E Siva Subramaniam Iyer, IIT Bombay Point Group Learning objective: The learner will learn to identify the point groups in molecules that have simple symmetry. ‏ Author E Siva Subramaniam Iyer, IIT Bombay

Point groups A set of symmetry operations together constitute a point group. Few symmetry are called special groups. They are Octahedral, tetrahedral and icosahedral. If moleculer are not any of this then the hunt of other symmetry elements begin and finally they are assigned point groups according to the symmetry elements they possess. A handy guide to identify the symmetry elements is shown in the flowchart. (flowchart on next page.)‏

Identifying the point gropus The flowchart was sure confusing. Lets simplify using simple examples. H2O NH3 Mo(CO)6 Mo(CO)5NH3 CH4 CO2 HCl PH3Cl2 CH2CCH2

The first step towards assigning the point group is to identify if the molecule belongs to any special point group. If not then proceed to find other elements of symmetry. Remember all groups have E operation! Special group are Ocatahedral perfectly symmetric eight faced figure. Tetrahedral four faced figure Icosahedral twelve faced figure Linear D∞h – symmetric linear molecules like CO2, H2 C ∞v- unsymmetric linear molecules like HCl Action Description of Action Audio narration 1. The slide appears. --

Lets learn to identify using few examples HCl The molecule is linear, hence has axis of rotation but there is no unique axis => it is a special group. And all angles of rotation leaves the molecule unchanged. But there are infinite planes that can bisect the molecule and contains the axis of rotation. Two such planes have been shown The point group is C∞v

CO2 The molecule is linear, hence has axis of rotation but there is no unique axis => it is a special group. And all angles of rotation leaves the molecule unchanged. there is plane perpendicular to axis of rotation that can bisect the molecule. Hence the point group is D∞h

. CH4 Methane The molecule is not linear. Action Description of Action Q1. Does the molecule have a unique axis of rotation? The answer is NO!. So it must belong to special group! With C as center the three Hydrogen form one face. And there are four such faces, hence it is a tetrahedral molecule Hence point group is Td Action Description of Action Audio narration The molecule with structure appears The statement in red comes Text in blue appears The figure rotates The molecule keeps rotation and each arrow one after other comes and disappears We shall identify the point group of the molecule. As we can see that there are four equivalent rotation axis, no specific axis of rotation, hence must belong to special group. There are four faces hence it is a tetrahedral point group.

The molecule is not linear. Mo(CO)6 The molecule is not linear. Q1. Does the molecule have a unique axis of rotation? The answer is NO!. So it must belong to special group! Q2 Is the molecule symmetric from all sides? Yes!! Q3 How many faces does it have? Eight! => It’s a octahedran! Point group is Oh Action Description of Action Audio narration The molecule with structure appears The statement in red comes Text in blue appears Text in green appears. The figure rotates The molecule keeps rotation and each arrow one after other comes and disappears The eight faces one after another glows and disappears. One face has been shown. We shall identify the point group of the molecule. There are eight faces hence it is a octahedral point group.

Other molecules We have learnt to identify the simple perfectly symmetric molecules. Now the next challenge is what if they are not….. We shall take up few examples and tell you how to identify the point groups of not so simple molecules. Action Description of Action Audio narration 1. Statements appear one after another The statements are read out. As and when they appear.

The water molecule H2O Q1. Is the molecule linear? No Q2. Is it a special symmetry Q3. Does the molecule have a unique axis of rotation? YES! It’s a C2 axis !! And it is the highest rotation symmetry! Q4. Is there any other axis perpendicular to this axis? No! Q5. Is there a plane of reflection? Yes!!! Hey there are two reflection planes…. Q6. Is there any plane which is perpendicular to the peincipal axis? Bingo!! This is a C2v symmery point group!!! Fig 1 Action Description of Action Audio narration 1.q1 one and two appear in sequence Q3 follwed by its answer appears Q4 appears Q5 appears Q6 appears followed by statements after it. The diagram appears the arrow appears and then molecule rotates clockwise by 180o about the axis Figure 2 appears. The two planes appear one after the other after the question and its answer has come. The molecule has a C2 axis of rotation. There are two reflection planes in the molecule. In cartesian coordinates they are in xy and yz plane if the axis of rotaion is in z axis. Lets refer to chart aswell ( flow chart on master slide. The molecule possess a C2v symmertry point group. Fig 2

