Precise potential harmonic approach to directly solving Schrödinger equations of helium-like three-body systems

A complete potential harmonic scheme is presented, including the linked coupled hyperradial ordinary differential equations and the secular equation of eigenenergy. It has been used to directly solve the Schrödinger equations of helium-like three-body systems (nuclear chargeZ = 1–9). and very accurate ground state eigenenergies as well as low-lying singlet excited state ones have been obtained.     

New theory of equation of state for surface monolayer

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.     

Volumetric and refractive properties of binary mixtures containing 1,3-dioxolane and isomeric chlorobutanes

The relation between refractive index deviations and excess volumes for binary mixtures formed by a cyclic ether and a haloalkane has been tested using several methods: refractive index mixing rules and equations of state. Refractive index deviations, excess volumes and molar refractions have been calculated from experimental data of refractive indices and densities at two temperatures 298.15 and 313.15 K. Results obtained have been discussed in terms of intermolecular interactions. Refractive indices were compared with those predicted by several mixing rules. Excess volumes have also been correlated using several cubic equations of state and finally a relation between parameter b from equations of state and molar refraction has been provided.     

Spin Flip Models in the Spin Coupling Method of Many-Particle Amplitudes

A special class of models is presented in which correlation effects for quasidegenerate electronic states are calculated without resorting to complete MRCI schemes. The high-spin reference determinant is transformed into the desired low-spin state by the spin flip procedure with concomitant electron elimination or addition. For the given spin flip process, variational equations that define the corresponding spin coupling matrix have been obtained. For the simplest spin flip model presented by A. Krylova as the SF-CIS method, a sequential spin projection procedure has been carried out. Illustrative calculations for the excited and dissociative states of small molecules have revealed the high quality of the suggested approximate schemes.Original Russian Text Copyright © 2004 by A. V. Luzanov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 771–782, September–October, 2004.     

Joule-Thomson inversion curve prediction by using equation of state

In this paper five equations of state are tested for checking their ability to predict the Joule-Thomson inversion curve.These five equations of state are:Mohsennia-Modarres-Mansoori(MMM),Ji-Lemp(JL),modified Soave-Redlich-Kwang(SRK)equation of state by Graboski(MSRK1),modified SRK equation of state by Peneloux and Rauzy(MSRK2),and modified Peng-Robinson (PR)equation of state by Rauzy(PRmr).The investigated equations of state give good prediction of the low-temperature branch of the inversion curve,except for MMM equation of state.The high-temperature branch and the peak of the inversion curve have been observed,in general,to be sensitive to the applied equation of state.The values of the maximum inversion temperature and maximum inversion pressure are calculated for each component used in this work.     

扩散控制的固相反应动力学模型

在许多由固相反应生成合金和无机材料的生产过程中,扩散传质控制着反应的过程。但是,对扩散控制固相反应系统的机理和动力学研究还很不成熟。Jander首先把平面扩散抛物线方程用于球体内部的扩散过程,导出了Jander方程,由于平面扩散截面积不变和球体扩     

Generalized interaction parameters in cubic equations of state for CO2—n-alkane mixtures

Five equations of state (including one recently proposed by the authors) have been applied to the calculation of vapour—liquid equilibrium (VLE) of CO₂—n-alkane mixtures. Interaction parameters for several systems have been obtained through regression analysis of experimental VLE data. These parameters have been correlated in terms of the temperature and the acentric factor of the hydrocarbon for three equations of state and for all systems. It is concluded that while all equations perform more or less with the same degree of accuracy, there are some advantages in using one or another for different VLE calculations.     

Equations of state for pure and mixture square-well fluids. II. Equations of state

New coordination number models for square-well (SW) fluids are incorporated with the generalized van der Waals partition function to develop equations of state for both pure and mixture SW fluids. The equations of state have been extensively tested with the Monte Carlo simulation data, of which three sets (18 data points) for the pure SW fluids are produced in this work. The results show that, without any parameters, our model reasonably describes not only the PVT behaviors but also the second and third virial coefficients of the model fluids. In addition, a comprehensive comparison has been made between our models and the other equations of state derived from the Lee-Chao and Lee-Sandler coordination number correlations.     

