Chemistry 125: Lecture 13 October 2, 2009 Overlap and Energy-Match Covalent bonding depends primarily on two factors: orbital overlap and energy-match. Overlap depends on hybridization. Bond strength also depends on the number of shared electrons. So quantum mechanics shows that Coulomb’s law and kinetic energy answer Newton’s query about what “makes the Particles of Bodies stick together by very strong Attractions.” A re-vote shows that class has gained insight into the sources of bonding. Energy mismatch between the constituent orbitals weakens the influence of their overlap. Predictions of this theory are confirmed experimentally by measuring relative bond strengths of H-H and H-F during heterolysis and homolysis. Because independent electron pairs must have no net overlap, hybridization can be related simply to molecular structure, which will help test our theory further. For copyright notice see final page of this file

Curiosity: Over most of this range 2s overlaps with 2p  better than either 2s with 2s or 2p  with 2p  Overlap Integral Å s-p  p-p  s-s p-p  sp 3 -sp 3 s 2 p-s 2 p CCCCCC sp 3 -sp 3 sp 2 -sp 2 sp-sp xx sp 2 -sp 2 sp-sp

Overlap Integral Å s-p  p-p  s-s p-p  sp 3 -sp 3 s 2 p-s 2 p CCCCCC sp 2 -sp 2 sp-sp Hybrids overlap about twice as much as pure atomic orbitals. sp gives best overlap, but only allows two orbitals (50% s in each) sp 3 can give four orbitals with nearly as much overlap (25% s in each) (because they allow nearly full measure of s with p overlap plus s with s, and p with p.)

Influence of Overlap on “MO” Energy of a One-Dimensional Double Minimum Case I: Perfect Energy Match

Degenerate Energy Rising Energy Falling Increasing Overlap No Significant Energy Difference Creates Splitting

Overlap Holds Atoms Together A B Electron Energy separate 1/√2 (A+B) 1/√2 (A-B) together < > with greater overlap

Electron Count and Bond Strength A B Electron Energy separate together # Effect 1Bonding 2Strongly Bonding 3Weakly Bonding 4Antibonding

Why Doesn’t Increasing Overlap Make Molecular Plum Puddings Collapse? H2H2 He ? Electrons do become 55% more stable (~650 kcal/mole) But proton-proton repulsion increases much more dramatically (  1/r) (already increases by 650 kcal/mole from H-H to 0.3 Å) Unless one uses neutron “glue” D 2  He fusion fuels the Sun (200 million kcal/mole)

Finally we understand the atom-atom …. force law! … …. Bonding Potential Electron pair becomes more stable with increasing overlap. Nuclear repulsion becomes dominant All from Coulomb’s Law and Schr ö dinger Kinetic Energy of Electrons (This curve provides the potential for studying molecular vibration.) Atom-Atom Distance Energy

Newton Opticks (1717) Query 31 There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the business of experimental Philosophy to find them out. shop.rpg.net

What Holds Atoms Together? GravityQuarks Kinetic Energy Quantum Forces Strange Attractors Magnetic Forces Electrical ForcesThe Strong Force Shared Electron Pairs Exchange of Virtual Particles Exchange of Photons The Weak Force Let’s Vote Again 0  0 59  50 (unanimous) 10  0 (plus sophisticated yesses) 5  50 (unanimous) 20  0 (no such thing) 58  50 (unanimous, but sophisticated) 0  0 7  0 12  1 (holdout) 3  0 (plus a sophisticated yes)) 5  0

Overlap & Energy-Match Bonding depends on

What if partner is lower in energy than A? A B Electron Energy separate 1/√2 (A+B) 1/√2 (A-B) together < > “Splitting”  Overlap ? B * *) approximately

Why use any of an“Inferior” Orbital? The 1s “core” AOs did indeed remain pure and unmixed during creation of molecular orbitals for CH 3 CHFOH : Sorry, I was confused. The sound recording presents a discussion of Frame 21 while showing this Frame (14). Wikis should follow the frame numbers, not the sound recording.

