Onsager's Method Research Articles

Enhanced Model for the Analysis of Thermoelectric Effects at Nanoscale: Onsager's Method and Liu's Technique in Comparison.

The aim of this paper is twofold. From the practical point of view, an enhanced model for the description of thermoelectric effects at nanoscale is proposed. From the theoretical point of view, instead, in the particular case of the proposed model, the equivalence between two classical techniques for the exploitation of the second law of thermodynamics is shown, i.e., Onsager's method and Liu's technique. An analysis of the heat-wave propagation is performed as well.

Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow

The rheological behavior of a material is strongly related to the energy dissipation, and the understanding and modeling of dissipation is important from the view point of rheology. To study rheological properties with some mesoscopic and macroscopic dynamics models, the modeling of dynamic equation which appropriately incorporates the dissipation is important. Although there are several methods to construct mesoscopic and macroscopic dynamic equations, such as the Onsager's method, their validity is not fully clear. In this work, we theoretically analyze the dissipation in a mesoscopic Langevin equation in detail, from the view point of stochastic energetics. We show that the dissipative heat flow from the heat bath to the system plays an important role in the mesoscopic dynamics. The dissipative heat flow is unchanged under the variable transform, and thus it is a covariant quantity. We show that we can construct the Langevin equation and also perform a coarse-graining based on the dissipative heat flow. We can derive the mobility tensor from the dissipative heat flow, and construct the Langevin equation by combining it and the free energy. Our method can be applied to various systems, such as the dumbbell model and the diffusion type equation for the density field, to give the coarse-grained dynamic equations for them.

Synthesis and spectroscopic properties of a copper(II) binuclear complex of a novel tetradentate asymmetrical Schiff base ligand and its DFT study

A new asymmetrical Schiff base ligand, N,N′-(salicylidene)-5-bromo-2-hydroxybenzaldehyde-p-phenylenediamine (SBHBP), and its binuclear Cu(II) complex have been synthesized. The molecular structures and spectroscopic properties of the ligand and its complex were experimentally characterized by elemental analysis, FT-IR, NMR and UV–Vis spectroscopic techniques and computationally by the density functional theory (DFT) method. The molecular geometry and vibrational frequencies of the SBHBP ligand in the ground state have been calculated using the B3LYP/6-31G(d,p) and 6-31++G(d,p) basis sets. A potential surface scan study was carried out and the most stable geometry of the SBHBP ligand was confirmed. The calculated results show that the optimized geometry can well reproduce the structural parameters, and the theoretical vibrational frequencies are in good agreement with the experimental values. On calculation of the electronic absorption spectra, TD-DFT calculations were carried out in both the gas and solution phases. The energetic behavior of the SBHBP ligand has been examined in solvent media using the B3LYP method with the 6-31G(d,p) and 6-31++G(d,p) basis sets by applying the Onsager method and polarizable continuum model (PCM). Additionally, Mulliken and NBO atomic charges, NMR analysis, molecular electrostatic potential (MEP) and frontier molecular orbitals (FMO) analysis of the SBHBP ligand were investigated using theoretical calculations.

Molecular Modeling Investigation of an Anti-cancer Agent Joint to SWCNT Using Theoretical Methods

The investigation of vinblastine intra single-walled carbon nanotube (SWCNT) has been studied by theoretical methods, and the best structural and functional vinblastine has been established. These results show the minimized structure of vinblastine intra SWCNT, calculated potential energy for important dihedral angles, and the effect of temperature on geometry of optimized structure. However, the vinblastine- SWCNT compound has been displayed different spectrum of gas phase and solvent NMR by GIAO and CSGT approximations, which appears the results of the determination of the number of active sites in vinblastine- SWCNT using the Onsager method that the O29 has the most shifting at indicated model, and it has been reflected mostly the transfer of vinblastine- SWCNT to a less polar environment.