二维相关荧光光谱技术

从发展历史、计算方程、一般规则和特有性质等方面系统地介绍了近年来在二维相关荧光光谱技术方面的方法探索和应用进展。以不同的外扰方式，如浓度、激发波长、猝灭以及其他如pH等分类，举例阐述了二维荧光相关光谱的可操作性及其应用，并与普通一维荧光光谱比较，说明了二维荧光相关光谱技术的优势。     

The performance of cubic equations of state on the critical isotherms of pure fluids

The potential of cubic equations of state for describing the critical isotherm of a pure fluid has been examined. Some mathematical results are derived which show that in this respect such equations have fundamental and far-reaching limitations, separate from their obvious failure in the critical region. The implications become clear in a numerical test of various equations on experimental critical-isotherm data. The present study provides insight into the relationship between the performance of a cubic equation of state and its parametric structure.     

A Novel Method for Fixed‐node Quantum Monte Carlo

In this paper, a novel method for fixed‐node quantum Monte Carlo is given. By comparing this method with the traditional fixed‐node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed‐node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 ¹A, state of CH₂, ¹A₂(C_4h, acet) state of C₈ and the ground‐states of H₂, LiH, Li₂, and H₂O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.     

Comparison of methods for calculating thermodynamic properties of binary mixtures in the sub and super critical state: Lee–Kesler and cubic equations of state for binary mixtures containing either CO2 or H2S

The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO₂ or H₂S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO₂ and H₂S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee–Kesler equation; (b) two equations that included new reference fluids for the Lee–Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO₂ mixtures while for H₂S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee–Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%.     

van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.     

Kinetic analysis of the mechanism of plasminogen activation by streptokinase

A kinetic study is made of plasminogen activation to plasmin catalyzed by streptokinase. The goal of the present paper is the resolution of the mechanism corresponding to the activation process by a global way, considering the mechanism as a whole and under less restrictive assumptions that those used by other authors. The kinetic equations describing the evolution with time of species involved in the system have been obtained. These equations are valid for both the transient phase and the steady state of the reaction. A kinetic data analysis procedure to evaluate the kinetic parameters, based on the derived kinetic equations has been suggested, for the first time, in the present paper. The validity of the results obtained has been checked by using simulated progress curves of the species involved. Finally, we have demonstrated that the time course equations obtained can be applied directly to different mechanisms of zymogen activation that could be considered to be particular cases of the general studied mechanism.     

Towards predictive association theories

Association equations of state like SAFT, CPA and NRHB have been previously applied to many complex mixtures. In this work we focus on two of these models, the CPA and the NRHB equations of state and the emphasis is on the analysis of their predictive capabilities for a wide range of applications. We use the term predictive in two situations: (i) with no use of binary interaction parameters, and (ii) multicomponent calculations using binary interaction parameters based solely on binary data. It is shown that the CPA equation of state can satisfactorily predict CO₂-water-glycols-alkanes VLE and water-MEG-aliphatic hydrocarbons LLE using interaction parameters obtained from the binary data alone. Moreover, it is demonstrated that the NRHB equation of state is a versatile tool which can be employed equally well to mixtures with pharmaceuticals and solvents, including mixed solvents, as well as phase equilibria in mixtures containing glycols. The importance of considering the solvation of CO₂-water (in CPA) when the model is applied to multicomponent mixtures as well as of the multiple associations in heavy glycol-water mixtures (in NRHB) is investigated.     

