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Homework Problems Chapter 2

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    Homework Problems

    Section 2

    Exercise 1

    Determine all symmetry elements and all unique symmetry operations of the following molecules:

    a) clipboard_e71f7300705f7b7904b5a0b89f18fe779.png

    b) clipboard_efebe6cd6e367d21c8fec0ff81221db25.png

    c) clipboard_ec6d716280ffb6af79d86e00ad667fc4c.png

    d) clipboard_e6e30e5a7bf3d020369c9f6b67437fb94.png

    e) bromine tetrafluoride

    clipboard_e435e2924704b16af2b32201a136fe351.png

    f) Boric acid

    clipboard_e01b0688e37c31938126398654198b8ca.png

    g) Dinitrogen tetroxide

    clipboard_e463967c19a82be7bdfdede0f6b94670e.png

    h) clipboard_ecbb4b6bb7e0eaef2268d0ee0df142410.png

    i) clipboard_e20716edf8e97ac457409c5a6b68cfdbf.png

    j) clipboard_e88ddb4744defc08607e47dbf1cb09ff7.png

    k) clipboard_e719dc28e149072e9850c4033b70912c8.png

    l) clipboard_e3cf3ee5cfbc318500a2be02472b7ca93.png

    m) clipboard_e871960f99e3339d997345c72c463948f.png

    Answer

    a) clipboard_e962a28b06b99d54f7572f2628279fc0e.png

    b) clipboard_e7f7922ff821b7d5844c205f7d3c3cee3.png

    c) clipboard_e4ced8ed1d374a9244f35f22f4f767594.png

    d) clipboard_eb83f73a794a13f92ce18c660ea074c9f.png

    e) clipboard_eca143893b75677595f7d126e641af5a3.png

    f) clipboard_e244cdf8825017217c40e800f7ddc5fee.png

    g) clipboard_ee97073076dd4e89b512d238b008d8b9a.png

    h) clipboard_e05fc76638c04edbd6ee287d17acd7721.png

    i) clipboard_ef7531acc8de39264a5422dfc59208699.png

    j) clipboard_e192b512620da41d498a6599f8d1e268f.png

    k) clipboard_e6ce6f0f27a6da250332dac7bb611f439.png

    l) clipboard_e98e7131475761d8fcfe9d90c98543068.png

    m) clipboard_e808de1f3740e34bea31934a214f5765a.png

    Exercise 2

    When is a molecule chiral?

    a) It has no mirror planes

    b) It is has no inversion center

    c) It has no principal axis

    d) It has no rotation reflections (improper rotations)

    Answer

    d) It has no rotation reflections (improper rotations)

    Exercise 3

    If a molecule has a principal axis Cn , and n additional C2 axes standing perpendicular to Cn then it belongs to

    a) A dihedral point group

    b) A rotational point group

    c) A low symmetry point group

    d) A high symmetry point group

    Answer

    a) A dihedral point group

    Exercise 4

    Which of the following molecules are chiral:

    a) CH4

    b) CHCl3

    c) HCFClBr

    d) HOF

    e) BHFCl

    Answer

    c) HCFClBr

    Exercise 5

    Determine the point groups of the molecules at symmetry.otterbein.edu/challenge/index.html until you feel that you can determine point groups effortlessly

    Section 3

    Exercise 1

    Can the following matrices be multiplied and if so what is the product matrix?

    a) clipboard_ee003225be8f7545fa1ce75f331626e31.png

    b) clipboard_e04b8d38e78fc69bd28e9a49e448a6e98.png

    c) clipboard_e1730f815abaab9b88814318e888c791e.png

    d) clipboard_e29aff0c84c94bc09f70f45a78e315029.png

    Answer

    a) clipboard_e7c2253e759540050e8b0ddfe53c402a8.png

    b) clipboard_e70fac56aca366cd4521a45d3af60b2f1.png

    c) clipboard_e69ce2876684ac1d13682315aba75aa65.png

    d) clipboard_ee82ea61ae57d99e6005ac7f319cbe475.png

    clipboard_e283766480b38c6c9fb6dcd8675e86753.png

    Exercise 2

    Determine the irreducible representations for the following orbitals in the point group D2h.

    The z axis is defined as the axis of the principal C2 axis. C2’ is defined as the axis rotating around y. σv is defined as the xz plane.

    clipboard_e2e7c3633964e1cee3e46ae3e7e9b800b.png

    Answer

    clipboard_e306fd0853de3c93edcd7b4bdf17b0d75.png

    Exercise 3

    Determine the matrix representations of the symmetry elements of the following point groups:

    a) D2

    Define principal C2 axis as the axis running along z. C2’ runs along x.

    b) C3

    If we define the principal C3 axis running along the z axis:

    Answer

    a) clipboard_e578879db86d0697318d1299f4f3b7d67.png

    b) clipboard_e03a9b59108b1fb21786531b2cbde1c62.png

    Dr. Kai Landskron (Lehigh University). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate.

    This page titled Homework Problems Chapter 2 is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kai Landskron.

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