NH3 molecule Action Description of Action Audio narration 1.q1 one and two appear in sequence Q3 follwed by its answer appears Q4 appears Q5 appears Q6 appears followed by statements after it. The diagram appears the arrow appears and then molecule rotates clockwise by 120o about the axis Figure 2 appears. The three planes appear one after the other after the question and its answer has come. The molecule has a C3 axis of rotation. There are three reflection planes in the molecule. They have a N and H in the plane Lets refer to chart aswell ( flow chart on master slide. The molecule possess a C3v symmertry point group. NH3 molecule C3 axis of symmetry. Q1. Is the molecule linear? No Q2. Is it a special symmetry? Q3. Does the molecule have a unique axis of rotation? YES! It’s a C3 axis !! And it is the highest rotation symmetry! It passes thru Nitrogen. Q4. Is there any other axis perpendicular to this axis? No! Q5. Is there a plane of reflection? Yes!!! Hey there are three reflection planes all are equivalent. It contains Nitrogen and one hydrogen and bisects the bond between other hydrogens. Q6. Is there any plane which is perpendicular to the principal axis? Bingo!! This is a C3v symmery point group!!! 11

PH3Cl2 Action Description of Action Audio narration 1.q1 one and two appear in sequence Q3 follwed by its answer appears Q4 appears The text in blue appears 5. Q5 appears Q6 appears followed by statements after it. The statement in black appears The fig 1appears The arrow appears and then molecule rotates clockwise by 120o about the axis Fig 2 comes up The arrow appears and then molecule rotates clockwise by 180o about the axis Fig3comes up Figure 4 appears. The three planes appear one after the other after the question and its answer has to come. Fig 5 appears, the plane comes which has all H and the P The molecule has a C3 axis of rotation. The molecule has a C2 axis of rotation and is perpendicular to C3 axis. The heighest symmetric axis is of C3, hence is the principal axis There are three reflection planes in the molecule. They have a P and H and 2 Cl in the plane There is another reflection plane perpendicular to the principal axis Lets refer to chart aswell ( flow chart on master slide. The molecule possess a D3h symmertry point group. PH3Cl2 Q1. Is the molecule linear? No Q2. Is it a special symmetry? Q3. Does the molecule have a unique axis of rotation? YES! It’s a C3 axis !! And it is the highest rotation symmetry! It has P and 2 Cl . Q4. Is there any other axis perpendicular to this axis? Yes! A C2 axis, passing through P and H. There are three such axis. The principal axis is C3 Q5. Is there a plane of reflection? Yes!!! Hey there are three reflection planes all are equivalent. It contains Phosphorus and one hydrogen and two chlorine and bisects the bond between other hydrogens. Q6. Is there any plane which is perpendicular to the principal axis? Yes!!! This plane has all the hydrogens and phosphorus => There is a C3 axis and plane perpendicular to this axis, so point group is D3H! Fig 2 Fig 1 Fig 3 Fig 4 Fig 5

Mo(CO)5NH3 Action Description of Action Audio narration 1.q1 one and two appear in sequence Q3 follwed by its answer appears Q4 appears The text in blue appears 5. Q5 appears Q6 appears followed by statements after it. The statement in black appears The fig 1appears The arrow appears and then molecule rotates clockwise by 90o about the axis Fig 2 comes up Figure 3 appears. The three planes appear one after the other after the question and its answer has to come. The molecule has a C4 axis of rotation. The molecule has a no other axis perpendicular to C4 axis. The highest symmetric axis is of C4, hence is the principal axis There are four reflection planes in the molecule. They have a Mo and CO and NH3 in the plane and has the principal axis There is no other reflection plane perpendicular to the principal axis Lets refer to chart aswell ( flow chart on master slide. The molecule possess a C4V symmertry point group. Q1. Is the molecule linear? No Q2. Is it a special symmetry? Q3. Does the molecule have a unique axis of rotation? YES! It’s a C4 axis !! And it is the highest rotation symmetry! It passes thru Mo , Co and NH3. Q4. Is there any other axis perpendicular to this axis? No!!!!. The principal axis is C4 Q5. Is there a plane of reflection? Yes!!! Hey there are four reflection planes all are equivalent. It contains Mo and one CO and NH3 and bisects the bond between two CO Q6. Is there any plane which is perpendicular to the principal axis? NO => The point group is C4v. Look that when one of the CO is replaced with NH3, the molecule changes its symmetry from octahedral to C4V. Fig 1 Fig 2 Fig 3

