WEBVTT 00:14.070 --> 00:22.110 hello i hope all of you doing well so i welcome you to the day four of this course 00:22.110 --> 00:31.150 so we stopped in the last class after finishing the plane symmetry and 00:31.150 --> 00:37.040 we just started the center of universal so we will start from itself ok so what is 00:37.040 --> 00:44.390 the symmetry inversion or also known as center of symmetry inversion symmetry so inversion 00:44.390 --> 00:54.480 symmetry is is a point ok and this point may not contain any atom if i consider 00:54.480 --> 01:02.420 molecule so if i take any point or any point of molecule and pass it through that 01:02.420 --> 01:09.640 particular point and go equal distance on the other side i will find an equivalent point 01:09.640 --> 01:17.210 and then this you know center point or origin through which i am passing is known as center 01:17.210 --> 01:18.710 of inversion 01:18.710 --> 01:28.840 let me take an example ok so i showed you this model in the previous class this is 01:28.840 --> 01:36.220 the benzene right now you can look at this molecule pickup any hydrogen atom here so 01:36.220 --> 01:43.390 i am picking up an hydrogen atom right here then i am passing through the center of this 01:43.390 --> 01:49.060 molecule ok the center of this mass of thismolecule and then going equal distance what i am finding 01:49.060 --> 01:54.369 i am finding another hydrogen ok so this is just equivalent through the previous hydrogen 01:54.369 --> 02:00.500 and i take anything i take these point particularly ok i take this point and pass through this 02:00.500 --> 02:06.450 central point again i get another similar point over here so similarly you take point 02:06.450 --> 02:14.360 any were on this molecule ok you pass through this point of the center and you know why 02:14.360 --> 02:20.970 the same amount same distance you will find exactly similar point on the another side 02:20.970 --> 02:26.830 so this point here in the center for this particular molecule will be the inversion 02:26.830 --> 02:36.260 symmetry point ok or the center of inversion so you you can take many other molecules let 02:36.260 --> 02:43.829 me show you another example so this particular model that you can see you can see if it 02:43.829 --> 02:53.070 is zoomed little bit more then this is model for ethylene ok c double c and then 02:53.070 --> 03:01.840 four hydrogens here so you suppose you mark here one two three four then you take one 03:01.840 --> 03:08.420 and you start walking which this midpoint of this c c bond and then keep going in the 03:08.420 --> 03:15.630 same direction by same amount you will reach here right so similar thing will happen for 03:15.630 --> 03:21.549 the this hydrogen this will reach here and the other one sitting here will come here 03:21.549 --> 03:30.199 correct so if i have started with a b c and d then a will go to the position of c c will 03:30.199 --> 03:38.320 go to the position of a and b will take the position of d and vise versa so i have to 03:38.320 --> 03:55.180 start with a b c d now after having this inversion symmetry i have c d a and b ok so this point 03:55.180 --> 04:01.100 of the center of c c bond this particular molecule is the inversion symmetry or center 04:01.100 --> 04:02.889 of inversion ok 04:02.889 --> 04:11.540 so if you like in the last class toward the end i i told you that if i can select 04:11.540 --> 04:18.160 any point or a molecule which pauses center of inversion then you consider any even point 04:18.160 --> 04:24.310 not necessarily you have to you know consider aim an atom but you can consider 04:24.310 --> 04:31.000 any point on in given bond ok you will find the exactly same point on the other side of 04:31.000 --> 04:38.720 the molecule once you pass through that center of inversion ok so now if you consider 04:38.720 --> 04:47.440 the you know screen that is being played in front of you i take another example of 04:47.440 --> 04:56.280 molecule ok so you can take this molecule like here any transition metal complex like 04:56.280 --> 05:05.370 you know c o is to whole six ok ignoring the metal charge so this will form an complex 05:05.370 --> 05:11.850 so all the c o bonds ok and if i take this o each as a you known like a ball so each 05:11.850 --> 05:19.570 of the ball is like an o l or you take it like you know co cl six cobalt chloride so 05:19.570 --> 05:29.500 each of this is you can take it a chloride chlorine atom ok and center is an co cobalt 05:29.500 --> 05:36.470 now they will occupy an octitle geometric right so they will all the chlorine atoms 05:36.470 --> 05:43.310 will be disposed at you know or six fertilizes of an octitle so we have here like one two 05:43.310 --> 05:51.270 three four five six so one and six they are occupied axial positions while the chlorine 05:51.270 --> 05:59.220 