A time-dependent polarizable continuum model: theory and application

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N,N-dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well.     

Dielectric properties of poly(4-methylphenylisocyanate) and poly(4-methoxyphenylisocyanate) in solution

In the range 200 Hz-2 MHz, the dielectric behaviour of two polyarylisocyanates depends on the solvent. In certain solvents, such as toluene, there is only one high frequency absorption for poly(4-methylphenylisocyanate) and it is independent of molecular weight. Its character corresponds to chains having a low kinetic flexibility. In other solvents, this polymer, as well as poly(4-methoxyphenylisocyanate), shows two regions of dielectric absorption. The low frequency relaxation is molecular weight dependent: a polarization due to solvent polymer interactions occurs along the main chain. Despite its solvent-dependence, the total dipole moment of these polyarylisocyanates which behave like coils is much lower than that of polyalkylisocyanates, which are known to be rod-like.     

Continuum treatment of electronic polarization effect

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.     

Solvatochromic behaviours and structure–spectra relationships of 4-carboxyl-2,6-dinitrophenylazohydroxynaphthalenes

Comprehensive electronic absorption spectra of a new dye series, 4-carboxyl-2,6-dinitrophenylazohydroxynaphthalenes have been investigated in solvents of varying polarities. The solvent dependent UV–vis spectral shifts were analysed using some solvent physical parameters such as refractive index, dielectric function, hydrogen bonding acceptor ability, orientation of polarization and others. The observed spectral shifts were correlated with different solute–solvent interaction mechanisms using simple and multiple linear regression analyses. The results of the curve fitting coefficients enabled us to classify the various interactions of solvents with the dyes and relate the solvatochromic behaviours to the substituent effects on the dye molecules. Charge-transfer complexation occurring between one of the congeners and N,N′-dimethylformamide was extensively studied and discovered to be both concentration- and temperature-dependent.The electronic character and the chemical nature of the solvents as well as the chemical nature of the other substituents, apart from the common hydroxyl group, are important factors for the observed solvatochromic properties of the 4-carboxyl-2, 6-dinitrophenylazohydroxynaphthalenes.     

Solvent friction effect on intramolecular electron transfer

U-shaped donor-bridge-acceptor molecules with different electronic couplings have been investigated as a function of temperature in solvents with slow polarization relaxation, in particular, N-methylacetamide (NMA) and N-methylpropionamide (NMP). At high temperature, the electron-transfer rate is well described by a nonadiabatic model; however, the rate at low temperature is controlled by the solvent friction. The change of the electron-transfer mechanism is discussed and compared with theoretical models.     

Electrophoretic mobilities of large organic ions in nonaqueous solvents: determination by capillary electrophoresis in propylene carbonate, N,N-dimethylformamide, N,N,-dimethylacetamide, acetonitrile and methanol

The mobilities of the monocharged permanent tertraphenylphosphonium cation and tetraphenylborate anion are determined by capillary zone electrophoresis in different organic solvents as a function of the ionic strength, I, of the background electrolyte. The nonaqueous solvents are propylene carbonate (PC), N,N-dimethylformamide (DMF), N,N,-dimethylacetamide (DMA), acetonitrile (MeCN) and methanol (MeOH). The ionic strength is between 5 and 50 mmol/L. The mobility as a function of I is in good agreement with the theory of Debye, Hückel and Onsager (DHO), extended by the ion size parameter as introduced by Falkenhagen and Pitts. The values of the limiting DHO slopes of the mobility vs. I curves (the slopes express the influence of the solvent on the reduction of the mobility with increase of I) decrease in the order MeCN > MeOH > DMF > DMA > PC. Absolute mobilities (obtained by extrapolation to I = 0) of a particular ion differ by a factor of about 7 between the solvents. However, constancy within 10% is observed for their Walden products (the absolute mobility multiplied with the solvent's macroviscosity). The role of dielectric friction on the mobility of the present monocharged, large analyte ions is discussed according to the theory of Hubbard and Onsager. Based on the radii of the ions, the static permittivity of the solvent and its permittivity at infinite frequency, and the relaxation time of polarization, an equal contribution of dielectric and hydrodynamic friction is predicted in MeOH as solvent. Experimental data are in contrast to this prediction, indicating the overestimation of dielectric friction, and the dominance of hydrodynamic friction on the migration of the analyte ions in all solvents under consideration.     

