Onsager Reaction Field Theory Research Articles

Size-dependent solvatochromism of CdS nanoparticles: Experimental absorption and fluorescence analyses

Owing to the quantum confinement effect, a nanocrystal shows a unique blend of molecular and solid properties: discrete energy levels with large polarizabilities which could respond to solvent environments. In this paper, we used steady-state fluorescence and absorption spectroscopy to study the size-dependent solvatochromism of CdS nanoparticles. The dipolar character of the ground state and the first excited state of the nanoparticle were also investigated with in the framework of Onsager reaction field theory using Ooshika–Mataga–Lippert equation. The results of the present study revealed that the solvatochromic responses were size dependent. Additionally, the responses increased with the particle size up to a certain size beyond which the response started to fall again. Hence, fine-tuning the nanoparticle's solvatochromic response and band gap is possible by appropriate choice of size. Moreover, size-dependent dipole moment values of CdS nanoparticles were determined. Based on the findings of the present study it was noted that steady-state fluorescence and absorption spectroscopy methods can efficiently be used to study the size-dependent solvatochromism of CdS nanoparticles.

Local Electric Fields in Aqueous Electrolytes.

Vibrational Stark shifts were explored in aqueous solutions of organic molecules with carbonyl- and nitrile-containing constituents. In many cases, the vibrational resonances from these moieties shifted toward lower frequency as salt was introduced into solution. This is in contrast to the blue-shift that would be expected based upon Onsager's reaction field theory. Salts containing well-hydrated cations like Mg2+ or Li+ led to the most pronounced Stark shift for the carbonyl group, while poorly hydrated cations like Cs+ had the greatest impact on nitriles. Moreover, salts containing I- gave rise to larger Stark shifts than those containing Cl-. Molecular dynamics simulations indicated that cations and anions both accumulate around the probe in an ion- and probe-dependent manner. An electric field was generated by the ion pair, which pointed from the cation to the anion through the vibrational chromophore. This resulted from solvent-shared binding of the ions to the probes, consistent with their positions in the Hofmeister series. The "anti-Onsager" Stark shifts occur in both vibrational spectroscopy and fluorescence measurements.

Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) [Formula: see text]. The ferromagnetic long-range interactions considered in this paper decay as [Formula: see text] with the distance [Formula: see text] between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of [Formula: see text] and [Formula: see text]. At finite temperatures and in the region [Formula: see text] in which [Formula: see text] is dependent of [Formula: see text], the ferromagnetic-paramagnetic phase transition survives for [Formula: see text] and no phase transition exists for [Formula: see text]. At [Formula: see text], the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for [Formula: see text]. The ground state of the system keeps ferromagnetic when [Formula: see text]. But for [Formula: see text], the system becomes antiferromagnetic at all temperatures.

Electrostatic Estimation of Intercalant Jump-Diffusion Barriers Using Finite-Size Ion Models.

We report on a scheme for estimating intercalant jump-diffusion barriers that are typically obtained from demanding density functional theory-nudged elastic band calculations. The key idea is to relax a chain of states in the field of the electrostatic potential that is averaged over a spherical volume using different finite-size ion models. For magnesium migrating in typical intercalation materials such as transition-metal oxides, we find that the optimal model is a relatively large shell. This data-driven result parallels typical assumptions made in models based on Onsager's reaction field theory to quantitatively estimate electrostatic solvent effects. Because of its efficiency, our potential of electrostatics-finite ion size (PfEFIS) barrier estimation scheme will enable rapid identification of materials with good ionic mobility.

Solvation Reaction Field at the Interface Measured by Vibrational Sum Frequency Generation Spectroscopy.

