Bonding in H2 The Molecular Orbital Model

The molecular orbital theory of chemical bonding rests on the notion that, as electrons in atoms occupy atomic orbitals electrons in molecules occupy molecular orbitals. Just as our first task in writing the electron configuration of an atom is to identify the atomic 

Generation of a and cr molecular orbitals of H2 by combining Is orbitals of two hydrogen atoms. 

For a molecule as simple as H2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear in molecules with more than two atoms. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular 

Two molecular orbitals (MOs) are generated by combining two hydrogen Is atomic orbitals (AOs). The bonding MO is lower in energy than either of the AOs that combine to produce it. 

The antibonding MO is of higher energy than either AO. Each arrow indicates one electron, and the electron spins are opposite in sign. Both electrons of H2 occupy the bonding MO. 

The molecular orbital approach to chemical bonding is based on the notion that, as electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Just as the first task in writing the electron configuration of an atom is to identify the atomic orbitals that are available to it, so too must we first describe the orbitals available to a molecule. In the molecular orbital method this is accomplished by representing molecular orbitals as combinations of atomic orbitals, the linear combination of atomic orbitals-molecular orbital (LCAO-MO) method. 

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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. 

Another model often used to describe bonding is the molecular orbital model. To introduce the assumptions, methods, and results of this model, we will consider the simplest of all molecules, H2, which consists of two protons and two electrons. A very stable molecule, H2 is lower in energy than the separated hydrogen atoms by 432 kj/mol. 

Historically, molecular orbital theory was preceded by an alternative and successful description of the bonding in H2. In 1927, W. Heitler and F. London proposed the valence bond theory, in which each electron resides in an atomic orbital. In other words, in this model, the identity of the atomic orbital is preserved. There are two ways in which the two electrons in H2 can be accommodated in the pair of Is atomic orbitals ... 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

An Elementary Molecular Orbital Model Bond Energies and Pauli Repulsions in Homonuclear Diatomics The Hydrogen Molecular Ion H2 (N=l)... 

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