Chemistry 125 Lecture 33 Conformational Energy and Molecular

Chemistry 125: Lecture 33 Conformational Energy and Molecular Mechanics Understanding conformational relationships makes it easy to draw idealized chair structures for cyclohexane and to visualize axial-equatorial interconversion. After quantitative consideration of the conformational energies of ethane, propane, and butane, cyclohexane is used to illustrate the utility of molecular mechanics as an alternative to quantum mechanics for estimating such energies. To give useful accuracy this empirical scheme requires thousands of arbitrary parameters. Unlike quantum mechanics, it assigns strain to specific sources such as bond stretching, bending, and twisting, and van der Waals repulsion or attraction. Synchronize when the speaker finishes saying “…in more detail than people wanted to hear about. ” Synchrony can be adjusted by using the pause(||) and run(>) controls. For copyright notice see final page of this file

Ernst Mohr Illustrations (1918) confirm Sachse’s 1890 insight.

Ernst Mohr Illustrations (1918) flagpole www. downunderchicago. com/pics/ol-la-lafuma-recliner--padded--la. jpg “chair” Red bonds rotate in & up. “boat” Blue bonds rotate in & down. inverted “ring flip” by 60° chair counter-rotation of two parallel bonds http: //beothic. blogspot. com/2007/01/dory_13. html bowsprit

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

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

Ernst Mohr Illustrations (1918) gauche OK within second ring of decalin, but not anti N. B. During 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!

Mol 4 D (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)

Mol 4 D (CMBI Radboud University, Nijmegen, NL) Click Points Ethane Click to Animate or go to http: //cheminf. cmbi. ru. nl/wetche/organic/nalkanesconf/ethane/jmindex. html Staggered Eclipsed barrier ~5. 2 k. J/mol 0. 239 = 1. 24 kcal/mol Should be ~2. 9 kcal/mol. Caveat emptor! Step Keys

Mol 4 D (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

Mol 4 D (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+ 10. 5 /sec 10 7. 5 1013 10 -3/4 3. 4 = 10 /sec OOPS! fully eclipsed 3. 4 kcal/mol ~ 4. 4 kcal/mol? (experimentally irrelevant) (tells how fast) Anti Gauche- Gauche + 0. 9 kcal/mol (tells how much) 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

Mol 4 D (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 Chair conformer Flexible or Twist-Boat conformer ~5. 5 kcal/mol

Mol 4 D (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

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

Conformational Energy of Ethane Energy 3 kcal/mol 0° 120° Torsional Angle 240° 360°

Conformational Energy of Butane 4. 4 kcal/mol Energy 3. 4 kcal/mol 0. 9 kcal/mol 0° CHCH 3 3 120° CH 3 0. 9 kcal/mol Torsional Angle CH 3 H CH 3 360° 240° CH H 3 CHCH 3 3

Molecular Mechanics (1946)

“Molecular Mechanics” programs calculate (and can minimize) strain assuming that molecules can be treated as 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).

“MM 2” Parameters 66 different atoms types (including 14 different types of carbon) 138 different bond stretches (41 alkane carbon-X bonds)

“MM 2” Parameters 66 different atoms types (including 14 different types of carbon) 624 different bond bendings (41 alkane-X angles)

“MM 2” Parameters 66 different atoms types (including 14 different types of carbon) Overall Butane 0. 5 180° is low “because of” reduced anti van der Waals repulsion kcal/mole tweaked by bond twistings 1494 different torsional energy 0 120° 240° (37 alkane-alkane-X twists)360° -0. 5 Sum: 1 -1 -1 -1 Torsional Contribution to Butane

After simplification “MM 3” has >2000 Arbitratily Adjustable Parameters ! Contrast with quantum mechanics, where there are no arbitrary parameters. (just particle masses, integral charges & Planck's constant)

1 e. g. gauche C-C-C-C (unfavorable) 21 43 4 5 23 e. g. favorable C…H “Ideal” Cyclohexane (by Molecular Mechanics) Strain (kcal/mol) 0. 33 Stretch 0. 00 0. 36 Bend 0. 00 0. 09 2. 15 -1. 05 4. 68 Stretch-Bend Easier Torsion (or harder? ) Non-1, 4 VDW to 1, 4 bend VDWa -0. 000 2. 12 -0. 55 6. 32 bond 7. 89 6. 56 stretched TOTAL

6 gauche butanes 6 0. 9 = 5. 4 (mnemonic) “Ideal” Minimized Stretches and flattens slightly to reduce VDW Relaxation of Cyclohexane (by Molecular Mechanics) 0. 33 Stretch 0. 00 0. 36 Bend 0. 00 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

H Axial - Equatorial = 1. 8 kcal/mol 8 gauchefor butanes CH 3 ! [ 2 gauche 2 anti ] “A-value” a measure of CH 3 group “size” Relaxed Axial Methylcyclohexane (by Molecular Mechanics) “Idealized” 0. 49 Stretch 0. 00 0. 96 Bend 0. 00 0. 14 Stretch-Bend -0. 00 3. 08 Torsion 2. 82 -1. 31 Non-1, 4 VDW 6. 12 5. 31 1, 4 VDW 7. 61 8. 66 TOTAL 16. 55

End of Lecture 33 Dec. 1, 2008 Copyright © J. M. Mc. Bride 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-Non. Commercial-Share. Alike 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. Mc. Bride, Chem 125. License: Creative Commons BY-NC-SA 3. 0