For copyright notice see final page of this file Chemistry 125: Lecture 34 December 2, 2009 The Conformation of Cycloalkanes Understanding conformational relationships makes it easy to draw idealized chair structures for cyclohexane and to visualize axial-equatorial interconversion. The conformational energy of cyclic alkanes illustrates the use of molecular mechanics, a useful, but highly empirical scheme for reckoning conformational energy. For copyright notice see final page of this file

Ernst Mohr Illustrations (1918) What o’clock? ? Z ? ? ? Drawing chair cyclohexane rings: opposite C-C bonds are parallel axial bonds are parallel to 3-fold axis equatorial bonds are (anti)parallel to next-adjacent C-C bonds

Cholic Acid (a Steroid) Glucose (a Carbohydrate)

For such problems D.H.R. Barton Invents Conformational Analysis (1950)  “up” ;   “down” (for molecule in conventional orientation, old-fashioned configuration notation, like cis / trans) Intermediates in steroid hormone synthesis Barton redraws Ring A A B C D   Baeyer observed only one c-Hexyl-COOH, but in these epimers,  and  OH groups have different reactivity! (configurationally diastereotopic)

For such problems D.H.R. Barton Invents Conformational Analysis (1950)  “up” ;   “down” (for molecule in conventional orientation, old-fashioned configuration notation, like cis / trans) ERRORS? ) (e) “equatorial” (p) “polar” (now axial) Ring Flip? Cf. ~1950 Stereochemistry: Bijvoet, Newman, CIP, (Molecular Mechanics) 3-fold axis (Nobel Prize 1969 for “development of the concept of conformation and its application in chemistry”)

Ernst Mohr Illustrations (1918) gauche, but not anti, is OK for the second ring of decalin. anti N.B. During ring flip equatorials become axials and vice versa. gauche fused chairs in "decalin" (decahydronaphthalene) Try with models if you’re skeptical. Ring flip impossible for trans decalin!

Mol4D (CMBI Radboud University, Nijmegen, NL) Conformational Jmol Animations Click for INDEX or go to http://cheminf.cmbi.ru.nl/wetche/organic/index.html (see Wiki to install Jmol)

Mol4D (CMBI Radboud University, Nijmegen, NL) Ethane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/ethane/jmindex.html Click Points Staggered Step Keys Eclipsed barrier ~5.2 kJ/mol  0.239 = 1.24 kcal/mol Should be ~2.9 kcal/mol. Caveat emptor!

Mol4D (CMBI Radboud University, Nijmegen, NL) Propane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/propane/jmproprot.html Eclipsed 3.3 kcal/mol Staggered

Mol4D (CMBI Radboud University, Nijmegen, NL) Butane (central bond) Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/butane/jmindex.html Anti Gauche+ 1013 10 -3/4  3.4 = 10 10.5 /sec fully eclipsed ~ 5.5 kcal/mol? (experimentally irrelevant) eclipsed 3.5 kcal/mol (tells how fast) + Anti Gauche 0.9 kcal/mol (tells how much) Gauche- Gauche / Anti = 10 -3/4  0.9 = 10-0.68 = 1 / 4.7 Gauche / Anti = 2  10 -3/4  0.9 = 2  10-0.68 = 1 / 2.4

Conformational Energy of Ethane Butane 5.5 0.9 (0.6?) 3.5 CH3 H 0° 120° 240° 360° Torsional Angle Energy (kcal/mole) 3 e.g. Journal of Molecular Structure: THEOCHEMVolume 814, Issues 1-3, 15 July 2007, Pages 43-49

Mol4D (CMBI Radboud University, Nijmegen, NL) Ring Flip of c-Hexane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/cyclohexane/jm/chxjmol.html Barrier (Half-Chair) ~ 11 kcal/mol Flexible or Twist-Boat conformer ~5.5 kcal/mol Chair conformer

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.html Barrier (Boat) ~ 1 kcal/mol Flexible or Twist-Boat Form The boat is not an isomer (an energy minimum), it is a barrier on the pleasantly smooth path between twist-boat isomers.

Shape, “Strain Energy” & Molecular Mechanics “Hooke’s Law” for Strain Energy

Molecular Mechanics (1946) N. E. Searle and Roger Adams, JACS, 56, 2112 (1935) At the barrier the C-C-Br angles  open by 12°. Activation Energy for Racemization obs. 19.5 kcal/mol Question: How did having COOH groups on the benzene rings facilitate the experiment? t1/2 = 9 min at 0°C (1013  10-(3/4)*20 ~ 10-2/sec) calc. 17.3 kcal/mol

to make energies match experiment (or reliable quantum calculations). “Molecular Mechanics” programs calculate (and can minimize) strain assuming that molecules can be treated as (electro)mechanical entities. To achieve useful precision they require a very large set of empirical force constants adjusted arbitrarily to make energies match experiment (or reliable quantum calculations).

138 different bond stretches (41 alkane carbon-X bonds) “MM2” Parameters 66 different atoms types (including 14 different types of carbon) 138 different bond stretches (41 alkane carbon-X bonds)

624 different bond bendings (41 alkane-alkane-X angles) “MM2” Parameters 66 different atoms types (including 14 different types of carbon) 624 different bond bendings (41 alkane-alkane-X angles)

“MM2” Parameters 1494 different bond twistings 66 different atoms types (including 14 different types of carbon) Overall Butane 180° is low “because of” low van der Waals repulsion 0.5 -0.5 just tweaked a bit by torsional energy in this scheme 1494 different bond twistings (37 alkane-alkane-alkane-X twists) kcal/mole 120° 240° 360° Sum: 1-1-1-1 Torsional Contribution to Butane

After simplification “MM3” has >2000 Arbitratily Adjustable Parameters ! Contrast with quantum mechanics, where there are no arbitrary parameters. (just particle masses, integral charges & Planck's constant)

We’ve come a long way from Couper, Catalogue of Molecular Mechanics Schemes from Wikipedia: Force Fields (Chemistry) We’ve come a long way from Couper, Crum-Brown, and Dewar

“Ideal” Cyclohexane (by Molecular Mechanics) e.g. (unfavorable) 1 2 3 4 e.g. gauche C-C-C-C 1 2 3 4 5 Strain (kcal/mol) 0.33 Stretch 0.00 0.36 Bend 0.09 Stretch-Bend -0.000 e.g. favorable C…H Easier (or harder?) to bend a stretched bond 2.15 Torsion 2.12 -1.05 Non-1,4 VDW -0.55 “Ideal” Cyclohexane (by Molecular Mechanics) 4.68 1,4 VDW 6.32 6.56 TOTAL 7.89

Relaxation of Cyclohexane (by Molecular Mechanics) 6 gauche butanes gauche butane 6  0.9 = 5.4 (mnemonic) Minimized “Ideal” 0.33 Stretch 0.00 0.36 Bend 0.09 Stretch-Bend -0.000 2.15 Torsion 2.12 -1.05 Non-1,4 VDW -0.55 4.68 1,4 VDW 6.32 6.56 TOTAL 7.89 Stretches and flattens slightly to reduce VDW Relaxation of Cyclohexane (by Molecular Mechanics)

End of Lecture 34 Dec. 2, 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). 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