Valence bond theory 4 orbitals with 4 electrons

Valence bond theory starts with the idea that a covalent bond consists of a pair of electrons shared between the bound atoms. Two resulting ideas make it easy to picture covalent bonds. The first of these is the concept that that the direction of a bond will be such as to make the orbitals of the bonding electrons... 

According to valence bond theory, atoms share electrons when an atomic orbital on one atom overlaps with an atomic orbital on the other. Each of the overlapping atomic orbitals must contain a single, unpaired electron. Furthermore, the two electrons shared by the bonded atoms must have opposite spins Section 6.6] nuclei of both atoms are attracted to the shared pair of electrons. It is this mutual attraction for the shared electrons that holds the atoms together. 

The previous section points out that the Born-Oppenheimer approximation is useful in that electronic parts of wavefunctions can be separated from nuclear parts of wave-functions. However, it does not assist us in determining what the electronic wavefunctions are. Electrons in molecules are described approximately with orbitals just like electrons in atoms are described by orbitals. We have seen how quantum mechanics treats atomic orbitals. How does quantum mechanics treat molecular orbitals Molecular orbital theory is the most popular way to describe electrons in molecules. Rather than being localized on individual atoms, an electron in a molecule has a wave-function that extends over the entire molecule. There are several mathematical procedures for describing molecular orbitals, one of which we consider in this section. (Another perspective on molecular orbitals, called valence bond theory, will be discussed in Chapter 13. Valence bond theory focuses on electrons in the valence shell.)... 

Write orbital diagrams (boxes with arrows in them) to represent the electron configurations— without hybridization—for all the atoms in PH3. Circle the electrons involved in bonding. Draw a three-dimensional sketch of the molecule and show orbital overlap. What bond angle do you expect from the unhybridized orbitals How well does valence bond theory agree with the experimentally measured bond angle of 93.3 ... 

According to valence bond theory, atoms share electrons when an atomic orbital on one atom overlaps with an atomic oibital on the other. Each of the overlapping atomic oibitals must... 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

A vexing puzzle m the early days of valence bond theory concerned the fact that methane is CH4 and that the four bonds to carbon are directed toward the corners of a tetrahedron Valence bond theory is based on the overlap of half filled orbitals of the connected atoms but with an electron configuration of s 2s 2p 2py carbon has only two half filled orbitals (Figure 2 8a) How can it have bonds to four hydrogens ... 

Valence bond theory (Chapter 7) explains the fact that the three N—O bonds are identical by invoking the idea of resonance, with three contributing structures. MO theory, on the other hand, considers that the skeleton of the nitrate ion is established by the three sigma bonds while the electron pair in the pi orbital is delocalized, shared by all of the atoms in the molecule. According to MO theory, a similar interpretation applies with all of the resonance hybrids described in Chapter 7, including SO S03, and C032-. 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

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... 

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. 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

Delocalization occurs in molecules wherever it is possible by symmetry considerations and wherever an energetic advantage can be gained from its operation. MO theory deals very satisfactorily with delocalization, but with valence bond theory the concept is somewhat clumsily incorporated as an addition to the conventional two-electron, two-centre bonding. In general, the stability conferred upon a molecule by delocalization is because the orbitals are more extensive, so that interelectronic repulsion is minimized. 

The VSEPR theory assumes that the four electrons from the valence shell of the carbon atom plus the valency electrons from the four hydrogen atoms form four identical electron pairs which, at minimum repulsion, give the observed tetrahedral shape. To rationalize the tetrahedral disposition of four bond-pair orbitals with those of the 2s and three 2p atomic orbitals of the carbon atom, sp3 hybridization is invoked. 

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