For trigonal bipyramidal coordination complex ML5 the correct point group symmetry and the relative order of the energies of the 3d orbitals in that crystal field, respectively are

For trigonal bipyramidal coordination complex ML₅ the correct point group symmetry and the relative order of the energies of the 3d orbitals in that crystal field, respectively are

$D_{3h}, d_{x^2-y^2} > d_{z^2}, d_{xy} > d_{xz}, d_{yz}$

$D_{3d}, d_{z^2} > d_{x^2-y^2}, d_{xz} > d_{xy}, d_{yz}$

$D_{3d}, d_{x^2-y^2} > d_{z^2} > d_{xy} > d_{xz}, d_{yz}$

$D_{3h}, d_{z^2} > d_{x^2-y^2}, d_{xy} > d_{xz}, d_{yz}$

Correct option is D

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid. This is one geometry for which the bond angles surrounding the central atom are not identical, because there is no geometrical arrangement with five terminal atoms in equivalent positions.

According to crystal field theory, the interaction between a transition metal and ligands arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand. The theory is developed by considering energy changes of the five degenerate d-orbitals upon being surrounded by an array of point charges consisting of the ligands. As a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the d-orbitals and farther away from others, causing a loss of degeneracy. The electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges. Thus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy.

The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands. It arises due to the fact that when the d-orbitals are split in a ligand field, some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five d-orbitals are degenerate.

For trigonal bipyramidal coordination complex ML₅ the correct point group symmetry and the relative order of the energies of the 3d orbitals in that crystal field, respectively are

$D_{3h}, d_{x^2-y^2} > d_{z^2}, d_{xy} > d_{xz}, d_{yz}$

$D_{3d}, d_{z^2} > d_{x^2-y^2}, d_{xz} > d_{xy}, d_{yz}$

$D_{3d}, d_{x^2-y^2} > d_{z^2} > d_{xy} > d_{xz}, d_{yz}$

$D_{3h}, d_{z^2} > d_{x^2-y^2}, d_{xy} > d_{xz}, d_{yz}$

Correct option is D

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For trigonal bipyramidal coordination complex ML5 ​the correct point group symmetry and the relative order of the energies of the 3d orbitals in that crystal field, respectively are​

​D3h,dx2−y2>dz2,dxy>dxz,dyzD_{3h}, d_{x^2-y^2} > d_{z^2}, d_{xy} > d_{xz}, d_{yz}D3h​,dx2−y2​>dz2​,dxy​>dxz​,dyz​​​

​D3d,dz2>dx2−y2,dxz>dxy,dyzD_{3d}, d_{z^2} > d_{x^2-y^2}, d_{xz} > d_{xy}, d_{yz}D3d​,dz2​>dx2−y2​,dxz​>dxy​,dyz​​​

​D3d,dx2−y2>dz2>dxy>dxz,dyzD_{3d}, d_{x^2-y^2} > d_{z^2} > d_{xy} > d_{xz}, d_{yz}D3d​,dx2−y2​>dz2​>dxy​>dxz​,dyz​​​

​D3h,dz2>dx2−y2,dxy>dxz,dyzD_{3h}, d_{z^2} > d_{x^2-y^2}, d_{xy} > d_{xz}, d_{yz}D3h​,dz2​>dx2−y2​,dxy​>dxz​,dyz​​​

Correct option is D

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For trigonal bipyramidal coordination complex ML₅ the correct point group symmetry and the relative order of the energies of the 3d orbitals in that crystal field, respectively are

$D_{3h}, d_{x^2-y^2} > d_{z^2}, d_{xy} > d_{xz}, d_{yz}$

$D_{3d}, d_{z^2} > d_{x^2-y^2}, d_{xz} > d_{xy}, d_{yz}$

$D_{3d}, d_{x^2-y^2} > d_{z^2} > d_{xy} > d_{xz}, d_{yz}$

$D_{3h}, d_{z^2} > d_{x^2-y^2}, d_{xy} > d_{xz}, d_{yz}$