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) “chair” “boat” bowsprit flagpole “ring flip” by 60° counter-rotation of two parallel bonds Red bonds rotate in & up.Blue bonds rotate in & down. inverted chair www. downunderchicago.com/pics/ol-la-lafuma-recliner--padded--la.jpg

Ernst Mohr Illustrations (1918) 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 What o’clock? ? ? ? ? Z

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

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

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

Mol4D (CMBI Radboud University, Nijmegen, NL) Click for INDEXClick for INDEX or go to Conformational Jmol Animations (see Wiki to install Jmol)

Mol4D (CMBI Radboud University, Nijmegen, NL) Ethane Click to Animate or go to to Animate Eclipsed barrier ~5.2 kJ/mol  = 1.24 kcal/mol Should be ~2.9 kcal/mol. Caveat emptor! Step Keys Click Points Staggered

Mol4D (CMBI Radboud University, Nijmegen, NL) Propane Click to Animate or go to to Animate Staggered Eclipsed 3.3 kcal/mol

Anti  Gauche  10 -3/4  3.4 = /sec OOPS! /sec Mol4D (CMBI Radboud University, Nijmegen, NL) Butane (central bond) Click to Animate or go to to Animate Gauche 0.9 kcal/mol (tells how much) eclipsed 3.4 kcal/mol (tells how fast) fully eclipsed ~ 4.4 kcal/mol? (experimentally irrelevant) Anti Gauche / Anti = 10 -3/4  0.9 = = 1 / 4.7 Gauche / Anti = 2  10 -3/4  0.9 = 2  = 1 / Gauche -

Mol4D (CMBI Radboud University, Nijmegen, NL) Ring Flip of c-Hexane Click to Animate or go to to Animate Flexible or Twist-Boat conformer ~5.5 kcal/mol Barrier (Half-Chair) ~ 11 kcal/mol Chair conformer

Mol4D (CMBI Radboud University, Nijmegen, NL) Flexible c-Hexane Click to Animate or go to to Animate Flexible or Twist-Boat Form Barrier (Boat) ~ 1 kcal/mol

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

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

Conformational Energy of Butane 0°120° 240° 360° Torsional Angle Energy 4.4 kcal/mol 0.9 kcal/mol 4.4 kcal/mol 0.9 kcal/mol 3.4 kcal/mol CH 3 H H

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).

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

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

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

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

“Ideal” Cyclohexane (by Molecular Mechanics) 0.33Stretch Bend Stretch-Bend Torsion ,4 VDW Non-1,4 VDW TOTAL7.89 Strain (kcal/mol) e.g. favorable C … H e.g. (unfavorable) e.g. gauche C-C-C-C Easier (or harder?) to bend a stretched bond

Relaxation of Cyclohexane (by Molecular Mechanics) 0.33Stretch Bend Stretch-Bend Torsion Non-1,4 VDW ,4 VDW TOTAL gauche butanes Stretches and flattens slightly to reduce VDW 6  0.9 = 5.4 (mnemonic) “Ideal” Minimized gauche butane

Axial Methylcyclohexane (by Molecular Mechanics) 0.49Stretch Bend Stretch-Bend Torsion Non-1,4 VDW ,4 VDW TOTAL16.55  8 gauche butanes ! Axial - Equatorial = 1.8 kcal/mol for CH 3 [ 2 gauche  2 anti ] Relaxed H CH 3 “A-value” a measure of group “size” “Idealized”

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