00000000000Daniel Nocera

# 00000000000Daniel Nocera - MIT OpenCourseWare...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 1: Symmetry Elements and Operations Consider the symmetry properties of an object (e.g. atoms of a molecule, set of orbitals, vibrations). The collection of objects is commonly referred to as a basis set J classify objects of the basis set into symmetry operations J symmetry operations form a group J group mathematically defined and manipulated by group theory A symmetry operation moves an object into an indistinguishable orientation A symmetry element is a point, line or plane about which a symmetry operation is performed There are five symmetry elements, which will be defined relative to point with coordinate ( x 1 ,y 1 ,z 1 ) : 1) identity , E E x ,y ,z = x ,y ,z 1 ) ( 1 1 1 ) ( 1 1 2) plane of reflection, σ σ ( )( 1 1 1 ) ( = 1 − 1 1 ) xz x ,y ,z x , y ,z 5.04, Principles of Inorganic Chemistry II Lecture 1 Prof. Daniel G. Nocera Page 1 of 5 3) inversion, i i ( x 1 ,y 1 ,z 1 ) ( = − x 1 , − y 1 , − z 1 ) 2 π 4) proper rotation axis, C n (where θ = ) n convention is a clockwise rotation of the point C 2 ( )( 1 1 1 ) ( = − 1 1 1 ) z x ,y ,z x , − y ,z 5) improper rotation axis, S n two step operation:...
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00000000000Daniel Nocera - MIT OpenCourseWare...

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