Chemical potential and thermodynamic functions of thermal radiation

Thermodynamic functions of the photon number of thermal radiation are described. The temperature dependence μ = 3.602kT of the chemical potential of thermal radiation is found by differentiation of these functions.     

电化学方法测定纳米材料的热力学函数

以纳米铜为例,首次采用电化学方法获取纳米材料的热力学函数.通过电化学沉积法制备了粒子尺寸约80nm的纳米铜电极,测定纳米铜与块体铜电极的电势差,以块体铜的热力学函数值为参考标准,根据纳米铜与块体铜的热力学关系式,求得纳米铜的标准摩尔生成焓、标准摩尔生成吉布斯自由能、标准摩尔熵分别为5.16kJmol-1、0.216kJmol-1、49.75JK-1mol-1,同时,求得纳米铜可逆电池反应的热效应为-4.95kJmol-1.     

A powerful truncated Newton method for potential energy minimization

With advances in computer architecture and software, Newton methods are becoming not only feasible for large-scale nonlinear optimization problems, but also reliable, fast and efficient. Truncated Newton methods, in particular, are emerging as a versatile subclass. In this article we present a truncated Newton algorithm specifically developed for potential energy minimization. The method is globally convergent with local quadratic convergence. Its key ingredients are: (1) approximation of the Newton direction far away from local minima, (2) solution of the Newton equation iteratively by the linear Conjugate Gradient method, and (3) preconditioning of the Newton equation by the analytic second-derivative components of the “local” chemical interactions: bond length, bond angle and torsional potentials. Relaxation of the required accuracy of the Newton search direction diverts the minimization search away from regions where the function is nonconvex and towards physically interesting regions. The preconditioning strategy significantly accelerates the iterative solution for the Newton search direction, and therefore reduces the computation time for each iteration. With algorithmic variations, the truncated Newton method can be formulated so that storage and computational requirements are comparable to those of the nonlinear Conjugate Gradient method. As the convergence rate of nonlinear Conjugate Gradient methods is linear and performance less predictable, the application of the truncated Newton code to potential energy functions is promising.     

The Gaussian equivalent representation in thermodynamic self-consistent field theory

Pair distribution functions and thermodynamic values for systems of classical particles with the Gauss and Morse interparticle interaction potentials were calculated using the approach based on the representation of the partition function and distribution functions in the form of functional integrals. The results are compared with those obtained in molecular dynamics simulations.     

A physically meaningful method for the comparison of potential energy functions

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semiquantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root-mean-square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined that overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated, and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2.     

Analysis of an energy minimization method for locating transition states on potential energy hypersurfaces

Conditions are given for the successful search for a transition state by an energy minimization method. Proofs for these guidelines are presented. Advantages of this method are discussed, including its use in establishing lower bounds to transition state energies. Comparisons are made with other searching methods.     

Comparison of minimization procedures for UHF wave functions

The Roothaan, McWeeny and Fletcher methods of minimizing the electronic energy in the SCF method are compared. The CN radical is used as an example using the abinitio UHF method. It is concluded that a combination of the Fletcher and Roothaan methods should be generally applicable and also highly efficient.     

Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.     

Calculation of thermodynamic solution functions in gas-liquid chromatography

The solubility of m- and p-isomers of xylene and fluorotoluene in aromatic stationary phases is investigated. It is shown that orientation interaction can be calculated from a lattice model, with the results compared with experiment. By calculating the orientation and dispersion forces it is possible to construct an enthalpy diagram for molecular rotation, on the basis of which the differences in heats of solution and rotational entropies of the isomers can be determined. An example is cited in which hydrogen bonding was found in systems containing fluorotoluenes. From increments in the heats of solution and rotational entropies of the homologous n-paraffins it is possible to determine the structural characteristics of the solvent, and the accuracy of the proposed structure can be evaluated by calculating the individual heats of solution. The presence of aromatic nuclei and aliphatic radicals in the molecule of the stationary phase can be determined from characteristic variations in the heat-of-solution increments. The size of the natural cavity in the solvent structure can be determined from the rotational entropy increment. It is shown that the selectivity of the stationary phase with respect to the n-paraffin homologs does not remain constant. Aromatic solvents give the highest selectivity.     