atoms at two four three and five they are in the equatorial plane now all the cc o cl 05:59.220 --> 06:08.240 bonds are equal now having that in mind you start from chlorine one ok and we have a point 06:08.240 --> 06:14.520 right here at the center of this you know cobalt atom ok 06:14.520 --> 06:22.690 now if we start from this chlorine one and keep walking through this bond and come here 06:22.690 --> 06:29.920 to this point and then keep going in the same direction an equidistance you know then 06:29.920 --> 06:39.680 we end up having you know chlorine finding this six chlorine atom ok so similar thing 06:39.680 --> 06:47.889 will happen for three three will go to the place of atom five two will come to opposition 06:47.889 --> 06:53.010 of four and four will go to the opposition of two ok so five will come to the position 06:53.010 --> 07:02.090 of third chlorine atom and six and one will interchange the position of an this inversion 07:02.090 --> 07:12.270 symmetry operation so what will be the structure structure is shown here in this right so you 07:12.270 --> 07:18.840 can see i say one will go to the place of six and six will come to the opposition of 07:18.840 --> 07:23.950 one that's what exactly this happening right six and one they are interchanging their position 07:23.950 --> 07:30.050 so whenever you have an center of inversion and you want to operate that particular operation 07:30.050 --> 07:40.160 on in given molecular structure the rule of thumb is all the you known atoms or bonds 07:40.160 --> 07:48.210 which are dispose the on two different sides of this particular you know point in 07:48.210 --> 07:56.810 space they will interchange their positions right so we can see here two four three five 07:56.810 --> 08:04.620 one six they are all interchanging their position so knowing this which should be able to 08:04.620 --> 08:11.700 right the structure of any molecule after operating inversion symmetry operation if 08:11.700 --> 08:18.550 the molecule causes a center of inversion you cannot operate any symmetry operation 08:18.550 --> 08:26.570 on a molecule which does not have it right so for example we talk about this 08:26.570 --> 08:34.579 ch cl right so in case of chloroform do you think there is a center of inversion answer 08:34.579 --> 08:42.450 is no because there is no such point through which i can pass and no which an equivalent 08:42.450 --> 08:48.890 point on the other side ok suppose i want to start from this hydrogen i will not find 08:48.890 --> 08:55.270 another you know hydrogen on the other side if i even consider any point so their actually 08:55.270 --> 09:02.150 is no such point in this particular molecule which can invert the structure center of inversion 09:02.150 --> 09:06.960 the symmetry operation actually inverse the structure ok 09:06.960 --> 09:11.800 so this molecule does not have work but the other molecule that i should used at benzene 09:11.800 --> 09:20.560 and ethylene they have an symmetry operation known as center of inversion now here in 09:20.560 --> 09:28.330 when you screen you can see that i have tried to compare this inversion symmetry with another 09:28.330 --> 09:36.190 similar kind of a symmetry operation that is rotational symmetry of order two that is 09:36.190 --> 09:42.300 by using a access ok so i have a molecule exactly the one that i showed you earlier 09:42.300 --> 09:47.430 that is ethylene ok so i have an ethylene molecule so if you look at screen you can 09:47.430 --> 09:57.820 see that all this hydrogen atoms of ethylene they are marked by a b and c and d and then 09:57.820 --> 10:06.410 we can perform the symmetry operations i or c two on this two structures so here clearly 10:06.410 --> 10:12.450 i that is inversion operation will invert the structures so we will go to opposition 10:12.450 --> 10:17.589 of d and vise versa so will this d and c will interchange their positions so you 10:17.589 --> 10:24.730 will ultimately get this particular structure of a inversion symmetry inversion operation 10:24.730 --> 10:33.820 now c two on a first it you know gives you a feeling that it will end up doing a 10:33.820 --> 10:39.399 same thing but will it really do that lets have a look at it so if you look at on screen 10:39.399 --> 10:47.740 you can see that the c two access which is in the plain of the molecule so this c 10:47.740 --> 10:54.040 two is not perpendicular to the plane of the molecule but it is in the plain of the molecule 10:54.040 --> 11:01.950 so what will happen this c two will you known make a rotation of hundred and eighty degree 11:01.950 --> 11:10.480 so this a will now go to this place c will go to this place and others will come here 11:10.480 --> 11:19.760 and here so i should have a structure like this correct so though apparently i n c two 11:19.760 --> 11:26.120 