Carbon valence orbitals

We could simply proceed to inspect these orbitals to see which overlap with each other, and then begin to make molecular orbitals in the way described in the previous section. Unfortunately, the situation is now quite complicated. The hydrogen number 1 interacts with allfour of the carbon valence orbitals. 

The methane molecule, CH4, has a tetrahedral structure. This structure is shown in Fig. 5-1. With the carbon in the center of the cube, the hydrogens are then placed at opposite corners of the cube, as defined by a regular tetrahedron. The origin of the rectangular coordinate system is chosen at the center of the cube, with the x,y, and z. axes perpendicular to the faces. All the carbon valence orbitals, 2s, 2px lp,j, and lp must be used to form an adequate set of ff molecular orbitals. 

The lowest energy electronic transitions in homocyclic aromatic hydrocarbons occur at near-ultraviolet, visible, and infrared wavelengths from 2500 A out to beyond 7000 A. They involve excitations of electrons in delocalized 7t-type MOs, which are composed principally of carbon 2p orbitals oriented perpendicular to the aromatic plane. The remaining minimal-basis carbon valence orbitals (the 2s orbitals and the 2p orbitals oriented in the molecular plane) are utilized to form in-plane ff-type MOs directed along the chemical bonds. Excitations of electrons in ff-type MOs to unoccupied MOs require far higher photon energies (in the vacuum ultraviolet), and are not considered in this Section. 

At a normal C-H bond length, we have the following overlap integrals between the carbon valence orbitals and the hydrogen Is orbital ... 

The overlap integrals between the carbon valence orbitals and the hydrogen Is orbital decreases in the order of HCsCH, CH2=CH2, and CH4 (with the hybridization index for the carbon atom equal to 1, 2, and 3, respectively). Assuming that the C-H bond strength increases with the overlap integral, we can conclude that the overlap integrals determined in (i) correlate well with the given spectral... 

Figure 35. Representation of the interaction between metal and carbon valence orbitals in the z.x-plane. The relative sizes of the orbitals are unknown. The negative lobe of the...

Figure 1.3 Pictorial representation of taking a linear combination of the four carbon valence orbitals to form sp -hybrid orbitals.

Figure 1.4 Result of hybridization of all four of the carbon valence orbitals.

Split-Valence Basis Sets. In split-valence basis sets, inner or core atomic orbitals ar e represented by one basis function and valence atomic orbitals are represented by two. The carbon atom in methane is represented by one Is inner orbital and 2(2s, 2pj., 2py, 2pj) = 8 valence orbitals. Each hydrogen atom is represented by 2 valence orbitals hence, the number of orbitals is... 

The first way that a basis set can be made larger is to increase the number of basis functions per atom. Split valence basis sets, such as 3-21G and 6-31G, have two (or more) sizes of basis function for each valence orbital. For example, hydrogen and carbon are represented as ... 

Boron is a unique and exciting element. Over the years it has proved a constant challenge and stimulus not only to preparative chemists and theoreticians, but also to industrial chemists and technologists. It is the only non-metal in Group 13 of the periodic table and shows many similarities to its neighbour, carbon, and its diagonal relative, silicon. Thus, like C and Si, it shows a marked propensity to form covalent, molecular compounds, but it differs sharply from them in having one less valence electron than the number of valence orbitals, a situation sometimes referred to as electron deficiency . This has a dominant effect on its chemistry. 

The chemical bonding occurs between valence orbitals. Doubling the 1 s-functions in for example carbon allows for a better description of the 1 s-electrons. However, the Is-orbital is essentially independent of the chemical environment, being very close to the atomic case. A variation of the DZ type basis only doubles the number of valence orbitals, producing a split valence basis. In actual calculations a doubling of tire core orbitals would rarely be considered, and the term DZ basis is also used for split valence basis sets (or sometimes VDZ, for valence double zeta). 

Divalent carbon species called carbenes are capable of fleeting existence. For example, methylene, CH2, is the simplest carbene. The two unshared electrons in methylene can be either spin-paired in a single orbital or unpaired in different orbitals. Predict the type of hybridization you expect carbon to adopt in singlet (spin-paired) methylene and triplet (spin-unpaired) methylene. Draw a picture of each, and identify the valence orbitals on carbon. 

The carbon-oxygen double bond of a carbonyl group is similar in many respects to the carbon-carbon double bond of an alkene. The carbonyl carbon atom is s/ 2-hybridized and forms three valence electron remains in a carbon p orbital and forms a tt bond to oxygen by overlap with an oxygen p orbital. The oxygen atom also has two nonbonding pairs of electrons, w hich occupy its remaining two orbitals. 

Here is a situation we haven t met before. After using the two available partially filled orbitals to form covalent bonds with hydrogen atoms, there remains a vacant valence orbital. In the electron dot formulation (36) we see that the carbon atom finds itself near only six electrons in CH2. The valence orbitals will accommodate eight electrons. Because one valence or-... 

It may be proper at this stage to lead the reader back to the stage where we constructed the localized orbitals of a CH2 group. At that time two valence orbitals were set aside—the 2pv orbital, and the outer (2s, 2pr) hybrid. Both of these orbitals lie in the. r, y plane. Now in our description of cyclopropane, we used bond orbitals to describe the CC bonding these bond orbitals are derived from in-plane (xy y) hybrids on each carbon. The two hybrids which are required on each carbon atom—in ordet to participate in two bond orbitals—are built precisely from the 2py orbital and the (2s, 2pj.) out combination on each CH2 group. 

Qualitatively, we can understand this variation by recalling that as the principal quantum number increases, the valence orbitals become less stable. In tin, the four n — 5 valence electrons are bound relatively loosely to the atom, resulting in the metallic properties associated with electrons that are easily removed, hi carbon, the four n — 2 valence electrons are bound relatively tightly to the atom, resulting in nonmetallic behavior. Silicon ( = 3) and germanium (a = 4) fall in between these two extremes. Example describes the elements with five valence electrons. 

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