Coupling quantum Monte Carlo to a nonlinear polarizable continuum model for spherical solutes

Starting from the nonlinear dielectric response model of Sandberg and Edholm, we derive an analytical expression of the polarization contribution to the solvation free energy in terms of the electronic density of the solute and the dielectric properties of the solvent. The solvent inhomogeneity is taken into account with the use of a smooth switching function whose spacial variation is established on the basis of how the solvent is arranged around the solute. An explicit form of a local potential representing the solvent effect on the solute is thus obtained by functional analysis. This effective potential can be combined with density functional or quantum chemical methods for the quantum mechanical treatment of the solute. Here, we use quantum Monte Carlo techniques for the solute and apply the method to the hydration of atomic ions finding very good agreement with experimental data.     

Self-consistent reaction field calculations of the solvent effect on absorption and emission n, π* transitions of diazines

A modified version of the self-consistent reaction field (SCRF) method has been accomplished in order to study the solvent effect on the electronic transition energies. The dielectric relaxation properties both of solvent and solute are directly taken into account in the Hartree—Fock equation. The method has been applied to calculate the solvent shifts, both in absorption and in emission, for n, π^* transitions of the three diazine isomers. It was found that the continuum model is able to describe experimental findings for aprotic solvents; the discrete plus continuum model is needed to account for the solvent shifts observed in water solution.     

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.     

A simple analysis of the influence of the solvent-induced electronic polarization on the <Superscript>15</Superscript>N magnetic shielding of pyridine in water

Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the ¹⁵N magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding constant is calculated as −58.7 ppm, in good agreement with the experimental value of −56.3 ppm. The explicit inclusion of hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of −61.8 ppm.     

Dynamics of a supercooled ionic liquid studied by optical and dielectric spectroscopy

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming ionic liquid dibutylammonium formate near its glass transition temperature Tg=153 K. The Stokes-shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical line width changes systematically along the solvation coordinate. The solvent dynamics in the viscous regime is compared with the rotational behavior of the solute and with the dielectric relaxation of the ionic liquid. Among the different quantities derived from the dielectric experiments, the relaxation of the macroscopic electric field, i.e., the modulus Mt, matches best the solvent response Ct regarding time scale and stretching exponent. Many other properties are reminiscent of the behavior of polar molecular liquids which lack the ionic character.     

Solvent response and dielectric relaxation in supercooled butyronitrile

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming dipolar liquid butyronitrile near its glass transition temperature T(g)=95 K. The Stokes shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical linewidth changes along the solvation coordinate in a nonmonotonic fashion. These features are characteristic of solvation in viscous solvents and clearly indicate heterogeneous dynamics, i.e., spatially distinct solvent response times. Using the dielectric relaxation data of viscous butyronitrile as input, a microscopic model of dipolar solvation captures the relaxation time, the relaxation dispersion, and the amplitude of the dynamical Stokes shift remarkably well.     

Dielectric properties for the binary mixture of dimethylsuphoxide and dimethylacetamide with 2-nitrotoluene at microwave frequencies

The dielectric properties of various organic solvents and binary solvent mixtures at different temperatures over the frequency range of 10 MHz–20 GHz, are investigated using the time domain reflectometry technique, at various temperatures from 15 to 45 °C. These solvent mixtures—dimethylacetamide–2-nitrotoluene and dimethylsulphoxide–2-nitrotoluene as well as pure solvents display a Debye type dispersion. Their frequency-dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters, for these solvent systems at various temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The static permittivity increases with increase in volume percentage of 2-nitrotoluene in dimethylacetamide as well as dimethylsulphoxide whereas the relaxation time decreases for both the systems.     

