ࡱ>  "'` =bjbjLULU .F.?.?cbbbbbbb[[[[ \4 n4^oooooooEGGGGGG$`hțkAbroorrkbbooxxxrboboExrExxbbӍo(^ 7̵[ ^ _ u v i j  " # 2 3 | } ABno01CDij"#vw  VWb hNsH* hNs6] hNs0JjhNsUhNs hNs0JWu aFo'=((,0"22335 & Fdd[$\$gdNs & Fdd[$\$gdNs & Fdd[$\$gdNs^gdNsgdNsgdNsgdNs=bcvw"#9:,-  ababc  ¼¼¼ hNs0JhNs0J5\jxhNsB*UphhNsB*phjhNsB*Uph hNs0JhNsjhNsUJ"$FH/01  \]lmop()56`aιάۦꟚۦۦۦۦ hNsH* hNs5\ hNs0JjhNsB*UphjhNsB*UphhNsB*phjhNsB*UphjhNsU hNs6]hNshNs0J5\hNs0J6]: M N ] ^ !!!!6!7!!!!!!!&"'">"?"##Y#Z#l#m##### $ $_$`$$$$$$$%%)%*%9%:%u%v%{%|%%% & &&&-&.&&&&&&&&&''''b'c'z'{''' hNs0JjhNsUhNs hNs0JH* hNsH*jhNsH*UU'#($(;(<(=(>(((((((=)>)F)G)y)z)))))));*<*N*O*^*_*******++++(+)+r+s+{+|+++++++,,X,Y,b,c,,,,,,,,,N-O-e-f-k-l-----7.8...........J/K//j(hNsU hNs0JjhNsUhNs[//////00%0&02030{0|000000000007181C1D111222 2"2#2]2^2_22222222333z3{3|3}3~333&4'42434;4<444444ʵʨjJhNsB*UphjrhNsB*UphhNsB*phjhNsB*Uph hNs0JH* hNsH*jhNsH*UhNs hNs0JjhNsUB4455/50545555555555555]6^6666666O7P7`7a7N8O88888888899 9 9X9Y9f9g9q9r9999999::':(:-:.:::::::;;;;7;8;;;;;;;W<X<`<a<f<g<<<<<==\=]=o= hNs0JhNsjhNsU^59f>>b??e@@ CCoDE}FRGHKsOPR VX & Fdd[$\$gdNs & Fdd[$\$gdNs & Fdd[$\$gdNsgdNs & Fdd[$\$gdNs & Fdd[$\$gdNso=p=u=v=======P>Q>c>d>f>g>h>>>>>>>>>>L?M?`?a?b?c???????G@H@c@d@e@f@g@@@@@@@@@@1A2A3A4AAAAAAAAASBTB\B]B C CRCSCTC̼̼hNs0J5\ hNs5\jhNs5U\ hNs0JjhNs0JU hNs0J hNs0JhNsjhNsUJTCUCVCWCCCCCCC D D D DDD_D`DmDnDoDpDDDDDDDEE&E'E+E,EEEEEEEEEEEFFqFrFzF{F}F~FFFFFFF+G,Ghamanaoapaaaaaaabb b bHbIbObPbQbRbnbbbbbbccccccccccdd"d#d$d%d&dmdndwdxdddddlemeqereseteeeeeeCfDfffffffffffffCgDgRgSg\gjhNsUhNs0J6]hNs hNs0J< hNs0JjhNs0JU hNs0JQ\gmgogpggggggg`hahehfhghhhhhhhhhfigikiliminiiiiiiiiiiiijj4j5j~jjjjjk,kIkJkkkkkkk:l;lHlIlJlnlllllmm&m'm)m*mmmmmm hNs6]jhNsUhNs hNs0J< hNs0JjhNs0JU hNs0JhNs0J6]Nmm"n#n4n5n6n7nSn_nrnsnnnnnnncodoqorosooopppvpwppppp q qqqqqqqqqqqqqqr?r@rGrHrIrJrerrrrrr"s#s=s>s@sAsssssss9t:tKtLtNtOtthNs0J5\hNs0J6]hNs hNs0J< hNs0J hNs0JjhNs0JUPttttttttuuuu]u^u`ubuuuuuuuuuu\v]vvv#w$wewfwwwwwwwwwwwwxxxxxxxyyyy"y#y/y0yKyNyQyYykylyyyyy9z*OJQJ^JhNsH*OJQJ^JhNsOJQJ^JhNsCJHOJQJ^JaJHhNs hNs0J hNs0JjhNs0JUDxyy#y0yLyNylyyy:z*CJ$OJQJ^JaJ$hNsCJ$OJQJ^JaJ$?}}}}}#~$~%~&~'~H~I~d~e~f~~~~~~~~~~~~fgbdhj "ʂ̂΂Ђ҂vxƒ؃ڃ܃IJKLMٻٳٳٳٳٳٳhNsOJQJhNs>*OJQJ^Jj~hNsUhNsH*OJQJ^JhNsOJQJ^JjBhNsUhNsjhNsUjhNsUFgj"҂L4 $$Ifa$gdNsgdNsgdNsM ކ012345 stcdڜhNs>*OJQJ^JhNsCJaJj hNsUj\hNsUjjhNsUhNsOJQJhNsH*OJQJ^JhNsOJQJ^Jj8hNsUj:hNsUjhNsUhNs<tg č8$a$gdNsgdNsgdNsgdNsakd $$IfF m+ rrr: 6    34aytNsdefgtu?