OPLS

The OPLS (Optimized Potentials for Liquid Simulations) force field was developed by Prof. William L. Jorgensen at Purdue University and later at Yale University. The OPLS (Optimized Potentials for Liquid Simulations) force field was developed by Prof. William L. Jorgensen at Purdue University and later at Yale University. 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 {displaystyle Eleft(r^{N} ight)=E_{mathrm {bonds} }+E_{mathrm {angles} }+E_{mathrm {dihedrals} }+E_{mathrm {nonbonded} }} E b o n d s = ∑ b o n d s K r ( r − r 0 ) 2 {displaystyle E_{mathrm {bonds} }=sum _{mathrm {bonds} }K_{r}(r-r_{0})^{2},} E a n g l e s = ∑ a n g l e s k θ ( θ − θ 0 ) 2 {displaystyle E_{mathrm {angles} }=sum _{mathrm {angles} }k_{ heta }( heta - heta _{0})^{2},} E d i h e d r a l s = ∑ d i h e d r a l s ( V 1 2 [ 1 + cos ⁡ ( ϕ − ϕ 1 ) ] + V 2 2 [ 1 − cos ⁡ ( 2 ϕ − ϕ 2 ) ] + V 3 2 [ 1 + cos ⁡ ( 3 ϕ − ϕ 3 ) ] + V 4 2 [ 1 − cos ⁡ ( 4 ϕ − ϕ 4 ) ] ) {displaystyle E_{mathrm {dihedrals} }=sum _{mathrm {dihedrals} }left({frac {V_{1}}{2}}left+{frac {V_{2}}{2}}left+{frac {V_{3}}{2}}left+{frac {V_{4}}{2}}left ight)} E n o n b o n d e d = ∑ i > j f i j ( A i j r i j 12 − C i j r i j 6 + q i q j e 2 4 π ϵ 0 r i j ) {displaystyle E_{mathrm {nonbonded} }=sum _{i>j}f_{ij}left({frac {A_{ij}}{r_{ij}^{12}}}-{frac {C_{ij}}{r_{ij}^{6}}}+{frac {q_{i}q_{j}e^{2}}{4pi epsilon _{0}r_{ij}}} ight)} with the combining rules A i j = A i i A j j {displaystyle A_{ij}={sqrt {A_{ii}A_{jj}}}} and C i j = C i i C j j {displaystyle C_{ij}={sqrt {C_{ii}C_{jj}}}} . Intramolecular nonbonded interactions E n o n b o n d e d {displaystyle E_{mathrm {nonbonded} }} 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 {displaystyle f_{ij}=0.5} , otherwise f i j = 1.0 {displaystyle f_{ij}=1.0} . All the interaction sites are centered on the atoms; there are no 'lone pairs'.