you can think that ok they are similar but you can see this two structures when i 11:26.120 --> 11:32.260 marked them with a b and c and d you can see they end up in a two different structures 11:32.260 --> 11:41.529 but if i forget about a b and c this marking then this two structures are equivalent ok 11:41.529 --> 11:48.430 so they are in that sense all right so that's about the inversion symmetry so here also 11:48.430 --> 11:56.230 i suggest you to take some molecules particularly the molecule model and you try to look at 11:56.230 --> 12:01.000 the inversion symmetry points ok the center of inversion in the given molecule 12:01.000 --> 12:05.690 so more you practice to find out about the symmetry elements it will be more 12:05.690 --> 12:15.040 better for you so lets move to the next symmetry element that we need to learn so 12:15.040 --> 12:23.750 the next symmetry element is known as improper axis of rotation so this is a symmetry element 12:23.750 --> 12:36.350 which is uh symbol is s n s substrate n so now you know we have something on 12:36.350 --> 12:41.150 improper because initially we started with proper access of rotation and i told that 12:41.150 --> 12:47.970 ok find the meaning of this you know proper this term will be clear it will be 12:47.970 --> 12:54.430 more clear when i discus something which is improper and here we come so the name itself 12:54.430 --> 13:02.810 suggest that ok probably there is no such existence of and you know access in 13:02.810 --> 13:09.190 reality ok [less/lets] lets have a look at it [wat/what] what does it mean so lets look 13:09.190 --> 13:16.170 at the definition of this improper access of rotation so this improper access of 13:16.170 --> 13:22.350 rotation if i think about this particular operation first so this operation is not a 13:22.350 --> 13:31.600 single operation but this a combination of two operations one rotation and one one 13:31.600 --> 13:46.990 reflection ok so you take a molecule you you can find an access which actually 13:46.990 --> 13:57.140 may not be one of these you know c that means it may not be along any proper access of symmetry 13:57.140 --> 14:07.339 now you suppose you find such an access about which you can have a certain degree of rotation 14:07.339 --> 14:13.890 followed by a reflection on a plain which is perpendicular to that previous access of 14:13.890 --> 14:23.620 rotation and you end up getting and structures then this access that you choose will be called 14:23.620 --> 14:33.690 an improper access of symmetry ok or improper access of rotation and as i said it not it 14:33.690 --> 14:42.550 does not necessarily mean that this particular access will also co inside with a proper access 14:42.550 --> 14:51.339 of you know rotation and that is why it is called improper access of rotation so essentially 14:51.339 --> 15:00.700 if i if i can write this s n operation i should write it in this way so s n this 15:00.700 --> 15:21.160 is an improper access of rotation improper access of rotation ok so this s n is first 15:21.160 --> 15:33.880 rotation operation followed by and reflection and this reflection is such that this plain 15:33.880 --> 15:43.310 sigma plain perpendicular to this c n ok so i can write this is a perpendicular ok perpendicular 15:43.310 --> 15:50.240 to this c n ok many occasion you will find in many books [at/that] that this is written 15:50.240 --> 15:58.260 as sigma h which may not be grammatically correct because [I/as] as i say this improper 15:58.260 --> 16:08.459 access of rotation may not be you know a long the you know proper access of rotation so 16:08.459 --> 16:13.530 sigma h is defined with respect to the proper access of rotation ok the principle access 16:13.530 --> 16:15.350 of symmetry 16:15.350 --> 16:22.760 now if i have the perpendicular plain two that access of rotation that i am talking 16:22.760 --> 16:30.860 about for s n operation and if this c n does not lie in the same direction as that 16:30.860 --> 16:38.660 of the principle access of rotation then this sigma cannot be called sigma h even 16:38.660 --> 16:44.950 though day it is perpendicular to this access so internal i will call it like sigma perpendicular 16:44.950 --> 16:56.120 ok so s n is an operation which is done in this way c n followed by uh followed 16:56.120 --> 17:04.189 by as sigma plane and that will return you an in distinguishable structure lets take 17:04.189 --> 17:13.689 one particular example ok so that he it is creative so here on your screen we have 17:13.689 --> 17:22.589 the molecule called methane ok so this is not a model methane though so now lets 17:22.589 --> 17:31.539 concentrate on the molecule that is on your screen right now so you look at this molecule 17:31.539 --> 17:45.830 methane and a consider an access which bisects two h c h angles simultaneously