Hi guys,

I compared the dihedral coefficients in the loplsaa.lt of the latest moltempalte (2019-8-28) with those of the original papers (Sui, Pluhackova, Böckmann, J.Chem.Theory.Comp (2012), 8(4), 1459 and Pluhackova,…,Böckmann, J.Phys.Chem.B (2015), 119(49), 15287), and I found some problems.

The dihedral style that Böckmann’s group use is Ryckaert-Bellemans (RB) function:

V = C0 + C1 cos(ϕ) + C2 cos(ϕ)^2 + C3 cos(ϕ)^3

In the moltemplate version (or more accurately, the Tinker version), the dihedral style is a Fourier function, which is called “opls” in LAMMPS:

V = 1/2 * [F1(1+cos(ϕ))+F2(1−cos(2ϕ))+F3(1+cos(3ϕ))+F4(1−cos(4ϕ))]

There is conversion relation to translate a Fourier function to the RB function:

C0 = F2 + (F1+F3)/2.0

C1 = 0.5 * (-F1+3*F3)
C2 = -1.0*F2 + 4*F4

C3 = -2 * F3

see Eq. (33) of this Gromacs doc:

http://manual.gromacs.org/current/reference-manual/functions/bonded-interactions.html

However, using the above relation to translate a RB function to a Fourier function could sometimes lead to mistake. If you use the above relation to convert the parameters for RB (C0~C3) to “opls” parameters (F1~F4), you’ll find you don’t really need C0, C1~C3 are sufficient to yield F1~F3, and F4 = 0. This is how Tinker convert the parameters to “opls” form. Then when you use these resulted F1~F4 to calculate back to C0’~C3’, you’ll find the C0’ don’t equal to the original C0. (I’ve tested the parameters from loplsaa.lt, trying to convert them back to the orignal RB form, and it turned out that I obtained correct C1~C3 but failed to get correct C0). Böckmann’s group also performed a conversion in their first lopls paper (Siu et al. 2012, see Table 2). If you use the above relation to convert their Fourier dihedral parameters (middle part of that table), you can’t get their correct C0 either.

Actually, given a RB function with C0,C1,C2,C3, the corresonding Fourier function should be:

V = 1/2 * [F0(1+cos(0)+F1(1+cos(ϕ))+F2(1−cos(2ϕ))+F3(1+cos(3ϕ))+F4(1−cos(4ϕ)]

= F0 + 1/2 * [F1(1+cos(ϕ))+F2(1−cos(2ϕ))+F3(1+cos(3ϕ))+F4(1−cos(4ϕ)]

I guess this may be what Böckmann’s group actually used for conversion. The constant term, F0, is essential to account for the C0. Using this form to translate their Fourier parameters, I successfully reproduced the C0~C4.

Therefore, I think we can’t use “opls” dihedral-style in LAMMPS to convert the RB dihedral function (like Tinker did). Instead, an option is to use “multi/harmonic” dihedral-style in LAMMPS which is the same form as the RB function.

I hope anyone can correct me if I’m wrong. Any comments or ideas are welcome!

Best,

Lingnan