二原子分子和三原子分子的周期表

门捷列夫元素周期表是自然科学中最重要的原则之一．然而,对于分子而言,却缺乏类似的表格．本文提出两个分别对应于二原子分子和三原子分子的周期表．这些分子周期表的格式和门捷列夫原子周期表相似．在这些表格中,分子依照它们各自的族数G和周期数P分类排列,G是价电子的数目而P则表示分子的尺寸．分子的基本性质,包括键长、结合能、力常数、电离势、自旋多重度、化学反应活性以及键角等等,都随着表中的G和P作周期性的变化．二原子分子和三原子分子的周期性因而被揭示开来．本文还进一步指出这种周期性是源出于分子的壳状电子构型．周期表中不仅包含了游离的分子,还包含了多原子分子中的“赝”分子．这些周期表可用来从本质上分类分子,广泛地预言分子的未知性质,了解在多原子分子中赝分子的作用,以及开拓新的研究领域,如芳香族、团簇或纳米微粒的周期性等．因此这些表格不仅能够引起多学科领域中科学工作者的关注,而且还能引起理科学生们的兴趣．     

Periodic tables of diatomic and triatomic molecules

The Mendeleev periodic table of atoms is one of the most important principles in natural science. However, there is shortage of analog for molecules. Here we propose two periodic tables, one for diatomic molecules and one for triatomic molecules. The form of the molecular periodic tables is analogous to that of Mendeleev periodic table of atoms. In the table, molecules are classified and arranged by their group number G, which is the number of valence electrons, and the periodic number P, which represents the size of the molecules. The basic molecular properties, including bond length, binding energy, force constant, ionization potential, spin multiplicity, chemical reactivity, and bond angle, change periodically within the tables. The periodicities of diatomic and triatomic molecules are thus revealed. We also demonstrate that the periodicity originates from the shell-like electronic configurations of the molecules. The periodic tables not only contain free molecules, but also the "virtual" molecules present in polyatomic molecules. The periodic tables can be used to classify molecules, to predict unknown molecular properties, to understand the role of virtual molecules in polyatomic molecules, and to initiate new research fields, such as the periodicities of aromatic species, clusters, or nanoparticles. The tables should be of interest not only to scientists in a variety of disciplines, but also to undergraduates studying natural sciences.     

Accurate electron affinities of several diatomic and triatomic molecules

The electron affinity of several diatomic and triatomic molecules is computed with an error of less than 0.1 eV using the second-order Møller-Plesset method and a 6.311 + G(2d,2p) basis set. The importance of the zero-point energy correction is tested and a comparison with the results obtained with other basis sets is made.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Surface tension of associating fluids by Monte Carlo simulations

Canonical Monte Carlo (NVT-MC) simulations were performed to obtain surface tension and coexistence densities at the liquid-vapor interface of one-site associating Lennard-Jones and hard-core Yukawa fluids, as functions of association strength and temperature. The method to obtain the components of the pressure tensor from NVT-MC simulations was validated by comparing the equation of state of the associative hard sphere system with that coming from isothermal-isobaric Monte Carlo simulations. Surface tension of the associative Lennard-Jones fluid determined from NVT-MC is compared with previously reported results obtained by molecular dynamics simulations of a pseudomixture model of monomers and dimers. A good agreement was found between both methods. Values of surface tension of associative hard-core Yukawa fluids are presented here for the first time.     

Universal scaling features of spectroscopic constants for diatomic systems

Based on a new criterion that was proposed to search for the universality of spectroscopic constants for bound ground-state diatomics [R. H. Xie and P. S. Hsu, Phys. Rev. Lett. 96, 243201 (2006)], we have found universal scaling relations between spectroscopic constants of diatomic systems with s-, p-, and d-type valence-shell constituents. Our study suggests a useful empirical approach for the prediction of molecular spectroscopic constants.     

Surface states in deformed and perturbed diatomic crystals

The electronic properties of a one-dimensional diatomic crystal have been analyzed by using the MO-LCAO method in the tight binding approximation, with mathematical techniques involved in setting up and solving difference equations. The approach gives the exact sets of analytic solutions for both localized and nonlocalized states. The theory of surface states is developed as a characteristic value problem. To illustrate the method the surface states for a semiinfinite crystal which contains a local imperfection at the surface were examined. It appears that this method has advantages over previous methods developed to solve surface problems in crystalline lattices.     

Some unexpected relationships between first,second and third derivative electron repulsion integrals for diatomic and triatomic molecules

It is demonstrated that for diatomic molecules, second and third derivative electron repulsion integrals need not be explicitly evaluated. Similarly for triatomic molecules an analogous simplification applies to all second derivative and 94% of all third derivative integrals. Such higher integral derivatives may be determined from intermediate quantities required in the evaluation of integral first derivatives, in conjunction with translational and rotational invariance properties. This result also has implications for theoretical studies of tetra-atomic and larger molecules. Specifically, the evaluation of most two- and three-center integral derivatives becomes very efficient.     