Combined experimental and computational modeling studies on 4‐[(2‐hydroxy‐3‐methylbenzylidene) amino]‐1,5‐dimethyl‐2‐phenyl‐1,2‐dihydro‐3H‐pyrazol‐3‐one

AbstractThe Schiff base compound, 4‐[(2‐hydroxy‐3‐methylbenzylidene)amino]‐1,5‐dimethyl‐2‐phenyl‐1,2‐dihydro‐3H‐pyrazol‐3‐one, has been synthesized and characterized by IR, UV–vis, and X‐ray single‐crystal determination. Molecular geometry from X‐ray experiment of the title compound in the ground state have been compared using the density functional method (B3LYP) with 6‐31G(d,p) basis set. Calculated results show that density functional theory (DFT) can well reproduce the structure of the title compound. The energetic behavior of the title compound in solvent media has been examined using B3LYP method with the 6‐31G(d,p) basis set by applying the Onsager and the polarizable continuum model (PCM). The results obtained with these methods reveal that the PCM method provided more stable structure than Onsager's method. By using TD‐DFT method, electronic absorption spectra of the title compound have been predicted and a good agreement with the TD‐DFT method and the experimental one is determined. The predicted nonlinear optical properties of the title compound are much greater than ones of urea. In addition, DFT calculations of the title compound, molecular electrostatic potential and NBO analysis were performed at B3LYP/6‐31G(d,p) level of theory. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Experimental and quantum chemical calculational studies on 2-[(4-propylphenylimino)methyl]-4-nitrophenol

The Schiff base compound 2-[(4-propylphenylimino)methyl]-4-nitrophenol has been synthesized and characterized by IR, UV–Vis, and X-ray single-crystal determination. The molecular geometry from X-ray determination of the title compound in the ground state has been compared using the Hartree–Fock (HF) and density functional theory (DFT) with the 6-31G(d) basis set. The calculated results show that the DFT and HF can well reproduce the structure of the title compound. The energetic behaviour of the title compound in solvent media was examined using the B3LYP method with the 6-31G(d) basis set by applying the Onsager and the polarizable continuum model (PCM). The results obtained with these methods reveal that the PCM method provides a more stable structure than Onsager's method. Using the TD-DFT method, electronic absorption spectra of the title compound have been predicted and good agreement with the TD-DFT method and the experimental determination was found. The predicted nonlinear optical properties of the title compound are much greater than those of urea. In addition, DFT calculations of the molecular electrostatic potential and NBO analysis of the title compound were carried out at the B3LYP/6-31G(d) level of theory.

Density functional computational studies on (E)-2-[(2-Hydroxy-5-nitrophenyl)-iminiomethyl]-4-nitrophenolate

Density functional calculations of the structure, atomic charges, molecular electrostatic potential and thermodynamic functions have been performed at B3LYP/6-31G(d,p) level of theory for the title compound (E)-2-[(2-hydroxy-5-nitrophenyl)-iminiomethyl]-4-nitrophenolate. The results show that the phenolate oxygen atom and all of the nitro group oxygen atoms have bigger negative charges, and the coordination ability of these atoms differs in different solvents. The energetic behavior of the title compound in solvent media has been examined using B3LYP method with the 6-31G(d,p) basis set by applying the Onsager method and the isodensity polarized continuum model (IPCM). The results obtained with these methods reveal that the IPCM method yielded a more stable structure than Onsager's method. In addition, natural bond orbital and frontier molecular orbital analysis of the title compound were performed using the B3LYP/6-31G(d,p) method.

Density functional theory studies on the reagent Ph3PBr2

We report density functional theory geometry optimizations at the B3LYP/6-311G(d,p) level of theory for the title reagent. Four stationary points on the molecular potential energy surface were located and characterized. Three of these stationary points are energy minima, one a saddle point. The minima correspond to the conventional Ph3PBr2 (three-fold Br-P-Br axis with twisted phenyl rings), the ion-pair [Ph3PBr]+Br- and a four-coordinated Ph3PBr2 spoke structure that can best be described as charge transfer on account of the substantial charge transfer from the Ph3P fragment to Br2 (as determined by a standard Mulliken population analysis and other considerations). The particular saddle point found corresponds to a three-fold Br-P-Br structure with coplanar phenyl rings. Single point B3LYP/6-311+g(3d,2p) calculations were done at the stationary point geometries in order to investigate possible deficiencies in the basis set. Solvent effects for the three solvents water, dichloroethane and cyclohexane were modelled using the self consistent reaction field Onsager method at the single point B3LYP/6-311+g(3d,2p) level of theory. In the gas phase, the charge transfer complex is the most stable of the four; in solution it is the least stable.

Ab initio and DFT studies on hydrolyses of phosphorus halides.