Interfacial electric fields are important in several areas of chemistry, materials sciences, and device physics. However, they are poorly understood, partly because they are difficult to measure directly and model accurately. We present both a spectroscopic experimental investigation and a theoretical model for the interfacial field at the junction of a conductor and a dielectric. First, we present vibrational sum frequency generation (VSFG) results of the nitrile (CN) stretch of 4-mercaptobenzonitrile (4-MBN) covalently attached to a gold surface and in contact with a variety of liquid dielectrics. It is found that the CN stretch frequency red-shifts with increasing dielectric constant. Second, we build a model in direct analogy to the well-known Onsager reaction field theory, which has been successful in predicting vibrational frequency shifts in bulk dielectric media. Clearly, due to the asymmetric environment, with metal on one side and a dielectric on the other, the bulk Onsager model is not applicable at the interface. To address this, we apply the Onsager model to the interface accounting for the asymmetry. The model successfully explains the red-shift of the CN stretch as a function of the dielectric constant and is used to estimate the reaction field near the interface. We show the similarities and differences between the conventional bulk Onsager model and the interfacial reaction field model. In particular, the model emphasizes the importance of the metal as part of the solvation environment of the tethered molecules. We anticipate that our work will be of fundamental value to understand the crucial and often elusive electric fields at interfaces.

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.

Solvent effect on the adduct formation of methyltrioxorhenium (MTO) and pyridine: enthalpy and entropy contributions

1:1 adduct formation between methyltrioxorhenium (MTO) and pyridine in different solvents (n-hexane, benzene, chloroform, ethyl acetate, dichloromethane and acetone) was studied using spectrophotometric techniques. The formation constants were determined from the absorbance change of the adduct versus pyridine concentration. The values of the formation constants vary from 114.5 to 752.5 L mol(-1) at T= 20 degrees C depending on the dielectric constant of the solvent (epsilon(r) = 1.89-20.7). Enthalpy and entropy changes during the adduct formation reactions were determined from van't Hoff plots. The measured enthalpy change of -37.0 to -22.2 kJ mol(-1) depends on epsilon(r), which is explained by Onsager's reaction field theory. The measured entropy change ranges from -71.2 to -36.6 J K(-1) mol(-1), and the dependence on the solvent is discussed in terms of the solvation effect.

Theoretical molecular structures for partially bonded complexes of trimethylamine with SO 2 and SO 3: ab initio and density functional theory calculations

The self-consistent reaction field (SCRF) method based on Onsager's reaction field theory is applied to investigate the effect of polar media on molecular structures of complexes of trimethylamime (TMA) with SO x ( x=2,3). The calculated SCRF N–S bond lengths at the MPW1PW91/6-311+G(3df) level are in satisfactory agreement with the experimental N–S bond lengths for the TMA–SO x upon crystallization. The results are enough to demonstrate the usefulness of the reaction field theory in providing qualitative understanding of the medium effect on the partially bonded system such as TMA–SO x .

Onsager reaction-field theory for magnetic models on diamond and hcp lattices

The Onsager reaction-field (ORF) theory is extended to apply to three-dimensional Bravais lattices with a basis. The ORF calculation is used to predict the critical temperature for classical Ising, $XY,$ and Heisenberg magnetic models, in particular, on diamond and hexagonal close-packed lattices. Results are compared with series extrapolations and other theoretical approaches where available. For the hcp lattice the ORF calculation is seen to be equivalent to a Green's-function approach by Adler [Physica B 107B, 207 (1981)].

Solvent Effects on the Complex Formation of Benzophenone Ketyl Radical and Triethylamine

The 1:1 complex formation between benzophenone ketyl radical (BPK) and triethylamine in various solvents was studied by means of nanosecond laser flash photolysis. The complex shows an absorption band slightly red-shifted from that of uncoupled BPK. The formation constants (Kf's) were determined from the absorbance change of the complex against amine concentration. The Kf values are in the range 60−103 M-1 depending on the dielectric constant of solvent (εr = 10.7−1.89). Enthalpy and entropy changes in the complex formation reactions were determined from van't Hoff plots around room temperature. The measured enthalpy change of −2.0 to −7.5 kcal mol-1 depends on εr, which is explained with an Onsager's reaction field theory. The measured entropy change varies from −16.5 cal K mol-1 to nearly zero, and the dependence on the solvent is discussed in terms of the solvation effect.

