Lennard-Jones’ 1930 Paper

L-J P Lennard-Jones Papers, Churchill College, Cambridge, UK... 

Hall, G. G. 1991. The Lennard-Jones paper of 1929 and the foundations of molecular orbital theory. Advances in Quantum Chemistry 22 1-6. 

Outer electrons, the ones involved in bonding, occupy exactly the sort of molecular orbitals discussed in the previous section with regard to MO calculations. Rather than discuss quantitative characteristics of specific wavefunctions, however, the Lennard-Jones paper highlights the general qualitative relationship between the electron density function corresponding to a particular wavefunction orbital and the energy associated with that orbital. These molecular wavefunctions are functionally more complex than atomic wavefunctions and their energies depend importantly on inter-nuclear distance. 

In 1937, Coulson s mentor, Lennard-Jones, wrote a series of papers on molecular orbitals applied to polyenes and aromatic molecules, discussing the variations in bond lengths in conjugated and aromatic molecules from a theoretical point of view. 92 He involved his student in the work. Coulson defined... 

One of the first studies of multiple ions at the water/solid interface was by Spohr and Heinzinger, who carried out a simulation of a system of 8 Li" and 81" ions dissolved in 200 water molecules between uncharged flat Lennard-Jones walls.However, the issues discussed in their paper involved water structure and dynamics and the single-ion properties mentioned earlier. No attempt was made to consider the ions distributions and ion-ion correlations. This work has recently been repeated using more realistic water-metal potentials. ... 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

Critical Phenomena in the Detonation of Gases. This subject was discussed in two papers published by J.E. Lennard-Jones A.F. Devonshire in ProcRoySoc 163A, 53-70(1937) and 165A, 1-11(1938). Abstracted very briefly in CA 32, 1533 6118(1938)... 

Equation of state discussed in these papers is given in this Volume under Detonation (and Explosion), Equations of State", as Lennard-Jones Devonshire Equation of State"... 

The problem of adsorption was first treated by Lenel in 1933. Lennard-Jones, Strachan, Devonshire and Goodwin18- followed, between 1935 and 1937, with a series of papers of a theoretical nature. During this period contributions were also made by Barrer,4 Goodwin5 and Orr.6 Since that time the problem has been re-examined by Crawford and Tomkins7 and by Rhodin8 during 1948 and 1949. 

Other comparisons of V-T transfer data with theory can be found in the literature. The reader is referred to the paper of Benson and Berend [48] for a comparison with the classical theory of those authors, in which both Morse and Lennard-Jones potentials have been employed. 

In equation (4), A is the number density of atoms per unit surface area A is the dispersion constant the subscripts 5 and / refer to the adsorbent and adsorbate, respectively and do = 0.S5 asf is the z-coordinate at which the 10-4 potential for a single planar surface passes through its zero-point value. The 10-4 potential is obtained by integration of the Lennard-Jones 12-6 potential over an infinite planar surface. The dispersion constants A and Aff represent the adsorbate-adsorbent and adsorbate-adsorbate interactions, respectively these coefficients are calculated from the Kirkwood-Muller equations in the original HK paper [6], Combining equations (2-4) yields an equation that relates filling pressure to pore width ... 

S.-B. Zhu and G. W. Robinson, Structure and Dynamics of Liquid Water between Plates, J. Chem. Phys. 94 (1991) 1403-1410 references to other simulations of this widely studied system are given in this paper see also E. Spohr, Molecular Dynamics Simulation Studies of the Density Profiles of Water between 9-3 Lennard-Jones Walls, J. Chem. Phys. 106 (1997) 388-391. 

It was shown by us J. Phys. Chem. B, 2006, 110, 12707) that the excess (deficit) of any species i around a central molecule j in a binary mixture is not provided by c,Gy (where c, is the molar concentration of species i in the mixture and Gy are the Kirkwood-Buff integrals) as usually considered and that an additional term, involving a volume F which is inaccessible to molecules of species i because of the presence of the central molecule j, must be included. In this paper, the new expression is applied to various binary mixtures and used to establish a simple criterion for preferential solvation in a binary system. First, it is applied to binary Lennard-Jones fluids. The conventional expression for the excess (deficit) in binary mixtures, c,Gy, provides always deficits around any central molecule in such fluids. In contrast, the new expression provides excess for one species and deficit for the other one. In addition, two kinds of binary mixtures involving weak (argon/krypton) and strong (alcohols/water) mtermolecular interactions were considered. 

To close this Section we comment on two papers that do not fit under any neat heading. The first of these is by Xiao et al,261 who study the final stages of the collapse of an unstable bubble or cavity using MD simulations of an equilibrated Lennard-Jones fluid from which a sphere of molecules has been removed. They find that the temperature inside this bubble can reach up to an equivalent of 6000 K for water. It is at these temperatures that sonolumines-cence is observed experimentally. The mechanism of bubble collapse is found to be oscillatory in time, in agreement with classical hydrodynamics predictions and experimental observation. The second paper, by Lue,262 studies the collision statistics of hard hypersphere fluids by MD in 3, 4 and 5 dimensions. Equations of state, self-diffusion coefficients, shear viscosities and thermal conductivities are determined as functions of density. Exact expressions for the mean-free path in terms of the average collision time and the compressibility factor in terms of collision rate are also derived. Work such as this, abstract as it may appear, may be valuable in the development of microscopic theories of fluid transport as well as provide insight into transport processes in general. 

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