Editing Molecular orbital theory (section)

== Magnetism explained by molecular orbital theory ==
For almost every covalent molecule that exists, we can now draw the Lewis structure, predict the electron-pair geometry, predict the molecular geometry, and come close to predicting bond angles. However, one of the most important molecules we know, the oxygen molecule O<sub>2</sub>, presents a problem with respect to its Lewis structure. 
[[File:Ossigeno molecolare con elettroni liberi.png|thumb|192x192px|In O₂, each oxygen atom forms a double bond and retains two lone pairs to achieve a full octet, as shown in the Lewis structure.]]
The electronic structure of O<sub>2</sub> adheres to all the rules governing Lewis theory. There is an O=O double bond, and each oxygen atom has eight electrons around it. However, this picture is at odds with the magnetic behavior of oxygen. By itself, O<sub>2</sub> is not magnetic, but it is attracted to magnetic fields. Thus, when we pour liquid oxygen past a strong magnet, it collects between the poles of the magnet and defies gravity. Such attraction to a magnetic field is called '''paramagnetism''', and it arises in molecules that have unpaired electrons. And yet, the Lewis structure of O<sub>2</sub> indicates that all electrons are paired. How do we account for this discrepancy?

Molecular orbital diagram of oxygen molecule:
[[File:Oxygen molecule orbitals diagram-en.svg|thumb|Molecular Orbital Energy-Level Diagrams for O2.]]
Atomic number of oxygen – 8

Electronic configuration – 1s²2s²2p<sup>4</sup>

Electronic configuration of oxygen molecule;

ó1s² < *ó1s² < ó2s² < *ó2s²  , [ π2px²  = π2py²] < ó 2pz²  < [*π2px¹ =*π2py¹] < *ó2pz  

Bond order of O<sub>2</sub> = (Bonding electrons − Anti bonding electrons) / 2

                        = (10 − 6) / 2  = 2

O<sub>2</sub> has unpaired electrons, hence it is paramagnetic.<ref>{{Cite web |title=Explain the Formation of O2 Molecule Using Molecular Orbital Theory |url=https://unacademy.com/content/question-answer/chemistry/explain-the-formation-of-o2-molecule-using-molecular-orbital-theory/ |access-date=2025-04-25 |website=Unacademy |language=en-US}}</ref>

Magnetic susceptibility measures the force experienced by a substance in a magnetic field. When we compare the weight of a sample to the weight measured in a magnetic field, paramagnetic samples that are attracted to the magnet will appear heavier because of the force exerted by the magnetic field. We can calculate the number of unpaired electrons based on the increase in weight.

Experiments show that each O<sub>2</sub> molecule has two unpaired electrons. The Lewis-structure model does not predict the presence of these two unpaired electrons. Unlike oxygen, the apparent weight of most molecules decreases slightly in the presence of an inhomogeneous magnetic field. Materials in which all of the electrons are paired are '''diamagnetic''' and weakly repel a magnetic field. Paramagnetic and diamagnetic materials do not act as permanent magnets. Only in the presence of an applied magnetic field do they demonstrate attraction or repulsion.

Water, like most molecules, contains all paired electrons. Living things contain a large percentage of water, so they demonstrate diamagnetic behavior. If you place a frog near a sufficiently large magnet, it will levitate.<ref>{{cite web |year=2011 |title=The Real Levitation |website=High Field Laboratory |publisher=[[Radboud University Nijmegen]] |url=http://www.ru.nl/hfml/research/levitation/diamagnetic/ |access-date=26 September 2011 |archive-date=27 August 2013 |archive-url=https://web.archive.org/web/20130827232750/http://www.ru.nl/hfml/research/levitation/diamagnetic/ |url-status=dead }}</ref>

Molecular orbital theory (MO theory) provides an explanation of chemical bonding that accounts for the paramagnetism of the oxygen molecule. It also explains the bonding in a number of other molecules, such as violations of the octet rule and more molecules with more complicated bonding (beyond the scope of this text) that are difficult to describe with Lewis structures. Additionally, it provides a model for describing the energies of electrons in a molecule and the probable location of these electrons. Unlike valence bond theory, which uses hybrid orbitals that are assigned to one specific atom, MO theory uses the combination of atomic orbitals to yield molecular orbitals that are ''delocalized'' over the entire molecule rather than being localized on its constituent atoms. MO theory also helps us understand why some substances are electrical conductors, others are semiconductors, and still others are insulators.

Molecular orbital theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the behavior of an electron in a molecule is still described by a wave function, ''Ψ'', analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is called a '''molecular orbital (''Ψ''<sup>2</sup>)'''. Like an atomic orbital, a molecular orbital is full when it contains two electrons with opposite spin.<ref>{{Cite web |title=4.3 Molecular Orbital Theory |url=https://chem-textbook.ucalgary.ca/version2/chapter-8-main/molecular-orbital-theory/ |access-date=2025-04-25 |website=UCalgary Chemistry Textbook |language=en-US}}</ref>