Molecular orbitals of hydrogen

Orbital Surfaces. Molecular orbitals provide important clues about chemical reactivity, but before we can use this information we first need to understand what molecular orbitals look like. The following figure shows two representations, a drawing and a computer-generated picture, of a relatively high-energy, unoccupied molecular orbital of hydrogen molecule, H2. 

Figure 2.5 Energy diagram molecular orbitals of hydrogen molecule...

Figure 1.6 The bonding and antibonding molecular orbitals of hydrogen. The dots in the drawing approximate the nuclei positions. The standing wave extends beyond the nuclei because the orbitals do.

Figure 1.9. A schematic representation of the formation of bonding (o) and antibonding (a ) molecular orbitals of hydrogen (Hj) by the combination of two equivalent Is hydrogen atomic orbitals. The signs (+) and (-) do not refer to charges but rather to the sign of the wave function /, whose square (t f ) gives the probabiUty of finding the electron(s) in the volume shown.

PROBLEM 1.67 Generate the molecular orbitals for hnear methylene, H—C—H, by combining the atomic orbitals of carbon with the molecular orbitals of hydrogen, Hj. 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

FIGURE 2 5 Genera tion of (T and a molecular orbitals of H2 by combining Is orbitals of two hydrogen atoms... 

Figure 1.17 Molecular orbitals of H2- Combination of two hydrogen 1 s atomic orbitals leads to two H2 molecular orbitals. The lower-energy, bonding MO is filled, and the higher-energy, antibonding MO is unfilled.

To get the molecular orbital of the hydrogen molecule, the orbital equations of the two atoms are combined. When the orbital equations are added together, the result is a bonding molecular orbital that extends over both atoms. Subtracting the orbital equations of the atoms produces an antibonding molecular orbital. This process is called the linear combination of atomic orbitals or LCAO. 

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.)... 

Figure 1.28 Formation of the bonding molecular orbitals of ethyne from two sp-hybridized carbon atoms and two hydrogen atoms. (Antibonding orbitals are formed as well but these have been omitted for simplicity.)...

In each of the B-H-B bridges, only two electrons bond the three atoms together by having the orbitals on the boron atoms simultaneously overlap the hydrogen Is orbital. A bond of this type is known as a two-electron three-center bond. In terms of molecular orbitals, the bonding can be described as the combination of two boron orbitals and one hydrogen orbital to produce three molecular orbitals, of which only the one of lowest energy is populated ... 

Relative contribution of each of these structures differs significantly and is determined by internal structural characteristics of the nitrones and by the influence of external factors, such as changes in polarity of solvent, formation of a hydrogen bond, and complexation and protonation. Changes in the electronic stmcture of nitrones, effected by any of these factors, which are manifested in the changes of physicochemical properties and spectral characteristics, can be explained, qualitatively, by analyzing the relative contribution of A-G structures. On the basis of a vector analysis of dipole moments of two series of nitrones (355), a quantum-chemical computation of ab initio molecular orbitals of the model nitrone CH2=N(H)0 and its tautomers, and methyl derivatives (356), it has been established that the bond in nitrones between C and N atoms is almost... 

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 raw material consists of the atomic orbitals of carbon, 2s, 2px, 2py and 2p, and the bonding and antibonding MOs of hydrogen, Tb and a- Considerations of energy and symmetry lead to the interactions shown in Figure 7.1. The interactions Tb 2i, and Fa i 2px give four of the six molecular orbitals of linear methylene. 

What atomic orbitals of the hydrogen atom are used to construct the molecular orbitals of the dihydrogen molecule ... 

Figure 5.4. The highest occupied molecular orbital of a Si911,2 dimer cluster. The top two silicon atoms comprise the surface dimer, and the remaining seven Si atoms contain three subsurface layers which are hydrogen terminated to preserve the sp3 hybridization of the bulk diamond cubic lattice. The up atom is nucleophilic and the down atom is electrophilic.

Although mixing of s and p orbitals is represented in Fig. 5.24 as a sepamle step preceding the formation of molecular orbitals, the entire process can be combined into a single step. For example, the bonding molecular orbital in hydrogen chloride may be considered to be formed as... 

The energies of the molecular orbitals of the adenine-thymine base pair have been calculated by several authors to elucidate the effect of hydrogen bond formation on the properties of the bases (for u-HMO calculations, see refs. 1, 140, 171, 263). 

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