Development of Polarizable Gaussian Model for Molecular Mechanical Calculations I: Atomic Polarizability Parameterization To Reproduce ab Initio Anisotropy

A set of atomic polarizability parameters for a new polarizable Gaussian model (pGM) has been developed with the goal to accurately reproduce the polarizability anisotropy, taking advantage of its ability to attenuate all short-range electrostatic interactions, by fitting the ab initio molecular polarizability tensors (Apq) calculated at the B3LYP/aug-cc-pVTZ level. For comparison, we also rederived the parameters for three Thole models in which the 1–2 (bonded), 1–3 (separated by two bonds), and 1–4 (separated by three bonds) interactions are fully included. The average percent errors (APEs) of molecular polarizability tensors for 4842 molecules or dimers are 2.98, 3.76, 3.28, and 3.82% for the pGM, Thole linear, Thole exponential, and Thole Amoeba models, respectively, with atom-type independent, universal screening factors (USF). The APEs are reduced further to 2.30, 2.69, 2.25, and 2.48% for the four corresponding polarizable models with atom-type dependent, variable screening factors (VSF). It is encouraging that the pGM with variable screening factors achieved APEs of 1.83 for 1155 amino acid analogs, dipeptides, and tetrapeptides, 1.39 for 28 nucleic acid bases, 0.708 for 1464 water clusters, and 1.99 for 85 dimers of water and biological building blocks. Compared to the new set of models, the APEs of the old Thole models that were fitted to isotropic molecular polarizabilities are 8.7% for set A (without the 1–2 and 1–3 interactions) and 6.3% for set D (with the 1–2 and 1–3 interactions) models, respectively. MPAD, a metric of molecular polarization anisotropy difference based on the diagonal terms of molecular polarizability tensors was defined and applied to assess the polarizable models in reproducing the ab initio molecular polarization anisotropy. The MPADs are 3.71, 4.70, 4.11, and 4.77% for the pGM, Thole linear, Thole exponential, and Thole Amoeba USF models, respectively. The APEs are reduced further to 2.85, 3.58, 2.90, and 3.15% for the four corresponding VSF models. Thus, the new pGM and Thole models notably improve molecular polarization anisotropy. Since pGM attenuates all short-range electrostatic interactions, its application is expected to improve stability in charge fitting, energy, and force calculations and the accuracy of multibody polarization.

本研究开发了一套全新可极化高斯模型（polarizable Gaussian model, pGM）的原子极化率参数，依托该模型可衰减所有短程静电相互作用的特性，以精准重现极化各向异性为目标，通过拟合B3LYP/aug-cc-pVTZ级别下计算得到的从头算分子极化率张量（Apq）完成参数拟合。为便于对比，我们还重新推导了三类托勒模型（Thole models）的参数，这三类模型分别完整包含1–2（成键）、1–3（间隔两个化学键）及1–4（间隔三个化学键）相互作用。针对4842个分子或二聚体体系，采用与原子类型无关的通用屏蔽因子（universal screening factors, USF）时，pGM、托勒线性模型、托勒指数模型及托勒Amoeba模型的分子极化率张量平均百分误差（average percent errors, APEs）分别为2.98%、3.76%、3.28%及3.82%。当采用与原子类型相关的可变屏蔽因子（variable screening factors, VSF）时，上述四类可极化模型的APEs进一步降至2.30%、2.69%、2.25%及2.48%。值得欣喜的是，采用可变屏蔽因子的pGM在1155个氨基酸类似物、二肽及四肽体系中取得了1.83%的APEs，在28个核酸碱基体系中为1.39%，在1464个水团簇体系中为0.708%，在85个水与生物构建单元的二聚体体系中为1.99%。相较于本研究提出的新型模型，此前基于各向同性分子极化率拟合得到的旧版托勒模型，在集合A（未包含1–2和1–3相互作用）与集合D（包含1–2和1–3相互作用）中的APEs分别为8.7%与6.3%。本研究定义了基于分子极化率张量对角项的分子极化各向异性差异度量（MPAD），用于评估可极化模型对从头算分子极化各向异性的重现能力。采用USF时，pGM、托勒线性、托勒指数及托勒Amoeba模型的MPAD分别为3.71%、4.70%、4.11%及4.77%；采用VSF时，上述四类模型的MPAD进一步降至2.85%、3.58%、2.90%及3.15%。由此可见，新型pGM与托勒模型显著提升了分子极化各向异性的重现精度。由于pGM可衰减所有短程静电相互作用，预计其在电荷拟合、能量与力场计算中可提升稳定性，并改善多体极化计算的准确性。