Introduction to Force Fields

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4 The Electrostatic Energy The Coulomb interaction potential between two charged particles is U el = q A q B 4πε 0 r AB , (7) € where q A and q B are the charges on particles A and B and r AB is the distance between atoms A and B. The attractive interaction between opposite charges in shown in Figure 5(a) and the repulsive interaction between like € charges is shown in Figure 5(b). € € Electrostatic Energy Electrostatic Energy 0 2 4 6 8 10 r AB (Å) 0 2 4 6 8 10 r AB (Å) (a) (b) Figure 5. Typical behavior of the electrostatic energy for (a) opposite charges and (b) like charges. Determination of Force Field Parameters The parameters that make up the force field generally are derived from experimental data. This can be done in many different ways; thus, there are many different force fields available in the literature. Some have been constructed to deal with small organic molecules, others have been generated to focus especially on biomolecules, and others are of general utility. Sample Force Field Parameters Molecular mechanics (MM) calculations rely on force fields constructed from empirical data. The force field parameters are obtained from experimental or quantum mechanical results. Shown in Tables 1 and 2 are some example bond stretching and angle bending force field parameters. These parameters are from the MM3 force field. Table 1. Example bond stretching parameters, MM3 force field Bond type r AB,eq k s,AB (Å) (kJ mol –1 Å –2 ) Csp 3 –Csp 3 € 1.523 € 1330 Csp 3 –Csp 2 1.497 1330 Csp 2 =Csp 2 1.337 2890 Csp 2 =O 1.208 3250 Csp 3 –Nsp 3 1.438 1540 Note that the stretching force constants for double bonds are in general larger than the stretching force constants for single bonds.
5 Table 2. Example angle bending parameters, MM3 force field Angle type θ ABC,eq k b,ABC (deg.) (kJ mol –1 deg –2 ) Csp 3 –Csp 3 –Csp 3 € 109.47 € 0.041 Csp 3 –Csp 3 –H 109.47 0.033 H–Csp 3 –H 109.47 0.029 Csp 3 –Csp 2 –Csp 3 117.2 0.041 Csp 3 –Csp 2 =Csp 2 121.4 0.051 Csp 3 –Csp 2 =O 122.5 0.042 Here, one of the most important things to note is that the angle bending force constants are much smaller than the bond stretching force constants. Also, note that even for a tetrahedral center (such as at an sp 3 -hybridized carbon), the angle bending force constants depend upon the end atoms. Because of the smaller H atoms one the ends, an H- C-H force constant will be smaller than a C-C-C force constant.
Page 1 and 2: Chemistry 380.37 May 2013 Dr. Jean
Page 3: 3 1.4 1.2 1.0 Ut (kJ/mol) 0.8 0.6 0

Introduction to Force Fields

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