ok 17:45.830 --> 17:52.730 so if i can show you that then it will be probably much better so i will show you 17:52.730 --> 17:57.299 using a model 17:57.299 --> 18:04.179 so this is what in shown on your screen so if you look at on this particular model which 18:04.179 --> 18:09.890 is the model for methane so you can see all red sticks represent this c h bonds 18:09.890 --> 18:17.700 now you can hold this molecule like this where you can see this c three you know access 18:17.700 --> 18:24.350 principle access of rotation but at the same time you can find the c two so c two will 18:24.350 --> 18:31.239 be like this like that one access passing through the middle of this angle right so 18:31.239 --> 18:37.759 you can see this angle if you if you oriented in such a way that you can see only c bond 18:37.759 --> 18:46.059 because the other one is such you know you know other c h bond and then 18:46.059 --> 18:51.450 this access obviously we cut this angle into half so essentially this access is cutting 18:51.450 --> 19:01.700 this angle and this angle into half so there i give a rotation it becomes like this so 19:01.700 --> 19:07.820 one twenty degree rotation will give you in indistinguishable structure that is 19:07.820 --> 19:08.820 a c two 19:08.820 --> 19:17.739 now that is fine now can i imagine an access to this one which will be an improper access 19:17.739 --> 19:26.239 of rotation answer is yes how so look at this properly so i am using that same c two ok 19:26.239 --> 19:33.139 i took an example which will be very easy to follow we can go to much complex structures 19:33.139 --> 19:38.159 as we and for the timing i should give the c two so that you can actually identify this 19:38.159 --> 19:47.090 s n access here also so i take an access through the same c two you know access here now instead 19:47.090 --> 19:55.779 of giving a c two rotation i give a rotation by ninety degree so what is do is about this 19:55.779 --> 20:00.889 access i give a ninety degree so [nine/ninety] ninety [if/if] if i give a ninety degree rotation 20:00.889 --> 20:10.639 this will go toward you right all right so now imagine a plain which is perpendicular 20:10.639 --> 20:18.899 to this access so any reflection will bring this molecule here this atom here and this 20:18.899 --> 20:26.490 angle will be like this now and this bond will be coming like this ok this will now 20:26.490 --> 20:33.470 go here and this bond will now go here because i am reflecting on a plain which is situated 20:33.470 --> 20:41.359 here so that will make the structure like this 20:41.359 --> 20:53.820 now if you just you know return to you know the this video couple 20:53.820 --> 21:00.169 of manys back then you will see we started with the structure so but doesnt mean i could 21:00.169 --> 21:08.389 find an access at a particular angle of rotation by which i can turn the molecule 21:08.389 --> 21:14.950 to structure which is not indistinguishable which is which is very much distinguishable 21:14.950 --> 21:23.440 but then if i give reflection perpendicular to that access then i get an indistinguishable 21:23.440 --> 21:31.250 structure so this combine effect of rotation followed by a reflection perpendicular to 21:31.250 --> 21:37.659 this access gives me an in structure now if you go back to the original definition 21:37.659 --> 21:45.169 of a symmetry operation we we said clearly that moment of a body which produces an distinguishable 21:45.169 --> 21:52.230 structure so obviously here this operation and rotation followed by reflection perpendicular 21:52.230 --> 21:59.229 to the rotational access if it gives an structure this is a symmetry element symmetry operation 21:59.229 --> 22:07.979 ok and then this all together c n sigma perpendicular as we showed here this all together 22:07.979 --> 22:13.879 solves the symmetry operations and that is denoted by s n so here i will also mention 22:13.879 --> 22:18.690 that a many times i am going back between these two terms symmetry operation and symmetry 22:18.690 --> 22:26.399 element i have discus what is what in my first or the second class so you should 22:26.399 --> 22:31.470 not be confused about symmetry element and symmetry operations and both symmetry elements 22:31.470 --> 22:38.730 symmetry operations are you know symbolize by the same letter so here this s n if i can 22:38.730 --> 22:44.259 find out suppose this particular molecule i will call this access as an s n access and 22:44.259 --> 22:52.289 then i can use this s n to symbolize as s n operation ok and then once i use it as an 22:52.289 --> 22:59.759 operation i change the molecular structure to another in indistinguishable you know 22:59.759 --> 23:04.989 this is the molecular structure to another distinguishable one ok 23:04.989 --> 23:16.620 so you have to practice a lot to find