ࡱ> 7 3bjbjUU "7|7|'lZZZZZZZnnH h#h#h#h#h#h#h#GGGGGGG$K MGZh#h#h#h#h#G#ZZh#h#sH###h#Zh#Zh#G#h#G# #,8?ZZ(Ah# nh#?(AH0H?6Nh#FN(A#nnZZZZCHEM 481 Spring 2003 Homework 1 Chapter 4 What are four basic symmetry elements and operations? Answer: A symmetry operation is the process of doing something to a shape or an object so that the result is indistinguishable from the initial state Identity (E) Proper rotation axis of order n (Cn) Plane of symmetry (s) Improper axis (rotation + reflection) of order n (Sn), an inversion center is S2 Identify the symmetry elements in NH3, H2O, CO2, CH4, and BF3. E2C3 (z)3 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v NH3 EC2 (z) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(xz) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(yz) H2O E2C INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET ... INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET vi2S INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET ... INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET C'2CO2 CH4 E8C36C26C43C2 =(C4)2i6S48S63 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h6 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET dE2C3 (z)3C'2 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h (xy)2S33 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET vBF3 Identify the symmetry elements and operations present in each of the following molecules: NH3 C3vE2C3 (z)3 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v H2O C2vEC2 (z) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(xz) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(yz) CO2 D INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET hE2C INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET ... INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET vi2S INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET ... INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/infinity.gif" \* MERGEFORMATINET C'2 CH4 OhE8C36C26C43C2 =(C4)2i6S48S63 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h6 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET d BF3 D3hE2C3 (z)3C'2 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h (xy)2S33 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v Chloroform  1,3,5-trichlorobenzene  Chair and boat cyclohexane  B2H6  Planar trans-H2O2  [Re2Cl8]2  The octahedral complex [Co(NH3)5(OH2)]3+, ignoring the hydrogen atoms  The room temperature form of elemental sulfur, S8  Identify symmetry elements and assign the point group of NH2Cl, SF4, PCl5 and SF6. CsE INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET hNH2Cl SF4 (sea-saw) C2vEC2 (z) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(xz) INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v(yz) PCl5 D3hE2C3 (z)3C'2 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h (xy)2S33 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET v SF6. OhE8C36C26C43C2 =(C4)2i6S48S63 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET h6 INCLUDEPICTURE "http://www.mpip-mainz.mpg.de/~gelessus/pics/sigma.gif" \* MERGEFORMATINET d Using symmetry elements and point groups predict the polarity/non polarity and optical activity achirality of molecules in problem 3 and 4. (a) NH3 (b) H2O (c) CO2 (d) CH4 (e) BF3 (f) Chloroform (g) 1,3,5-trichlorobenzene (h) Chair and boat cyclohexane (i) B2H6 (j) Planar trans-H2O2 (k) [Re2Cl8]2 (l) The octahedral complex [Co(NH3)5(OH2)]3+, ignoring the hydrogen atoms (m) The room temperature form of elemental sulfur, S8 NH3C3vH2OC2vCO2DahCH4OhBF3Point GroupPolarityChiralityChloroform , CHCl3C3vyesno1,3,5-trichlorobenzene D3hnonoChair cyclohexaneD3dnonoBoat cyclohexane C2vyesnoB2H6 D2hnonoPlanar trans-H2O2 C2hyesno[Re2Cl8]2D4hnonoThe octahedral complex [Co(NH3)5(OH2)]3+, ignoring the hydrogen atomsC4vyesnoThe room temperature form of elemental sulfur, S8D4hnono Determine the point group to which each of the following belongs: CCl4 (b) Benzene (c) Pyridine (d) Fe(CO)5 (e) Staggered and eclipsed ferrocene, (h5-C5H5)2Fe (f) Octahedral W(CO)6 (g) fac- and mer-Ru(H2O)3Cl3 CCl4: Td  Benzene: D6h  Pyridine: C2v  Fe(CO)5 D3h  Ferrocene Staggered: D5d  Ferrocene Eclipsed: D5h  (Octahedral W(CO)6 Oh  Ru(H2O)3Cl3 fac: C3v  Ru(H2O)3Cl3 mer: C2v Water, H2O belongs to C2v point group. Using character table for C2v,what are the symmetry labels of atomic orbitals, 2s, 2px, 2py, 2pz) on O atom and the two linear combinations of two atomic orbtials (two 1s) of hydrogen atoms.  