Molecular Orbitals and Atomic Models

By Vijay Damodharan - Natural Sciences Student @ Christ College, Cambridge

 

Understanding the electronic structure of atoms and molecules is one of the key requirements to explain many physical phenomena in physics and chemistry. One of the earliest models to describe atoms was the plum pudding model. Later, the discovery of the nucleus led to the Bohr model. However, after the quantum revolution, a far more sophisticated, accurate, and complete model of the atom was developed - the quantum model.


Before we discuss the quantum model, it is worth briefly mentioning why the Bohr model of the atom is wrong. The Bohr model states that electrons ‘orbit’ the nucleus. However, from the theory of electromagnetism, we know that accelerating charges emit electromagnetic radiation and lose energy. This means that the electrons cannot maintain a stable orbit and should just spiral into the nucleus.


This does not happen because electrons are not just particles. They also have a wave-like nature which must be accounted for, hence the need for quantum mechanics.


The wave-particle nature of electrons is encapsulated by the idea of an orbital. When the electron is not being observed, it behaves like a wave. This is described by a wave function, where the absolute value squared of the wave function gives the probability of measuring the electron at a particular position in time. An atomic orbital is the wave function, so it is related to the probability of finding the electron.

More fundamentally, the atomic orbitals are the wave function solutions to the Schrodinger equation describing the atom.


Every atom contains an infinite number of these atomic orbitals. Electrons populate the atomic orbitals by obeying the Pauli Exclusion Principle, since they are Fermions. The Pauli Exclusion Principle is understood by the idea of quantum numbers; however, the overall result is that each atomic orbital can only occupy two electrons.


Classically, when two atoms approach each other, we imagine that the negatively charged electrons are attracted to the positively charged nuclei of the two atoms and shared between them. Depending on the strength of the attraction to each nucleus (the electronegativity) the electron can be shared equally, or it may be much closer to one atom than the other. Based on this, the bonds are described as covalent or ionic, where ionic means the electron density is almost completely concentrated over one atom.


In the quantum picture, when two atoms approach, the atomic orbitals of the two atoms interact. Because the orbitals are wavelike in nature, they can interact in phase or out of phase. The in-phase interaction creates a new orbital which is lower in energy than either of the atomic orbitals, and the out-of-phase interaction creates a new orbital which is higher in energy than either of the atomic orbitals. Therefore, these are called bonding and anti-bonding molecular orbitals, respectively.


The electrons, which previously populated the atomic orbitals, now populate the molecular orbitals. If more electrons populate bonding molecular orbitals than anti-bonding ones, the overall energy of the molecule is lower than the energy of the individual atoms. This reduction in energy makes it favourable for a molecule to form.


The reverse is true if more electrons populate the anti-bonding molecular orbitals than bonding ones.


Molecular orbitals are similar to atomic orbitals, but the wave function is now spread over the entire molecule, and not just an atom. Different atoms will contribute different amounts to the molecular orbital, and this leads to the classical idea of electronegativity.


This quantum picture is quite different to the classical picture. Classically, if we have a molecule made of different atoms covalently bonded to each other, we imagine that each pair of atoms has some electrons shared between them. Quantum mechanically, what we have are molecular orbitals spread over the entire molecule, and the electrons populate these molecular orbitals. Moreover, these molecular orbitals, like atomic orbitals, only tell us the probability of finding an electron when we make a measurement. Until we make a measurement, the electron exists as just a mathematical wave function, described by the molecular orbital.

Figure 1: molecular orbital formed by constructive overlap of the two hydrogen 1s AOs and oxygen 2pz AO

The interaction of Oxygen 2p and Hydrogen 1s AOs to form a molecular orbital in water is shown below. The colour indicates the phase, the same colour means the orbitals are in-phase, and different colours mean they are out of phase.


This theory explains many features of molecules, such as bond lengths and bond strengths. We can also use it to determine whether two molecules will interact or not because strong interaction requires the individual atomic orbitals to be similar in energy and have the same symmetry. So molecular orbital picture is a basis for explaining many chemical reactions and mechanisms, especially in organic chemistry.