Quantum corrections to second virial coefficients for the diatomic Lennard-Jones potential

1982 ◽  
Vol 86 (8) ◽  
pp. 1469-1472 ◽  
Author(s):  
S. H. Ling ◽  
M. Rigby
Keyword(s):  
Virial Coefficients ◽  
Quantum Corrections ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Second Virial Coefficients ◽  
Lennard Jones

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: IX. SECOND VIRIAL COEFFICIENTS AND THE INTERMOLECULAR POTENTIAL OF NEON

1955 ◽  
Vol 33 (4) ◽  
pp. 589-596 ◽  
Author(s):  
G. A. Nicholson ◽  
W. G. Schneider
Keyword(s):  
Low Temperature ◽  
High Temperatures ◽  
Pressure Range ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Second Virial Coefficients ◽  
Lennard Jones

The second virial coefficients of neon have been determined in the temperature range 0° to 700 °C. and the pressure range 10 to 80 atmospheres. These data were combined with published low temperature (−150° to 0 °C.) second virial data, to investigate the intermolecular potentials of neon using both a Lennard-Jones potential, with a 9th and 12th power repulsion term, and also a modified Buckingham exponential–six potential. The agreement between observed and calculated values of B(T) was excellent for both the exponential–six and the Lennard-Jones 12:6 potentials and slightly less satisfactory for the Lennard-Jones 9:6 potential.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

The behaviour of fluids of Quasi-Spherical molecules. I. Gases at low densities

1954 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
SD Hamann ◽  
JA Lambert
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
Good Description ◽  
Virial Coefficients ◽  
Polyatomic Molecules ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

Consideration of the spherically smoothed mutual potential energy between nearly spherical polyatomic molecules leads to the conclusion that it can often be well represented by a (28,7) type of Lennard-Jones potential. Second and third virial coefficients have been calculated for this potential and also for (∞,6) and (∞,7) potentials. The (28,7) interaction energy gives a good description of the properties of gases of quasi-spherical molecules. For these gases it is markedly superior to the more usual (12,6) potential.

scholarly journals Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

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