Volumetric properties of 1-iodoperfluorohexane+<Emphasis Type="Italic">n</Emphasis>-octane binary system at several temperatures

New densities are reported over the whole composition range for 1-iodoperfluorohexane+n-octane system at temperatures from 288.15 to 308.15 K at atmospheric pressure. These data have been used to compute the excess molar volumes, V _m ^E. Large positive V _m ^E values have been obtained over the entire range of composition, which increases when the temperature rises. The experimental data were used to calculate the isobaric thermal expansivity, and the quantities (∂V _m ^E/∂T)_p and (∂H _m ^E/∂p)_T. Furthermore, the results have been used to investigate the volumetric prediction ability of the equations of state Soave–Redlich–Kwong, Peng–Robinson, Patel–Teja and Soave–Redlich–Kwong with volume translation.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Vapor pressures of pure compounds using the Peng–Robinson equation of state with three different attractive terms

Accurate representation of pure compounds vapor pressures is required to increase the robustness of equations of state when predicting phase equilibria for mixtures. Using cubic equations of state, this representation largely depends on improving the temperature-dependent attractive term of the equation of state (EOS) to cover data from the triple to critical points. With this purpose, the Peng–Robinson equation of state is applied with three different attractive terms: Mathias, Mathias–Copeman, and Carrier–Rogalski–Péneloux. Experimental vapor pressures for 311 pure compounds (9000 experimental values) have been fitted. The studied compounds include nitrogen compounds, oxides, sulfides, chlorides, oxyhalides, inorganic compounds, alkanes, cycloalkanes, alkenes, alkadienes, alkynes, aromatic hydrocarbons, halogenated alkanes, halogenated cycloalkanes, halogenated alkenes, halogenated aromatic hydrocarbons, alcohols, ethers, aldehydes, ketones, alkanoic acids, esters, phenols, heterocyclic oxygen compounds, heterocyclic nitrogen compounds, hydrocarbon nitrogen compounds, and sulfur compounds. Overall average absolute deviations of 0.416, 0.214 and 0.276% have been found for the resulting Peng–Robinson–Mathias (PRM), Peng–Robinson–Mathias–Copeman (PRMC), and Peng–Robinson–Carrier–Rogalski–Péneloux (PRCRP) equations of state, respectively.     

Caloric properties of mixtures of refrigerants R22 / R114

The nonazeotropic refrigerant mixture chlorodifluoromethane (R22) and 1,2-dichlorotetrafluoroethane (R114) has been frequently suggested as a working fluid in cooling systems and heat pump applications. However, especially for mixtures exact and reliable measurements of the caloric properties are often missing, so that calculations with equations of state yield results of great uncertainty. In spite of the CFC-ozone problem of this mixture it can be considered as an exemplary mixture to set up accurate equations of state.

Therefore measurements with an isenthalpic throttle calorimeter were carried out for three different compositions of the mixture. The measured isenthalps could be reproduced within the experimental accuracy by polynomials. Together with the specific heat capacity of the pure components the measurements lead to several caloric properties in the liquid-, vapour- and critical region. The caloric properties can also be calculated by equations of state (EOS). It turned out that the results obtained from Bender's EOS with interaction parameters fitted to the experiments lead to a good agreement with the experimental data.     

A crossover SAFT-VR equation of state for pure fluids: preliminary results for light hydrocarbons

SAFT is perhaps the most versatile, fundamentally, based engineering equation of state in use today. However, in common with all analytic equations of state, SAFT exhibits classical behavior in the critical region rather than the non-analytical, singular behavior seen in real fluids. Recently, so-called crossover equations of state have been developed which solve this shortcoming by incorporating the scaling laws valid asymptotically close to the critical point while reducing to the original classical equation of state far from the critical point. We have combined the SAFT-VR equation of state with an analytical crossover technique to obtain the SAFT-VRX equation of state. The SAFT-VRX approach combines the accurate low temperature behavior of SAFT-VR with a precise representation of the critical region. Preliminary results are presented for hydrocarbon systems which illustrate the accuracy of the SAFT-VRX approach over the entire fluid phase region.