Molecular orbitals

Molecular orbitals that are orbitals that no longer belong to a single nucleus to become dependent on two or more nuclei. The mathematical treatment that Quantum Mechanics uses to calculate molecular orbitals is the method of linear combination of atomic orbitals, or CLOA method, which considers the molecular orbital, and, is the result of linear combination, that is, an addition, or a subtraction, of the two atomic orbitals involved, F1 and F2.


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  • 1 Origin
  • 2 Classification
    • 1 The types of orbitals are
  • 3 Smolecular Orbit Theory
    • 1 S molecular orbitals
    • 2 Molecular orbitals p
  • 4 Molecular electrons
  • 5 External links
  • 6 Source


The simplest case is that of the interaction of two atoms, each with a single atomic orbital occupied by a single electron, that is, the case already considered from the point of view of the valence bond theory, of the formation of the hydrogen molecule. It will be seen that the description of the HH bond is the same, or at least very similar to the description of the bonds in more complex molecules. When the two 1s orbitals of two hydrogen atoms interact, they transform into two molecular orbitals, one bonding, which is occupied by the two electrons, which no longer belong to a single nucleus to become part of the two atomic nuclei, and another anti-bonding agent. , which will be empty. The bonding molecular orbital is lower in energy than the original atomic orbitals and the anti-bonding higher in energy than these.

The bonding orbital, yE, is the result of the sum, F1 + F2, of the two atomic orbitals: Molecular orbitals are mathematical functions that define the wave behavior of electrons within molecules, always from the point of view of chemistry quantum. Mathematical functions are used to find physicochemical properties, such as the probability of finding the electron in a given space. The word orbital was used by Robert S. Mulliken for the first time in 1925., being the translation of the word “Eigenfunktion”, used by the German Schrödinger. Molecular orbitals are generally made up of a linear set of atomic orbitals, in each atom of a molecule. The quantitative form can be found using methods like the one known as Hartree-Fock.

Molecular orbitals are used to determine the electronic configuration in molecules. Almost all methods in quantum chemistry start by calculating molecular orbitals, in order to describe the behavior of an electron in the electric field that nuclei create around themselves. If two electrons are in the same orbital, they are bound to have opposite spins according to the Pauli exclusion principle.


  • Bonding: they have less energy than the atomic orbitals that contributed to their formation. They collaborate in the bond in such a way that the positive nuclei overcome the electrostatic forces of repulsion due to the attraction that the negative electronic cloud creates, between them there is a distance known as the bond length.
  • Anti-linkers: They have greater energy and that is why they create repulsion, unlike linkers.

The types of orbitals are

  • Bonding σ Orbitals: These are the s and p atomic orbitals, which combine with each other in all possible ways (ss, pp, sp, ps). They have simple links
  • Binding π orbitals: They are those that coordinate the p atomic orbitals, perpendicular to the axis. They have highly delocalized electrons that interact with great ease.
  • Anti-bonding σ * orbitals: these are higher energy orbitals than the bonding orbitals. Anti-bonding π * orbitals: These are high-energy π orbitals.
  • N orbitals: They occur in heteroatomic molecules, such as N or O. Electrons that are unpaired occupy these orbitals.

In the same way as atomic orbitals, molecular orbitals are filled with electrons, in increasing order of energy level, according to the Pauli exclusion principle, or applying Hund’s rule.


Smolecular orbit theory

The molecular orbital theory applied to the hydrogen molecule is relatively simple because only two atomic orbitals and only two electrons are involved. But in polyatomic molecules with more than two nuclei and several atomic orbitals, the treatment is much more complicated, since, to get to know exactly the most stable situation of all the atoms in the molecule, one would have to consider molecular orbitals that comprise more than two nuclei or even the entire molecule.

To obviate the study of such a complex situation, especially from the mathematical point of view, certain simplifications are used and admitted, such as the consideration that, in general, molecular orbitals are located essentially between two unique nuclei and that their shape and orientation they maintain some similarity with the shape and orientation of the corresponding atomic orbitals. This approach coincides with the classic ideas of considering each bond as the bonding force between two atoms, disregarding the influence that the rest of the molecule can exert on it. With these simplifications, most, but not all, molecules can be interpreted and approximated to the interpretation of the covalent bond given by the valence bond theory.

S molecular orbitals

The linker molecular orbital described for the hydrogen molecule, which is ellipsoidal in shape (symmetric about the axis of union of the two nuclei), is called the molecular orbital s (sigma) and the resulting covalent bond, bonds. Similarly, the corresponding anti-bonding molecular orbital is called orbitals * (star sigma or asterisk sigma). By overlapping or interacting two type s atomic orbitals, type s molecular orbitals are always formed. But also from orbitals p orbitals and bonds can be formed. Thus, for example, when a p orbital interacts with an s orbital, we arrive at two molecular s orbitals, one binding:

As in the case of the combination of two s orbitals, in the bonding orbital formed from one s and one p orbital, due to the significant decrease experienced by the lobe not involved in the overlap of the p orbital, the highest electron density is found between the two nuclei and the resulting molecular orbital it has practically ellipsoidal symmetry with respect to the axis that joins the two nuclei. It is therefore a molecular orbital s similar to that of the hydrogen molecule.

Molecular orbitals p

But from two atomic p orbitals, another type of molecular orbital can originate. Indeed, the overlap or interaction between the two p atomic orbitals can take place laterally to give rise to two molecular orbitals of the p (pi) type, one bonding, of lower energy than the starting atomic, and another anti-bonding, of higher energy and with a node: Like the starting atomic orbitals, the p-type molecular orbitals also have different sign zones separated by a nodal plane. The bonding molecular p orbital is made up of two lobes of different sign in which the probability of finding the electrons is maximum, separated by a nodal plane that passes through the two nuclei. That is, in the bonding orbital, the two nuclei of the atoms that provide the p orbitals are joined by two zones or p clouds, one upper and one lower of different signs. In the anti-bonding orbital, the nodal zones are two, that of the plane that passes through the two nuclei and that of a plane perpendicular to the first one that causes the upper and lower zones to be divided in turn into two parts of different signs:

Molecular electrons

We have already seen that the “localized” way of describing the electron-based bonds directed to specific sites according to the geometry of the molecule, is very useful to have an interpretation of the bonds. However, there are some problems that are fixed through the use of Molecular Orbital Theory, OM. The latter differs from the treatment based on Hybrid Orbitals in several aspects, the main one is that Hybrids are built to show the formation of “directed” bonds, unlike OMs that are more general in their approach to describe the configuration. electronics in molecules. They allow correcting various difficulties present in hybrids, such as:

Hybrids assume that e’s are local to links, which is not entirely correct. Rather, what exists is a high possibility that electronic charge is located in the direction of the bonds, not ruling out that it can also occupy other regions of the molecule. This anomaly is correctable by means of the so-called “resonance structures” as already seen.

To form bonds involving hybrids, it is necessary to have pairs of electrons, shared or not, to direct them towards specific positions in the geometry of the molecules. But what happens in molecules that have unpaired electrons? This situation is not contemplated by the molecular hybrid scheme.

Link Energy is also not a concept that appears in hybrids, in circumstances that we know are that links are more difficult to break than others.


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