Evidence of dissociative collision induced diatomic and triatomic hydrogen ion formation from hydrocarbon ion interaction with silicon surface

A singly charged hydrocarbon ion CH(x) (+) (x=0,1,2,3,4) was extracted from an electron bombardment type ion source using methane as the reagent gas and irradiated onto the Si(100) surface at glancing angle. Scattered ion spectrometry using an electrostatic energy analyzer revealed that H(+), H(2) (+), and H(3) (+) ions were clearly formed at the scattering angle of 15 degrees , associated with dissociative collisions of hydrocarbon ion species of incidence energy of 1000 eV. The formation of H(3) (+) was tentatively interpreted as resulting from combination of excited atomic hydrogen produced by dissociative collisions of CH(4) (+) ions with Si(100) surface.     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

Anisotropic colloidal particles in critical fluids

We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluid mixture. The orientation-dependent long-ranged universal interactions mediated by the critical solvent between a particle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to the correlation length and interparticle distances. Exact results are obtained using a "small particle operator expansion." The amplitudes of the isotropic and anisotropic operators in the expansion depend on the size and aspect ratio of the dumbbell or lens and are determined by density profiles in the Ising model at the critical point in a wedge geometry with symmetry-breaking fixed-spin boundary conditions. Dumbbells and ellipsoids with a symmetry preserving surface are also considered.     

Fluctuation theory of critical phenomena in fluids

It is assumed that critical phenomena are generated by density wave fluctuations carrying a certain kinetic energy. It is noted that all coupling equations for critical indices are obtained within the context of this hypothesis. Critical indices are evaluated for 15 liquids more accurately than when using the current theory of critical phenomena.     

Liquid-vapor equilibrium and surface tension of nonconformal molecular fluids

Molecular dynamics simulations at constant temperature have been performed on the liquid-vapor interface for fluids characterized by a recently introduced three-parameter potential. This potential is a modification of the well-known spherical Kihara interaction and is termed approximate nonconformal (ANC). It has been used successfully to describe many real molecules in the gaseous phase. Besides the usual molecular energy and size, the ANC potential introduces a third parameter s, called softness, to measure the form of the potential profile. Study of these systems shows that their critical and interfacial properties follow very closely those of four selected substances: argon, methane, propane, and hexane. Deviations of the properties predicted from the experimental values are analyzed and their probable causes are determined. The critical properties of ANC fluids and their dependence on s are also obtained via first-order perturbation theory in the form of an augmented van der Waals model. Analysis of the results shows that ANC potential functions can be used as reliable effective interactions for real dense fluids.     

A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

Universal scaling behaviour of surface tension of molecular chains

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments interacting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different intermolecular potentials.     

Phase equilibria and interfacial tension of fluids confined in narrow pores

Correlation between phase behaviors of a Lennard-Jones fluid in and outside a pore is examined over wide thermodynamic conditions by grand canonical Monte Carlo simulations. A pressure tensor component of the confined fluid, a variable controllable in simulation but usually uncontrollable in experiment, is related with the pressure of a bulk homogeneous system in equilibrium with the confined system. Effects of the pore dimensionality, size, and attractive potential on the correlations between thermodynamic properties of the confined and bulk systems are clarified. A fluid-wall interfacial tension defined as an excess grand potential is evaluated as a function of the pore size. It is found that the tension decreases linearly with the inverse of the pore diameter or width.     

Surface tension of electrolyte solutions

A simple analytic expression is derived for the excess surface tension of electrolyte solutions, which is in good agreement with the experimental data on NaCl in the concentration range up to as high as 1 M. This expression is consistent with the following two theories: (i) The recent theory of Levin and Flores-Mena (Europhys Lett (2001) 56:187), who demonstrated the important contribution of the formation of an ion free layer at the air–electrolyte solution interface, and (ii) the Onsager–Samaras theory (J Chem Phys (1934) 2:528) modified by taking into account the ion-free layer effect. It is shown that the excess surface tension consists of three parts: the contributions of the ion-free layer, the image interaction between the electrolyte ions and the ion-free layer, and the image interaction between the electrolyte ions and air.     

Surface tension of polymer solutions

Summary Heats of dilution and surface tensions of a polystyrene-cyclohexane solution have been measured in a wide temperature range covering the theta-temperature. Surface tensions as well as interaction parameters obtained from heats of dilution show no discontinuity at0. Concentration of polymer adsorbed on the surface has been calculated, it decreases with increasing temperature. Plots of interaction parameter vs.1/T give two straight lines which cut at the theta-temperature.

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Zusammenfassung Verdünnungswarmen and Oberflächenspannungen einer Polystyrol-Cyclohexan-Lösung wurden in einem großen Temperaturbereich gemessen, der die Thetatemperatur einschließt. Aus den Verdünnungswärmen wurden die Wechselwirkungsparameter berechnet. Sowohl Oberflächenspannung als such Wechselwirkung zeigen gegen die Temperatur aufgetragen keine Diskontinuität an der Thetatemperatur. Die Konzentration des an der Oberfläche adsorbierten Polymeren wurde berechnet, sic nimmt mit steigender Temperatur ab. Auftragungen des Wechselwirkungsparameters gegen die reziproke Temperatur ergeben zwei Gerade, die sich bei der Thetatemperatur schneiden.

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With 5 figures