone pairs on the oxygen atom of ethanol. The EDA interaction between ethanol and CO2 as well as that between CO2 molecules themselves leads to significant deviations from linearity in the geometry of the CO2 molecule. The vibrational spectra of carbon dioxide obtained from the atomic velocity correlation functions in the bulk system as well as from isolated complexes show splitting of the nu2 bending mode that arises largely from CO2-CO2 interactions, with ethanol contributing only marginally because of its low concentration in the present study. The stretching frequency of the hydroxyl group of ethanol is shifted to lower frequencies in the bulk mixture when compared to its gas-phase value, in agreement with experiments.

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.

Solvation Dynamics in Acetonitrile: A Study Incorporating Solute Electronic Response and Nuclear Relaxation

The solvent reorganization process after electronic excitation of a polar solute in a polar solvent such as acetonitrile is related mainly to the time evolution of the solute-solvent electrostatic interaction. Modern laser-based techniques have sufficient time resolution to follow this decay in real time, providing information to be confirmed and interpreted by theories and models. We present here a study aimed at the investigation of the different steps involved in the process taking place after a vertical S(0) --> S(1) excitation of a large size chromophore, coumarin 153 (C153), in acetonitrile, from both the solute and the solvent points of view. To do this, we use accurate quantum mechanical calculations for the solute properties within the polarizable continuum model (PCM) and classical molecular dynamics (MD) simulations, both equilibrium and nonequilibrium, for C153 in the presence of the solvent. The geometry of the solute is allowed to change in order to study the role of internal motions in the time-dependent solvation process. The solvent response function has been obtained from the simulation data and compared to experiment, while the comparison between equilibrium and nonequilibrium MD results for the solvation response confirms the validity of the linear response approximation in the C153-acetonitrile system. The MD trajectories have also been used to monitor the structure of the solvation shell and to determine its change in response to the change in the solute partial charges.