Method valence bond, limited

The approach used first, historically, and the one this book is about, is called the valence bond (VB) method today. Heitler and London[8], in their treatment of the H2 molecule, used a trial wave function that was appropriate for two H atoms at long distances and proceeded to use it for all distances. The ideal here is called the separated atom limit . The results were qualitatively correct, but did not give a particularly accurate value for the dissociation energy of the H—H bond. After the initial work, others made adjustments and corrections that improved the accuracy. This is discussed folly in Chapter 2. A cmcial characteristic of the VB method is that the orbitals of different atoms must be considered as nonorthogonal. 

However, using the newly developed nonorthogonal Valence Bond SCF (VBSCF) method these VB structures can be constructed directly from purely carbene localized orbitals, without the uncertainty introduced by the orthogonality tails15,16. The orthogonal LMO analysis described above (OVB) is more convenient computationally, but a limited number of real VB calculations need to be carried out on actual heteronuclear doublebond systems to compare with and to validate the LMO results. This analysis has been carried out here using ab initio VBSCF computer codes. 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

Finally we discuss the Generalized Valence Bond (GVB) method as proposed by Hunt, Hay and Goddard./180,181,182/ This is a method aimed at improving some of the HF procedures, for instance to obtain the correct dissociation limit, and to partially include correlation effects. The basic idea is that the type... 

Continuum effective Hamiltonian needs a definition of the electronic charge distribution pMe. All quantum methods giving this quantity can be used, whereas other methods must be suitably modified. Quantum methods are not limited to those based on a canonical molecular orbital formulation. Valence Bond (VB) and related methods may be employed. The interpretation of reaction mechanisms in the gas phase greatly benefits by the shift from one description to another (e.g. from MO to VB). The same techniques can be applied to continuum effective Hamiltonians. We only mention this point here, which would deserve a more detailed discussion. 

The ab initio calculations which have so far been performed have, on the whole, been rather limited. The most extensive treatments have been for the systems H3, 62-95 H385-97 and H2F.108 The ab initio method which at present seems to offer the most practical means of calculating reliable surfaces is the iterative natural orbital (INO) method.92 108 Relatively little effort has as yet been put into the application of valence-bond methods which, from a theoretical point of view, provide the most natural description of processes involving the breaking and making of chemical bonds. The Hartree-Fock or SCF method, which is the most convenient and widely used of all the ab initio methods, gives an inadequate description of these processes and often yields qualitatively incorrect results.13107... 

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