# Introduction

In this particular article, Crystal field theory and shape of d-orbitals, We are going to discuss the theory of crystal field and its assumption. We will also discuss the shape of d-orbital.

## Crystal field theory and shape of d-orbital

Let’s know about crystal Field theory in detail

### Crystal field theory (CFT)

valence bond theory is used to visualize the bonding in complexes. But it fails to explain the nature of ligands, color, and electronic spectra, The effect of temperature on the magnetic moment and magnetic susceptibilities. Why some complexes are high spin and others are low spins, the stability of complexes. To explain these properties Bethe and van Vleck proposed the crystal field theory. This theory was originally applied to ionic crystals and is, therefore, called crystal field theory.

#### Assumptions of crystal field theory

This theory is based on the following assumptions.

1) Ionic ligands such as CI, OH, CN are regarded as the negative point charges and The neutral ligands such as H₂O, NH₃, py are regarded as a point dipole. Because these ligands are dipolar. If the ligand is a neutral molecule like H₂O, NH₃, The negative end of the dipole is directed towards the metal ion.

2) Metal- ligands bond is not covalent i.e., there is no overlapping of orbitals. Instead, the bonding in complexes is purely electrostatic in nature. In complexes, two types of electrostatic forces come into account. One is the attraction between the metal cation and the negative charge ligand or the negative end to the polar ligand. The second type of electrostatic interaction is the electrostatic repulsion between the lone pairs of electrons on the ligands and The electrons in the d-orbitals of the metal cation and The repulsion between nuclei of the metal cation and the ligands but to a small extent. Another repulsion also comes into account that occurs among the ligands.

3) The five d-orbitals in a free metal ion are degenerate. When a complex is formed, the electrostatic field of the ligands destroy the degeneracy of these d-orbitals i.e., These orbitals now have different energies. The orbitals lying in the direction of the ligands are raised in energy more than those lying away from the ligands, Because of the repulsion between the d-electrons and the ligands.

In order to understand the CFT, it is necessary to know the geometry and orientations of the five d-orbitals.

##### Shape of d-orbitals

In fact, there are six d-orbitals each of them have four lobes. These orbitals are dxy*, *d*yz, *d*zx, *d*x²-y², *dz²-*x*², and dz*²-y². T*he three orbitals d*xy, *d*yz, *and d*zx *lie in between the axes and the three orbitals d*x²-y², *d*z²-x² *and d*z²-y² *lie on axes.

In so far as there are only five independent d-orbitals, one of them is regarded as the linear combination of the d*z²-x²* and d*z²-y² *orbitals. Because of the fact that these two orbitals have no independent existence.

The orbital d*z²-x² *has the probability of finding electron along the *z *and x-axes whereas the orbitals d*z²-y² *has the probability of finding electron along the z and x-axes. Therefore, when these two orbitals are combined, The resulting d*z*² orbitals have the probability of finding electron along z-axis twice that of along the x-and y-axes. The dz² orbitals also have some fraction of probability along the x and y-axes. This xy component has a doughnut shape. Therefore the five d-orbitals shown in the figure are dxy,dyz, dzx, dx²-y², and dz².

The three orbitals dxy, dyz and dzx lie in between the axes. These three orbitals lie in xy, yz, and zx planes respectively. The dx²-y² orbital on x and y-axes and the dz² orbital on the z-axis. The shape of dz² is different from the other four.

All the five d-orbitals are gerade. Because The opposite lobes have an inversion center with respect to the phase of the wave function. The plus and minus signs indicate the different phase of the lobes of orbitals.

###### The conclusion of Crystal field theory and shape of d-orbitals

In this article Crystal field theory and shape of d-orbitals. We have widely discussed the crystal Field theory and its assumptions. Along with that we have also discussed the shape of d-orbital in the easiest way possible.