In the extreme magnetic fields of white dwarves and neutron stars, a third type of chemical bonding can occur. That is the finding of theoretical chemists in Norway, who have used computer simulations to show that as-yet-unseen molecules could form in magnetic fields much higher than those created here on Earth.
High-school chemistry students are taught that there are two types of chemical bond – ionic bonds, in which one atom donates an electron to another atom; and covalent bonds, in which the electrons are shared. In fact, real chemical bonds usually fall somewhere in between.
When two atoms come together, their atomic orbitals combine to form molecular orbitals. For each two atomic orbitals combined, two molecular orbitals are formed. One of these is lower in energy than either atomic orbital and is called the bonding orbital. The other “anti-bonding” orbital is higher in energy than either atomic orbital. Whether or not the atoms will actually bond is determined by whether the total energy of the electrons in the molecular orbitals is lower than the total energy of the electrons in the original atomic orbitals. If it is, bond formation will be energetically favoured and the bond will be formed.
Bonding and anti-bonding
The Pauli exclusion principle forbids a single orbital from holding more than two electrons (it can hold two if they have opposite spins). If the atomic orbital of each atom contained just one electron, both can go into the bonding orbital when the orbitals combine. Both electrons are therefore lowered in energy and the bond formation is energetically favoured. But if the atomic orbitals contained two electrons each, two of the four electrons would have to go into the anti-bonding molecular orbital. Overall, therefore, two electrons would have their energy lowered by bond formation, while two electrons would have their energy raised.
Under normal circumstances, the anti-bonding orbital is always raised in energy farther above the energy of the higher-energy atomic orbital than the bonding orbital is lowered below the energy of the lower-energy atomic orbital. This means that a chemical bond with both its bonding and its anti-bonding orbitals full would always have a higher energy than the atomic orbitals from which it would be formed. Such a bond would therefore not form. This is why noble-gas atoms, which have full outer atomic orbitals, almost never form molecules on Earth.
But now Kai Lange and colleagues at the University of Oslo have used a computer program developed by their group called LONDON to show this is not always true elsewhere. LONDON creates mathematical models of molecular orbitals under the influence of magnetic fields of about 105 T. This is much stronger than the 30–40 T fields that can be made in laboratories and that have little effect on chemical bonds.
Changing the rules
Large fields could be relevant to those studying astronomical objects such as white dwarves – where magnetic fields can reach 105 T – and neutron stars, where fields could be as high as 1010 T. Under such conditions, the team has shown that the rules of bonding change. In particular, the anti-bonding orbital is lowered in energy when a diatomic molecule is subjected to a strong perpendicular magnetic field. Molecules with full bonding and anti-bonding orbitals, such as diatomic helium, can still be energetically favoured.
Team leader Trygve Helgaker explains the sophistication of LONDON enabled the group to perform calculations that others have found impossible. “We can do accurate calculations with all orientations of the molecule to the magnetic field,” he says. “People have done the same kinds of electronic-structure calculations before, but I believe their calculations were limited to the situation where the field is parallel to the molecular axis.”
The research is published in Science; in an accompanying commentary, Peter Schmelcher of the Institute for Laser Physics at the University of Hamburg, Germany, said “Atoms, molecules and condensed-matter systems exposed to strong magnetic fields represent a fascinating topic, and this work has added a key bonding mechanism.” Interestingly, while he accepts the fields present around a white dwarf will be unachievable in a laboratory in the foreseeable future, he sees an alternative way the group’s models might be tested experimentally. Rydberg atoms are highly excited atoms that can be the size of the dot of an “i”. Because the bond length between Rydberg atoms is so great, the Coulomb interaction is much smaller, and Schmelcher believes it might therefore be possible to use them to produce magnetic fields of comparable strength.