Molecular Mechanics as an Organic Chemistry Laboratory Exercise Ronald M. ~arretland Ny Sin College of the Holy Cross, Worcester, MA 016 10
Conventional (hand-held) molecular models have been (and continue to be) useful in visualizing molecular structures in three dimensions. However, many students still have difficulty dealing with intramolecular relationships, despite the aid of models. This seems related to the fact that models can be constructed by simply joining pieces, rather than by thoughtful consideration of spatial relationships. The molecular models are also useful for examining steric interactions but give no quantitative information about steric energy. A more complete approach to the instruction of spatial relationships and stereochemistry is to combine molecular models with computer-based calculations. The wide variety of programs currently available for various computers (and graphics capabilities) on a commercial basis (1) and from the Quantum Chemistry Program Exchange (2) has made it possible for many institutions to integrate molecular modeling into the chemistry curriculum. We have introduced this exercise into the organic chemistry course for chemistry majors. Currently, sophomores perform force field calculations (3) with a VAX-8600 computer using VT-100 terminals (without enhanced graphics capabilities). A force field based program like MM2 (4) requires far less computer time and resources than programs that use either an ab initio or semiempirical approach (e.g., GAUSSIAN82 and MNDO, respectively). The force field method of molecular modeling is therefore most amenable to an undergraduate "laboratory exercise"; it can be performed, as a computer dry lab, outside of scheduled laboratory time or during free time of some wet-lab experiment. The total steric energy for the optimized geometry of a molecule is perhaps the most widely used piece of information obtained from a force field calculation. The absolute value for the steric energy varies from program to program Author to whom correspondence should be addressed.
and is of little or no use; however, the relative size of individual interactions (compression, bending, stretch-bend, van der Waal, torsional) that compose the total steric energy can be helpful in identifying specific sites and types of strain. The interatomic distances and specific details of the optimized geometry can also be useful in this regard. In general, however, it is most informative to compare steric energies and establish relative stabilities of structural isomers, stereoisomers, and rotomers in staggered conformations. The dihedral driver can be activated to fix certain dihedral angles and examine energies of rotomers in eclipsed conformations as well. In order to perform any molecular mechanics calculation, the location of each atom must be entered. One method (which encourages students to consider intramolecular relationships) is to construct a physical model of (or draw) a molecule and then describe each atom's position relative to the location of a bonded atom ( 5 ) . This is the approach employed for defining atomic positions in STRFIT (6);this program is completely compatible with and serves as input for MM2. The location of atom B (in molecule ABCD) is defined by its directional orientation from atom A. This A-B path is described by a sum of vectors that form a threedimensional axis system: u(p) and d(own), i(n) and o(ut), l(eft) and r(ight). For example, the heavy atoms of 2,2-dimethylcyclobutanone (carbon ring in plane of screen) are defined by the following string of directions: C l C2 dr, C2 C3 dl, C3 C4 ul, C l C4 (closes the ring), C2 C5 ro, C2 C6 ri, C l 0 1 u C l 0 1 (repeated to create the double bond of C=0). The appropriate number of hydrogen atoms is automatically positioned on all carbon atoms present in the molecule; alternatively, hydrogen atom positions may be entered with bond directions like any other MM2-recognizable element. With only a brief introduction, our students learn to use STRFIT (by Saunders and Jarret) for structure input and to
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Number 2
February 1990
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run Allinger's MM2 program (QCPE 395) for geometry optimization and energy computation. We present the computational results (Tables 1 and 2) obtained for a series of compounds, selected to encourage students to think about spatial relationships of atoms within a molecule, and demonstrate how steric energies vary among geometrical isomers, rotomers, conformers and stereoisomers in the context of reaction products (eqs 1-3 below). Results and Discussion
In order for the act of conducting molecular mechanics computations to serve as a pedagogical tool, it is imperative that the operator realize that the algorithm used in structure refinement is designed to locate the local energy minimumwhich may or may not correspond to the global energy minimum. Thus the program will generally not rotate bonds through an eclipsed conformation (energy maximum) in search of an energy minimum (unless the dihedral driver is activated). This "steepest descent" approach prevents conversion of a given input staggered rotomer into a different output staggered rotomer (e.g., gauche to anti butane) and conversion between conformers (e.g., twist-boat to chair cyclohexane). If an eclipsed form is used as input, however, then it is technically possible to end up at an energy minimum on either side of this energy maximum. Thus, if eclipsed butane is entered (with two C-H atoms eclipsed), structure refinement could generate either anti or gauche butane (Table 1); likewise, if planar cyclohexane is entered, optimization could proceed to either the chair or twist-boat conformation (Table 2). This approach of entering unstable conformations can be useful in introducing the student to preferred orientations. For example, it is not intuitively obvious to most students that, while cyclohexane is often drawn as a planar molecule, Table 1.
