Chemistry 125: Lecture 35 December 3, 2010 Understanding Molecular Structure & Energy through Standard Bonds The conformational energy of cyclic alkanes illustrates the use of molecular mechanics, a useful, but highly empirical scheme for reckoning conformational energy. Although molecular mechanics is imperfect, it is useful for discussing molecular shapes in terms of standard covalent bonds. The Cambridge Structural Database provides geometric details for more that 50,000,000 bonds. For copyright notice see final page of this file Preliminary

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 3.5 66 different atoms types (including 14 different types of carbon) 0.9 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 e.g. favorable C…H Stretch-Bend -0.000 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)

Axial Methylcyclohexane (by Molecular Mechanics) Relaxed “Idealized” 0.49 0.96 0.14 3.08 -1.31 5.31 8.66 0.49 Stretch 0.00 0.96 Bend 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 Axial Methylcyclohexane (by Molecular Mechanics)

Substituted Cyclohexanes CH3 Axial - Equatorial = 1.7 kcal/mol for CH3 6 gauche butanes  8 gauche butanes ! [ ~2 gauche  2 anti ] “A-value” a spectroscopic measure of group “size” F Cl Br I 0.3 0.6 kcal/mol values from Eliel, Wilen, & Mander, Stereochemistry of Organic Compounds (1994) 0.6 Substituted Cyclohexanes 8.66 VDW radius increase is offset by increasing C-X distance.

Substituted Cyclohexanes Axial - Equatorial = 1.7 kcal/mol for CH3 “A-value” a spectroscopic measure of group “size” CH3 Et i-Pr t-Bu 1.7 1.8 2.2 kcal/mol values from Eliel, Wilen, & Mander, Stereochemistry of Organic Compounds (1994) Substituted Cyclohexanes 4.8 no “good” torsional angle

Cyclobutane Puckering (by Molecular Mechanics) 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 Stretch Bend Stretch-Bend Torsion Non-1,4-VDW 1,4-VDW TOTAL Torsion vs. Bend Cyclobutane Puckering (by Molecular Mechanics)

Cyclopentane Puckering (by Molecular Mechanics) 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 Stretch Bend Stretch-Bend Torsion Non-1,4-VDW 1,4-VDW TOTAL "Envelope" Cyclopentane Puckering (by Molecular Mechanics)

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

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

"allowed" locus for Br neighbors within 5Å Br•••Br Contact van der Waals Radius (1.9Å) C Br 5Å

? • Br•••Br Contact Br C "allowed" locus for Br neighbors within 5Å positions <5Å from many crystals (CSD) Nyburg & Faerman, Acta Crystallographica B41, 274-279 (1985) "allowed" locus for Br neighbors within 5Å Br•••Br Contact Bonded bromine atoms may not be “spherical”! ? Molecular Mechanics Programs assume they are! C Br • S.C. Nyburg and C.H. Faerman,A Revision of van der Waals Atomic Radii for Molecular Crystals - N, O, F, S, Cl, Se, Br, and I Bonded to Carbon.Acta Crystallographica B41, 274-279 (1985). In order to balance attraction from more distant atoms, the closest atoms must be "too" close and repulsive.

Angiostatin anti-cancer drug Despite its problems MM is necessary for complex structures Angiostatin anti-cancer drug largest molecule calculated by quantum mechanics “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

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

Cambridge Structural Database http://www.ccdc.cam.ac.uk >50,000,000 BONDS Total X-Ray Structures 36,334,442 atomic positions Jan 2010 Atoms per Structure 27 44 56 Year 73 75

End of Lecture 35 Dec. 3, 2010 Copyright © J. M. McBride 2009, 2010. 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