1. Chemistry 125: Lecture 35 December 4, 2009 Understanding Molecular Structure and Energy through Standard Bonds Although molecular mechanics is imperfect, it is useful for discussing molecular shapes in terms of standard covalent bonds. Analysis of the Cambridge Structural Database shows that predicting bond distances to within 1% requires detailed categorization of bond types. Early attempts to predict heats of combustion in terms of composition proved adequate for physiology, but not for chemistry. Group- or bond-additivity schemes are useful for understanding heats of formation, especially when corrected for strain. Heat of atomization is the natural target for bond- energy schemes, but experimental measurement requires spectroscopic determination of the heat of atomization of elements in their standard states. For copyright notice see final page of this file PRELIMINARY

2. Mol4D (CMBI Radboud University, Nijmegen, NL) Flexible c-Hexane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/cyclohexane/jm/twist_boat.htmlClick to Animate Flexible or Twist-Boat Form Barrier (Boat) ~ 1 kcal/mol The boat is not an isomer (an energy minimum), it is a barrier on the pleasantly smooth path between twist-boat isomers.

3. Axial Methylcyclohexane (by Molecular Mechanics) 0.49Stretch0.00 0.96Bend0.00 0.14Stretch-Bend-0.00 3.08Torsion2.82 -1.31Non-1,4 VDW6.12 5.311,4 VDW7.61 8.66TOTAL16.55 “Idealized ” 0.49 0.96 0.14 3.08 -1.31 5.31 8.66 Relaxed

4. H CH 3 Substituted Cyclohexanes 6 gauche butanes  8 gauche butanes ! Axial - Equatorial = 1.7 kcal/mol for CH 3 [ ~2 gauche  2 anti ] “A-value” a spectroscopic measure of group “size” 8.66 0.6 F Cl Br I 0.3 0.6 kcal/mol VDW radius increase is offset by increasing C-X distance.

5. Axial - Equatorial = 1.7 kcal/mol for CH 3 Substituted Cyclohexanes “A-value” a spectroscopic measure of group “size” 4.8 CH 3 Et i-Pr t-Bu 1.7 1.8 2.2 kcal/mol no “good” torsional angle

6. Stretch Bend Stretch-Bend Torsion Non-1,4-VDW 1,4-VDW TOTAL Cyclobutane Puckering (by Molecular Mechanics) Torsion vs. Bend Relaxed 0.77 16.07 -0.92 11.23 -0.26 2.35 29.24 Planar 0.66 13.48 -0.78 14.81 -0.28 2.27 30.16

7. Stretch Bend Stretch-Bend Torsion Non-1,4-VDW 1,4-VDW TOTAL Cyclopentane Puckering (by Molecular Mechanics) "Envelope" Relaxed 0.31 2.14 -0.09 6.38 -0.51 3.19 11.42 Planar 0.19 0.51 0.02 11.53 -0.48 4.34 16.10

8. e.g. What is the source of the barrier to c-hexane ring flip? two butane gauche  eclipsed (~7 kcal/mole) But why does the plastic model click? Baeyer Angle Strain +7° +5° -3° +5° Like a plastic model, molecular mechanics is satisfying because not only does it say what a structure should be, it can also say “why”. (the actual transition state is thought to be a “Half- Chair”)

9. Are They “True”? YES Are Molecular Mechanics Programs Useful? NO As we work with more complex systems, they become ever more indispensable. This is why Wikipedia alone lists 34 different schemes of 11 types for various purposes.

10. C Br van der Waals Radius (1.9Å) Br Br Contact 5Å

11. Br neighbor positions <5Å from many crystals (CSD) Nyburg & Faerman, Acta Crystallographica B41, 274-279 (1985) C Br In order to balance attraction from more distant atoms, the closest atoms must be "too" close and repulsive. Bonded bromine atoms may not be “spherical”! Molecular Mechanics Programs assume they are! ? Br Br Contact

12. 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

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

14. Cambridge Structural Database Total X-Ray Structures Year Atoms per Structure 27445673 >500,000 predicted by 2010 33,532,769 atomic positions Jan 2009 http://www.ccdc.cam.ac.uk >50,000,000 BONDS 75

15. CSD1

16. 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

17. 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%

18. 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

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

20. 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

21. We want to understand all “Stuff” Its Properties & Transformations Keys: Structure (Bonds) (Bonds?) & Energy

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

23. 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…

24.  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

25. 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 + 1/2 O 2 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 !

26. End of Lecture 35 Dec. 4, 2009 Copyright © J. M. McBride 2009. 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