Hi,
I'm
wondering if someone can help me gain some wisdom about mixing (combination)
rules in MD simulations. The classical simple point charge models for
water -- SPC and SPC/E -- seem to be widely used to the present day in MD
simulations of aqueous systems. At the same time, it seems that there are
two widely used sets of mixing
(combination)
rules for calculating Lennard-Jones (LJ) interaction parameters for the
interaction of different atomic species. If I understand correctly, these
two most common sets are:
(1)
Lorentz-Berthelot mixing rules: arithmetic for sigma [ sigma_ij = 1 / 2 *
(sigma_i + sigma_j) ], geometric for epsilon [ epsilon_ij = \sqrt{epsilon_i *
epsilon_j} ]
(2) Geometric mixing rules: geometric for sigma
[ sigma_ij = \sqrt{sigma_i * sigma_j} ],
geometric for epsilon [ epsilon_ij = \sqrt{epsilon_i * epsilon_j} ]
and the
Lennard-Jones (LJ) interaction I am referring to is
U_LJ(r_ij) = 4 epsilon_ij * [(sigma_ij / r_ij)^12
- (sigma_ij / r_ij)^6].
Many of the papers reporting MD
simulations of SPC-only or SPC/E-only systems (mostly from the 1980s, 1990s, and
2000s) state that they used the
Lorentz-Berthelot mixing rules (1). However, in the case of SPC or
SPC/E water, epsilon for the hydrogens is 0, so (1) and (2) will give the same
result.
However, the situation becomes less
straightforward when one introduces, for example, Na and Cl ions modeled by the
OPLS-AA force field. OPLS-AA uses mixing rules (2) above: geometric
combination for both sigma and epsilon, as described in the second page of the
Jorgensen group's classic paper (Jorgensen et al., JACS 1996, 118, 45,
11225--11236):
https://doi.org/10.1021/ja9621760
So,
my question is, if I have an OPLS-modeled solute in SPC or SPC/E water, do I use
mixing rules (1) or (2) above?
One possible lead is
this paper from the Frenkel group (Espinosa et al., J. Chem. Phys. 2018, 149,
224501):
https://doi.org/10.1063/1.5054056 In that paper, they
state, "As OPLS/AA has been parameterized for being used in combination
with SPC, TIP3P, and TIP4P water models, we have chosen these models for
simulating water despite them being less accurate than other models in
reproducing the behavior of pure water." Sure enough, when I look at
what appears to be the original OPLS paper -- albeit united-atom, not all-atom
-- Jorgensen et al. state, "The potential functions have the simple Coulomb
plus Lennard-Jones form and are compatible with the widely used models for
water, TIP4P, TIP3P, and SPC" (Jorgensen & Tirado-Rives, JACS 1988,
110, 1657--1666:
https://doi.org/10.1021/ja00214a001
)
But I'm still a little confused... does the
discussion above mean it is legitimate to use mixing rules (2) when simulating
an OPLS solute in
SPC or SPC/E water? As far as I know, most people, and most MD codes, use
either mixing rules (1) or mixing rules (2) -- not a "mixture" of
mixing rules (1) and (2), so to speak.
Does anyone have
wisdom on this? Thank you very much for your
time!
Andrew DeYoung, PhD
Department of Chemistry
Carnegie
Mellon University