On the Temperature Transferability of Force Field Parameters for

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Molecular Mechanics

On the Temperature Transferability of Force Field Parameters for Dispersion Interactions Zheng Gong, Huai Sun, and Bruce E. Eichinger J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00104 • Publication Date (Web): 25 May 2018 Downloaded from http://pubs.acs.org on May 26, 2018

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Journal of Chemical Theory and Computation

On the Temperature Transferability of Force Field Parameters for Dispersion Interactions Zheng Gong1, Huai Sun1*, Bruce E. Eichinger2

1

School of Chemistry and Chemical Engineering, Materials Genome Initiative Center, Shanghai Jiao Tong University, Shanghai, 200240, China

2

Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA *

To whom correspondence should be addressed: [email protected]

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Abstract

The accuracy of force fields is a key to the successful prediction of the thermodynamic properties of materials. In simulations of organic molecules over large temperature ranges, atomistic force fields that are parameterized at, or near, ambient temperatures are found to systematically underestimate the intermolecular dispersion interactions at elevated temperatures. Analysis of the underestimates using diatomic molecules indicates that a minor part is due to the change in molecular polarizability, while the major part is due to the reduced dielectric constant of the bulk liquid as the density decreases with increasing temperature. By writing the dispersion parameter as a linear function of temperature, we have successfully enhanced the temperature transferability of atomistic force fields. This approach is tested on 66 molecular liquids covering four functional groups - alkane, aromatic, ether, and ketone-aldehyde – over a broad range of temperatures by calculating liquid density, heat of vaporization, isobaric heat capacity and shear viscosity.


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1.

Introduction

It is highly desirable to quantitatively predict thermodynamic and transport properties of molecular liquids using molecular simulations. Many chemical processes take place at broad range of temperature and pressure, however, experimental data is often absent for the purpose of designing or optimizing processes. To advance the goal of computing properties with simulations, the Industrial Fluid Properties Simulation Challenge (IFPSC) was organized over a decade ago to promote the development of simulation techniques.1-3 The success of simulation predictions depends critically on the accuracy of the force fields used to describe both inter- and intra-molecular interactions. Most atomistic force fields such as OPLS/AA4, COMPASS5, CGenFF6 and our recently developed TEAM7 are optimized at one temperature, which it is well known that these force fields are valid for applications for a range of temperature encompassing the data set used for parameterizations.8-11 However, the transferability of atomistic force fields over wider temperature ranges is questionable. To illustrate the problem, we show the densities calculated for dodecane, benzene, diethyl ether and acetone over wide temperature ranges at experimental vapor pressures using three published force fields - CGenFF6, OPLS/1.14*CM1A12 and TEAM-AMBER7 in Figure 1. Using these force fields, as temperature increases, the predicted densities decrease more rapidly than the experimental data. The deviations indicate that the



cohesive strength of the intermolecular interactions are gradually underestimated as the temperature increases. For these molecules the intermolecular interactions are predominantly the London dispersion interactions, which are induced dipole-dipole interactions. Given that the critical issue in many-body quantum theory is the proper account of dielectric screening between interacting charges that are separated by other charges, we have been led to contend that most molecular force fields do not explicitly account for all of the contributions that screening makes to modulating the strength of cohesive interactions. Our simulation data indicates that the attractive dispersion energy of the commonly accepted force fields should be made temperature dependent to improve the fit to experiment at elevated temperature. As shown in the Figure 1, with a correction to the dispersion energy as explained below, we can predict the densities accurately. In this work, we demonstrate that two factors, the molecular polarizability and bulk dielectric constant, account for the underestimation of dispersion interactions at elevated temperature in classical force fields. By writing the dispersion interactions as a function of temperature, a new force field is optimized using experimental density and heat of vaporization over broad ranges of temperature. The resulting force field is validated by calculating various thermodynamic properties of molecules.


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2.

Temperature dependent dispersion interaction

The polarizabilities of noble-gas molecules, diatomic molecules and methane in the gas phase have been measured experimentally.13 It has been shown that the polarizabilities of the noble gas-molecules are independent of temperature, but the polarizabilities of polyatomic molecules increase with the temperature in the order of 1 % per 1000 K, which is attributed to the increased average molecular volume due to increasing occupation of higher energy levels of rotation and vibration at elevated temperatures.14,15 We calculated the polarizabilities of a group of diatomic molecules, H2, N2, O2 and F2 at CCSD(T)/aug-cc-pVQZ16,17 level of theory using Gaussian 09 software18. The polarizability of the diatomic molecule increases ca. 1% as the bond length increases 1%. However, the contribution from the increased molecular polarizability accounts for only a small part of the total increased dispersion energy. Using the liquid data as shown in Figure 1, we see that about 1.4 % increase in the strength of the dispersion energy per 100 K temperature change accounts for a significant improvement in predictions for alkanes and ethers in the temperature range of 100-600 K. A major contribution of the increased dispersion energy in liquid phase is due to the reduced dielectric constant as the temperature increases. According to the ClausiusMossotti theory of polarization, the dielectric constant, , without a permanent dipole is



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given as:

=

(1.)

where is molecular polarizability and is the number density. The equation may be inverted to: =

(2.)

Choose a density and expand to first order around to obtain: = 1 +

− + ⋯

= 1 + − + ⋯

(3.)

It should be noted that is positive definite. Therefore, the dielectric constant decreases as the density decreases as the temperature increases. Because the dispersion energy is the interaction between induced-dipoles, the reduced dielectric constant leads to an apparent increase in the dispersion energy. A reduction in the dielectric constant also increases the strength of the charge-charge interactions. In normal atomistic (nonpolarizable) force fields, the electrostatic interactions are represented by columbic interactions of static point charges. For the molecules of interest here, the charge-charge interactions are not large and tend to be screened by neighboring charges, similar to Debye-Huckel screening. Although the dynamic polarization (e.g. rotation of electric dipole moments) is modeled by using the static charge model, the induced polarization is not. The induced polarization contributes to additional dielectric screening, which has an


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impact on the long-range interactions. In normal practice, the force field parameters are optimized effectively to represent the averaged interaction over a limited range of temperature; as we have shown, deviations become apparent over large temperature ranges. Both factors discussed above can be included in a scaled constant of the dispersion term: ∗ = where the scaling factor

!"#$ % is

!"#$ %

(4.)

temperature dependent. Using the approximately

linear dependence, we parameterize a linear function !"#$ %

= 1 + &'% − %()* +.

(5.)

The reference temperature %()* is conveniently fixed at 298 K. Using the most common Lennard-Jones (LJ-12-6) function, the well-depth and diameter parameters are expressed as: ,% = /% =

!"#$ %,-.

0 1

!"#$

%/-.

(6.) (7.)

To test our model, we implemented the temperature dependent terms with the TEAM-AMBER7 force field. The functional form is: 2=

3:,< 34 37 6 − 6 + 8 − 8 + 9 1 − cos@A + B 2 2 2

On the Temperature Transferability of Force Field Parameters for

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