On the Transferability of Three Water Models Developed by Adaptive Force Matching

Hongyi Hu; Zhonghua Ma; Feng Wang1    Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas, USA
1 Corresponding author: email address: fengwang@uark.edu

Abstract

Water is perhaps the most simulated liquid. Recently, three water models have been developed following the adaptive force matching (AFM) method that provides excellent predictions of water properties with only electronic structure information as a reference. Compared to many other electronic structure-based force fields that rely on fairly sophisticated energy expressions, the AFM water models use point-charge-based energy expressions that are supported by most popular molecular dynamics packages. An outstanding question regarding simple force fields is whether such force fields provide reasonable transferability outside of their conditions of parameterization. A survey of three AFM water models, B3LYPD-4F, BLYPSP-4F, and WAIL, are provided for simulations under conditions ranging from the melting point up to the critical point. By including ice-Ih configurations in the training set, the WAIL potential predicts the melting temperate, TM, of ice-Ih correctly. Without training for ice, BLYPSP-4F underestimates TM by about 15 K. Interestingly, the B3LYPD-4F model gives a TM 14 K too high. The overestimation of TM by B3LYPD-4F mostly likely reflects a deficiency of the B3LYP reference. The BLYPSP-4F model gives the best estimate of the boiling temperature TB and is arguably the best potential for simulating water in the temperature range from TM to TB. None of the three AFM potentials provides a good description of the critical point. Although the B3LYPD-4F model gives the correct critical temperature TC and critical density ?C, there are good reasons to believe that the agreement is reached fortuitously. Links to Gromacs input files for the three water models are provided at the end of the chapter.

Keywords

Force matching

Critical point

Surface tension

Liquid-vapor

Ab initio

Force field

Melting

1 Introduction

Water is ubiquitous and generally considered to be one of the most versatile liquids. It is not surprising that a significant amount of simulation has been done to investigate various properties of water. There are probably more potentials developed for water than any other liquids (1). Early models that gained significant popularity include SPC (2), SPC/E (3), TIP3P (4), and TIP4P (5). All of these models were developed by fitting to experimental properties. Of these, arguably, SPC/E and TIP4P are considered to be the most successful. In recent years, new members in the TIP4P family, such as TIP4P-Ew (6) and TIP4P-2005 (7), have been created and are generally believed to be more accurate than the earlier ones.

Although maybe not as popular as experiment-based potentials, quite a few water models were developed by fitting to electronic structure calculations. Early electronic structure-based models, such as the Matsuoka, Clementi, Yoshimine (MCY) model (8), fail to predict several key properties, such as the density of water. Consequently, these models are not as widely used as experiment-based potentials. In recent years, electronic structure-based potentials, such as the Thole-Type Model (TTM) family (9,10), Distributed Point Polarizable (DPP) family (11,12), Huang, Braams, Bowman (HBB) family (13,14), and many others (15,16), are more sophisticated and accurate. However, these potentials are rather expensive to evaluate and have only limited support in public domain molecular dynamics (MD) packages.

Although experiment-based potentials satisfactorily reproduce the most important properties, it is very hard to judge if a property is reproduced for the correct reason. Also, it is hard to determine if such potentials can reliably predict properties not being fit. In this sense, a potential fit only to electronic structure information is more robust in that if such a potential does reproduce an experimental property, it is more likely that such an agreement is obtained by correctly capturing the underlying physics.

Recently, several water potentials were developed based on the adaptive force matching (AFM) approach (17-21). These water models were created by only fitting to electronic structure calculations. With AFM, the fit was done iteratively in the condensed phase. Obtaining reference forces in the condensed phase allows fitting of relative simple energy expressions that implicitly capture many-body effects. Only energy expressions that are supported by popular MD packages, such as Gromacs, were used in typical force fields developed by AFM (20-23). With simple point-charge-based energy expressions, the three water models investigated in this work require computational resources comparable to that of TIP4P for each force evaluation. It is worth mentioning that these models are generally a factor of two slower than TIP4P due to the requirement for smaller time steps. However, the use of deuterium to replace hydrogen in simulations alleviates this disadvantage.

Although simple energy expressions lead to efficient force fields, they may limit the transferability of the potential. The philosophy of AFM is to fit a force field for a specific condition. This is achieved by including, in the training set, only reference configurations representative of the condition of interest. This is actually not very different from the development of some, if not most, experimental-based force fields, where only experimental properties under limited conditions were fit. For example, the TIP4P potential was fit only to properties at 1 atm and 25 °C (5). Nonetheless, these water models are frequently used under thermodynamic conditions not tested during parameterization (24-27).

Several water models have been created based on AFM. Some of the models (20,21) were designed to be used with ab initio free energy perturbation theory (28,29). Three recent water models, B3LYPD-3F, BLYPSP-4F, and WAIL, offer similar performance and are capable of simulating the liquid states (17-19). The objective of this chapter is to investigate the performance of these three models outside of the thermodynamic conditions of parameterization. Under the conditions of parameterization, the AFM models have been found to be highly competitive with experiment-based potentials. For example, the WAIL potential designed for the modeling of ice and water gives a very good description of the melting temperature (TM) of ice and temperature of maximum density (TMD) of water. It is interesting to check if these models are better or worse than experimental-based potentials outside their "comfort zone." These results should establish the applicability of these models as general purpose potentials for water.

In order to accomplish this purpose, we investigate TM, diffusion constant (D), viscosity (?), surface tension (?), static dielectric constant (?s), TMD, boiling temperature (TB), critical temperature (TC), critical density (?C), and critical pressure (PC). In this chapter, we will provide a brief review of the AFM procedure in Section 2, and a brief summary of the three water models in Section 3. Computational details are reported in Section 4. Results and summary are presented in Section 5. Conclusion is given in Section 6.

2 The Adaptive Force-Fitting Procedure

AFM was designed to fit a force field to best reproduce electronic structure forces obtained under a particular thermodynamic condition or a set of thermodynamic conditions of interest. AFM requires an initial guess to the force field. From such a force field, a typical realization of AFM contains three steps as illustrated in Figure 2.1.

The first step in AFM is the sampling step. In this step, the phase space associated with thermodynamic conditions of interest is traversed with a sampling algorithm, such as MD or Monte Carlo (MC). The guess force field will be used to integrate MD or MC trajectories. Configurations are randomly selected from the trajectories to form the training set. Standard sampling algorithms traverse the phase space according to the Boltzmann weight of each microstate. More important regions of the phase space are thus better represented in the...