Chem 125 Lecture 10 9/27/06 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed further. It is not readily understood without reference to notes from the lecture.

Exam :30-11:30 Friday, Sept. 29 ! Covers Lectures through Today Including: Functional Groups X-Ray Diffraction 1-Dimensional Quantum Mechanics (Sections I-IV of webpage & Erwin Meets Goldilocks)Erwin Meets Goldilocks Early Exam 10:15-11:15, Room SCL 111 Help Available Today 8-10 PM, WLH 120 Thursday 7-10:30 PM, WLH 114

Morse Quantization Morse Potential : Quantized; Probability Spreads to Right Because low kinetic energy means low curvature 7 Å ~ Exponential Decay (e -x ) (~ constant negative kinetic energy)

Morse Quantization Morse Potential : Quantized; Probability Spreads to Right Energies not evenly spaced as for Hooke’s Law 7 Å As the energy increases, along with the number of nodes, the well widens more than it would for a Hooke’s Law parabola. Thus wavelengths become longer, and energies lower, than expected for Hooke’s Law.

Morse Continuum Morse Potential : Not Quantized above Dissociation Limit ~ sin(x) (~ constant positive kinetic energy) Total Potential Kinetic

Coulombic Spacing 50 Å e - in Coulombic Potential of a Proton ! High Curvature (Erwin Program is approximate)

Coulomb Three E = k n2n2 50 Å Higher levels spread way out

Reward for Finding  Knowledge of Everything e.g. Allowed Energies Structure Dynamics Bonding Reactivity

Change mass Single-bonded H Increase mass from 1 to 14 (H to C 14 ) C  Curvature of  m Greater mass means more curvature for the same energy.

Change mass Single-bonded H Increase mass from 1 to 14 (H to C 14 ) Need to lower energy (curvature) for m=14 C  Curvature of  m Greater mass means more curvature for the same energy.

Mass Effect What about U 235 or a marble? m = 1 m = 14

Mass Effect and Vibration C H Higher-energy H shifted to right in unsymmetrical Morse Potential. half-maximum probability density

Mass Effect and Vibration H C

H C H C ±0.05Å (3% of X-C) ±0.1Å (9% of X-H)

Vib Dunitz et al. (1981) Typically vibrating by ±0.050 Å in the crystal

Reward for Finding  Knowledge of Everything e.g. Allowed Energies Structure Dynamics Bonding Reactivity

Single- vs. Double Minimum For Hooke's Law the Blue Energy is too Low and the Red Energy is too High. The Correct Energy must lie between these values. Single-Mimimum For Double-Minimum the Blue and Red are correct!

far apart far apart in Ain B Total Energy of Particle close together in AB "Mixing"   s Stabilzation of Particle Holds A & B together Bonding Antibonding Black line is energy Blue line is 

Dynamics: Tunneling The word "Tunneling" is one of my pet peeves: It is misleading and mischievous because it suggests that there is something weird about the potential energy in a double minimum. In fact it simply involves the same negative kinetic energy that one sees in the tails of EVERY bounded wavefunction. The word reveals a profound naiveté about quantum mechanics.

Bonding: Double Minimum 1.4 kcal/mole  ~4  sec to get from well to well. Well-to-Well time  5  sec  Energy (kcal/mole) Assertion - Involves time-dependent q. mech.

Reward for Finding  Knowledge of Everything e.g. Allowed Energies Structure Dynamics Bonding Reactivity Coming soon After Exam, Atoms, Molecules

Payoff for Organic Chemistry! What's Coming for Next Exam? Atoms 3-Dimensional Reality (H-like Atoms) Hybridization Orbitals for Many-Electron Atoms Molecules Plum-Pudding Molecules ("United Atom" Limit) Understanding Bonds (Pairwise LCAO) "Energy-Match & Overlap" (Wrong!) Recovering from the Orbital Approximation Reactivity HOMOs and LUMOs Recognizing Functional Groups Structure (and Dynamics) of XH 3 Molecules

Good Luck on the 1st Exam