A perturbation theory and simulations of the dipole solvation thermodynamics: Dipolar hard spheres

Padé truncation of the thermodynamic perturbation theory is used to calculate the solvation chemical potential of a dipolar solute in a model fluid of dipolar hard spheres. Monte Carlo simulations of the solvation thermodynamics are carried out over a wide range of solute and solvent dipoles in order to address the following major issues: (i) testing the performance of the Padé perturbation theory against simulations, (ii) understanding the mechanism of nonlinear solvation, and (iii) elucidating the fundamental limitations of the dielectric continuum picture of dipole solvation. The Padé form of the solvation chemical potential constructed in the paper agrees with the whole body of simulation results within an accuracy of 3%. Internal energy and entropy of solvation are also accurately described by the perturbation treatment. Simulations show a complex nonlinear solvation mechanism in dipolar liquids: At low solvent polarities the solvation nonlinearity is due to orientational saturation that switches to the electrostriction mechanism at higher dipolar strengths of the solvent. We find that the optimum cavity radius of the Onsager reaction-field theory of solvation depends substantially on solvent polarity. A general method of testing the performance of linear solvation theories is proposed. It shows that the fundamental failure of continuum theories consists in their inaccurate description of the internal energy and entropy of solvation.

UV-Vis spectroscopic studies of solute–solvent and solute–cosolvent interactions in supercritical carbon dioxide

The keto–enol tautomeric equilibria of ethyl acetoacetate in supercritical (SC) CO2 with and without ethanol cosolvent were investigated over the pressure range from 75.9 to 185 bar at 308.2 K using UV-Vis spectroscopy. In order to obtain the local densities of solvent and cosolvent about the solute, we correlated the standard Helmholtz free energy of the tautomerization with a solvent parameter based on the Onsager reaction field theory. In both SC CO2 and SC CO2–ethanol, the local density enhancement of CO2 in the vicinity of the solute is most remarkable at the reduced density close to unity. The highest degree of aggregation of cosolvent about the solute takes place at the lowest pressure investigated, which is slightly above the critical pressure. Moreover, the clustering of ethanol with the solute competes with that of CO2. In addition, the local concentration enhancement of ethanol was studied in the concentration range of 0 to 6 mol%. It was found that the local concentration of ethanol is enhanced significantly at lower cosolvent concentrations.

Onsager reaction field theory for the three-dimensional anisotropicXYmodel

We discuss coupled $\mathrm{XY}$ spin chains in three dimensions and calculate the transition temperature and spin correlation lengths as functions of the ratio of the interchain exchange coupling ${J}^{\ensuremath{'}}$ to the intrachain coupling $J,$ for chainlike spatial anisotropy ${J}^{\ensuremath{'}}<J.$ We use two different approaches of the Onsager reaction-field (ORF) formalism. First we use the standard ORF theory, in which both the intrachain and interchain couplings are treated equally. Second, we treat one chain exactly and consider it in the effective field caused by the other chains, with the ORF formalism applied to the interchain interaction. The transition temperatures obtained are compared with results from Monte Carlo simulations.

Spectroscopic study of 4-aminobenzophenone in supercritical CF 3H and CO 2: local density and Onsager's reaction cavity radius

The measured bathochromic shifts of 4-aminobenzophenone (4ABP) in CF 3H are explained by Onsager's reaction field theory (ORFT) if the cavity radius is the sum of Van der Waals radii of solute and solvent, while in CO 2, the cavity radius is the solute's Van der Waals radius. The experimental local densities around 4ABP have been estimated and show a maximum at a reduced density of 0.5 for CF 3H and 0.7 for CO 2. Simulations are consistent with the high local densities found at low bulk densities and suggest possible explanations for the different radii used for CF 3H and CO 2.

