force constant (the critical feature of a transition state), and for parameterization force constants of transition states could be calculated by quantum mechanical methods. 1 Indeed, MM has been used to calculate geometries and energies of transition states, but these studies have used force fields developed for very specific reactions, perhaps the best example being the dihdroxylation of alkenes with osmium tetroxide under the influence of a chiral catalyst . However, MM is not at present a generally applicable tool for studying transition states. This is probably because force constants are not as transferable between transition states (are more variable from one transition state to another) as they are between ordinary molecules, making a forcefield that works for one kind of reaction inapplicable to another. References 1. (a) Lucht RP (2007) Science 316:207. (b) Rawls RL (2000) Chemical and Engineering News, May 22, 35 2. Norrby P-O, Rasmussen T, Haller J, Strassner T, Houk KN (1999) J Am Chem Soc 121:10186 1 Such as ab initio, density functional, and semiempirical methods. The reliability of the geometries and energies of calculated transition states can be gauged by comparing activation energies calculated from them with experimental activation energies. 608 Answers
Chapter 3, Harder Questions, Answers Q10 How many parameters do you think a reasonable forcefield would need to minimize the geometry of 1,2-dichloroethane? C C H H H H Cl Cl Look at the structure of the molecule: At a bare minimum, we would need parameters for these seven contributors to the energy (here C is the atom type sp 3 C): (1) E stretch (C–C) (2) E stretch (C–H) (3) E stretch (C–Cl) (4) E bend (HCC) (5) E bend (ClCC) (6) E bend (HCCl) (7) E torsion (ClCH 2 –CH 2 Cl) For each of the three E stretch (X–Y) terms, k stretch (X–Y) and l eq (X–Y) are needed, for a total of 6 parameters. For each of the three E bend (XYZ) terms, k bend (XYZ) and a eq (XYZ) are needed, for a total of 6 parameters. The torsional curve likely requires at least 5 parameters (see chapter 3, section 3.2.2 ) for reasonable accuracy. This makes a total of 6 þ 6 þ 5 ¼ 17 parameters. But this would be a very stunted forcefield; it has no parameters for nonbonded interactions and so is not suitable for molecules with bulky groups, and it is parameterized only for the atom types sp 3 C, H, and Cl. It cannot handle other kinds of carbon and other elements, and it has no special parameters for electrostatic interactions. A reasonable forcefield would be of more general applicability: it should be able to handle the eight common elements C(sp 3 , sp 2 , sp), H, O(sp 3 , sp 2 ), N(sp 3 , sp 2 , sp), F, Cl, Br, I; we are focussing for convenience on an organic chemistry forcefield. Yet this would have only 13 atom types, compared to the typical organic forcefield with 50–75 . Similar considerations applied to the stretching of C–H, C–O, C–N, C–F, ..., H–O, H–N, etc. bonds, to the bending of various C–C–C, CO–C, etc.
- Fall '19
- dr. ahmed