A THEORETICAL INVESTIGATION ON 10–12 POTENTIAL OF HYDROGEN–HYDROGEN COVALENT BOND

This is an analytical investigation of well-known 10–12 potential of hydrogen–hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6–12 Lennard–Jones potential in case of this type of bond. Though the results are illustrated in many text books and literature, an analytical analysis for these potentials is missing almost everywhere. The power laws are valid for small radial distances, which are calculated to some extent. The internuclear separation as well as the binding energy of the hydrogen molecule are evaluated with success.

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THREE-BODY RECOMBINATION OF GASEOUS IONS

Canadian Journal of Chemistry ◽

10.1139/v60-235 ◽

1960 ◽

Vol 38 (10) ◽

pp. 1693-1701 ◽

Cited By ~ 6

Author(s):

Takayuki Fueno ◽

Henry Eyring ◽

Taikyue Ree

Keyword(s):

Binding Energy ◽

Theoretical Approach ◽

Rate Constants ◽

Lennard Jones Potential ◽

Internuclear Separation ◽

Jones Potential ◽

Lennard Jones ◽

Three Body ◽

Body Recombination ◽

Complex Ion

The recombination of gaseous ions in the presence of third bodies is assumed to follow a sequence of two bimolecular steps: M + X+ [Formula: see text] MX+ and MX+ + Y− [Formula: see text] XY + M. The termolecular rate constants of the over-all processes are calculated for several ionized gases at various temperatures. For the calculation, the equilibrium internuclear separation and the corresponding binding energy of a complex ion, MX+, are obtained by minimizing the interaction energy between M and X+, which is approximated to the sum of the Lennard-Jones potential for the M–X interaction and the polarization energy between M and X+. The recombination coefficients of some ionized gases at 288 °K and various pressures are calculated and compared with the observed data. The agreement is found to be satisfactory. The limitations of this theoretical approach are discussed.

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Virial Coefficients of Modified Lennard-Jones Potential

Ukrainian Journal of Physics ◽

10.15407/ujpe59.02.0172 ◽

2014 ◽

Vol 59 (2) ◽

pp. 172-178 ◽

Cited By ~ 10

Author(s):

Ushcats M.V. Ushcats M.V. ◽

Keyword(s):

Virial Coefficients ◽

Lennard Jones Potential ◽

Jones Potential ◽

Lennard Jones

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

International Journal of Molecular Sciences ◽

10.3390/ijms22115914 ◽

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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