Hydrolyses of phosphorus halides, (RO)(2)POX where R = H or Me and X = F or Cl, in the gas phase and in the reaction field have been investigated theoretically with ab initio and the density functional theory (DFT). The free energy of activation in the reaction field was also estimated using the Onsager method with a correction of entropy change and basis set superposition error (BSSE). The reaction of (MeO)(2)POF proceeds through a path with bifunctional catalysis regardless of the medium, but the reaction of (MeO)(2)POCl proceeds through bifunctional and general base catalysis in the gas phase and in water, respectively. The estimated free energy barrier of 23 kcal/mol for the hydrolysis of (MeO)(2)POF is in good agreement with the experimental values of 24 kcal/mol, and relative barrier of 3 kcal/mol to the (MeO)(2)POCl is also in good agreement with the experimental values of 5 kcal/mol of diisopropyl phosphorus halides ((Pr(i)O)(2)POX, X = F and Cl).

Molecular structure and vibrational assignment of dimethyl oxaloacetate

A complete conformational analysis of the keto and chelated enol forms of dimethyl oxaloacetate (DMOA), a β-dicarbonyl compound, was carried out by ab initio calculations, at the density functional theory (DFT) level. In addition to nine stable enol conformers, which are stabilized by intramolecular hydrogen bonds, twelve stable keto conformers were also obtained. The considerably higher energy of the keto compared to that of the most stable enol conformer makes the presence of keto form, at least in the gas phase, unlikely. Theoretical calculations in the solution, using the Onsager Method, suggest two coexisting enol conformers in the solution. This finding is in agreement with the experimental data. The hydrogen bond strength of the most stable conformer of DMOA is compared with that of acetylacetone (AA). Harmonic vibrational frequencies of this stable enol form and its deuterated analog were also calculated and compared with the experimental data. According to the theoretical calculations, the enolated proton in dimethyl oxaloacetate moves in an asymmetric single minimum potential with a hydrogen bond strength of 31.1 kJ/mol, 35.3 kJ/mol less than that of AA. This weakening of hydrogen bond is consistent with the frequency shifts for OH/OD stretching, OH/OD out-of-plane bending and O⋯O stretching modes. The calculated O ⋯O distance is about 0.07–0.08 Å longer than that of its parent AA.

A theoretical and experimental study on the structure and dipole moment of phloroglucinol in ethanol

The dipole moment and structural properties of phloroglucinol in ethanol have been investigated using experimental dielectric procedures and theoretical ab initio and density functional methods. Applying Buckingham's method, it was determined that the dipole moment of phloroglucinol in ethanol is 7.70 D. It was proposed that phloroglucinol interacts with the solvent by means of moderate hydrogen bonds, in which the solvent exerts its hydrogen-bond-donor capability forming solvent–solute association complexes of 3:1 stoichiometry. The main molecular regions implied in these interactions comprise the hydroxyl groups of phloroglucinol. On the other hand, the calculated data at the B3LYP/6-31G(d) level of theory with Onsager's method permitted to conclude that two related association complexes for a conformational equilibrium are the predominant species of phloroglucinol in ethanol. Also, the percentages of these complexes in equilibrium determine the magnitude of the analyzed properties of phloroglucinol.

Solvent effects on the structure and dipole moment of resorcinol

With the specific aim of explaining the dipole moment (DM) of resorcinol in water, we investigated the molecular conformations and solute–solvent interactions of resorcinol in ethanol, methanol and water. In this work, experimental dielectric procedures and theoretical ab initio and density functional methods were used. Basis sets at the levels of theory HF/6-31G(d) and B3LYP/6-31G(d) were used for calculations. Onsager's method was used to analyze the solvent effects on the conformers of resorcinol. A conformational equilibrium between the two main conformers of non-solvated resorcinol was proposed. The total energies, DMs, structural molecular and reactivity parameters of the conformers and transition states involved were calculated. These theoretical magnitudes were correlated with parameters of the solvating solvents. The properties of the solute–solvent association complexes formed by a molecule of resorcinol and two molecules of water by means of intermolecular hydrogen bonds were also calculated. It was concluded that the DM of resorcinol in water (8.66 D) is due to these solute–solvent association complexes, which are the predominant forms of resorcinol in aqueous solutions.

