In tight-binding wikipedia article it is said that bonding and anti-bonding orbitals correspond to different $k$-values in a single energy band. At the same time in Cordona Fundamentals of Semiconductors book there is the following picture.
Bonding It says that bonding and anti-bonding orbitals correspond to different energy bands. Please help me understand this.


1 Answer 1


Simply, different orbitals correspond to different energy bands, whereas anti bonding and bonding orbitals correspond to the change in energy between lines that make up a band. For example, the p orbital band of a certain element (say silicon) may look different than the s band; that is, the distance/bandgap between certain bands - which represent certain orbitals - may differ due to the structure of the atom, as well as the bonding of the atom. Furthermore, the figure depicts silicon's atomic orbital, where the distance between the anti-bonding and bonding orbitals represents a change in energy states (delta E). Nevertheless, the k value which measures the energy and reactivity of electrons, which in this case refers to that of occupied orbitals because it is (+)k, corresponds to the wave mechanics of electrons as described by the Pullmans in their volume, "Quantum Biochemistry," so the difference in energy states does correspond to different k values that define donor-acceptor characteristics of a molecule. However, it may help to recall what the band both demonstrates and means; the band represents the continuum of individual energy states of electrons in a mole of an element or molecule, in which individual orbitals decrease in distance from each other as you increase the number of orbitals. Moreover, the band is important to understand because it indicates the general properties of an element or molecule, such as conductivity and even thermal properties.

Understanding the Molecular Orbital (MO) theory is the key to understanding bands and their intricacies. In MO theory, atomic orbitals combine to form molecular orbitals, and the antibond and bond states simply demonstrate different energy levels; this is where electrons, more accurately recognized as wave functions constructively (bond) and destructively (anti bond) interfere to form molecular orbitals - which defines the covalent bond - between constituent atoms; this distinction of bonding is also the 1st principle of Molecular Orbital (MO) theory. Additionally, the overlap between atomic orbitals directly corresponds to the change in energy between bonding and anti-bonding orbitals, where a large overlap correlates to a large change in energy in the molecular orbital. Furthermore, in determining MO configuration, the stability of a molecule (bond order) - as well as its overall structure - can be identified, which helps retain an accurate picture of the molecule and its fundamental properties as a whole.

Though, if you need more clarification or details, visit the MIT Solid State Chemistry playlist on YouTube; I referenced lectures 12-16. Information related to the Pullman K is from Albert Szent-Gyorgyi's book, Bioelectronics.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.