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Molecular Mechanics
Development of Polarizable Gaussian Model for Molecular Mechanical Calculations I: Atomic Polarizability Parameterization to Reproduce Ab Initio Anisotropy Junmei Wang, Piotr Cieplak, Ray Luo, and Yong Duan J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00603 • Publication Date (Web): 15 Jan 2019 Downloaded from http://pubs.acs.org on January 15, 2019
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Journal of Chemical Theory and Computation
Development of Polarizable Gaussian Model for Molecular Mechanical Calculations I: Atomic Polarizability Parameterization to Reproduce Ab Initio Anisotropy
Junmei Wang,† Piotr Cieplak,‡ Ray Luo,⊥ and Yong Duan§ †Department
of Pharmaceutical Sciences, University of Pittsburgh, 3501 Terrace St Pittsburgh,
PA 15261, United States ‡ SBP
Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037,
United States ⊥Departments
of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering,
Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States §UC
Davis Genome Center and Department of Biomedical Engineering, University of California,
Davis, One Shields Avenue, Davis, California 95616, United States
Corresponding authors: Junmei Wang, 412-383-3268,
[email protected] Yong Duan, 530-754-7632,
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ABSTRACT 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 the Set A (without the 1-2 and 1-3 interactions) and 6.3% for the 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.
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Journal of Chemical Theory and Computation
List of Abbreviations Used in the text: A:
Molecular polarizability tensor
AA:
Set A Applequist model
AE:
Set A Thole exponential model
AL:
Set A Thole linear model
APE:
Average percent error
AT:
Set A Thole Amoeba model
AUE:
Average unsigned error
DA:
Set D Applequist model
DE:
Set D Thole exponential model
DL:
Set D Thole linear model
DT:
Set D Thole Amoeba model
ESP:
Electrostatic potential
FF:
Force field
MPAD:
Molecular polarization anisotropy difference
pGM:
Polarizable Gaussian Model
RMSE:
Root-mean-square error
Set A:
Thole polarizable models with 0% 1-2 and 1-3 and 100% 1-4 interactions
Set D:
Thole polarizable models with 100% 1-2, 1-3 and 1-4 interactions
USF:
universal screening factor
VSF:
variable screening factor
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1. INTRODUCTION Force field is an integral and critical component that forms the foundation for molecular modeling. Because of its simplicity and robustness, the effective functional form (Eq. 1) has been extensively used in many biomolecular force fields, which include AMBER FF94,1 FF99,2 FF99SB,3 FF034, FF12SB,5 FF14SB,6 CHARMM,7 OPLS,8-9 and GROMACS,10 and numerous others. 2
𝑉𝐴𝐹𝐹 = ∑ 𝐾𝑟 (𝑟 − 𝑟𝑒𝑞 ) + ∑ 𝐾𝜃 (𝜃 − 𝜃𝑒𝑞 ) 𝑏𝑜𝑛𝑑𝑠
2
𝑎𝑛𝑔𝑙𝑒𝑠 𝑁
+
∑ 𝑑𝑖ℎ𝑒𝑑𝑟𝑎𝑙𝑠
𝑞𝑖 𝑞𝑗 𝐴𝑖𝑗 𝐵𝑖𝑗 𝑉𝑛 [1 + cos(𝑛𝜙 − 𝛾)] + ∑ ( + 12 − 6 ) 2 𝑅𝑖𝑗 𝑅𝑖𝑗 𝑅𝑖𝑗
(1 )
𝑖
