Carbon, atomic orbitals

Carbon atom, 4. See also Atomic orbitals Carbon dioxide hydration, 197-199. See also Carbonic anhydrase Carbonic anhydrase, 197-199,200 Carbonium ion transition state, 154, 159 Carboxypeptidase A, 204-205 Catalysis, general acid, 153,164,169 in carboxypeptidase A, 204-205 free energy surfaces for, 160, 161 in lysozyme, 154... 

Atomic Orbitals Carbon has six electrons, i.e. and is placed in second period of the periodic table. In it there are two shells of atomic orbitals available for these electrons. The first shell closest to the nucleus has a single 5 orbital-the Is orbital. The second shell has a single s orbital (the 2s orbital) and three p orbitals (3 2p). Therefore, there are a total of five atomic orbitals into which these six electrons can fit. The s orbitals are spherical in shape with the 2s orbital being much larger than the Is orbital. The p orbitals are dumb-bell-shaped and are aligned along the x, y and z axes. Therefore, they are... 

The familiar octet rule, which states that atoms are most stable when their valence shell is full, suggests that carbon in a molecule will take on four more electrons from other atoms so as to possess an octet of electrons and thereby attain a noble gas configuration. The number of bonds that an atom can make is called its valence number. If each bond that carbon makes is created by the donation of a single electron from an adjacent atom s atomic orbitals, carbon will make four bonds. Carbon is said to have a valence of four. This valence is by far the most common bonding arrangement for C. When carbon has fewer than four bonds it is in a reactive form, namely a carbocation, radical, carbanion, or carbene. When a similar analysis is done for N, O, and F, it is found that these atoms prefer three, two, and one bond(s), respectively. 

When elements in Period 2 form covalent bonds, the 2s and 2p orbitals can be mixed or hybridised to form new, hybrid orbitals each of which has. effectively, a single-pear shape, well suited for overlap with the orbital of another atom. Taking carbon as an example the four orbitals 2s.2p.2p.2p can all be mixed to form four new hybrid orbitals (called sp because they are formed from one s and three p) these new orbitals appear as in Figure 2.9. i.e. they... 

The orbitals used for methane, for example, are four Is Slater orbitals of hydrogen and one 2s and three 2p Slater orbitals of carbon, leading to an 8 x 8 secular matrix. Slater orbitals are systematic approximations to atomic orbitals that are widely used in computer applications. We will investigate Slater orbitals in more detail in later chapters. 

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... 

Butadiene The ti molecular orbitals of 1 3 butadiene are shown m Figure 10 10 The four sp hybridized carbons contribute four 2p atomic orbitals and their overlap... 

The picture of benzene as a planar framework of ct bonds with six electrons m a delo cahzed rr orbital is a useful but superficial one Six elecfrons cannof simulfaneously occupy any one orbifal be if an afomic orbifal or a molecular orbifal We can fix fhis wifh the more accurate molecular orbital picture shown m Figure 114 We learned m Section 2 4 that when atomic orbitals (AOs) combine to give molecular orbitals (MOs) the final number of MOs musf equal fhe original number of AOs Thus fhe six 2p AOs of SIX sp hybridized carbons combine fo give six tt MOs of benzene... 

Many of the reactions in which acetylene participates, as well as many properties of acetylene, can be understood in terms of the stmcture and bonding of acetylene. Acetylene is a linear molecule in which two of the atomic orbitals on the carbon are sp hybridized and two are involved in 7T bonds. The lengths and energies of the C—H O bonds and C=C<7 + 27t bonds are as follows ... 

Fig. 1.16. Interaction of atomic orbitals of carbon and oxygen leading to molecular orbitals of carbon monoxide.

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

The lowest energy molecular orbital of singlet methylene looks like a Is atomic orbital on carbon. The electrons occupying this orbital restrict their motion to the immediate region of the carbon nucleus and do not significantly affect bonding. Because of this restriction, and because the orbital s energy is very low (-11 au), this orbital is referred to as a core orbital and its electrons are referred to as core electrons. 

The lowest-unoccupied molecular orbital is called the LUMO (+0.1 au). The LUMO has nonbonding character, and looks like a 2p atomic orbital on carbon. If this molecule... 

For electron movement to occur, the donor and acceptor molecules must approach so that the donor HOMO and acceptor LUMO can interact. For example, the LUMO of singlet methylene is a 2p atomic orbital on carbon that is perpendicular to the molecular plane. Donors must approach methylene in a way that allows interaction of the donor HOMO with the 2p orbital. 

The usefulness of spin density surfaces can be seen in the following models of methyl radical, CH3, and allyl radical, CH2=CHCH2. In each case, the surface is shaped somewhat like a 2p atomic orbital on carbon. There are some interesting differences between the two radicals, however. While the unpaired electron is confined to the carbon atom in methyl radical, it is delocalized over the two terminal carbons in allyl radical. 

For the minute, imagine an HF-LCAO treatment of just the jr-electrons in ethene where each carbon atom contributes just one electron and one atomic orbital of the correct symmetry to the conjugated system. Without any particular justification except chemical intuition, we make the following assumptions. 

In the PPP model, each first-row atom such as carbon and nitrogen contributes a single basis functiqn to the n system. Just as in Huckel theory, the orbitals x, m e not rigorously defined but we can visualize them as 2p j atomic orbitals. Each first-row atom contributes a certain number of ar-electrons—in the pyridine case, one electron per atom just as in Huckel 7r-electron theory. 

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

When we discussed sp3 hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent sp3 hybrids. Imagine instead that the 2s orbital combines with only two of the three available 2p orbitals. Three sp2 hybrid orbitals result, and one 2p orbital remains unchanged- The three sp2 orbitals lie in a plane at angles of 120° to one another, with the remaining p orbital perpendicular to the sp2 plane, as shown in Figure 1.13. 

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