Linear Combination Of Atomic Orbitals

Molecules are formed with more than one atom participating in the bonding method. This bonding can occur variably, participating under different conditions with the exchange of one or more electrons. The atomic orbitals are considerably the single electron single-center functioning method. It is generally utilized to define the electron position in a certain space. Variable atomic orbitals overlap and build the molecular orbital which describe the position and associated properties of an electron. The bond order, bond strength, etc., are described easily and accurately through the molecular orbital. 

Atomic Orbital: Concept

The atomic orbital concept is considered the simplified refinement of Bohr’s orbit. The atomic orbital is defined as the process of describing the wave type behavior and location of an electron in any particular orbit. It is considered a mathematical function that is used effectively to get the probable location of an electron. This location can be found in any region around the nucleus. 

Hence according to certain theories, the orientation of an atomic orbital is governed by the space where there is a probability to find an electron. This information about the placement is generally calculated in a quantitative mathematical format. In each orbital, a maximum of two electrons can be placed and attain different shapes and sizes. Atomic orbitals of different molecules can vary in physical and chemical properties, bond order, and bond strength etc. 

Every atomic orbital attains different properties and features. Each electron and atom are described by three basic quantum numbers, i.e., angular momentum, electron energy, and vector component. These three are represented mathematically as l, n, and ml. Each electron attains its specific projection rate (ms) and attains only two electrons in its arena for forming an atomic orbital. The simplified names such as ‘s,’ ‘p,’ ‘d’, and ‘f’ orbitals are represented in quantum mathematics as l = 0,1,2,3, respectively. 

‘S’ Orbital:

The ‘s’ orbital attains specific functions concerning the molecule type and the number of electrons present in the orbital. The properties also vary by exchanging several electrons and briefly explain what atomic is orbital. The ‘s’ orbitals attain the representation of a three-dimensional graph and are spherically symmetrical where the surface reflects ninety percent of the electron density. The most common example of ‘s’ orbital is Hydrogen which attains electrons in 1s, 2s, and 3s. Below are some of the properties of the ‘s’ orbital described. Let us have a look:

• The’ s’ orbital increases and gets large as they travel in the far region from the nucleus. 
• The number of nodes in the ‘s’ orbitals is greater. It is similar to the standing wave, which attains the notable amplitude, which gets separated by the zero, nodes, and points amplitude. 
• For certain atoms, the energy of ‘s’ becomes higher concerning the angular momentum, which also increases due to the constant increase of the distance of electrons from the nucleus.

‘P’ Orbital:

The shape of the ‘s’ orbital is symmetrical, but in the ‘p’ orbital, the shape of an orbital relies on certain points. When the value of angular momentum (l) increases, the quantity of atomic orbitals in the specific subshell decreases. Hence the shape of the ‘p’ orbitals becomes quite complicated. It is because the value in the 2p subshell is l=1, with three basic values: ml (-1, 0, +1). In general, there are three 2p orbitals. Considering the example of Hydrogen for the electron distribution probability, it attains two lobes, and electron density varies according to their arrangement in three different axes.  

Linear Combination Of Atomic Orbitals (LCAO) Method:

The linear combination of atomic orbitals is the mathematical method of forming molecular orbitals. The LCAO method governs the orientation of an atomic orbital. It mentions that repeated overlapping of two or more atomic orbitals is the basic formation process of molecular orbitals.

This method is the quantum superposition of explaining what atomic is orbital and a quantitative method to get the molecules’ configuration, pattern, and structured arrangement. By determining the molecular orbitals and position of the placement of an electron within the orbit, any information relating to the molecule is calculated mathematically. 

Dihydrogen (H2+) is the most common example of the molecular orbital, where each hydrogen atom comprises an atomic orbital and forms a bond with the exchange of a single electron. Combining two hydrogens (H) atomic orbital, two Hydrogen (H2) molecular orbital is formed. Both types of molecular orbitals attain lower and higher energy, and thus it affects the molecule’s linear combination and bond formation. 

Conclusion:

Atomic orbitals are an integral part of quantum mechanics defining the probable position of an electron. The atomic orbitals attain variable properties and characteristics through which complex quantitative calculations are solved. The overlapping of two or more atomic orbitals forms the molecular orbitals, which eventually determines the details like bond order, bond strength, configuration, etc. Atomic orbital defines the placement of electrons and atoms with the set of quantum numbers that relate to angular momentum, vector component, and electron energy.