Projection operator method: vibrations of water (H₂O)

01:12 Reducible representation for 3N degrees of freedom
06:12 Reduction of reducible representation
18:03 Subtracting out rotations and translations
20:46 Effect of each symmetry operation on representative bond stretch
22:13 A1 stretch
22:53 B1 stretch
25:23 Effect of each symmetry operation on representative bond bend
26:33 A1 bend
Derivation of the normal modes of vibration for water (H₂O) - point group C₂v - by the projection operator method.
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[@lseinjr1]

(For mobile users)
01:12 Reducible representation for 3N degrees of freedom
06:12 Reduction of reducible representation
18:03 Subtracting out rotations and translations
20:46 Effect of each symmetry operation on representative bond stretch
22:13 A1 stretch
22:53 B1 stretch
25:23 Effect of each symmetry operation on representative bond bend
26:33 A1 bend

[@bijayapathak8271]

I seriously don't know why your channel doesn't have many subscribers .I discovered it two days back. Your teaching skills are really awesome. Thank you very much for the efforts.

[@lseinjr1]

You are very kind!

[@ellyhung6861]

thank you soooo much for making this great teaching video!!!

[@lseinjr1]

You're very welcome!

[@terrypaske3321]

This is great. My only suggestion would be to include a small character table in the screen so the viewer can follow along with that part of it instead of you just saying what it is. Thank you so much for all your videos, they have been so helpful!

[@lseinjr1]

Thanks, and great suggestion!

[@superideaful]

Great job explaining!

[@amitkumarkundu5187]

Like it... Thank you sir...

[@ΜαριαΠ-λ2η]

How many vibrations does it have [Co(NH3)6]?

[@lseinjr1]

Linear molecules have 3N - 5 vibrations, and non-linear molecules have 3N - 6, where N is the number of atoms. [Co(NH3)6] is non-linear, and N = 25, so 75 - 6 = 69 vibrations.

[@ΜαριαΠ-λ2η]

@@lseinjr1 Thank you very much

[@yasershowman3865]

Great Explanation

[@fayizali0324]

Sir, last video BCl3 projection operation you count bonds, like for identity value of 'R' is 3 but in that video you count atoms which don't change it place, kindly tell me which I consider?

[@lseinjr1]

It depends on whether you are deriving molecular orbitals, or deriving normal modes of vibration.

[@bhagyashreec2543]

My sir said we also do projection operation for bending modes ..can you please explain???

[@lseinjr1]

When we derived the vibrational modes, there were two (2) A1's and one B1. One of the A1's and the B1 were stretches. The final A1 is the bending motion. This step is shown at 25:21. For water, it is somewhat trivial.
To see the derivation of bending motions for a more complicated molecule, please see:
th-cam.com/video/vxwKbWz0m1o/w-d-xo.html

[@ahmedamer7794]

how to know the activity in IR or Raman Spectra ?

[@ahmedamer7794]

It will be active in IR and Ramon, right or wrong?

[@lseinjr1]

We know about IR and Raman activity by looking at the character table for C2v. IR active modes nave an "x", "y", or "z" basis function (modes A1, B1, and B2).
Raman active has quadratic basis functions (like x^2, xy, yz, xz. This would be any representation in C2v (A1, A2, B1, B2))

[@ahmedamer7794]

@@lseinjr1 please sir, can you make a video for C4v example
Like XeOF4

[@riggidyrickt7574]

what is the trace of sigma d?

[@lseinjr1]

The trace of any mirror, whether sigma v, sigma d, or sigma h, is always "1". This is one reason that the trace is such a useful property of a matrix.