3-1 1 Improper Rotation (Sn) Improper rotation : Consists of a rotation followed by a reflection in the plane perpendicular to the rotation axis. Example, Methane, CH 4 S4 σh 4 1 4 2 2 4 C 4 σh 1 3 2 1 3 3 Molecule is left unchanged. 3-2 2 NOTE: Neither C 4 nor σh is a symmetry operation of methane but their product C 4×σh is (i.e. S 4) S1 ≡ reflection, S 2 = i Pictorially S1 rotate reflect reflect σ i h 3-3 3 OK That’s it: We can now identify molecules by their symmetry elements. i.e. E, Cn, σ, i, S ↑ σh, σv Whether or not a molecule has all or some of these can easily be classified by assigning a label. This identifies the point group of the molecule. Point Group Labels look like this C2v , D∞h, Oh, Td - - - - - - - - - - 3-4 4 Assigning Point Groups VERY IMPORTANT! - Assigning a point group to a molecule depends on listing the symmetry elements of the molecule and then looking them up in a table. - It is often easier (at first) to work through a YES/NO TREE. I don’t like it. 3-5 5 Decision Tree For Assigning Point Groups (a) Molecule Y Linear N Y i ? Two or Y more N N Cn , n>2 ? Y i ? N ⇓ Go to Y N C5? (b) D∞h Ih Oh C∞ v Td Linear groups Cubic groups From (a) (b) N Cn? Y Y N σ ? Select C n with Y highest n i then, is Y N nC 2 ⊥ Cn ? i ? N Y N Y σh? σh? N N nσd? σ Y Y n v? Y S2n ? D D D nh nd n N S2n Let’s do a few examples. Cn Cnv Cnh Cs Ci Cl 3-6 6 H2O: Start at Top of Tree Linear – NO Two or More C 2’s – NO Cn – Yes (C 2) Select Highest C n – NO Is nC 2 C2 POINT GROUP FOR WATER IS C 2v σh - NO σv’s - YES ⇓ Cnv Or we can identify the symmetry elements 3-7 7 e.g. NH 3 C3 Molecule possesses: N Identity (E) H H H C3 axis 3 σσσv planes ⇒ C3v or go through tree Linear ? – no , 2 or more C n – no Cn ?– yes , C2 C3 ?– no σh ?– no , nσv ?– yes ⇓ Cnv (n = 3) Point group for ammonia is C 3v 3-8 8 Be Careful With σσσh And σσσv! In both examples so far we had to answer questions concerning the minor planes. Is it σh or σv? σh’s are to main rotation axis. C2 water σ v σ'v E, C2, 2σv 3-9 9 BF 3: F F B Planar F Linear ? – no 2 or more C n (n > 2)? – no Cn ? – yes (C 3) Is C 2 C3 ? – yes σh ?– yes ⇓ POINT GROUP Dnh FOR BF 3 D3h PCl 5 has the same point group Why? 3-10 10 Examples: O H In H H W H F F F F F F F F C4ν C4ν C5ν C∞ν One infinite-fold rotation axis with infinite number of symmetry planes which include the rotation axis. D2 Three mutually perpendicular two-fold rotation axes. D3 One three-fold rotation axis and two-fold rotation axes perpendicular to the three-fold axis. The two-fold axes are at C∞ν D2 D3 3-11 11 Making sense of the truth table • search is for highest order C n axis NO C2 axes C2 axes DC (Difference between D & C) • “D” IF D AND σ – Dnh (See later σd’s bisect C 2’s) σd – Dnd (σd’s bisect C 2’s) NO σ – Dn .