out if molecule has a improper access of rotation 23:16.620 --> 23:27.779 so now on your screen you have an example of generalized example of a some 23:27.779 --> 23:36.789 s n access so this n is [th/the] the order of rotation ok this pretty much similar to 23:36.789 --> 23:48.090 what we had in case of proper access of rotation so s n when n equals to one 23:48.090 --> 23:54.539 it would mean at three sixty rotation right and s two would mean hundred and eighty degree 23:54.539 --> 24:00.059 of rotation is s three would mean hundred and twenty degree and so on and in every cases 24:00.059 --> 24:06.739 it is implied that rotation about the particular angle followed by a reflection in to perpendicular 24:06.739 --> 24:19.700 plain so when i talk about s one ok so s one is c one followed by sigma perpendicular c 24:19.700 --> 24:25.269 one is nothing but identity so c one doesnt do anything and then we are left with a sigma 24:25.269 --> 24:32.460 perpendicular so if there is a any reflection perpendicular to this c one access if there 24:32.460 --> 24:39.299 is a access are imagine then essentially s one means nothing but reflection so if you 24:39.299 --> 24:45.229 if you see any where that somebody has use s one operation you know s one is nothing 24:45.229 --> 24:55.029 but you know operation by plain of symmetry ok so just an reflection on a 24:55.029 --> 24:56.029 plane 24:56.029 --> 25:05.090 now come to s two this is interesting s two is like a you look at the screen and suppose 25:05.090 --> 25:17.869 a molecule has an s two so what does mean so i will i will rotate by hundred and 25:17.869 --> 25:24.769 eighty degree so whatever was on this side it will now come back to this side correct 25:24.769 --> 25:30.470 because s n hundred and eighty degree rotation so it is a you know this part will come 25:30.470 --> 25:38.139 here now if i give a rotation what will happen so now after the c two it has come here now 25:38.139 --> 25:46.379 after the reflection on a perpendicular plain it will go here down here so essentially this 25:46.379 --> 25:52.759 two operations it produces you know it it actually inverse the position of this object 25:52.759 --> 25:59.479 which we started with ok so it goes over here so that means it will have an center of inversion 25:59.479 --> 26:06.919 so s two is necessarily inversion which exactly shown here so we start from this particular 26:06.919 --> 26:14.659 point give a an hundred and eighty degree rotation and then we will reflect it here 26:14.659 --> 26:27.789 now i cloud easily get it through an inversion symmetry ok so s two is nothing but center 26:27.789 --> 26:36.759 of inversion ok so you can go to like a s three if you look at so that will have 26:36.759 --> 26:45.859 a c three followed by sigma perpendicular s four as you showed we this methane molecule 26:45.859 --> 26:53.799 it will have c four followed by sigma perpendicular and so on ok so you can try to look at different 26:53.799 --> 26:59.720 molecular models and try to find out if try to find out what are the difference 26:59.720 --> 27:07.220 symmetry elements so by now i have showed you pretty much all the symmetry 27:07.220 --> 27:13.809 operations symmetry elements and and the symmetry operations that you can have 27:13.809 --> 27:16.220 in a given molecular structure 27:16.220 --> 27:23.100 now you should try finding out all though symmetry elements that are possible in a molecular 27:23.100 --> 27:34.070 structure ok so we are come to pretty end of this particular lecture 27:34.070 --> 27:40.630 so we have learned so far all the symmetry elements symmetry operations and we tried 27:40.630 --> 27:45.849 to find out some of the symmetry elements uh symmetry elements from some of the molecules 27:45.849 --> 27:55.580 now in a next step our intention is to find quantity way so that i can say 27:55.580 --> 28:01.399 we can talk about the nature of symmetry of a given molecule if one is you know higher 28:01.399 --> 28:10.139 symmetry then other or not and we should be able to utilize the symmetry elements present 28:10.139 --> 28:17.999 in a molecular structure in a proper way that can actually help me having application 28:17.999 --> 28:24.330 of this symmetry elements and operations so for that we need an mathematical frame work 28:24.330 --> 28:27.509 which is actually a group theory 28:27.509 --> 28:35.229 so in the following class we will try to learn what group theory is basic mathematical 28:35.229 --> 28:41.989 concept of group theory and then in the following classes we try to see how this 28:41.989 --> 28:48.909 symmetry is being you know assimilated into the group theory and how it helps us 28:48.909 --> 28:52.279 in solving various problems in chemistry 28:52.279 --> 28:54.799 thank you very much for your attention see you in the following class