@ "čƍ68띎hNsCJH*OJQJ^JaJhNsCJOJQJ^JaJjR1hNsUjr%hNsUjhNsUhNsOJQJhNs>*OJQJ^JhNsH*OJQJ^JhNsOJQJ^JhNsjhNsUjhNsU8ďȏʏЏҏtv~ΐАҐ6789:25bcٓړ02RTbdflnp8:<>@L׿jzIhNsUjBhNsUj6<hNsUjhNsUhNshNsH*OJQJ^JhNsOJQJ^JhNsOJQJJА:35cړn@z~ $$Ifa$$IfgdNsgdNsgdNsLN24 xƗȗʗ̗ΗЗҗԗ֗ؗڗܗޗպպղպպղպպղպպղպhNsCJaJhNsOJQJ hNsH*jUhNsOJQJU^JhNsj?ShNsOJQJU^JhNsOJQJ^JjhNsOJQJU^JFE<<<<< $$Ifa$kdV$$Ifra8 0B 634abytNs—ƗΗԗE<<<<< $$Ifa$kdW$$Ifra8 0B 634abytNsԗ֗ܗE<<<<< $$Ifa$kdX$$Ifra8 0B 634abytNs E<<<<< $$Ifa$kdKY$$Ifra8 0B 634abytNs И֘ ԙؙ֙ڙܙ45"#$%12ǛțOP)*BRWβΤΖ܉hNs>*OJQJ^JUj?_hNsOJQJU^Jj]hNsOJQJU^JjM\hNsOJQJU^JjZhNsOJQJU^JjhNsOJQJU^JhNsOJQJ^JhNsCJaJhNsOJQJhNs hNsH*6Ҙ֘ޙE@;@;@gdNsgdNskdZ$$Ifra8 0B 634abytNsțP* $$Ifa$$a$gdNsgdNsgdNsgdNs Certain symmetry operations can be present simultaneously, while others cannot. There are certain combinations of symmetry operations which can occur together. Symmetry Groups combine symmetry operations that can occur together. Symmetry groups contain elements and there mathematical operations. For example, one of the symmetry element of H2O is a C2-axis. The corresponding operation is rotation of the molecule by 180 about an axis. Point Groups Low Symmetry Groups C1: only E  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image26.gif" \* MERGEFORMATINET Cs: E and s only  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image27.gif" \* MERGEFORMATINET Ci: E and i only  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image28.gif" \* MERGEFORMATINET Cn, Cnv, Cnh Groups Cn: E and Cn onlyC2:  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image29.gif" \* MERGEFORMATINET C3:  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image30.gif" \* MERGEFORMATINET  Cnv: E and Cn and n sv'sC2v: E, C2, 2 sv H2O C3v: E, C3, 3 sv NH3 C v: E, C , sv HF, HCN Cnh: E and Cn and sh (and others as well)C2h: E, C2, sh, i  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image31.gif" \* MERGEFORMATINET Dn, Dnv, Dnh Groups Dn: E, Cn, n C2 axes ^ to CnD3: E, C3, 3 ^ C2 [Co(en)3]3+  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image32.gif" \* MERGEFORMATINET  Dnh: E, Cn, n C2 axes ^ to Cn, shD3h: E, C3, 3 ^ C2, sh  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image33.gif" \* MERGEFORMATINET  D3h: E, C3, 3 ^ C2, sh eclipsed ethaneD6h: E, C6, 6 ^ C2, sh  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image34.gif" \* MERGEFORMATINET WX`azCDEFGHIJMORT۸۸ۨ۸۸ۨے۸۸ۨjmhNsU