Effects of hydrogen bond and solvent polarity on the C=O stretching of bis(2-thienyl)ketone in solution

The optimized structural parameters, the absorption and the resonance Raman spectra have been investigated for the bis(2-thienyl)ketone in gas phase, in cyclohexane, methanol, and acetonitrile solvents by means of time dependent density functional theory calculations, the solvent electronic polarization effect on the solvation shift is examined and in well accordance with the calculation. The effect of increasing the polarity of the solvent is well represented by the polarizable continuum model, both for the absorption spectra and resonance Raman intensities. The Raman spectra of the C=O stretching mode, which is sensitive to the intermolecular interaction for bis(2-thienyl)ketone dissolved in solvents, were systematically studied. It was found that the hydrogen bond effect plays an important role in reducing the carbonyl stretching wavenumbers. The results of Raman shifts were interpreted through the dilution effect, solvation effects, and hydrogen bond-forming effects. Furthermore, the excitation profiles of several important Raman bands of bis(2-thienyl)ketone molecule in different solvents have been critically analyzed. The solvent effects on structural and symmetry properties of the molecule in S2 electronic state as well as the short-time photo relaxation dynamics have been discussed.     

Solvent effect on intramolecular electron transfer rates of mixed-valence biferrocene monocation derivatives

Intramolecular electron transfer (ET) rates in various solvents of mixed-valence biferrocene monocation (Fe(II), Fe(III)) and the 1',1' '-diiodo and 1',1' '-diethyl derivatives (respectively abbreviated as BFC(+), I(2)BFC(+), and Et(2)BFC(+)) were determined by means of the spin-lattice relaxation times of the protons, taking into account the local magnetic field fluctuation caused by the electron hopping between the two ferrocene units. We also determined the ET rates of a mixed-valence diferrocenylacetylene monocation (DFA(+)) in order to examine the effect of the insertion of an acetylene bridge between the two ferrocene units. The insertion of the bridge decreased the ET rate, while the effect of substitution on the cyclopentadienyl rings on the rate was minor. The observed rates for each mixed-valence monocation in various solvents did not correlate with the reorganization energies, but we did find a significant contribution of the solvent dynamics. The observed rates were considerably higher than those expected on the basis of the Sumi-Marcus-Nalder model in which the solvents were regarded as dielectric continua. The slope of the logarithm plot of the pre-exponential factors in various solvents for each mixed-valence monocation versus the inverse of the longitudinal dielectric relaxation times of the solvents was significantly smaller than unity, and the slope for DFA(+) was larger than those for BFC(+), I(2)BFC(+), and Et(2)BFC(+). These results were ascribed to a partial contribution of the dielectric friction to the dynamics along the solvent coordinate; the extent of the contribution decreased with a reduction in the ET distance. For the dynamics along the solvent coordinate of the ET reactions in methanol, the observed rates indicated an important contribution by the minor dielectric relaxation components with faster relaxation times, rather than the major component with an extraordinarily long relaxation time.     

Solvent effect on hydrogen bonded Tyr⋯Asp⋯Arg triads: Enzymatic catalyzed model system

The hydrogen bond plays a vital role in structural arrangement, intermediate state stabilization, materials function, and biological activity of certain enzymatic reactions. The solvent and electronic effects on hydrogen bonds are illustrated employing the polarizable contimuum model at B3LYP/6–311++G(d,p) level. Geometry optimizations reflect the significant solvent and electronic effect. The proton departs spontaneously upon oxidation from the hydroxyl group of tyrosyl in hydrogen bonded Tyr⋯Asp⋯Arg triads in both gas phase and solvents. The electron transfer isomers are observed for anionic triads, no matter what the solvent is. The difference of distance between two hydrogen bonds is enlarged in solvent as compared to that in gas phase. The electronic effect on IR spectra is distinctive. The tyrosyl fragment tends to be oxidized and the arginine moiety is easier to bind an excess electron. The variations of chemical shift and spin-spin coupling constant are more significant upon electron transfer than upon solvent dielectric constant. The augmentation of solvent dielectric constant stabilizes the system, enhances the difference of isomers, and increases the vertical ionization potential and vertical electron affinity values.     

