London energy theory

In view of the complications of the intermolecular potential (as compared to the interatomic potential of the rare gas atoms) the comparisons for molecules in Tables II, III, and IV should be judged with caution. The apparent discrepancies from the theories for single atoms can be misleading. An example is the calculation for CH4 on the Slater-Kirkwood theory where Table IV shows the absurd value of 24 for the effective number of electrons. Pitzer and Catalano32 have applied the Slater-Kirkwood equation to the intermolecular potential of CH4 by addition of all the individual atom interactions and, with N = 4 for carbon and 1 for hydrogen, obtained agreement within 5 per cent for the London energy at the potential minimum. 

Van der Waals forces are derived from the energy of interaction between two molecules, Vss. These can be derived from London s theory as follows ... 

Heitler-London covalence theory phys chem A calculation of the binding energy and the distance between the atoms of a diatomic hydrogen molecule, which assumes... 

Relation (2) is introduced in the theory of de Boer and Hamaker energy constant in London s theory in which the two atoms are represented by three-dimensional harmonic oscillators with a characteristic frequency v and a polarizability a. h is Planck s constant. 

A Review of Correlations for ky. Justification for using the geometric mean for ey—and for Tcij—is provided by London s theory of dispersion forces. When Londons expression for the intermolecular energy is equated to the attractive part of the Lennard-Jones (LJ) 12 6 potential, the following relationship obtains ... 

An accurate equation of state of fluids is used to test the combining rules for the interaction energy uy of mixtures derived from the theories of London energy between small or large (chain) molecules. The tests are based mostly on comparisons with the thermodynamic excess functions of binary systems at P = 0. For long chains the parameter r)/k, determining the dependence of u/k on the temperature, depends on the reduced density p = V°/V of the system (where V° is the close-packed volume) and /k—>0 when P > 0.75 (solid state). 

Casimir and Polder showed, in 1948, that London s theory must be modified if the molecules are some distance (in molecular terms) apart. This is because the electrostatic forces are not propagated instantaneously but take a finite, if small, time pass between two molecules. The net result of such retarded dispersion forces is that the energy of interaction between two particles with distance between them being greater than 20 nm is proportional to r instead of... 

A continuation of London s theory of adiabatic chemical reactions, especially for atomic reactions. The total binding energy of single atom pairs is obtained as a function of atomic distance from optical data euid using the Heitler-London calculations corrected for the Coulomb energy. Linear reactions of the systems... 

Pendry J B 1974 Low Energy Eiectron Diffraction The Theory and its Appiication to Determination of Surface Structure (London Academic)... 

The semiempirical methods combine experimental data with theory as a way to circumvent the calculational difficulties of pure theory. The first of these methods leads to what are called London-Eyring-Polanyi (LEP) potential energy surfaces. Consider the triatomic ABC system. For any pair of atoms the energy as a function of intermolecular distance r is represented by the Morse equation, Eq. (5-16),... 

The atomization energy, electron affinity and ionization potential have been calculated for 1//-azepine. and a difference in energy between the boat and chair forms of 64.8 kJ mol -1 deduced.98 The calculated dipole moment for l//-azepine is 4.67 D.98 Hiickel-London theory has been applied to calculate the ring-current octopole hypersusceptibilities of l//-azepine."... 

The key element in London s approach is the expansion of the electrical potential energy in multipole series. Since neutral molecules or portions of molecules are involved, the leading term is that for dipole-dipole interaction. While attention has been given to higher-order terms, these are usually small, and the greater need seems to be for improved treatment of the dipole-dipole terms. London used second order perturbation theory in his treatment, but Slater and Kirkwood38,21 soon followed with a variation method treatment which yielded similar results. Other individual papers will be mentioned later, but the excellent review of Mar-genau26 should not be overlooked. 

London theory U — I = ionization energy empirical evaluate U from El and correlate (U/I) with number of electrons in system. 

Hall, G. G., Proc. Roy. Soc. [London) A213, 113, The molecular orbital theory of chemical valency. XI. Bond energies, resonance energies and triplet state energies. ... 

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