1. Chem 125 Lecture 35 12/5/08 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 or the wiki from the lecture.

2. Are They “True”? YES They are indispensable. Are Molecular Mechanics Programs Useful? NO

3. C Br van der Waals Radius Br Br Contact

4. Br neighbor positions from many crystals (CSD) Nyburg & Faerman, Acta Crystallographica B41, 274-279 (1985) C Br To balance attractive and repulsive forces between neighboring molecules, the closest atoms must be "too" close. Bromine atoms seem not to be spherical! Molecular Mechanics Programs Assume They Are! ? Br Br Contact

5. Angiostatin anti-cancer drug “We optimized kringle 1 with the AM1 method using Gaussian 03. Plasminogen kringle 1 contains 1200 atoms, which are made up of 642 heavy atoms and 578 hydrogen atoms. The job takes about 650 optimization steps starting from the MM+ geometry.” M. J. Frisch, Gaussian, Inc., 2003 largest molecule calculated by quantum mechanics Despite its problems MM is necessary for complex structures

6. Is the standard Structural Model realistic in geometric detail? X-Ray Diffraction

7. Cambridge Structural Database Total X-Ray Structures Year Atoms per Structure 27445473 >500,000 predicted by 2010 30,572,792 atomic positions Jan 2008 http://www.ccdc.cam.ac.uk >40,000,000 BONDS

8. CSD1

9. Number of Mean Bond Lengths Tabulated. (specialized because of influence of neighbors on precise bond distance) 175 CC 97 CN 119 CO 119 different types of CO bonds 27 different types of C sp 3 -C sp 3 bonds

10. CSD1 mean high 1/4 median low 1/4 # obs std dev 3 C* means C bearing C,H only C# means any Csp 3 crowding stretches bond even moreso short long R 2 CH CR 3 R 2 CH CHR 2 R 3 C CR 3 RCH 2 CH 3 R 2 CH CH 3 R 3 CH CH 3 ~1%

11. C-C bond lengths single 1.53 Å double 1.32 triple 1.18 aromatic 1.38 (one-and-a-half bonds) single: sp 3 -sp 2 1.50 sp 2 -sp 2 1.46

12. N to C aromatic Bond Lengths N PlanarN Pyramidal N N + _ poor  overlap  Twist Bimodal ? N :

13. How Complex Must a Model be to Predict Useful Structures? To get standard deviations in bond distance of 0.015Å (~1%) the Cambridge crew defined: 682 kinds of bonds altogether 175 different kinds of CC bonds (differing in multiplicity, hybridization, attached groups, rings, etc.) 97 different types of CN bonds 119 different types of CO bonds

14. We want to understand all “Stuff” Its Properties & Transformations Key: Structure & Energy Bonds?

15. How Standard are Bond Energies? Obviously there will be correction for conformation and strain, but is there an underlying energy for composition or constitution?

16. Adolph Oppenheim: On the Relationship of Heat of Combustion with the Constitution of Substances. 1868 Ludimar Hermann: On the Regularity and Calculation of Heat of Combustion of Organic Compounds. By a frequently expressed need of physiology to be able to calculate heats of combustion, I have been led to study the current situation…

17.  H Combustion by C / H Content? Substance Carbons atoms/mole Hydrogens atoms/mole Theory  H combust kcal/mole Error kcal/mole Error % Graphite [1] 0 -94.05 - - Hydrogen 0 2 -57.8 - - c-Hexane 6 12 -911.1 -881.6 -29.5 -3 c-Hexanol 6 12 -911.1 -842.7 -68.4 -8 Ethene 2 4 -303.7 Glucose 6 12 -911.1 -670.4 -240.7 -36 Not too bad for fuel purposes, especially if one were to include some kind of correction for partial oxidation. [-57.8]  per H 2 [-94.05]  per C = 2  94.05 + 2  57.8 H 2 C=CH 2 has extra energy to give off. One of its bonds (  ) is not very stabilizing, so it starts unusually high in energy. O1O1 O6O6 partially "pre-oxidized" -316.2 +12.5 +4 Composition: Atom Additivity

18. How Complex Must a Model be to Predict Chemically Useful Energies? For physiology purposes you might be content with ± 5% in heat of combustion. But for predicting the equilibrium constant between c-hexane and c-hexanol, being off by 1% (9 kcal/mole) means being off in K eq by a factor of A useful model must go beyond composition. How about constitution? 10 7 !

19. C 6 H 12 Energy -911.1 = -29.5 CO 2 / H 2 O graphite / hydrogen -881.6  H combustion  H formation Energy (kcal/mole) Compared to What? easily measured How to measure? ( elements in their “standard states”)

20. HfHf APPENDIX I HEATS OF FORMATION From Streitwieser, Heathcock, & Kosower

21. HfHf APPENDIX I HEATS OF FORMATION From Streitwieser, Heathcock, & Kosower

22. HfHf APPENDIX I HEATS OF FORMATION From Streitwieser, Heathcock, & Kosower

23. formation cyclo minimum Expt. - Theory  H f + n  4.9 Group Additivity “unstrained” 2  -4.9 = -9.8 Strainless Theory (n  -4.9) ? From Streitwieser, Heathcock, & Kosower “Transannular” Strain similar c-hexane c-octane Small-Ring Strain

24.  ve Bond Energies Can one sum bond energies to get useful "Heats of Atomization"? Bond Additivity (between atoms and groups) From Streitwieser, Heathcock, & Kosower

25. How well can “Bond Energies” predict  H atomization ? Where does  H atomization come from?

26. C 6 H 12 Energy 1680.1 atoms  H atomization 1650.6 -911.1 -29.5 CO 2 / H 2 O graphite / hydrogen -881.6  H combustion  H formation Energy (kcal/mole) Compared to What? How Can You Know  H formation for an atom? = - 881.6 + 911.1 + 1650.6 How to measure?

27. Atom Energy from Spectroscopy light energy X-Y X + Y H-H 104.2 kcal/mole (  H f H = 52.1) O=O 119.2 kcal/mole (  H f O = 59.6) CO 257.3 kcal/mole X* + Y Maybe this is the observed transition at 257.3 ? 141? 257.3  H f C=O = -26.4  H f H 0 2 _ _ _  H f O 0 2 _ _ _ X*’ + Y Or maybe this is the observed transition at 257.3 ? 125? 257.3 spectroscopic value precise, but uncertain Which to choose? CO Hf CHf C Hf OHf O graphite O 2 C + O graphite O (  H f C = 171.3) But Nobel Laureates Worried.

28. End of Lecture 35 Dec. 5, 2008