Hybridization involving s, p and d-Orbitals

• The process of mixing of the atomic orbitals is called hybridization.
• There are different types of hybridization like sp², sp³, sp, sp³d, sp³d², sp³d, dsp²,d²sp^3.
• The atoms of third period elements have vacant d orbitals.
• Since, the energy of 3d orbitals is comparable to the energy of the occupied 3s and 3p orbitals (the energy difference is very small), hence quite often d orbitals also get involved in the bonding process.
• The paired electrons in the 3s or 3p orbitals can be promoted to the vacant 3d orbitals, thereby, opening up the possibilities of hybridization of s, p and d.
• the different types of hybridization involving only s, p and d orbitals are:

i) The sp³d hybridization: Trigonal bi-pyramidal hybridization

• In sp³d hybridization, one s, three p and one d orbital (d_z²) of the same energy level (e.g., n=3) are involved in hybridization.
• These five orbitals combine to give five hybrid orbitals.
• These hybrid orbitals designated as sp³d orbitals, are oriented towards the corners of trigonal bi-pyramid.
• Three orbitals forming a plane are directed towards the corner of the equilateral triangle (angle of inclination = 120⁰), while the other two are oriented at right angles to the plane of the triangle, above and below it.
• A typical example of this type of hybridization is the formation of PCl₅ molecule.
• The ground state outer electronic configuration of phosphorous is 3s² 3p_x¹ 3p_y¹ 3p_z¹ 3d⁰.
• The promotion of one 3s electron to 3d level gives the outer configuration, 3s¹ 3p_x¹ 3p_y¹ 3p_z¹ 3d¹.
• These five orbitals hybridize to give five new sp³d orbitals.
• Each hybrid orbital is singly occupied.
• One of the p orbitals of chlorine is singly occupied.
• These singly occupied p orbitals of Cl form five P-Cl bonds due to the overlap with five sp³d orbitals.
• This gives a trigonal by-pyramidal geometry for PCl₅ molecule.
  
  

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ii) The sp³d² hybridization : Octahedral hybridization

• The orbitals which take part in sp³d² hybridization are ns, n(p_x, p_y, p_z), n(d_z², d_x²_-y²). E.g., 3s, 3(p_x, p_y, p_z), 3(d_z², d_x²_-y²).
• In this case, the total number of atomic orbitals which hybridize is six.
• The six hybridized orbitals are directed towards the corner of an octahedron, and are inclined at an angel of 90⁰ to each other.
• The sp³d² hybridization is observed for sulphur in SF₆.

• The ground state outer electronic configuration of sulphur is 3s² 3p_x² 3p_y¹ 3p_z¹ 3d⁰.
• Promotion of two electrons, one each from 3s and 3p_x to two 3d (d_z², d_x²_-y²) orbitals, followed by hybridization yields six sp³d² hybrid orbitals.
• These six hybrid orbitals are directed towards the corner of a regular octahedron.
• Each hybrid orbital is occupied by one electron.
• These hybrid orbitals overlap with the half-filled p orbitals of F atoms to form six S-F bonds. This gives an octahedral geometry for SF₆.

iii) The d²sp³ hybridization: Octahedral hybridization

• The d²sp³ hybridization involves two d orbitals belonging to (n-1)^th energy level and the s and p orbitals belonging to nth energy level, i.e., (n-1) (d_z², d_x²_-y²), ns, n(p_x, p_y, p_z).
• For example: 3d_z², 3d_x²_-y², 4s, 4(p_x, p_y, p_z) orbitals.
• A typical example of this type of hybridization is the formation of a complex ion, [Co(NH₃)₆]³⁺.

• The outer configuration of Co is 3s² 3p⁶ 3d⁷ 4s².
• Therefore, the configuration of Co³⁺ is 3s² 3p⁶ 3d⁶ 4s⁰ 4p⁰.
• When the reaction takes place, the six electrons in 3d orbitals pair up. This makes two d-orbitals available.
• These two 3d orbitals combine with one 4s and three 4p orbitals to form six d²sp³ hybrid orbitals.
• These six orbitals are oriented along the six corners of a regular octahedron.

iv) The dsp² hybridization : Square planar hybridization

• In this type of hybridization, one d orbital belonging to (n-1)^th energy level, and one s and two p orbitals belonging to the nth energy level, viz., (n-1) d_x²_-y², ns, np_x, np_y, np_z.
• For example: 3 d_x²_-y², 4s, 4p_x, 4p_y, 4p_z are involved.
• A typical example of this kind of hybridization is the formation of complex ion [Ni(CN)₄]^2-.

• Nickel (atomic no. = 28) has the outer configuration 3s², 3p⁶, 4s², 3d⁸. The electronic configuration of Ni²⁺ is 3s² 3p⁶ 3d⁸.
• During the reaction, these eight d electrons pair up to occupy four of the d orbitals. This leaves one of the 3d orbitals vacant.
• This 3d orbital combines with one 4s and two 4p orbitals to give four dsp² hybrid orbitals.
• Thee four hybrid orbitals are directed towards the four corners of a square in the xy plane.
• This gives a square planar geometry to the complex ion [Ni(CN)₄]^2-.

References: 

i) https://www.masterorganicchemistry.com/2018/01/16/a-hybridization-shortcut/

ii) https://www2.chem.wisc.edu/content/hybridization#

iii) https://www.organicchemistrytutor.com/topic/hybridization/

Hybridization involving s, p and d-Orbitals