molecspec

molecspec - Principles of Molecular Spectroscopy What...

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Principles of Molecular Spectroscopy What variables do we need to characterize a molecule? Nuclear and electronic configurations: What is the structure of the molecule? What are the bond lengths? How strong or stiff are the bonds? What is the symmetry? Where is the electron density? Molecular Behavior: How much do the nuclei move (vibration/rotation)? How do the structural variables change with time? EXAMPLE: H-F What is your picture of the structure of this molecule? 2 nuclei + 10 e ? Molecular orbitals? ψ ab b H F ψ= c ψ+ c ψ 1 1 s 2 2 p z 1s ab H F ψ = c ψ c ψ 2pz 1 2 z ψ b We quantitatively characterize the structure through the electronic energy as a function of nuclear configuration: E elec 0 -D o b ψ ab ψ attractive forces repulsive forces H + F r e r E elec = electronic energy relative to isolated atoms 5.33 Lecture Notes: Principles of Molecular Spectroscopy Page 1
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If we characterize this energy curve, we have learned much about our molecule: 1) r e : What is the equilibrium separation between atoms? 2) D 0 : What is the strength of the bond? How stable is molecule? 3) Shape of ψ b or ψ ab : Is r e fixed? How stiff is bond? How does r e change if you put energy into bond? 4) Splitting between surfaces: What is the nature and energy of the e orbitals involved in bonding? How can you probe these energy surfaces with light? Light resonant with the motion of charged particles such as electrons or nuclei will be absorbed. We need rules for the frequency or energy of motion of nuclei and electrons. These will be related to the parameters above. What we will find is that different spectroscopies will tell us about different variables: Rotational spectroscopy: will tell us where r e is. Vibrational spectroscopy: will tell us how stiff the bond is and about the curvature of potential. Electronic spectroscopy: will tell us about where electronic states lie potential energy curves, barriers, dissociation energies Change to a new frame of reference - molecular coordinates z For any free particle (nucleus or electron): ¾ Kinetic and potential energy associated with the motion of a particle ¾ Translation along x, y, z n particles 3n degrees of freedom (d.o.f). y x In a molecule the positions of these particles is not independent. To solve problems in molecular structure and motion, chose a molecular frame of reference: ¾ Coordinates along symmetry axes ¾ Origin (often) at the center of mass r o = 1 m i r i M i 5.33 Lecture Notes: Principles of Molecular Spectroscopy Page 2
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To simplify problem, treat nuclear and electronic motion separately. Electrons are much lighter than nuclei. Therefore, we expect that the electrons will occupy a fixed distribution in space about a nuclear configuration.
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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molecspec - Principles of Molecular Spectroscopy What...

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