Kim method: vibrations of boron trifluoride (BF₃)

01:18 Assignment of coordinates for stretches
03:41 A1' irreducible representation / basis function (stretch)
05:47 E1' irreducible representation / first basis function (stretch)
07:09 E1' irreducible representation / second basis function (stretch)
08:00 Assignment of coordinates for bends
09:59 A1' irreducible representation / basis function (bend)
11:01 E1' irreducible representation / first basis function (bend)
11:57 E1' irreducible representation / second basis function (bend)
Derivation of the molecular vibrations of BF₃ (boron trifluoride) - point group D₃ₕ - by the correspondence theorem (the Kim Method). Boron trifluoride is an important catalyst for Friedel-Crafts alkylations and acylations.
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[@lseinjr1]

(For mobile users)
01:18 Assignment of coordinates for stretches
03:41 A1' irreducible representation / basis function (stretch)
05:47 E1' irreducible representation / first basis function (stretch)
07:09 E1' irreducible representation / second basis function (stretch)
08:00 Assignment of coordinates for bends
09:59 A1' irreducible representation / basis function (bend)
11:01 E1' irreducible representation / first basis function (bend)
11:57 E1' irreducible representation / second basis function (bend)

[@omdwivedi9323]

Can you explain how kim method and projection method differ? If possible suggest some books for the reading purpose. It will be greatful

[@lseinjr1]

The Kim method is particularly powerful for highly symmetric systems, systems with a large number of symmetry operations, such as octahedral Oh (48 operations) or tetrahedral (24).
When there is degeneracy (multiple states with the same energy), the projection operator method requires you to find one first, and then derive the others from that.
The Kim method, on the other hand, allows one to derive each member of the degenerate pair (e symmetry) or triple (t symmetry) directly from the basis functions.
The downside of the Kim method is that is not well known I learned it at Temple University from a colleague of Dr. Kim, and then from Dr. Kim himself. Once it is learned, it allows derivations of vibrations and orbitals (and much else besides) with much less effort than the projection operator method.
Dr. Kim published an excellent book on group theory, which includes details of his method (which he calls the "Correspondence Theorem"):
"Group Theoretical Methods and Applications to Molecules and Crystals" by Shoon K. Kim, Cambridge University Press, 1999, ISBN-13 : 978-0521640626.

[@arshikhan2256]

Sir would u plz tell us whats purpose 4 the kim method as we know that projection method is use find out vibration mode in or out of the phase. What we getting by this and how this method is useful

[@lseinjr1]

The Correspondence Method (the "Kim Method") has the same uses as the projection operator method - to derive the normal modes of vibration and molecular orbitals.
There are two difficulties with the projection operator method: (1) the method does not directly derives all members of a degenerate (E or T) representation at the same time (so that you have to do additional work after you have found the first degenerate representation, and (2) the method becomes more and more tedious as the number of symmetry operations in the group grows.
The Kim Method shows the greatest advantages with high symmetry groups like Td (24 operations) and Oh (48 operations).