Atomic orbitals description

Microscopic to Atomic Orbital Description of Soil Chemical Characteristics... 

In terms of an atomic-orbital description, the carbonyl bond can be represented as shown in Figure 16-1. The carbon is. sp2-hybridized so that its [Pg.674]

Figure 16-1 Atomic-orbital description of the carbonyl group. The a bonds to carbon are coplanar, at angles near to 120° the two pairs of unshared electrons on oxygen are shown as occupying orbitals n.

The origin of this problem can be seen by substituting the atomic orbital description of the molecular orbital (4) into the molecular orbital wave function (13), leading to... 

The other type of interpretation of /S is a delocalization of the partly filled shell into the ligands (in octahedral complexes due to formation of the a antibonding yg and -n antibonding y ). The usual L.C.A.O. (hnear combination of atomic orbitals) description is probably not very adequate for the actual M.O. formed but if we make the simplification that the proportion x of the electron density (the squared wave function y> ) is distributed in the ligands, and — x) still resides in the central ion [that does not mean that the L.C.A.O. coefficients are y x and (1 — x)i, since the overlap integrals may be rather large], we would expect a relation of the form... 

The Extended Iliickel method also allows the inclusion ofd orbitals for third row elements (specifically, Si. P, Sand CD in the basis set. Since there arc more atomic orbitals, choosing this option resn Its in a Ion ger calc ii 1 at ion. Th e m ajor reason to in cin de d orbitals is to improve the description of the molecular system. 

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

The researchers established that the potential energy surface is dependent on the basis set (the description of individual atomic orbitals). Using an ab initio method (6-3IG ), they found eight Cg stationary points for the conformational potential energy surface, including four minima. They also found four minima of Cg symmetry. Both the AMI and PM3 semi-empirical methods found three minima. Only one of these minima corresponded to the 6-3IG conformational potential energy surface. 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2, but in somewhat different ways. Both assume that electron waves behave like more familiar waves, such as sound and light waves. One important property of waves is called interference in physics. Constructive interference occurs when two waves combine so as to reinforce each other (in phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2.2). Recall from Section 1.1 that electron waves in atoms are characterized by then- wave function, which is the same as an orbital. For an electron in the most stable state of a hydrogen atom, for example, this state is defined by the I5 wave function and is often called the I5 orbital. The valence bond model bases the connection between two atoms on the overlap between half-filled orbitals of the two atoms. The molecular orbital model assembles a set of molecular- orbitals by combining the atomic orbitals of all of the atoms in the molecule. 

Notice that the 2s and 2p orbitals have a slightly different exponent. Such basis sets, where we simply use the same number of atomic orbitals that we would use in everyday descriptive chemistry, are referred to as minimal basis sets. 

There is a second point to note in dementi s paper above where he speaks of 3d and 4f functions. These atomic orbitals play no part in the description of atomic electronic ground states for first- and second-row atoms, but on molecule formation the atomic electron density distorts and such polarization functions are needed to accurately describe the distortion. 

The stability order of alkenes is due to a combination of two factors. One is a stabilizing interaction between the C=C tr bond and adjacent C-H a bonds on substituents. In valence-bond language, the interaction is called hyperconjugation. In a molecular orbital description, there is a bonding MO that extends over the four-atom C=C—< -H grouping, as shown in Figure 6.6. The more substituents that are present on the double bond, the more hyperconjugation there is and the more stable the alkene. 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

Conjugated enones are more stable than nonconjugated enones for the same reason that conjugated dienes are more stable than nonconjugated dienes (Section 14.1). Interaction between the tt electrons of the C=C bond and the tt electrons of the C=0 group leads to a molecular orbital description for a conjugated enone that shows an interaction of the tt electrons over all four atomic centers (Figure 23.3). 

Molecular orbital (MO) theory (Section 1.11) A description of covalent bond formation as resulting from a mathematical combination of atomic orbitals (wave functions) to form molecular orbitals. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

Another important polyatomic molecule is benzene, C6f I6, the parent of the aromatic compounds. In the molecular orbital description of benzene, all thirty C2s-, C2p-, and Hls-orbitals contribute to molecular orbitals spreading over all twelve atoms (six C plus six H). The orbitals in the plane of the ring (the C2s-, C2px, and ( 2/ -orbitals on each carbon atom and all six Hls-orbitals) form delocalized o-orbitals that bind the C atoms together and link the H atoms to the C atoms. The six C2pz-orbitals, which are perpendicular to the ring, contribute to six delocalized tt-orbitals that spread all the way around the ring. However, chemists... 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

The structure of CaB contains bonding bands typical of the boron sublattice and capable of accommodating 20 electrons per CaB formula, and separated from antibonding bands by a relatively narrow gap (from 1.5 to 4.4 eV) . The B atoms of the B(, octahedron yield only 18 electrons thus a transfer of two electrons from the metal to the boron sublattice is necessary to stabilize the crystalline framework. The semiconducting properties of M B phases (M = Ca, Sr ", Ba, Eu, Yb ) and the metallic ones of M B or M B5 phases (Y, La, Ce, Pr, Nd ", Gd , Tb , Dy and Th ) are directly explained by this model . The validity of these models may be questionable because of the existence and stability of Na,Ba, Bft solid solutions and of KB, since they prove that the CaB -type structure is still stable when the electron contribution of the inserted atom is less than two . A detailed description of physical properties of hexaborides involves not only the bonding and antibonding B bands, but also bonds originating in the atomic orbitals of the inserted metal . ... 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

Lewis structures are blueprints that show the distribution of valence electrons in molecules. However, the dots and lines of a Lewis structure do not show any details of how bonds form, how molecules react, or the shape of a molecule. In this respect, a Lewis structure is like the electron configuration of an atom both tell us about electron distributions, but neither provides detailed descriptions. Just as we need atomic orbitals to understand how electrons are distributed in an atom, we need an orbital view to understand how electrons are distributed in a molecule. 

The n molecular orbitals described so far involve two atoms, so the orbital pictures look the same for the localized bonding model applied to ethylene and the MO approach applied to molecular oxygen. In the organic molecules described in the introduction to this chapter, however, orbitals spread over three or more atoms. Such delocalized n orbitals can form when more than two p orbitals overlap in the appropriate geometry. In this section, we develop a molecular orbital description for three-atom n systems. In the following sections, we apply the results to larger molecules. 

---