Valence bond theory 6-electron system

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

Heterocyclic systems have played an important role in this historical development. In addition to pyridine and thiophene mentioned earlier, a third heterocyclic system with one heteroatom played a crucial part protonation and methylation of 4//-pyrone were found by J. N. Collie and T. Tickle in 1899 to occur at the exocyclic oxygen atom and not at the oxygen heteroatom, giving a first hint for the jr-electron sextet theory based on the these arguments.36 Therefore, F. Arndt, who proposed in 1924 a mesomeric structure for 4//-pyrone, should also be considered among the pioneers who contributed to the theory of the aromatic sextet.37 These ideas were later refined by Linus Pauling, whose valence bond theory (and the electronegativity, resonance and hybridization concepts) led to results similar to Hiickel s molecular orbital theory.38... 

The Hy-CI function used for molecular systems is based on the MO theory, in which molecular orbitals are many-center linear combinations of one-center Cartesian Gaussians. These combinations are the solutions of Hartree-Fock equations. An alternative way is to employ directly in Cl and Hylleraas-CI expansions simple one-center basis functions instead of producing first the molecular orbitals. This is a subject of the valence bond theory (VB). This type of approach, called Hy-CIVB, has been proposed by Cencek et al. (Cencek et.al. 1991). In the full-CI or full-Hy-CI limit (all possible CSF-s generated from the given one-center basis set), MO and VB wave functions become identical each term in a MO-expansion is simply a linear combination of all terms from a VB-expansion. Due to the non-orthogonality of one-center functions the mathematical formalism of the VB theory for many-electron systems is rather cumbersome. However, for two-electron systems this drawback is not important and, moreover, the VB function seems in this case more natural. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

M. A. Fox, F. A. Matsen, J. Chem. Educ. 62, All (1985). Electronic Structure in Tr-Systems. Part II. The Unification of Hiickel and Valence Bond Theories. 

Ab initio modem valence bond theory, in its spin-coupled valence bond (SCVB) form, has proved very successful for accurate computations on ground and excited states of molecular systems. The compactness of the resulting wavefunctions allows direct and clear interpretation of correlated electronic structure. We concentrate in the present account on recent developments, typically involving the optimization of virtual orbitals via an approximate energy expression. These virtuals lead to higher accuracy for the final variational wavefunctions, but with even more compact functions. Particular attention is paid here to applications of the methodology to studies of intermolecular forces. 

According to Pauling [6-9], valence bond theory can also be used to describe metallic systems. At a first glance, this seems to be contradictory, since VB deals with localized chemical bonds and a metallic bond is thought of as completely delocalized. Pauling s argument is that the metal atoms in the crystal have an available orbital to receive an extra electron and thus form an extra covalent bond, through a mechanism he called unsynchronized resonance. 

Pauling s use of valence bond theory had a direct connection with the types of structures commonly used by organic chemists, and was relatively easy to understand, provided one did not delve too deeply into its details. The basic postulate was that compounds having n-electron systems that can be described by more than one structure will be stabilized by "resonance" and will have a lower energy than any of the contributing structures. Thus, for benzene one would write... 

Valence bond theory, in the terms defined by Pauling, is not able to account for the 4n+2 rule, and the properties of cyclobutadiene and cyclooctatetraene. It has been suggested that the problem with these molecules is the strain associated with the bond angles in the planar structures.10 However, this was shown to be incorrect by the observation that the addition of two electrons to cyclooctatetraene leads to the planar dianion. It is only recently that it has been recognized that cyclic permutations must be included in order to properly treat cyclic systems via valence bond theory.11 One of Pauling s few failures in structural theory is his nonrecognition of the problems associated with the 4n molecules. 

The yellow to orange compounds 804(118207)2, 864(84 013)2, and 8e4(8b2Fii)2 have been prepared. Crystallographic studies on 804(118207)2 have shown that the cation 8c4 + has square-planar D h) geometry. The structure can be described by valence bond theory in terms of four resonance structures equivalent to (la), or by simple molecular orbital theory in which three of the four n molecular orbitals are filled. " The 8e4 + ions are examples of six-jr-electron systems, and they are thus examples of inorganic aromatic compounds (lb). 

The Fermi hole for the reference electron at a bonded maxima in the VSCC of the carbon atom has the appearance of the density of a directed sp hybrid orbital of valence bond theory or of the density of a localized bonding orbital of molecular orbital theory. Luken (1982, 1984) has also discussed and illustrated the properties of the Fermi hole and noted the similarity in appearance of the density of a Fermi hole to that for a corresponding localized molecular orbital. We emphasize here again that localized orbitals like the Fermi holes shown above for valence electrons are, in general, not sufficiently localized to separate regions of space to correspond to physically localized or distinct electron pairs. The fact that the Fermi hole resembles localized orbitals in systems where physical localization of pairs is not found further illustrates this point. 

Consider a diatomic, AB, interacting with a surface, S. The basic idea is to utilize valence bond theory for the atom-surface interactions, AB and BS> along with AB to construct AB,S For each atom of the diatomic, we associate a single electron. Since association of one electron with each body in a three-body system allows only one bond, and since the solid can bind both atoms simultaneously, two valence electrons are associated with the solid. Physically, this reflects the ability of the infinite solid to donate and receive many electrons. The use of two electrons for the solid body and two for the diatomic leads to a four-body LEPS potential (Eyring et al. 1944) that is convenient mathematically, but contains nonphysical bonds between the two electrons in the solid. These are eliminated, based upon the rule that each electron can only interact with an electron on a different body, yielding the modified four-body LEPS form. One may also view this as an empirical parametrized form with a few parameters that have well-controlled effects on the global PES. 

It is possible to apply theoretical models working exactly in the frame of the Valence Bond theory. Another way is to employ empirical models for the above mentioned purpose. The aim of this review is to show how molecular geometry may be employed to solve these kinds of problems. As a useful method, an empirical model called Harmonic Oscillator Stabilization Energy (HOSE) can be used. Its the chief aim is to serve as a tool for determining the weights of canonical structures in 7i-electron systems [44,45], which may be either molecules or their fragments. 

An entirely different way to treat the electronic structure of molecules is provided by valence bond theory, which was developed at about the same time as the molecular orbital approach. However, valence bond theory was not so amenable to calculations on large molecules, and molecular orbital theory came to dominate electronic structure theory for such systems. Nevertheless, valence bond theories are often considered to be more appropriate for certain types of problem than molecular orbital theory, especially when dealing with processes that involve bonds being broken and/or formed. Recall from Figure 3.2 that a self-consistent field wavefunction gives a wholly inaccurate picture for the dissociation of H2 by contrast, the correct dissociation behaviour is naturally built into valence bond theories. 

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