CH2CCH2 Allene Action Description of Action Audio narration 1.q1 one and two appear in sequence Q3 follwed by its answer appears Q4 appears The text in blue appears 5. Q5 appears Q6 appears followed by statements after it. Q7 appears followed by the answer The statement in black appears The fig 1appears without any axis shown The arrow appears and then molecule rotates clockwise by 180o about the axis Fig 1 Figure 2 appears Figure 2a appears. The two planes appear one after the other after the question and its answer has to come. Figure 3 appears The molecule has a C2 axis of rotation. The molecule has Two more C2 axis The highest symmetric axis is of C2, hence is the principal axis. But ther are more than one axis hence the molecule is of D symmetry. There are two reflection planes in the molecule. The molecule has an improper axis of rotation There is no plane perpendicular to principal axis, and has improper axis of rotation, hence is a D2d point groups Lets refer to chart aswell ( flow chart on master slide. The molecule possess a D4d symmertry point group. CH2CCH2 Allene Q1. Is the molecule linear? No Q2. Is it a special symmetry? Q3. Does the molecule have a unique axis of rotation? YES! It’s a C2 axis !! And it is the highest rotation symmetry! It has c=c=c . Q4. Is there any other axis perpendicular to this axis? Yes! two C2 axis, both axis passing through central c. There are no axis of higher order. Because there are two C2 axis , the molecule is of D type Q5. Is there a plane of reflection? Yes!!! Hey there are two reflection planes and are equivalent. It contains three carbons and two hydrogens Q6. Is there any other interesting feature? There is an S4 Axis!!! But there are other symmetry elements, so S4 point group is ruled out. Q7. Is there any plane which is perpendicular to the principal axis? No => There is no plane perpendicular to principal axis, and has improper axis of rotation, hence is a D2d point groups 90 o rotation Fig 1 Fig 2 Fig3 rotoreflection reflection C2’ After rotaion the hydrogen from one corner comes to another 14 Fig 2a Fig 4 σd plane

Summary The molecules possess different symmetry. They depend on the molecular structure. The various point groups are C1,C2—Cn, C2v, C3v… Cnv, C∞v D3h,D4h… Dnh, D ∞ h, Dnd Oh, Ih, Td, O, I, T, Th There can be molecules with no symmetry. It requires a great amount of practice to identifying these groups.

MCQ ( answers in red) What is the symmetry of CH2Cl2 ? a) C2v b) C3v c) C1 d) No symmetry What is the symmetry of CH3Cl ? a) C2v b) C3v c) D3h d) No symmetry What do you get after C4 and σh in allene? a) S4 b) Cant be predicted c) C4 d) σh Which of these is a special group? a) Octahedral b) Linear c) C5h d) D∞v What is the symmetry of CFHIBr ? a) Td b) T c) C4v d) No Symmetry

Glossory bond going into the plane Bond coming out of the plane Bond on the plane Rotation axis Reflection plane

References Reference website http://www.reciprocalnet.org/edumodules/symmetry/index.html Books: Chemical Application of Group theory, F A Cotton, 3rd edition, john Wiley and Sons., 1990 Group Theory and Chemsitry, David Bishop, Dover Publication, New York, 1973. Note to animator: There might be few places whre nomenclature of point groups might have been violated. Please ensure that the format is Axy : first letter caps, rest all small and subscript 18