1. Chem 125 Lecture 14 10/6/08 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.

2. Hybridization Reality Check: Structure and Dynamics of XH 3 BH 3 CH 3 NH 3 valence electrons of X 345

3. sp 1 sp 3 There should be a relationship between Hybridization and Structure angle sp m -sp n = cos -1 (mn)(mn) 1 mnangle 11 22 33 00  * 125.3° * to avoid net overlap between different e-pairs (Pauli Principle) 13125.3° ? 180° linear 120° trigonal 109.5° tetrahedral 90° 

4. The three X-H Bonds say, “Use 3  sp 2 to maximize overlap” How to Optimize Hybridization of the X Atom in XH 3 ? The X Atom says, “O.K. make 3 bonds, but Maximize s-orbital occupancy” B (3 e - ) N (5 e - ) C (4 e - ) 3  p 2  s2  s (One X-electron in each of 3 bonding AOs; remainder in the 4th AO) 3  sp 2 vacant p Whatever (all sets of four 1-electron valence AOs use same amount of 2s)

5. How to Optimize Hybridization of the X Atom in XH 3 ? The X Atom says, “O.K. make 3 bonds, but Maximize s-orbital occupancy” B (3 e - ) N (5 e - ) C (4 e - ) (One X-electron in each of 3 bonding AOs; remainder in the 4th AO) B (3 e - ) N (5 e - ) C (4 e - ) BH 3 STRONGLY prefers sp 2 bonds (planar) CH 3 Less Strongly prefers sp 2 bonds (planar) NH 3 must compromise sp >2 bonds (pyramidal) 3  sp 2 1  p Whatever The three X-H Bonds say, “Use 3  sp 2 to maximize overlap” 3  sp 2 vacant p 3  p 2  s2  s

6. Hybridization Reality Check: Structure and Dynamics of XH 3 BH 3 CH 3 NH 3 valence electrons of X 345 Competes with bonds for s-character

7. BH 3 STRONGLY prefers sp 2 bonds (planar) CH 3 less strongly prefers sp 2 bonds (planar) NH 3 must compromise sp >2 bonds (pyramidal) Are these Predictions True? Experiment: X-Ray? Distortion from plane weakens bonds and deprives electrons of s-character. Distortion from plane weakens bonds and shifts s-character to lone electron (not wasted). Distortion from plane weakens bonds but shifts s-character from single electrons to pair of electrons. 2 BH 3  B 2 H 6 2 CH 3  C 2 H 6 Gas IR & ESR Spectroscopy

8. Infrared: Out-of-Plane Bend X H H H X H H H X H H H X H H H X H H H X H H H X H H H X H H H X H H H This “umbrella” vibration may be treated as a 1-dimensional “Erwin” problem with a fictious “mass” that reflects the amount of motion of the four atoms.

9. Infrared: Out-of-Plane Bend Weaker Planar Preference Hooke’s Law potential energy adjusted to give proper energy difference Amount of deformation 34.2 Terahertz18.7 THz 34,210,000,000,000 vibrations per sec 1141 cm -1 606 cm -1 Strong Planar Preference 3.26 kcal/mole 1.73 kcal/mole H H Amount of deformation Stiffer “Spring”

10. Two closely-spaced absorptions Infrared: Out-of-Plane Bend 932 cm -1 968 cm -1 37 cm -1 “Tunnel” Splitting: 1 cm -1 Potential Energy “Inversion” Barrier 3 kcal/mole 2 cal/mole  Ground State Tunneling ~10 11 /sec Umbrella Clock! Not a Hooke’s Law pattern Double Minimum potential energy adjusted to give proper energies 5  10 -14 sec 0.002 (kcal) 0 & 1 node 2 & 3 nodes Lect. 9 frame 9

11. Electron Spin Resonance Spectrum measures s-orbital character of the SOMO electron in CH 3. A line separation due to magnetic interaction between the unpaired electron and the 13 C nucleus occurs only if the electron spends time ON the nucleus, which happens only for s-orbital.

12. CH 3 SOMO PlanarBent

13. CH 3 SOMO PlanarBent

14. Structural Isotope Effect: CH 3 spends more time more bent than CD 3 (thus uses more s-character for SOMO electron) CH 3 38 Gauss  2% s 36 Gauss  less s CD 3 on average

15. CF 3 Repulsion between F atoms?  Less Bent (flatter) than CH 3 Since Fluorine holds the lion's share of the bonding electron pair, Carbon has less reason to use its valuable s-character in the bonding orbitals. Uses more for the SOMO.  More Bent than CH 3 OR

16. CF 3 SOMO 271 Gauss!  20% s (vs. 38 for CH 3 )  sp 4

17. Tension! Differing Goals Computer Chem 125 Student Minimize kinetic plus coulomb energies of electrons and nuclei by “settling down” Minimize total energy using Schrödinger equation with “realistic” constraints Understand structure and reactivity with the simplest “realistic” model Experimental Molecule e.g. limited set of AOs, SCF, some correlation, delocalized MOs e.g. localized bonds, lone pairs; hybridization E-match/overlap HOMO/LUMO Qualitative Insight Validation by Experiment & Computer Useful Predictions of Properties Validation by Experiment Structure Total e-Density (X-Ray) Energies (IR) Nuclear e-Density (ESR) Dipole Moment, etc.

18. End of Lecture 14 Oct. 6, 2008