Sigma, a-orbitals

Sigma (a) orbital A molecular orbital resulting from head-on overlap of two atomic orbitals. 

A sigma a) orbital lies along the axis between two bonded atoms a pair of electrons in a sigma orbital is called a sigma bond. 

Bond Formation. The sp bond formation is illustrated in Fig. 3.7. By convention, a directional (or stereospecific) orbital such as the spP is called a sigma (a) orbital, and the bond a sigma bond. The direction of the four bonds produces a tetrahedral symmetry which is found in structures such as diamond or silicon carbide bere the carbon atom is bonded to four... 

The transfer of a solvated electron to a chlorinated aliphatic hydrocarbon occurs with the simultaneous loss of chloride because tiiere are no available n orbitals available. Therefore, the electron must add to a carbon-chlorine antibonding sigma (a) orbital, thereby breaking the C-Cl bond. This process is called dissociative electron transfer (see Scheme 2). The resulting radical can add a second solvated electron followed by loss of another chloride, as long as a chlorine is still present on that carbon. Ihis is illustrated in Scheme 2 for tire dechlorination of CCI4 in Na/NHa. 

All of these orbitals are sigma (a) orbitals and formed by the direct head-on or end-to-end overlap of atomic orbitals resulting in electron density concentrated between the nuclei of the atoms. 

A bond m which the orbitals overlap along a line connecting the atoms (the inter nuclear axis) is called a sigma (a) bond The electron distribution m a ct bond is cylm drically symmetric were we to slice through a ct bond perpendicular to the mternuclear axis Its cross section would appear as a circle Another way to see the shape of the elec tron distribution is to view the molecule end on... 

To answer this question, it is necessary to consider the shape or spatial distribution of the orbitals filled by bonding electrons in molecules. From this point of view, we can distinguish between two types of bonding orbitals. Ihe first of these, and by far the more common, is called a sigma bonding orbital. It consists of a single lobe ... 

See text below.) When p orbitals from two different atoms (a) overlap, there are two quite different possibilities. If they overlap head to head (b), two sigma molecular orbitals are produced. If. on the other hand, they overlap side to side (c). two pi molecular orbitals result. 

Figure 1.17 The hypothetical formation of the bonding molecular orbitals of ethane from two sp -hybridized carbon atoms and six hydrogen atoms. All of the bonds are sigma bonds. (Antibonding sigma molecular orbitals — are called a orbitals — are formed in each instance as well, but for simplicity these are not shown.)... 

However, the electron density between the atoms approaches zero at the nodal plane for the anti-bonding a orbital, which destabilizes the system. As an example, see below for the overlap of 2 Is orbitals (from Figure 9-2). Figure 9-3 shows the bonding and antibonding sigma orbitals formed by the combining head-on of two p orbitals. 

Fig.4 (see p. 74/75) shows all localized orbitals for the ground state of the BH molecule and the 12 excited state of B2.37) These are again rotationally symmetric orbitals, i.e., sigma type orbitals, and the complete contour surfaces can be obtained by spinning around the indicated axis. In all orbitals shown the outermost contour corresponds to a wavefunction value of 0.025 Bohr-3/2. For all valence shell orbitals the increment from one contour to another is 0.025 Bohr-3/2. For the inner shells the increment is again 0.2 Bohr 3/2, but only three contours and the wavefunction values at the nuclear positions are shown. 

The relation between F2 and FH is similar to that observed between B2 and BH. The FH molecule has a sigma bonding orbital and has three trigon-ally equivalent lone pairs which are almost identical in character and shape to the corresponding lone pairs of F2. These contracted lone pairs are less sensitive to the other atom than those on B. We also find nearly complete transferability between the inner shells. Here again the outermost contour is 0.025 Bohr 3/2 and the increment of those contours which are shown is 0.2 Bohr 3/2. 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

The formation of bonding molecular orbitals by an overlap of atomic orbitals applies not only to the Is orbitals of hydrogen, but also to other atomic orbitals. When the atomic orbitals overlap along the axis of the bond, a covalent bond, called a sigma (a) bond, results. This is normally referred to as end-on overlap. Some examples of the formation of a bonds from overlapping atomic orbitals are shown in the diagrams. 

The basis of the VSEPR theory is that the shape of a molecule (or the geometry around any particular atom connected to at least two other atoms) is assumed to be dependent upon the minimization of the repulsive forces operating between the pairs of sigma (a) valence electrons. This is an important restriction. Any pi (7t) or delta (8) pairs are discounted in arriving at a decision about the molecular shape. The terms sigma , pi and delta refer to the type of overlap undertaken by the contributory atomic orbitals in producing the molecular orbitals, and are referred to by their Greek-letter symbols in the remainder of the book. 

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