Spin-lattice relaxation and rotational motion of aromatic triplet-state molecules in supercooled alkane solvents (part 1)

The phosphorescence of phenazine (PZ) and quinoxaline (QX) was investigated after pulsed laser excitation in the glass-transition range of several alkane solvents. Three relaxation processes of PZ and QX in the metastable triplet state, T1, were studied as a function of temperature: (1) the decay of the selective population of the strongly phosphorescent triplet substate T1x due to spin-lattice relaxation (SLR), (2) the time-dependent red shift of the phosphorescence spectrum due to the solvation of triplet-state molecules, and (3) the decay of the phosphorescence polarization due to orientational relaxation (OR). Various aspects and connections of the mechanisms governing the three relaxation phenomena are discussed. The relaxation dynamics were characterized at temperatures above the glass-transition temperature of the respective solvent, where the fundamental processes involved are strongly dependent upon the solvent viscosities. For the systems treated here, OR and solvation were satisfactorily described by a Vogel-Fulcher-Tammann temperature behavior. SLR also depends on properties of the alkane solvent above the glass transition. Upon cooling, SLR becomes independent of the specific solvent properties and is based on mechanisms that are typical for amorphous glasses or solids. (This particular aspect will be the subject of a subsequent publication, part 2).     

Toward an understanding of the catalytic role of hydrogen-bond donor solvents in the hetero-Diels-Alder reaction between acetone and butadiene derivative

A detailed theoretical investigation of the catalytic role of hydrogen-bond- (HB-) donor molecules (water, methanol, chloroform, dichloromethane, and chloromethane) in the hetero-Diels-Alder reaction between acetone and N,N-dimethyl-1-amino-3-methoxy-1,3-butadiene is presented. This work extends a previous study (Domingo, L. R.; Andres, J. J. Org. Chem. 2003, 68, 8662) in which the importance of weak HB-donor solvents to catalyze more effectively than solvents with a higher dielectric constant but no HB-donor capability was analyzed. Now, based on density functional theory (DFT) at B3LYP/6-31+G(d) level calculations, different techniques for analyzing the nature of HB interaction, namely, natural bond orbital (NBO) theory, topological analysis of the electron density (atoms in molecules, AIM, theory), and the electron localization function (ELF) and decomposition of the interaction energy between monomers (energy decomposition analysis, EDA), have been applied to understand why only some HB-donor solvents are able to catalyze the reaction. The catalytic effect of the solvent arises from the improved HB-acceptor capability of the oxygen atom at the transition structure (TS) due to the strong polarization of the carbonyl group. The HB acceptor presents three lone pairs (NBO analysis), and the ELF shows an increment of the electronic charge of the lone pairs of 0.50e with respect to the reactant. All solvent molecules form stronger HB interactions at the TS, but only those presenting larger charge-transfer interactions (water, methanol, chloroform) benefit more from the polarization of the carbonyl group than other solvents (dichloromethane, chloromethane) with less "covalent" character.     

Dipolar solvation dynamics in room temperature ionic liquids: an effective medium calculation using dielectric relaxation data

Solvation dynamics in four imidazolium cation based room temperature ionic liquids (RTIL) have been calculated by using the recently measured dielectric relaxation data [ J. Phys. Chem. B 2008, 112, 4854 ] as an input in a molecular hydrodynamic theory developed earlier for studying solvation energy relaxation in polar solvents. Coumarin 153 (C153), 4-aminophthalimide (4-AP), and trans-4-dimethylamino-4'-cyanostilbene (DCS) have been used as probe molecules for this purpose. The medium response to a laser-excited probe molecule in an ionic liquid is approximated by that in an effective dipolar medium. The calculated decays of the solvent response function for these RTILs have been found to be biphasic and the decay time constants agree well with the available experimental and computer simulation results. Also, no probe dependence has been found for the average solvation times in these ionic liquids. In addition, dipolar solvation dynamics have been predicted for two other RTILs for which experimental results are not available yet. These predictions should be tested against experiments and/or simulation studies.