OPLS

Functional form

The functional form of the OPLS force field is very similar to that of AMBER:

$E (r^{N}) = E_{b o n d s} + E_{a n g l e s} + E_{d i h e d r a l s} + E_{n o n b o n d e d}$

$E_{b o n d s} = \sum_{b o n d s} K_{r} (r - r_{0})^{2}$

$E_{a n g l e s} = \sum_{a n g l e s} k_{θ} (θ - θ_{0})^{2}$

$E_{d i h e d r a l s} = \sum_{d i h e d r a l s} (\frac{V_{1}}{2} [1 + \cos (ϕ - ϕ_{1})] + \frac{V_{2}}{2} [1 - \cos (2 ϕ - ϕ_{2})] + \frac{V_{3}}{2} [1 + \cos (3 ϕ - ϕ_{3})] + \frac{V_{4}}{2} [1 - \cos (4 ϕ - ϕ_{4})])$

$E_{n o n b o n d e d} = \sum_{i > j} f_{i j} (\frac{A_{i j}}{r_{i j}^{12}} - \frac{C_{i j}}{r_{i j}^{6}} + \frac{q_{i} q_{j} e^{2}}{4 π ϵ_{0} r_{i j}})$

with the combining rules $A_{i j} = \sqrt{A_{i i} A_{j j}}$ and $C_{i j} = \sqrt{C_{i i} C_{j j}}$ .

Intramolecular nonbonded interactions $E_{n o n b o n d e d}$ are counted only for atoms three or more bonds apart; 1,4 interactions are scaled down by the "fudge factor" $f_{i j} = 0.5$ , otherwise $f_{i j} = 1.0$ . All the interaction sites are centered on the atoms; there are no "lone pairs".

2 more chapters are free with a Lably account.

Functional form

Parameterization

Implementation

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