Valence bond method definition

This last sentence makes clear Slater s attitude toward quantum chemistry. Contrary to Pauling, who was definitely in favor of the valence bond method as the mathematical expression of a chemical theory such as resonance. Slater considered both methods as mathematical approximations used in order to gain access to more fundamental physical principles. What really attracted Slater was the search for a unified view of the problem of molecule formation, in which both approximate methods would be treated so that one would manage to get at the essential physical features of the problem situation, forgetting, in the process, the particular method of approximation used. 

Aromaticity is one of a number of remarkably important but fuzzy concepts in chemistry that does not lend itself easily to widely applicable clear-cut definitions. One of the more recent attempts to summarise what chemists with dilferent backgrounds see in this term was made by Schleyer. Valence bond theory has been, since Kekule s times, a major source of qualitative and quantitative interpretations of aromaticity, and it is surprising that it has not been mentioned, even once, in Schleyer s editorial. Of course, this omission does not diminish the importance that VB methods have had and still have in providing easy-to-understand ideas about aromatic behaviour which are often markedly superior to those coming from other theoretical sources. In order to justify this claim from a current perspective, in this section we look at the recent VB studies of the aromaticity of a series of benzenelike rings, and of clamped benzenes. 

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. 

In using the determinantal method, the explicit use of a spin coordinate and spin-orbitals for each electron has provided the simplest mathematically elementary technique for ensuring that this permutational symmetry is obeyed and retained. No new algebraic or analytical tools were required the definition of spin integration is all that is needed. But the price which had to be paid for this mathematical simplicity was the entanglement of space emd spin variables. It would be physically and chemically attractive to be able to remove any explicit appearance of electron spin from the valence bond model and concentrate on the main physical features of the model which are ... 

Polansky OE, Fratev F (1976) Pars orbital method character orders in CNDO calculations and a new definition for bond orders in all valence electron methods. Chem Phys Lett 37(3) 602-607... 

This article provides a comprehensive review of modem approaches to analysis of electronic wavefunctions. Diverse definitions of properties such as atomic charges, energies, and valences, bond orders and energies, specialized orbitals, and similarities of atoms and molecules are presented. The merits and shortcomings of these definitions are discussed, Particular emphasis is placed on rigorous interpretive tools which produce quantities that can be regarded as tme quantum mechanical observables. Because of their lack of generality, approaches to quantification of chemical concepts that are limited to certain classes of molecules or electronic stmcture methods (such as n -electron bond orders in Hiickel theory) are not mentioned. 

Very often a specific semiempirical MO method was adopted to represent Hqu and a specific MM method was used for //mm and the coupling term / qm-mm introduced additional empirical parameters to allow the combined energy to reproduce experiments. Thus they are specific to the MO method and the MM method adopted at the initial definition of the method. The empirical valence bond approach has also been combined with MM for more complex systems. There have been other approaches attempting to incorporate different procedures which show the importance of combining these methods and the difficulty in doing so. Numerous QM/MM studies have been made in the past, including various versions, some applications, " the treatment of charges, application to zeolites and biochemistry, molecular dynamics, and solvent effects. These variations of the so-called QM/MM methods are treated in separate articles. 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

The GVB and SC methods provide wave functions that are, of course, much more compact than the corresponding valence—CASSCF one (e.g., only 14 spin-coupling modes for methane with the SC method, and a single one with the GVB method). Owing to this difference in size, the GVB and SC methods cannot be expected to include the totality of the nondynamical correlation, even if these two methods treat well, by definition, the left—right correlation for each bond of the molecule. Physically, this is because the various local ionic... 

As explained in the preceding section, the bond index and the valency have definite physical meanings only when basis functions are orthonormalized. MOPAC satisfies this assumption(6), but general MO methods, including DV-Xa, don t satisfy it. Fortunately basis functions can be orthonormalized after MO calculation without any loss of accuracy, provided that all overlap integrals are known. 

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