hNsQJjfhNsUhNsOJQJhNsCJaJj`hNsUjhNsUhNs5H*OJQJ\^JhNs5OJQJ\^JhNshNs>*OJQJ^JhNsOJQJ^JhNsH*OJQJ^J6 $$Ifa$jkdZf$$IfT0634abytNsTG $$If^a$ $$Ifa$jkdql$$IfT0634abytNsTGH\n $$Ifa$$a$gdNsjkdks$$IfT0634abytNsTT[\]^ghmnoprstuGHIJKLNOQZ[  (*,02468<HJRTV\^`b򼴼򼬼hNsOJQJjU}hNsUjthNsUjhNsUhNsCJaJhNsH*OJQJ^JhNs5H*OJQJ\^JhNs5OJQJ\^JhNshNsOJQJ^J?not $$Ifa$jkd t$$IfT0634abytNsTK $$Ifa$jkd|$$IfT0634abytNsTKLN $$Ifa$$a$gdNsjkdۅ$$IfT0634abytNsT 6` $$Ifa$jkd{$$IfT0634abytNsTbdfhtv|~  ",.:<FHJLNȽйнȽйнȽйнннйнннj[hNsUjhNsU hNs<hNsCJaJhNshNsH*OJQJ^JhNsOJQJhNsOJQJ^JhNs5H*OJQJ\^JhNs5OJQJ\^JhNs5OJQJ\= $$Ifa$$a$gdNsjkd$$IfT0634abytNsT $$Ifa$jkd$$IfT0634abytNsTJ $$Ifa$$a$gdNsjkd$$IfT0634abytNsTJLpZ $$Ifa$jkd$$IfT`0~634abytNsTNP\^fhln~RTVXZ\^`dpr|~ооЮЮооЮ hNsQJjhNsUhNs5OJQJ\^J hNs<hNsCJaJjVhNsUjhNsU hNsH* hNsH*hNshNsOJQJhNsH*OJQJ^JhNsOJQJ^JhNs5H*OJQJ\^J8Z\^ $$Ifa$$a$gdNsjkdC$$IfT`0~634abytNsT $$Ifa$jkd$$IfTR0~634abytNsT $$Ifa$ $$If^a$jkdZ$$IfTR0~634abytNsT $&(*,$$$$ $ $$$ $"$$$&$*$,$0$2$4$6$8$%%%ļĴĴļĴĴjhNsUhNs5OJQJ\U hNsQJjhNsUjhNsUhNsCJaJhNshNsOJQJhNsH*OJQJ^JhNsOJQJ^JhNs5H*OJQJ\^JhNs5OJQJ\^J9* $$Ifa$jkd$$IfTR0~634abytNsT6$%% $$Ifa$ $$If^a$jkdM$$IfTR0~634abytNsT D h: E, C , ^ C2, sh  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image35.gif" \* MERGEFORMATINET  H2 Dnd: E, Cn, n C2 axes ^ to Cn,  D3d: E, C3, 3 ^ C2, 3 sd staggered ethaneSn Group S2n: E, Cn, S2n (no mirror planes) S4, S6, S8, etc. (Note: never S3, S5, etc.)S4: E, C2, S4  INCLUDEPICTURE "http://chemistry.rutgers.edu/undergrad/chem207/img/Image36.gif" \* MERGEFORMATINET High Symmetry Cubic Groups, Td, Oh, Ih Td: E, 8 C3, 3 C2, 6 S4, 6 sd Tetrahedral stru%%% % %%%%%%&%(%2%4%@%B%L%N%R%T%V%X%\%^%b%n%p%x%z%~%%%%%%%%%%%%%%%%%%%& & &&&&&&H&J&P&R&`&b&d&f&h&t&v&|&~&ɻ֭ɻɻɻ hNsQJhNsOJQJhNs5H*OJQJ\^JhNs5OJQJ\^JhNsCJaJhNsH*OJQJ^JhNsOJQJ^JhNsjhNsUD%%%T% $$Ifa$$a$gdNsjkd$$IfTR0~634abytNsTT%V%%% $$Ifa$ $$If^a$jkd!$$IfTR0~634abytNsT%%% &b& $$Ifa$$a$gdNsjkd$$IfTR0~634abytNsTb&d&&R' $$Ifa$jkda$$IfT0634abytNsT~&&&J'L'N'P'R'T'''''''''''''''''''''(8 88888888888888888889 9 9999 9"9$9&9P9R999999:´ڬڪ´ڬڬUhNsOJQJhNs5H*OJQJ\^JhNs5OJQJ\^JhNsH*OJQJ^JhNsOJQJ^JhNsCJaJjhNsUjhNsUhNsCR'T'''888~~$If $$Ifa$$a$gdNsjkd$$IfT0634abytNsTctures No need to identify all the symmetry elements - simply recognize Td shape. methane, CH4Oh: E, 8 C3, 6 C2, 6 C4, i, 6 S4, 8 S6, 3 sh, 6 sd Octahedral structures No need to identify all the symmetry elements - simply recognize Oh shape.  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