Valency bonds, spatial direction

The valence bond model constructs hybrid orbitals which contain various fractions of the character of the pure component orbitals. These hybrid orbitals are constructed such that they possess the correct spatial characteristics for the formation of bonds. The bonding is treated in terms of localised two-electron two-centre interactions between atoms. As applied to first-row transition metals, the valence bond approach considers that the 45, 4p and 3d orbitals are all available for bonding. To obtain an octahedral complex, two 3d, the 45 and the three 4p metal orbitals are mixed to give six spatially-equivalent directed cfisp3 hybrid orbitals, which are oriented with electron density along the principal Cartesian axes (Fig. 1-9). 

Among the countless concepts that Linus Pauling introduced from Quantum Mechanics into chemistry[l,2], and that became standard principles of the trade, there is the idea of hybridization . In the framework of the valence-bond description of a system, it is useful to mix atomic orbitals of the same n-quantum number , or of similar spatial extent, to construct directed, asymmetric atomic contributions. Although hybrids are not needed in an LCAO-MO description of the system, they have so much become part of the language of both organic and inorganic chemistry, that people will go out of their way to arrive at descriptions that are compatible with them. 

There is no quantum-mechanical evidence for spatially directed bonds between the atoms in a molecule. Directed valency is an assumption, made in analogy with the classical definition of molecular frameworks, stabilized by rigid links between atoms. Attempts to rationalize the occurrence of these presumed covalent bonds resulted in the notion of orbital hybridization, probably the single most misleading concept of theoretical chemistry. As chemistry is traditionally introduced at the elementary level by medium of atomic orbitals, chemists are conditioned to equate molecular shape with orbital hybridization, and reluctant to consider alternative models. Here is another attempt to reconsider the issue in balanced perspective. 

Two theories go hand in hand in a discussion of covalent bonding. The valence shell electron pair repulsion (VSEPR) theory helps us to understand and predict the spatial arrangement of atoms in a polyatomic molecule or ion. It does not, however, explain hoav bonding occurs, ] ist where it occurs and where unshared pairs of valence shell electrons are directed. The valence bond (VB) theory describes how the bonding takes place, in terms of overlapping atomic orbitals. In this theory, the atomic orbitals discussed in Chapter 5 are often mixed, or hybridized, to form new orbitals with different spatial orientations. Used together, these two simple ideas enable us to understand the bonding, molecular shapes, and properties of a wide variety of polyatomic molecules and ions. 

Werner recognized that the secondary valence bonds in his theory were directed in space, with the result that geometrical and optical isomersion is possible. For example, there are nine isomers with the empirical formula Co(NH3)3(N02)3, corresponding to different spatial arrangements of the MH3 and NO2 group. In 1916... 

In general, in its application to an electron and a nucleus the ifj function passes through maxima and minima as the radial distance of the former from the latter increases, and finally it dies away asymptotically to zero at great distances. The electric density rises and falls and finally drops to zero. The places where the density is zero are called nodes. According to the various relations of n, I, and m, there are varying numbers of nodes and the cloud possesses either spherical symmetry or various kinds of axial symmetry. The symmetry and the values of the wave function in various directions prove to be very significant in problems of valency and determine the spatial orientation of valency bonds. These matters will be illustrated more fully in a later section. 

Detailed calculations about the more complex atoms are virtually impossible to perform, but the Pauli principle provides the general rules of valency, and, furthermore, certain empirical extensions of wave mechanics prove of great utility in the treatment of such matters as the spatial direction of valency bonds. 

Certain two-dimensional 5 = quantum antiferromagnets can imdergo a direct continuous quantum phase transition between two ordered phases, an antiferromagnetic Neel phase and the so-called valence-bond ordered phase (where translational invariance is broken). This is in contradiction to Landau theory, which predicts phase coexistence, an intermediate phase, or a first-order transition, if any. The continuous transition is the result of topological defects that become spatially deconfined at the critical point and are not contained in an LGW description. Recently, there has been a great interest in the resulting deconfined quantum critical points. ... 

The problem of directed valence is treated from a group theory point of view. A method is developed by which the possibility of formation of covalent bonds in any spatial arrangement from a given electron configuration can be tested. The same method also determines the possibilities of double and triple bond formation. Previous results in the field of directed valence are extended to cover all possible configurations from two to eight s, p, or d electrons, and the possibilities of double bond formation in each case. A number of examples are discussed. 

Each constituent atom of a covalent crystal is linked to its neighbours through directed covalent bonds. The crystal structure is determined by the spatial dispositions of these bonds. Because primary valence forces are involved, such solids are hard and have high melting points, e.g. diamond, silicon carbide, etc. Relatively few entirely covalent solids have been studied at elevated temperatures and it is, therefore, premature to comment on their decomposition characteristics. 

In the above equation, d is the antisymmetrizer the set of orbitals, 4>di, are the set of doubly occupied core and valence orbitals, and the set of orbitals, (pat), are the set of Ha singly occupied active valence orbitals. The total number of electrons is Ng — 2nd + a- The doubly occupied valence orbitals do not directly participate in bonding, although, as we shall see, they can affect which type of bonds are formed. The active orbitals are distinct, singly occupied and non-orthogonal orbitals. The spatial product of orbitals in Eq. (1) is multiplied by a product of spin functions associated with the doubly occupied orbitals times a spin function, 0, for the electrons in the active orbitals. This spin function is a linear combination of spin... 

Indeed, contrary to transition metal ions, lanthartide ions, due to the timer eharacter of their 4f valence orbitals, exhibit very little preference in bonding direction (Kanaker, 1970). The bonds between lanthartide ions and ligands are essentially ionic and the spatial arrangement of the ligand around the lanthartide ions are mainly due to steric hindrance and inter-ligand interactions. Further more it is well known that the earboxylate ions presents several eoordination modes (see scheme 2) (Ouehi, 1988). 

It is difficult to evaluate the relative contributions oflk j), and (I J ai to the observed quadrupole interaction in [( -C5H5)Fe(CO)2]2. The similar values of A observed for both the cis and trans isomers do however indicate similar values for each isomer. In addition the spatial disposition of the ligands on one iron site must have a small influence on the quadrupole interaction on the second iron site. If the influence were large, one would expect to see different quadrupole interactions in the two isomers. This may be an indication that the valence contribution is dominant, a conclusion that would also be supported by the apparent absence of a direct iron-iron bond. 

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