Hydrogen bond molecular orbital

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 1.8 The overlapping of two hydrogen Is atomic orbitals with the same phase sign (indicated by their identical color) to form a bonding molecular orbital.

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.)...

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. 

Now we can consider the bonding in methane. Using orbital overlap as in the hydrogen molecule as a model, each sp orbital of carbon can now overlap with a 1 orbital of a hydrogen atom, generating a bonding molecular orbital, i.e. a ct bond. Four such... 

The equations for the bonding and anti-bonding molecular orbital wave functions for the linear combinations of the two Is atomic orbitals of the two hydrogen atoms may now be written in the forms ... 

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... 

S. G. Anderson and D. P. Santry, J. Chem. Phys., 74, 5780 (1981). Nonempirical Molecular Orbital Calculations for Hydrogen-Bonded Molecular Solids Molecular Dipole and Quadruple Moments for Solid Hydrogen Fluoride and Hydrogen Chloride. 

The hydrogen molecule molecular orbital and valence bond treatments... 

Fig. 2. CASSCF, orthogonal localized, non-orthogonal localized, and generalized valence bond molecular orbitals for the hydrogen molecule.

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