Group Theory and Chemistry Intermediate Topics 1: Group Multiplication

In this video three different ways to represent symmetry operations will be introduced: 1) visually, 2) a transformation matrix on atomic positions, and 3) a transformation matrix on a 3D vector. We will use these concepts to construct a multiplication table for the C2v point group.

[@mrsage4489]

Thank you so much for all your videos. You really helped me.

[@arvinmontederamos4335]

10:22 , I think there's a mistake in the orientation (labels) on sigma xz because sigma xz showed similar orientation as the identity E. I think the C and D should swap places to achieve sigma xz.

[@hansenyang4014]

9:55 I am confused by the first and second terminology. You said the cell corresponding to row sigma(xz) and column sigma(yz) corresponds to sigma(xz) first and then sigma(yz), but the matrix multiplication is sigma(xz)*sigma(yz). Wouldn't sigma(xz)*sigma(yz) mean yz first and then xz? I thought the opreations of matrix multiplication should be read from right to left.