INCLUDEPICTURE "F:\\Inetpub\\wwwroot\\chem481\\481HW\\Image45.gif" \* MERGEFORMATINET  based on x2,y2, z2 2s : a1 Based on translationbal symmetry z 2pz: a1 Based on translationbal symmetry x 2px: b1 Based on translationbal symmetry y 2py : b2 Two linear combinations of two atomic orbtials (two 1s) of hydrogen atoms. a 1 symmetry:  b2 symmetry:  Construct a molecular orbital diagram for H2O from the information you obtained in previous question The symmetry operators of the C2v group all commute with each other (each is in its own class). Molecualr orbitals should have symmetry operators E, C2, sv1, and sv2. Building a MO diagram for H2O Symmetry of a1 orbital of H2O  INCLUDEPICTURE "http://138.47.34.166/chem481/image7V4.JPG" \* MERGEFORMATINET  Symmetry of b1 orbital of H2O  INCLUDEPICTURE "http://138.47.34.166/chem481/imageBB2.JPG" \* MERGEFORMATINET  Symmetry of b1 orbital of H2O, cont.  INCLUDEPICTURE "http://138.47.34.166/chem481/image8IA.JPG" \* MERGEFORMATINET  Symmetry of b2 orbital of H2O  INCLUDEPICTURE "http://138.47.34.166/chem481/image20U.JPG" \* MERGEFORMATINET  Symmetry of b2 orbital of H2O, cont.  INCLUDEPICTURE "http://138.47.34.166/chem481/imageDV5.JPG" \* MERGEFORMATINET  MO diagram for H2O  INCLUDEPICTURE "http://138.47.34.166/chem481/imagePD7.JPG" \* MERGEFORMATINET  INCLUDEPICTURE "http://138.47.34.166/chem481/imageJEQ.JPG" \* MERGEFORMATINET  How many molecular vibrations a non-linear molecule containing N atoms would have? If the molecule has N atoms then we need 3N displacement coordinates to fully describe all possible motions, ie each atom's movement may be described by giving the components of its displacement (from the stable geometry) along the x, y and z directions. Therefore the sum of the number of modes of translation + of rotation + of vibration = 3N NUMBER OF MODES OF VIBRATION Vibrational modes = 3N - (the number of modes of translation) - (the number of modes of rotation) How many translations are there? The molecule as a whole can move along the x, y or z direction, so we have 3 translations. How many rotations are there? FOR A NON-LINEAR MOLECULE:The molecule as a whole can rotate around the x, y or z direction, so we have 3 rotations. BUT, FOR A LINEAR MOLECULE: The molecule has only 2 axes around which to rotate, the third is chosen to point along the molecular linear axis. (Rotation about the molecular axis must be, if you think about it, some combination of electronic orbital and nuclear spin motions. As such it is not regarded as part of molecular rotation). So we have 2 rotations. How many vibrations are there? FOR A NON-LINEAR MOLECULE of N atoms: 3N-6 FOR A LINEAR MOLECULE of N atoms: 3N-5 Determine the number of degrees of vibrational freedom for each of the following: SO2 SiH4 HCN H2O BF3 Solution: The number of vibrational degrees of freedom of a molecule with N atoms is given by 3N-6 for a nonlinear molecule and 3N-5 for a linear molecule. Nonlinear molecule, 3 atoms - 3 Nonlinear molecule, 5 atoms 12 Linear molecule, 3 atoms 4 Nonlinear molecule, 3 atoms 3 Nonlinear molecule, 4 atoms 6 The molecule BF3 has symmetry D3h. It has 6 vibrations of symmetry, A1, E, E, and A2" (remember that E vibrations are doubly degenerate and count as two vibrations). Which ones are IR active? BF3 has symmetry D3h . Tt is nonlinear molecule, (3N-6) N= 4 atoms  6 vibtational modes BF3 (trigonal planar) The reducible representation for B is D3hE2C33C2sh2S33sv1201301 Symmetries of the normal modes. Activity of each mode in the infrared. Activity of each mode in the infrared. Determine the symmetries of each of the following types of internal modes: B%F stretching modes; Out-of  plane bending motions; F%B%F angle deformations. Since the normal modes transform as A1 , E , E , and A2", observing that A2" and E' are IR-active, while A1' , E' and E" are Raman-active, the number of active modes are 1*1+2*2 = 3 in IR (2 are double degenerate), and 1*1+1*2+1*2 = 5 in Raman (4 are double-degenerate). 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