Histogram-Free Reweighting with Grand Canonical Monte Carlo: Post-simulation Optimization of Non-bonded Potentials for Phase Equilibria

Histogram reweighting (HR) is a standard
approach for converting
grand canonical Monte Carlo (GCMC) simulation output into vapor–liquid
coexistence properties (saturated liquid density, ρliqsat, saturated
vapor density, ρvapsat, saturated vapor pressures, Pvapsat, and enthalpy
of vaporization, ΔHv). We demonstrate that a histogram-free reweighting approach, namely,
the Multistate Bennett Acceptance Ratio (MBAR), is similar to the
traditional HR method for computing ρliqsat, ρvapsat, Pvapsat, and ΔHv. The primary advantage of MBAR is
the ability to predict phase equilibria properties for an arbitrary
force field parameter set that has not been simulated directly. Thus,
MBAR can greatly reduce the number of GCMC simulations that are required
to parameterize a force field with phase equilibria data. Four different
applications of GCMC-MBAR are presented in this study. First, we validate
that GCMC-MBAR and GCMC-HR yield statistically indistinguishable results
for ρliqsat, ρvapsat, Pvapsat, and ΔHv in a limiting test case. Second, we utilize GCMC-MBAR to optimize
an individualized (compound-specific) parameter (ψ) for 8 branched
alkanes and 11 alkynes using the Mie Potentials for Phase Equilibria
(MiPPE) force field. Third, we predict ρliqsat, ρvapsat, Pvapsat, and ΔHv for force field j by simulating force field i, where i and j are common force fields from the
literature. In addition, we provide guidelines for determining the
reliability of GCMC-MBAR predicted values. Fourth, we develop and
apply a post-simulation optimization scheme to obtain new MiPPE non-bonded
parameters for cyclohexane (ϵCH2, σCH2, and λCH2).

直方图重加权法（Histogram reweighting, HR）是将巨正则系综蒙特卡洛（grand canonical Monte Carlo, GCMC）模拟结果转换为气液共存性质的标准方法，此类性质包括饱和液态密度ρliqsat、饱和蒸气密度ρvapsat、饱和蒸气压Pvapsat与汽化焓ΔHv。本研究证实，无直方图重加权方法——即多态贝内特接受比法（Multistate Bennett Acceptance Ratio, MBAR）——在计算ρliqsat、ρvapsat、Pvapsat及ΔHv时，与传统HR方法的表现相近。MBAR的核心优势在于，可直接预测未经直接模拟的任意力场参数集对应的相平衡性质，因此能够大幅减少利用相平衡数据拟合力场参数所需的GCMC模拟次数。本研究展示了GCMC-MBAR的四类不同应用场景：其一，在极限测试案例中验证了GCMC-MBAR与GCMC-HR在计算ρliqsat、ρvapsat、Pvapsat及ΔHv时的统计结果无显著差异；其二，基于相平衡米氏势场（Mie Potentials for Phase Equilibria, MiPPE），利用GCMC-MBAR为8种支链烷烃与11种炔烃优化了专属（化合物特异性）参数ψ；其三，通过模拟力场i来预测力场j的ρliqsat、ρvapsat、Pvapsat与ΔHv，其中i与j均为文献中常见的力场；此外，本研究还给出了判断GCMC-MBAR预测值可靠性的指导准则。其四，开发并应用了一套模拟后优化方案，以获取环己烷的新型MiPPE非键相互作用参数（ϵCH2、σCH2与λCH2）。