chem2000_lecture01-02_molecular_orbitals_and_hydrogen

chem2000_lecture01-02_molecular_orbitals_and_hydrogen -...

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CHEMISTRY 2000 Topic #1: Bonding – What Holds Atoms Together? Spring 2012 Dr. Susan Lait
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2 Why Do Bonds Form? An energy diagram shows that a bond forms between two  atoms if the overall energy of the system is lowered when the  two atoms approach closely enough that the valence electrons  experience attraction to both nuclei: It is important to consider both the attractive and repulsive  forces involved!   Also, remember that atoms are in constant motion above 0 K.   Bonds are NOT rigid!
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3 The Quantum Mechanics of H 2 + To get a better understanding of bonding, it’s best to start with  the simplest possible molecule, H 2 + .  H 2 +  consists of: What forces do we need to consider? This is a three-body problem, so there is no exact solution. The nuclei are much more massive than the electrons (1 u for a  proton; 0.0005u for an electron).  To simplify the problem, we  use the  Born-Oppenheimer approximation .  We assume that  the motion of the nuclei is negligible compared to the motion of  the electrons and treat the nuclei as though they were immobile.
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4 The Quantum Mechanics of H 2 + If we set the internuclear distance to R, we are then able to  solve for the wavefunction of the electron in H 2 +  and its energy: This is possible because H 2 +  has only one electron and simple  (cylindrically symmetric) geometry.  The resulting ground-state  orbital looks like this: Electron energy = kinetic energy + electron-nuclear attraction
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5 The Quantum Mechanics of H 2 +
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chem2000_lecture01-02_molecular_orbitals_and_hydrogen -...

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