W2013CHM2311 Part 3b Notes(1)

The oxygen is placed at 000 z h o x y h now

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Unformatted text preview: umbers in the body of the table are called “characters” C2v E C2 σv (xz) σv’ (yz) A1 1 1 1 1 z x2, y2, z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz The character under a given symmetry opera0on tells us how the orbitals (and func0ons) listed on the right in the same row are affected by the symmetry opera0ons. Characters Orbitals have regions in which the wave func0on is either posi0ve or nega0ve. Character = 1 ➜  The shading of the lobes stay the same (i.e. the wave func0on is not affected) upon carrying out the symmetry opera0on ➜  The orbital is said to be symmetric with respect to the opera0on Character = - 1 ➜  The shading of the lobes reverses (i.e. the wave func0on changes sign) upon carrying out the symmetry opera0on ➜  The orbital is said to be an:symmetric with respect to the opera0on Example: Water Looking at a water molecule (C2v point group), what is the effect of a C2 rota0on on a pz atomic orbital on the oxygen atom? C2v E C2 σv (xz) σv’ (yz) A1 1 1 1 1 z x2, y2, z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz Transforma0ons of Oxygen pz- Orbital in Water Water is placed in the Cartesian coordinate system according to the “right hand rule” and with the z- axis (principal axis of rota0on) poin0ng up. The oxygen is placed at (0,0,0). z H O x y H Now we can draw in the pz orbital of oxygen. It does not maier whether you draw the orbital with the dark lobe up or down. At this point it is arbitrary! Transforma0ons of Oxygen pz- Orbital in Water Carry out the desired transforma0on on the whole molecule. z H O x y H If the shading of the lobes reverses (i.e., the wave func0on changes sign), the orbital is an:symmetric with respect to the opera0on. If the shading of the lobes stay the same (i.e., the wave func0on is not affected), the orbital is symmetric with respect to the opera0on. Transforma0ons of Oxygen pz- Orbital in Water C2 opera0on on the pz orbital: z z x H O x y H C2 y H O H Shading of lobes is unchanged: the pz orbital is symmetric with respect to the C2 opera0on. Using this method, the transforma0on proper0es (i.e., symmetric vs. an0symmetric) can be visually determined for all of the p- orbitals of water with respect to each of the symmetry opera0ons in the C2v point group....
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