Tautomeric Rearrangements in Mono- and Dichalcogenide Analogs of Formic Acid, HC(X)YH (X, Y = O, S, Se, Te): A Theoretical Study

Theoretical calculations are reported at the Hartree−Fock (HF), MP2, and Becke3LYP (B3LYP) levels on a complete series of 16 chalcogenic derivatives of formic acid HC(X)YH (X, Y = O, S, Se, Te) using all-electron basis sets. The periodic variations observed on substituting the chalcogens are discussed. The transition structures for the tautomeric rearrangement of these formic acid derivatives are also characterized. The variations in relative energies corrected for zero-point vibrations show that the barrier for tautomerism is reduced as the electronegativity of chalcogens is decreased. The trends of natural charges on atoms of chalcogenides are described. At the correlated level of calculations both MP2 and B3LYP methods give comparable results. The solvent effects on tautomeric equilibrium are assessed by performing self-consistent reaction field (SCRF) calculations at the HF level. A comparative study is provided for two solvation models: the electrostatic solvation model based on Onsager's reaction field theory and the self-consistent isodensity polarized continuum model (SCI-PCM). The latter is shown to be a better model for solvation. The solvents with dielectric constants 2.0, 7.6, and 35.9 are shown to be less effective on the thermodynamic stabilities of these reactions. The dipole moments show significant variations between solvents of lower dielectric medium, while the variations are insignificant between solvents of higher dielectric media. A comparison of thermodynamic preferences for keto and enol forms in monochalcogeno acetc acids with the solvent model SCI-PCM at the HF and B3LYP levels is also provided. Chemical shifts calculated using the GIAO method (at the B3LYP/6-311+G(2D,P)//B3LYP/6-31G(D) level) correlate well with the experimental results. However we conclude from these results that the thion form of CH3C(S)OH is less predominant.

Unique determination of the cavity radius in Onsager reaction field theory

A method based on the combined use of classical Maxwell field theory and modern quantum chemistry reaction field theory is outlined for determining the spherical cavity radius of pure liquids in the Onsager reaction field model. For each electronic structure model the method provides a unique value for the radius of the spherical cavity.

Onsager reaction field theory of Josephson junctions arrays

Josephson junctions arrays, in the limit where the order parameter has a fixed modulus, can be described by the classical XY model. We calculate the transition temperature for a model of classical XY spin chains coupled to their nearest neighbor chains. The interchain interaction is treated within the Onsager reaction field formalism, whereas each chain, in the effective field caused by the other chains, is treated exactly.

Onsager reaction field theory of the one-dimensional ferromagnet with long-range interactions.

Onsager reaction field theory of the one-dimensional ferromagnet with long-range interactions.

Onsager reaction field theory of a spatially anisotropic Heisenberg model.

Onsager reaction field theory of a spatially anisotropic Heisenberg model.

Calorimetric study of the solution process of tetramethylsilane in alcohols

Calorimetrically measured enthalpies of solution of tetramethylsilane into 16 alcohols, containing from 1 to 6 carbon atoms, are reported at 25°C and infinite dilution. These values are combined with the vaporization enthalpy of the solute to obtain standard enthalpies of gaseous tetramethylsilane and data are analysed in terms of the solvent structures. The solution functions for tetramethylsilane (TMS) are compared with the solution functions for tert-butyl halides ( t-BuX) in order to obtain information on ert-butyl halide-alcohol interactions. For this purpose, values of solution enthalpies are also determined for tert-butyl chloride, bromide and iodide in pentan-3-ol, 2-methylbutan-2-ol and hexan-1-ol. The limitations of the use of TMS as “inert” model solute of t-BuX are discussed. However, the application of the Onsager reaction field theory is found to be useful in the analysis of the influence of the eccentricity factor on the interaction enthalpy and leads us to conclusions regarding the relative importance of dipolar solute-solvent interaction and solvent reorganization on the solution process of t-BuX in alcohols.