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Unit 5: Quantum Chemistry: Molecular Structure   In our daily life, only certain rare gasses exist as single atoms (e.g., helium, etc).  The matter and materials we deal with everyday are mainly in their molecular (e.g., plastics or gasoline), crystalline (salt), or metallic (aluminum cans) state.  In these states, atoms of one or more elements combine to form larger molecules, crystals, and so forth.  In this unit, you will start to go over techniques of quantum chemistry designed to study large molecular systems.  Of course, you will start from simple models, such as the H2+ molecule-ion and the H2 molecule.  Bonds will initially be described in terms of Valence Bond Theory before approaching the Molecular Orbital Model.

Unit 5 Time Advisory
This unit will take you 14.5 hours to complete.

☐    Subunit 5.1: 2 hours

☐    Subunit 5.2: 4.5 hours

☐    Subunit 5.3: 3 hours

☐    Subunit 5.4: 5 hours

Unit5 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

  • Account for more than of nucleus and additional electrons in the wavefunction of the system.
  • Identify the parameters necessary for energy calculations for the hydrogen molecule/ion.
  • Explain the difference in terms of energy calculations between homonuclear and heteronuclear and diatomic molecules.
  • Apply the Born-Oppenheimer approximation to energy calculations.
  • Describe bonding using Molecular Orbital Theory for diatomic and polyatomic molecules.
  • Describe and compare new techniques of approximations such as the Huckel Approximation, Hartree-Fock method, and Density Functional Theory.

5.1 Separating Electronic and Nuclear Motion  

  • Reading: Boston University: Professor Dan Dill’s “Molecular Structure: Separating Electronic and Nuclear Motion” Link: Boston University: Professor Dan Dill’s “Molecular Structure: Separating Electronic and Nuclear Motion” (PDF)
     
    Instructions: For Professor Dill’s notes, please click on the link above, scroll down to the italic heading “Molecular Structure: Separating Electronic and Nuclear Motion,” and select the hyperlink next to this heading to download the PDF file.  Please read the entire text (4 pages).  Pay attention to how and why the motion of nuclei in a molecule can be separated from the motion of electrons.  Studying this resource should take approximately 2 hours to complete.  Note that this resource also covers the material you need to know for subunits 5.1.1–5.1.2.  

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.1.1 Adiabatic Approximation   Note: This subunit is covered by the readings assigned beneath subunit 5.1.  In particular, please focus on pages 1–2 to learn about the adiabatic approximation.

5.1.2 The Born-Oppenheimer Approximation   Note: This subunit is covered by the readings assigned beneath subunit 5.1.  In particular, please focus on pages 3–4 to learn about the Born-Oppenheimer approximation.

5.2 Molecular Orbitals Theory  

  • Reading: MIT’s OpenCourseWare Professor Griffin and Professor Voorhis’s Physical Chemistry: “Molecular Orbital Theory – Part I” and “Part II” and “Modern Electronic Structure Theory” Links: MIT’s OpenCourseWare: Professor Griffin and Professor Voorhis’s “Molecular Orbital Theory – Part I” and “Part II” and “Modern Electronic Structure Theory” (PDF)

    Instructions: Please click on the links to download the PDFs. In these resources, you will learn how to carry out a linear combination of atomic orbitals to form molecular orbitals and how to compute the energies of these molecular orbitals.  Please read these three PDFs in their entirety (11 pages, 14 pages, and 8 pages, respectively).  Studying these resources should take approximately 4.0 hours to complete.

    Terms of Use: Terms of Use: Robert Guy Griffin and Troy Van Voorhis, Physical Chemistry 5.61, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed August 16, 2012). License:Creative Commons BY-NC-SA 3.0. The original version can be found here.

  • Reading: Everyscience.com’s “Molecular Orbital Theory” Link: Everyscience.com’s “Molecular Orbital Theory” (HTML)

    Instructions: Please click on the “Molecular Orbital Theory” link and read this webpage for a glance at MO Theory.  Pay attention to the difference between a bonding and an antibonding molecular orbital.  Studying this resource should take approximately 0.5 hours to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.3 Molecular Orbitals Description of Diatomic Molecules   5.3.1 The Hydrogen Molecule  

  • Reading: University of Waterloo: Professor Chung (Peter) Chieh’s “Molecular Orbitals of H2” Link: University of Waterloo: Professor Chung (Peter) Chieh’s “Molecular Orbitals of H2” (HTML)
     
    Instructions: Please read the webpage.  While studying this resource, reproduce the LCAO and build your own MO energy diagram.  Studying this resource should take approximately 1 hour to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.3.2 Bonding in Homonuclear of Diatomic Molecules  

  • Reading: Cartage.org’s “Molecular Orbitals of Homonuclear Diatomics” Link: Cartage.org’s “Molecular Orbitals of Homonuclear Diatomics” (HTML)
     
    Instructions: Please read the webpage.  While studying this resource, reproduce the LCAO and build your own MO energy diagram.  In contrast to the hydrogen molecule MO (subunit 5.3.1) that was built just using the H 1s atomic orbitals, these MOs are constructed using a larger set of atomic orbitals, resulting in a more complex MO diagram.  Studying this resource should take approximately 1 hour to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.3.3 Bonding in Heteronuclear Diatomic Molecules  

  • Reading: Institut für Physikalische und Theoretische Chemie der Technischen Universität Carolo – Wilhelmina zu Braunschweig’s “Heteronuclear Molecules AB” Link: Institut für Physikalische und Theoretische Chemie der Technischen Universität Carolo – Wilhelmina zu Braunschweig’s “Heteronuclear Molecules AB” (HTML)
     
    Instructions: Please read the webpage.  While studying this resource, reproduce the LCAO and build your own MO energy diagram.  In contrast to subunit 5.3.2, these MOs have an “unsymmetrical” look, as they have been built using atomic orbitals from different atoms, thus with different energies.  Studying this resource should take approximately 1 hour to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.4 Molecular Orbitals Description of Polyatomic Molecules   5.4.1 The Huckel Theory and Applications  

  • Reading: Oxford University: Professor Mark Brouard’s “Huckel Theory for Polyatomic Molecules” Link: Oxford University: Professor Mark Brouard’s “Huckel Theory for Polyatomic Molecules” (PDF)
     
    Instructions: Please click on the link and select the “Notes for lectures 7 and 8” link under the “Valence” section to access the PDF file and visualize some practical applications of the Huckel Theory to molecules with conjugated bonds.  Please read this entire lecture (11 pages).  Studying this resource should take approximately 1 hour to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: Tennessee Tech University: Professor Northrup’s “Huckel Molecular Orbital Theory (HMO Theory)” Link: Tennessee Tech University: Professor Northrup’s “Huckel Molecular Orbital Theory (HMO Theory)” (PDF)
     
    Instructions: Read these lecture notes to learn about Huckel Theory. 

    Studying this resource should take approximately 1 hour.  
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.4.2 Self-Consistent Field (Hartree-Fock Method) Calculations and Density Functional Theory  

  • Reading: Cambridge University: Professor Nicholas Handy’s “Self Consistent Field Theory” Link: Cambridge University: Professor Nicholas Handy’s “Self Consistent Field Theory” (HTML)
     
    Instructions: Please click on the “Self Consistent Field Theory” link above, and read Professor Handy’s webpage to learn about self-consistent field theory.  Studying this resource should take approximately 3 hours to complete.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: The Saylor Foundation’s “Assessment 9” Link: The Saylor Foundation’s “Assessment 9” (DOC)
     
    Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
     
    Completing this assessment should take approximately 1 hour.