The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

scholarly journals Drug Design Outlook by Calculation of Second Virial Coefficient as a Nano Study

2017 ◽  
Vol 56 (2) ◽  
Author(s):  
M. Monajjemi ◽  
F. Naderi ◽  
F. Mollaamin ◽  
M. Khaleghian
Keyword(s):  
Potential Energy ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Basis Set ◽  
Intermolecular Potential ◽  
Energy Curve ◽  
Basis Set Superposition Error ◽  
Second Virial Coefficients ◽  
Calculated Potential Energy

Intermolecular potential energy surface for an interaction of drug with Na has been examined using HF level of theory with 6-31G* basis set. The name of drug is meso-tetrakis (p-sulphonatophenyl) porphyrin (here after abbreviated to TSPP) . The numbers of Na<sup>+</sup> have a significant effect on the calculated potential energy curve (including position, depth, and width of the potential well). Counterpoise (CP) correction has been used to show the extent of the basis set superposition error (BSSE) on the potential energy curves obtained for TSPPNa. The second virial coefficients are calculated by these data.

Measurement of the temperature variation of virial coefficients. II. The second virial coefficients of benzene

1966 ◽  
Vol 19 (8) ◽  
pp. 1331 ◽  
Author(s):  
GA Bottomley ◽  
TH Spurling
Keyword(s):  
Potential Energy ◽  
Temperature Variation ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Energy Functions ◽  
Second Virial Coefficients ◽  
Potential Energy Functions ◽  
Direct Measurements

New measurements of the temperature variation of the second virial coefficient of benzene from 35� to 184� are reported, combined with selected direct measurements up to 33j0, and used to evaluate the parameters for various intermolecular potential energy functions.

The virial coefficients of the carbon dioxide-ethylene system I. Pure gases

1964 ◽  
Vol 277 (1371) ◽  
pp. 448-467 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Direct Determination ◽  
Expansion Method ◽  
National Physical Laboratory ◽  
Intermolecular Potential ◽  
Gaseous Mixtures ◽  
Physical Laboratory ◽  
The Relationship

This paper describes the first part of an investigation of the thermodynamic properties of gases and gaseous mixtures undertaken a few years ago at the National Physical Laboratory, with the main object of providing data on the relationship between the properties of mixtures and those of the pure constituents. The virial coefficients of carbon dioxide and ethylene have been determined by the series-expansion method over the range —10 to 200 °C, and the representation of the results by several forms of intermolecular potential has been investigated. In the case of ethylene it appears that the second virial coefficient may be represented accurately in terms of a Lennard-Jones 6:12 potential, the parameters of which are determined. In the corresponding representation for carbon dioxide there is a small but systematic discrepancy and evidence is adduced that this may be rectified by the introduction of a quadrupole interaction term on the lines of the theory developed by Pople. The value of the quadrupole moment suggested by this calculation proves to be in fairly close agreement with a recent direct determination. Work on the virial coefficients of mixtures of the two gases will be described in a further paper.

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
Keyword(s):  
Methyl Acetate ◽  
Virial Coefficient ◽  
Methyl Formate ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Ethyl Formate ◽  
Carbonyl Oxygen ◽  
Second Virial Coefficients ◽  
Theoretical Significance ◽  
Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

The second virial coefficients of mixed organic vapours

1952 ◽  
Vol 210 (1103) ◽  
pp. 557-564 ◽  
Keyword(s):  
Hydrogen Bonding ◽  
Binary Mixtures ◽  
Diethyl Ether ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Corresponding States ◽  
Linear Variation ◽  
Second Virial Coefficients

The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.

Pairwise additive third virial coefficients for multipolar molecules : Application to water vapour

1971 ◽  
Vol 24 (8) ◽  
pp. 1567 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Water Vapour ◽  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Axially Symmetric ◽  
Multidimensional Integration ◽  
Third Virial Coefficient ◽  
Qualitative Effect ◽  
Experimental Values

Pairwise additive third virial coefficients for axially symmetric multipolar molecules have been calculated using a non-product multidimensional integration formula. Results for the Stockmayer potential agree with the corrected results of Rowlinson. It is found that the inclusion of the dipole-quadrupole and quadrupole-quadrupole terms in the potential function has a marked qualitative effect on the shape of the C-T curve. Values of the third virial coefficient for water vapour calculated using a potential function derived from gaseous viscosity and second virial coefficient data are in good agreement with the experimental values.

Parameters of the Morse Potential from Second Virial Coefficients of Gases

1987 ◽  
Vol 42 (5) ◽  
pp. 447-450 ◽  
Author(s):  
Akira Matsumoto
Keyword(s):  
Temperature Dependence ◽  
Morse Potential ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Polyatomic Molecules ◽  
Inert Gases ◽  
Second Virial Coefficients ◽  
Analytic Expression

An analytic expression for the second virial coefficient in case of the Morse potential is derived. The parameters of the Morse potential are determined for eighteen species comprising inert gases, diatomic and polyatomic molecules, and mixtures of gases using experimental second virial coefficients. The calculated second virial coefficients based on the obtained Morse potential agree well with the empirical second virial coefficients and their temperature dependence.

scholarly journals Predicting second virial coefficients of organic and inorganic compounds using Gaussian process regression

2021 ◽  
Vol 23 (4) ◽  
pp. 2891-2898
Author(s):  
Miruna T. Cretu ◽  
Jesús Pérez-Ríos
Keyword(s):  
Gaussian Process ◽  
Virial Coefficient ◽  
Inorganic Compounds ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Gaussian Process Regression ◽  
Temperature Dependent ◽  
Second Virial Coefficients ◽  
Molecular Features

Intuitive and accessible molecular features are used to predict the temperature-dependent second virial coefficient of organic and inorganic compounds with Gaussian process regression.

Second Virial Coefficients and Transport Properties of Hexafluoride Gases from an Improved Intermolecular Potential

1997 ◽  
Vol 52 (10) ◽  
pp. 748-756
Author(s):  
Ilioara Coroiu ◽  
D. E. Demco
Keyword(s):  
Transport Properties ◽  
Transport Coefficients ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Predictive Ability ◽  
Uranium Hexafluoride ◽  
Chem Phys ◽  
Intermolecular Potential ◽  
Second Virial Coefficients ◽  
Temperature Range

Abstract Second virial coefficients and a large number of Chapman-Cowling collision integrals were calculated for gases obeying an improved intermolecular potential proposed by Aziz et al. [J. Chem. Phys. 94, 1034 (1991)]. The results are tabulated for a large reduced temperature range, kT/ε from 0.1 to 100. The treatment was entirely classical, and no corrections for quantum effects were made. The higher approximations to the transport coefficients were also calculated and tabulated for the same temperature range. These results should be applicable to characterize the bulk properties of various spherical molecules, especially to predict gaseous transport properties. Evaluation of the potential parameters for uranium hexafluoride, together with fitting to second virial coefficient, viscosity, thermal conductivity and self-diffusion data are also presented. This potential appears to have the best overall predictive ability for gaseous hexafluoride data.

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