On the functional representation of bond energy functions

Ab initio calculations are used to test the ability of various representations to reproduce bond energies. It is found that expansion in 1/R, where R is the bond length, is remarkably efficient and is consistently better than the usual R expansion. A quadratic form in 1/R is better than a cubic representation in R and sometimes even as good as a quartic representation. A cubic function in 1/R is, in all cases studied, better performing than the quartic expansion in R. It is also found that parameters derived with the 1/R expansion are defined more sharply than those derived for the R expansion. It is suggested that the 1/R expansion may be computationally more efficient for simulations of large biomolecules and for constructions of reactive force fields than the standard bond functions. © 1994 by John Wiley & Sons, Inc.     

Conformational studies of double-helical polynucleotides by the method of pair-wise potential functions

Double-helical polynucleotide conformations, poly(dA)·poly(dT), poly(d(A-T))·poly(d(T-A))·poly(dG)·poly(dC), and poly(d(G-C))·poly(d(C-G)) are analyzed by the atom–atom potential method. The energy optimization is carried out in the space of eight independent geometric parameters using analytical procedures for the constraints, taking into account the flexibility of the β-D -deoxyribose rings. At the first stage, the full screening of atomic partial charges was assumed. The structures of the calculated B and the A forms of DNA are characterized by low energy and absence of short contacts; the dihedral angles are near the average values in the monomers. With the typical energy difference of 3–5 kcal/mol nucleotide pairs in all cases, the B form is more preferable as compared to the A form. At the final step the effect of the Coulomb term is evaluated for poly(dA)·poly(dT) using various values of the effective dielectric constant (? = 28, 24, 20, 18, 14, 12, 10, 8, 6, 4, and 1). If ? ?24, the energy optimization leads A to B. We discuss the stereochemical details of the intermediate conformations on the A–B path and hypothesize the nature of stability of the A and the B forms and the mechanism of the A–B transition.     

Additive prediction of thermodynamic functions of hydrofluorides

Summary The experimental data available on the thermodynamic functions ⁰ forMF·nHF hydrofluorides [M=Li, Na, K, Rb, Cs, NH₄, Ag(I) and Tl(I);n=1–3] have been evaluated additively. The unknown values of ⁰ forn=0÷7 are predicted.

---

Additive Voraussagen der thermodynamischen Funktionen von Hydrogenfluoriden (Kurze Mitt.)

Zusammenfassung Die vorhandenen experimentellen Daten über die thermodynamischen Funktionen ⁰ von HydrogenfluoridenMF·nHF [M=Li, Na, K, Rb, Cs, NH₄, Ag(I) und Tl(I);n=1–3] werden linear ausgeglichen und die fehlendenden Werte für ⁰ mitn=0÷7 vorausgesagt.

     

The determination of the thermodynamic characteristics of Lennard-Jones fluids under isobaric conditions by the method of molecular functions

Integral equation theory for partial distribution functions was used to suggest an effective method for calculating the derivative of radial distribution function with respect to temperature under isobaric conditions. The thermodynamic expansion, compression, and pressure coefficients and isobaric and isochoric heat capacities were calculated for Lennard-Jones fluids. The calculation results were in close agreement with the known thermodynamic relations.     

Heat capacity and thermodynamic functions of ferrocenemethanol

The heat capacity (C _{p, m}) of ferrocenemethanol (FM) C₅H₅FeC₅H₄CH₂OH have been measured by the low-temperature adiabatic calorimetry method in the range 6–371 K. The triple point temperature, the enthalpy of fusion, and the purity of the substance under consideration have been determined. The ideal gas thermodynamic functions of FM—absolute entropy S _m(g) ⁰ and change in the enthalpy Δ ₀ ^T H _m at 298.15 K—have been derived from the heat capacity data and the known values of the saturation vapor pressure and enthalpy of sublimation. The ideal gas thermodynamic functions C _{p, m} ⁰ and S _m(g) ⁰ and the enthalpy of formation of FM have been calculated by the empirical difference method at T = 298.15 K. The experimental and calculated values of the thermodynamic functions are consistent within error limits, which proves their reliability.     

Accuracy in the determination of thermodynamic solution functions from retention indexes

Conclusions Equations are proposed for evaluating the accuracy in the determination of the relative distribution coefficients, separation factors, differences in partial molar enthalpies, entropies, and free energies of solution from retention indexes which give an error of the same order of magnitude as the gas-chromatographic method of determination from specific retention volumes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 632–635, March, 1972.