Steric Energies (MM2) vs. Dihedral Angle for Butane Derivatives
Dihedral Angle (C 1-C2-C3-C4)
Steric Energy (Kcallmol)
Dihedral Angle (C 1-C2-C3-C4)
Steric Energy (Kcal/mol)
Butane: 0,360 60,300 120,240 180
Table 2.
Steric Energies (MM2) for Cyclohexane Derivatives
Compound Cyclohexane(chair) methyl (eq) methyl (ax) 1, ldimethyl 1,2dimethyl (eq,eq) 1,2-dimethyl (ax,eq) 1,2-dimethyl (ax,ax) 1,3dimethyl (eq,eq) 13-dimethyl (ax,eq) 1,3dimethyl (ax,ax) 1,4dimethyl (eq,eq) 1,4dimethyl (ax,eq) 1,4dimethyl (ax,ax) Cyclohexane (twist-boat)
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this is actually a high-energy conformation of the six-membered ring. However, if the student performs the calculation on this structure, shelhe finds that the energy is enormousrelative to that of the chair conformation. Moreover, the change in geometry accompanying the energy minimization can be readily monitored with the C-C-C-C dihedral angles. In the initial planar structure, the dihedral angles are 0'; in the optimized chair form, they are nearly 60°in the twistboat conformation of cyclohexane, the dihedral angle is about 30'. To optimize the geometry of boat cyclohexane (energy maximum), a dihedral angle must be fixed at, or near, 0' with the dihedral driver (Table 2). The dihedral driver is also useful in generating an energy diagram (steric energy vs. dihedral angle) for the rotation about C-C single bonds in acyclic hydrocarbons. This year a group of 12 chemistry majors worked on this problem. Each student was assigned a dihedral angle between 0' and 330' (at 30' intervals) and asked to calculate the energy for the corresponding rotomer of butane, 2-methylbutane, 2,3-dimethylbutane, and 2,2-dimethylbutane (Table 1). By pooling the data and presenting the results for each compound in the form of an energy diagram, certain points are clearly made: (1) energy surfaces differ, depending on the substitution pattern about the C-C bond; (2) staggered rotomers are energy minima and eclipsed forms are energy maxima; (3) these stationary points are connected through rotation about C-C single bonds (skewed forms); (4) compounds may have energetically distinct energy minima (local and global) and maxima for rotomers of a particular compound; (5) a methyl-methyl gauche interaction results in destabilization (about 0.9 kcallmol relative to methyl-hydrogen); (6) compounds do not exist as a statistical distribution of rotomers (at all temperatures); (7) certain rotomers are chiral and have an enantiomer. Molecular mechanics is an ideal tool for examing stereoisomers; enantiomers have identical steric energy, while diastereomers need not. We use a series of dimethylcyclobutan01derivatives (which would be produced by the reduction of dimethylcyclobutanone) or trimethylcyclobutanol derivatives (which would result from the addition of methylmagnesium bromide to dimethylcyclobutanone) for this purpose. These computational results help identify stereochemical relationships between anticipated reaction products (eqs 13).
Energy (Kcal/mol)
Compound
6.55 6.89 8.67 9.27 8.46 10.08 10.90 7.21 9.02 12.55 7.22 8.97 10.80 11.9 1
Cyclohexane (chair) chloro (eq) chloro (ax) 1,ldichloro 1,2dichloro (eq,eq) 1,2dichloro (ax,eq) 1,2dichloro (ax,ax) 1,3dichloro (eq,eq) 1,3-dichloro (ax,eq) 1,3dichloro (ax,ax) 1,4dichloro (eq,eq) 1,4dichloro (ax,eq) 1,4dichloro (ax,ax) Cyclohexane (boat)
Journal of Chemical Education
Energy (Kcal/mol)
32.09 kcallmol
31.05 kcallmol
33.19 kcallmol
33.19 kcallmol
total energy. For example, the energies of dimethylcyclohexanes show a predictable dependence on steric interactions, with total energy for diequatorial
