1. Physics 3313 - Lecture 20 4/14/20101 3313 Andrew Brandt Wednesday April 14, 2010 Dr. Andrew Brandt 1.Molecules 2.Bonds 3.Energy Diagram

2. Molecules Except for inert gasses elements generally combine to form chemical compounds Basic unit is the molecule—group of neutral atoms held together strongly enough to act as a single particle Molecules can be studied by examining their absorption or emission spectra and through chemical properties Molecules of a certain type have definite composition and substructure Ex. Hydrogen always has 2 H atoms; water H 2 O; salt Na Cl If one atom is removed or another becomes attached then you have a different molecule with different properties If the energy of the molecule is > < or = to the sum of the atoms energy a molecule can be formed? < How are molecules formed? 4/14/20103313 Andrew Brandt2

3. Covalent Bond 4/14/20103313 Andrew Brandt3 Covalent bond-one or more pairs of electrons shared between two atoms. Electrons spend more time between the atoms leading to a net attractive force The attractive force of electrons counterbalances repulsive force of nuclei, leads to stable equilibrium for H 2 atom with a separation of 0.0742 nm and a total molecule energy of -4.5 eV. So if you add 4.5 eV the molecule will split into H+H

4. Consider Carbon Has 6 electrons -> shell half filled 4/14/20103313 Andrew Brandt4

5. Ionic Bond An ionic bond is formed between oppositely charged ions The electron is transferred from one atom to another, and the oppositely charged ions attract each other Example NaCl: Cl has 17 electrons so one more closes sub shell, while Na has 11 electrons so losing one also closes a shell, Na + and Cl - ions attract each other. Note the molecular structure of NaCl is an aggregate of ions, not as regular a molecular structure as covalent bond atoms. Some molecules not purely covalent or ionic: HCl, CL atom attracts shared electron more strongly than H (like kids some share better than others) 4/14/20103313 Andrew Brandt5

6. Simplest Molecule is H 2 + 4/14/20103313 Andrew Brandt6 This molecule is one electron shared by two protons If barrier is not too wide electron can tunnel between the two potentials If R=0.1 nm electron transits 1 quadrillion times a second. If R=1nm transits only 1/second According to uncertainty principal electron confined to a larger distance has less momentum and KE, so total energy of H 2 + electron is less than that of electron in H with an H + (proton) nearby, so if repulsion between protons not too great H 2 + could be stable

7. Symmetric Wave Functions for H 2 + Molecule 4/14/20103313 Andrew Brandt7 Solving Schrodinger Equation for this system is possible, but complicated. Start with conceptual approach considering symmetric wave function:

8. 4/14/20103313 Andrew Brandt8 Anti-Symmetric Wave Functions for H 2 + Molecule

9. Energy Approach for H 2 + 4/14/20103313 Andrew Brandt9