 1  1s (F) Core 1

 2  1s(O) Core 2

 3  1s(C 1 ) Core 3

 4  1s(C 2 ) Core 4

Why use any of an“Inferior” Orbital? but the valence-level AOs were heavily mixed. The compact 1s “core” AOs did indeed remain pure and unmixed during creation of molecular orbitals for CH 3 CHFOH,

 5 “1s(valence)” 2s of F 2sp hybrid of O 2s of C

a << b B A (aA + bB) 2 = a 2 A 2 + b 2 B 2 + 2abAB Why use any of an“Inferior” Orbital? Suppose the energy of the A orbital is much higher (less favorable) than that of the B orbital. Can one profit from shifting electron density toward the AB overlap region (from the “outside” region) without paying too much of the high-energy“cost” of A? Yes, because for a small amount ( a ) of A in the MO, the amount of A 2 probability density ( a 2 ) is REALLY small, while the amount of shifted by overlap (2ab) is much larger. e.g. a = 0.03, b = 0.98 means a 2 = 0.001, b 2 = 0.96, 2ab = 0.06 (Incidentally, this is normalized, since the integral of AB is ~0.6, and 0.6 x 0.06 is ~0.04 = ) (Preliminary audio discussion of this frame appears out of order at 17:18-20:05 in the record lecture, and it exchanges A and B)

Influence of Overlap on “MO” Energy of a One-Dimensional Double Minimum Case II: Poor Energy Match

Degenerate Energy Rising Energy Falling Increasing Overlap Splitting due only to Original Well Offset Fights Well Difference Note Small Energy Mismatch still Mixing non-degenerate AOs Negligible Mixing Still Biased Mostly Left Mostly Right

What if partner is lower in energy than A? What are the ultimate energies? A B Electron Energy separate 1/√2 (A+B) 1/√2 (A-B) together < > ? C A-CA-C A+CA+C larger energy shifts smaller energy shifts looks mostly like C in shape & energy looks mostly like A

B A given overlap yields this splitting for perfect E-match How much smaller is the bonding shift when energy is mismatched? C A Electron Energy separate together Average of A and C Energy- mismatch

B How much smaller is the bonding shift when energy is mismatched? C A Electron Energy separate together With E-mismatch larger splitting for same overlap A given overlap yields this splitting for perfect E-match Energy- mismatch

B How much smaller is the bonding shift when energy is mismatched? C A-CA-C A+CA+C A Electron Energy separate together (shift up a bit for >,< normalization) Splitting is less sensitive to lesser contributor of mismatch / overlap For a given overlap, bonding shift is reduced by energy mismatch. (Still A+ C ends lower than A+B, because C starts lower.) e.g. when mismatch is relatively large, a given amount of overlap doesn’t make much difference

Important Generalizations Mixing two overlapping orbitals gives one composite orbital that is lower in energy than either parent and one that is higher in energy than either parent. The lower-energy combination looks more like the lower-energy parent, both in shape and in energy (ditto for higher-). For a given overlap, increasing energy mismatch decreases the amount of mixing and decreases the magnitude of energy shifts.

Which Bond is Stronger A-B or A-C? A B Electron Energy separate C Compared to What? A-B stronger if forming Ions (A + B - ) together A-C electrons clearly lower in energy, but…

Which Bond is Stronger A-B or A-C? A B Electron Energy separate C Compared to What? A-B stronger if forming Ions (A + B - ) A-C stronger if forming Atoms (A C) together mismatch aids Heterolysis mismatch hinders Homolysis

Experimental Evidence Is All This True?

H-H vs. H-F  ** Homolysis to A B kcal/mole HF Bond is Stronger Heterolysis to A + B - kcal/mole (gas phase) HF Bond is Weaker Big on F Big on H "Hydrofluoric Acid " antibonding molecular orbital : empty (match)(mismatch) ABN (antibonding node) AON (atomic orbital node)

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

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

End of Lecture 13 Oct. 2, 2009 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0