Lecture 3: Hydrogen

Read sections 1.13, 9.1, 9.4 from your textbook.

There will be a quiz due on this and the next lecture by 10 PM, Tuesday, January 23.

Overview of Hydrogen

Earth's primordial atmosphere was probably similar to the gas cloud that created the sun and planets. It consisted mainly of hydrogen and helium, along with methane, ammonia, and water. Much of this was lost from the planet. The second atmosphere included gases from volcanic activity (including CO₂ and N₂) along with more water from collisions with comets.

Hydrogen, H₂, is the simplest of the molecules. What do we know about hydrogen?

Hydrogen is a lighter-than-air, flammable, diatomic gas.
It boils at -253.5 deg C.
Platinum metal or heat can catalyze the reaction of hydrogen with oxygen to form water.
In hydrogen fuel cells, the chemical oxidation of hydrogen to water produces electricity. (This is an area of intense activity of inorganic chemists because fuel cells may replace fossil fuels to power automobiles and reduce our reliance on petroleum. We need better inorganic materials to store hydrogen, separate components of the fuel cell, and catalyze the oxidation/reduction reactions.)
We'll see later that many transition metal complexes add H₂ and form either dihydrogen complexes, M(H₂), or di-hydrides, M(H)₂. These metal complexes catalyze the addition of H₂ to alkenes and other unsaturated organic molecules.

The linear hydrogen molecule has high symmetry. Hydrogen has a proper rotation axis along the H-H bond. There are an infinite number of planes that include this axis. Because the two atoms are identical, there is also a mirror plane (and a C₂ axis) that bisects the bond. Between the hydrogen atoms is an inversion center.

Bonding

A molecular orbital diagram represents the interaction between the atomic orbitals. We represent orbitals as shapes corresponding to regions of highest probability of electron density. Each hydrogen atom has one electron in one atomic orbital (1s). We represent the 1s orbital as a sphere. The combination of two atomic orbitals must give two molecular orbitals. The bonding molecular orbital, H1(1s) + H2(1s), is lower in energy than the atomic orbitals. It puts most electron density between the positive nuclei for electrostatic stabilization. The antibonding molecular orbital, H1(1s) - H2(1s), has much less electron density between the nuclei and a nodal plane (with zero electron density) bisecting the bond axis. Repulsion between the nuclei raises the energy of this orbital. The energy stabilization of the bonding molecular orbital equals the destabilization of the antibonding molecular orbital.

The sigma anti-bonding orbital has a nodal plane that bisects the H-H unit.

Both of the molecular orbitals have sigma symmetry. That is, rotation around the bond axis doesn't change those orbitals. The bonding orbital is unchanged by rotation around the perpendicular C2 axis but the antibonding orbital is inverted by this rotation.

(Note that in the picture, blue represents the positive sign of the mathematical function describing the electron density and red represents the negative mathematical function.)

Atomic orbitals combine to form molecular orbitals when that have the same symmetry and when they are close in energy.

The number of atomic orbitals combined will always equal the number of molecular orbitals.

The bond order indicates the strength of the interaction. A bond order of 2 is stronger (but not necessarily twice as strong) as a bond order of 1. When the bond order is 0, there is no bonding interaction between the atoms. Bond order is the number of electrons in bonding molecular orbitals minus the number of electrons in antibonding molecular orbitals divided by 2, or...

In the picture below, we see that the maximum stabilization (and destabilization) of molecular orbitals occurs when the atomic orbitals have the same energy. As the energy gap between ao1 and ao2 increases, the stabilization and destabilization of the molecular orbitals decreases. When the two atomic orbitals, ao1 and ao2, are far apart in energy, the molecular orbitals are essentially "perturbed" atomic orbitals. They are shifted only slightly in energy.

The first molecular orbital diagram is for a diatomic with a non-polar bond between atom 1 and atom 2.

There is a somewhat polar bond between the atoms in the second molecular orbital diagram with greater electron-density around atom 2.

The last molecular orbital diagram indicates a highly polar bond. The bonding molecular orbital is essentially a perturbed atomic orbital of atom 2 with a small contribution from atom 1.

Ionization

Ionization of atoms usually refers to the loss of electrons (forming cations and free electrons). The UV radiation in the thermosphere (uppermost region of the atmosphere) is sufficient in energy to strip all atoms of electrons. If most of the atoms or molecules in a region are ionized, the resulting state of matter corresponds to a plasma. How much energy is required for ionization? See the NIST table of ionization energies. Ionization energy describes how tightly an electron is held and is related to electron affinity.

The energy required to remove an electron from a particular atomic orbital tells us about the energy of that orbital. This is important when we consider the combination of atomic orbitals to make molecular orbitals because, for two orbitals with the same symmetry, the overlap of the orbitals becomes greater as the energy difference decreases. The H-H bond in molecular hydrogen is strong because the two atomic orbitals that make up the molecular orbital have the same energy.

Let's look at a simple example. Consider a hydrogen atom in the upper atmosphere. This neutral atom has a single electron in a 1s orbital and a single proton. The electron is strongly held but if the atom absorbs 13.6 electron volts of energy, the electron will separate from the proton. This amount of energy corresponds to a photon of light of frequency = 3.3 x 10¹⁵ Hz, or wavelength = 91 nm, in the vacuum UV.

Bond Energy

Bond energy is determined by monitoring the energy of the light required to break a chemical bond. Bond length is related to bond energy and is determined by analyzing the diffraction pattern of X-rays passing through a crystal of the substance.