London model

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

The elastic moduli of the vortex lattice around the transition field H j of have been analyzed within the nonlocal London model by Miranovic and Kogan (2001). In particular, the square vortex lattice was found to be soft with respect to shear displacement along the square sides [110] or [110]. 

Our VB program TURTLE [3] allows for both a more extensive and a more restrictive description of benzene and cyclobutadiene than was available in the previous studies. We included full orbital and full geometry optimisation. Two orbital models were used. The first has p-like (pn) orbitals strictly localised on the carbon atoms. This corresponds to the classical Heitler-London model [48], but with optimal orbitals. The second uses delocalised fully optimised [68] p orbitals, which include tails to neighbouring atoms. 

Calculate the singlet-state and triplet-state energies for the Heitler-London model of the H2 molecule using the Ising model. 

It has been pointed out that any relationship between the exchange integral and the Weiss field is only valid at 0 K, since the former considers magnetic coupling in a pair-wise manner and the latter results from a mean-field theory (Goodenough, 1966). Finally, it is also essential to understand that Eq. 8.43 is strictly valid only for localized moments (in the context of the Heitler-London model). One might wonder then whether the Weiss model is applicable to the ferromagnetic metals, in which the electrons are in delocalized Bloch states, for example, Fe, Co, and Ni. This will be taken up later. 

The basic idea of the Heitler-London model for the hydrogen molecule can be extended to chemical bonds between any two atoms. The orbital function (10.8) must be associated with the singlet spin function cro,o(l > 2) in order that the overall wavefunction be antisymmetric [cf. Eq (8.14)]. This is a quantum-mechanical realization of the concept of an electron-pair bond, first proposed by G. N. Lewis in 1916. It is also now explained why the electron spins must be paired, i.e., antiparallel. It is also permissible to combine an antisymmetric orbital function with a triplet spin function, but this will, in most cases, give a repulsive state, such as the one shown in red in Fig. 10.2. 

Hamiltonian, 139 Heitler-London model, 141-142 ion and molecular orbital theory, 157-160... 

Heitler-London model - An early quantum-mechanical model of the hydrogen atom which introduced the concept of the exchange interaction between electrons as the primary reason for stability of the chemical bond. 

Valence bond theory is usually introduced using the famous Heitler-London model of the hydrogen molecule [Heitler and London 1927] This model considers two non-interacting hydrogen atoms (a and b) in their ground states that are separated by a long distance. The wavefunction for this system is ... 

Considerations like these mean that the VB model, although it has seen a considerable resurgence of interest over the past few years with several key breakthroughs being made, is still predominantly perceived as a specialist area with applications confined to smcJl numbers of electrons. The so-called Generalised Valence Bond (GVB) method which is a self-consistent development of the Heitler-London model is developed in Chapter 22 and, for the moment, this is as far as we shall go with the details of the more classical VB model until we have been able to develop the tools necessary to continue in Chapter 21. 

We can obviously set up an heuristic primitive for the spatial part using the very idea which was used to generate Q/(. If each electron pair is a localised bond then the spatial part should be capable of being generated from a product of spatial orbitals similar to the primitive product used in the Heitler-London model of the electron-pair bond. Clearly, if these individual orbitals are formed from some set of basis functions, then the matrix which defines the orbitals in terms of the basis functions forms a familiar variational problem... 

The pair-NO extension of the simple Heitler-London model. 

It is possible to obtain an analytical expression for the variation of V (R) = (E (R )) with R in the case of simple diatomic molecules. Sugiura 60) obtained an analytical expression for the variation of the intemuclear potential V (R) in H2 for both the bonding and antibonding states of the electronic ground state, in terms of the HeiUer and London model (61), using the Bom-Oppenheimer approximation (see Section 2 above). The result is an involved expression in g, where g — Klao ... 

The Heitler-London model for H2 is the simplest model both for chemical bonding of two neutral species, here the bonding to two H atoms, as well as for electron exchange and energy transfer. (See e.g. Hermann Haken and Hans Christoph Wolf, Molecular Physics and Elements of Quantum Chemistry,... 

Only the first of these truly originates from him. In the first paper of the series, Pauling took up the idea of spatially directed bonds. By a generalization of the Heitler-London model for hydrogen, a normal chemical bond can be associated with the spin pairing of two electrons, one from each of the two atoms. While an s orbital is spherically symmetrical, other atomic... 

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