Experimental and Theoretical Studies of Rotational Barriers in Aceto-, N-Methylaceto- and N-Phenylacetohydroxamic Acid

Experimental and theoretical calculations for the E and Z forms of aceto-, N-methylaceto- and N-phenylacetohydroxamic acid are reported. The experimental method was NMR spectroscopy, while the computational methods included Hartree-Fock, Møller-Plesset and density functional theory calculations, with and without solvation, using either the Onsager or Tomasi's PCM method. In all calculations zero point energy corrections were included. The computed results when compared with the experimental ones show that, irrespective of the method used, the differences in the rotational barriers, ∆(E-TS) and ∆(Z-TS), are slight and below the 3 kcal mol-1 limit of the theoretical methods. In general the results using the PCM method were worse than the ones obtained from gas phase calculations or using the Onsager method, even though the PCM method is computationally most expensive. The calculations show, using either the Hartree-Fock or the B3LYP approach, that considering solvation using the Onsager method improves agreement with the experiment results. The calculated barrier heights, excluding the PCM method, agree broadly with the experimental results. Thus using the Onsager approach or gas phase calculations adequate results for barrier heights, but not for relative differences, were obtained.

Dipolar Complexation in Binary Mixtures of Tri-n-Butyl Phosphate (TBP) with Long-Chain Aliphatic Alcohols

The mean square dipole moments of the 1:1 complexes of tri-n-butyl phosphate (TBP) with 1-hexanol, 1-heptanol and 1-octanol in benzene are determined following two different methods i.e., one based on Onsager's method and the other using modified Palit's method. The interaction dipole moment for the thermodynamically most favoured geometry of 1:1 complexes of the system involving 1-hexanol, 1-heptanol, 1-octanol as the first components and TBP as the second component is evaluated. The results indicate that complexation is predominantly due to polarization effect involving charge redistribution. Furthermore, the induced excess polarization and apparent complexation constant in these mixtures are calculated.

Dielectric Studies of Hydrogen Bonded Association Complexes—Butanols with Aniline and Pyridine

Abstract The mean square dipole moments of 1:1 complexes of n-butanol, i-butanol and r-butanol with aniline and pyridine in benzene are determined following two different methods: one uses Onsager's method based on dipole-dipole interaction and the other uses the help of modified Palit's method involving a limiting polarization measurement technique. The interaction dipole moments Δμ for the thermodynamically most favoured geometry of 1:1 complexes of the system involving butanol-aniline and butanol-pyridine were calculated. The value of Δμ indicated that complexation is due to polarization interaction. Furthermore, Δμ is found to be in the order pyridine > aniline. The dipole moment of the complexes involving butanol-aniline and butanol-pyridine is found to be in the order pyridine > aniline. These results have been used in interpreting of the structures of the complexes.

Liquid-crystalline ordering in the solution of partially flexible macromolecules

Abstract The liquid-crystalline ordering in the solution of persistent chains which length, L, is comparable with the length of the effective Kuhn segment, l, is considered by means of a generalization of the Onsager method. The orientational entropy for this case is calculated using the method proposed by I.M. Lifshitz (for another problem) in 1968. It is shown that a slight flexibility of the persistent chain is sufficient for the complete change in the properties of the liquid-crystalline transition: for example, at L l ∼0.1 these properties are more similar to those which are characteristic for the semi-flexible limit ( L l ⪢1), than for the rigid rod limit ( L l ⪡1), although at such L l the geometric form of the macromolecule is much closer to the rodlike one.

Liquid-crystalline ordering in the solution of long persistent chains

Abstract The orientational ordering in the solution of long persistent macromolecules is studied by means of the Onsager method. It is shown that the liquid-crystalline transition occurs at significantly higher concentrations and that the order parameter at the transition point is much smaller than for the model of freely-jointed segments. It is concluded that the orientational ordering in the solutions of semiflexible chains depends essentially on the flexibility distribution along the chain contour.

Liquid-crystalline ordering in the solution of semiflexible macromolecules

Abstract The solution of semiflexible polymer macromolecules with steric repulsion between the parts of the polymer chains is considered. The conditions for formation of the liquid-crystalline phase in this solution are determined by means of the Onsager method.

XY model and algebraic methods

A systematic study of properties of a set of operators leads to a new approach to solve the XY model. The algebraic solution refers only to a subalgebra of spin operators. Through the connection with the algebra of related fermion operators is apparent, these need not be referred to. As a by-product, Onsager's method for the Ising model results in a very simple form, and its relationship to the approach of Schultz, Mattis and Lieb (1961) becomes apparent.

A Graphical Exposition of the Ising Problem

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.