Molecular Orbital Theory: The Hydrogen Molecule
		The bonding of many molecules can be explained using valence bond theory. However, another bonding description, the molecular orbital model (abbreviated MO), is necessary for a more complete and accurate picture of the electronic structure of some species. In the Interactive Student Tutorial Chapter 5 we learned about atomic orbitals. You'll recall that an atomic orbital is a mathematical wave function, whose square gives the probability of finding an electron within a given region of space in an atom. In molecular orbital theory, we consider the molecule as a whole rather than concentrating on individual atoms. Molecular orbital A wave function whose square gives the probability of finding an electron within a given region of space in a molecule. Molecular orbitals have some similarities to atomic orbitals. Each molecular orbital has a specific energy-level and a specific shape, and each can be occupied by a maximum of two electrons with opposite spins. Let's use MO theory to examine the simple diatomic molecule H2. When two hydrogen atoms approach each other, the 1s orbitals begin to blend together and the electrons spread out over both atoms. According to MO theory, there are two ways for orbital interaction to occur: an additive interaction or a subtractive interaction. The additive interaction leads to formation of a molecular orbital that is roughly egg-shaped, whereas the subtractive interaction leads to formation of a molecular orbital than contains a node between the atoms.
		The additive combination, denoted , is lower in energy than the two isolated 1sorbitals and is called a bonding molecular orbital. Electrons in bonding orbitals spend most of their time in the region between the two nuclei, binding the atoms together. The subtractive combination, denoted * ("sigma star"), is higher in energy than the two isolated 1s orbitals and is called an antibonding molecular orbital. Any electrons in an antibonding orbital do not occupy the central region between the nuclei and do not contribute to bonding. The energy relationships of the various orbitals are illustrated in bonding diagrams,
		Note that bond orders—the number of electron pairs shared between atoms (see the Interactive Student Tutorial section of Chapter 7.5)—can be calculated from MO diagrams by subtracting the number of antibonding electrons from the number of bonding electrons and dividing by 2, as follows: The H2 molecule has a bond order of 1 because it has two bonding electrons and no antibonding electrons. Key Ideas of Molecular Orbital Theory Molecular orbitals are to molecules what atomic orbitals are to atoms. Molecular orbitals describe regions of space in a molecule where electrons are most likely to be found, and they have a specific size, shape, and energy level. Molecular orbitals are formed by combining atomic orbitals on different atoms. The number of molecular orbitals formed is the same as the number of atomic orbitals combined. Molecular orbitals that are lower in energy than the starting atomic orbitals are bonding; MOs that are higher in energy than the starting atomic orbitals are antibonding. Electrons occupy molecular orbitals beginning with the MO of lowest energy. Only two electrons occupy each orbital, and their spins are paired. Bond order can be calculated by subtracting the number of electrons in antibonding MOs from the number in bonding MOs and dividing by 2.
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