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Sep 17, 2014 - We examine the performance of the general AMBER force field (GAFF) and the CHARMM general force field (CGenFF) within the context of ...
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Evaluation of the Performance of GAFF and CGenFF in the Prediction of Liquid−Vapor Saturation Properties of Naphthalene Derivatives Vaibhaw Kumar,† Kaustubh S. Rane,† Scott Wierzchowski,‡ Majeed Shaik,§ and Jeffrey R. Errington*,† †

Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States ‡ Shell International Exploration and Production Inc., Houston, Texas 77079, United States § Shell India Markets Private Limited, Bangalore 560048, India S Supporting Information *

ABSTRACT: We examine the performance of the general AMBER force field (GAFF) and the CHARMM general force field (CGenFF) within the context of capturing the liquid−vapor saturation properties of naphthalene derivatives. Molecular simulation is employed to construct phase diagrams for naphthalene, tetralin, trans-decalin, quinolone, 1-methylnaphthalene, 1naphthol, indole, benzo[b]furan, and benzo[b]thiophene over a range of temperatures that spans from room temperature to the critical point. A general histogram-based approach introduced by Rane and co-workers (J. Chem. Theory Comput. 2013, 9, 2552) is used to calculate saturated densities, vapor pressures, and enthalpies of vaporization. Results for GAFF and CGenFF are compared to experimental data, available correlations, and literature results for the transferable potentials for phase equilibria force field (TraPPE). GAFF and CGenFF provide reasonable descriptions for the saturation properties of the naphthalene derivatives studied. Specifically, GAFF and CGenFF capture the critical temperature to within average errors of 5.6 and 6.3%, respectively, and the boiling temperature to within average errors of 4.0 and 4.4%, respectively. The models generally produce estimates of the critical temperature and boiling temperature that are low relative to experiment. The two models provide a relatively consistent description of the six molecules studied containing two fused six-membered rings, whereas their description of the three molecules examined containing fused five- and six-membered rings often differs appreciably. In terms of an overall comparison, our results do not indicate that one force field clearly outperforms the other. and versatile force field.2 Existing general force fields, such as CHARMM3 and AMBER,4,5 are progressively finding widespread use among the modeling community. They are relatively easy to implement and provide model parameters for a wide range of molecular species, including naphthalene derivatives. The CHARMM and AMBER force fields were originally developed to describe biomolecular systems.3−5 For example, both force fields provide parameter sets for all 20 common amino acids, nucleic acids, and carbohydrates. More recently, the developers of these force fields have released generalized versions, specifically the general AMBER force field (GAFF)6 and the CHARMM general force field (CGenFF),7 which provide parameter sets for a wide range of organic molecules. The models describe nonbonded interactions (interactions between atoms connected by three or more bonds) via a combination of atom-based Lennard-Jones 12−6 interactions and point charges. The intramolecular configuration of the molecule is further governed by a series of bonded interactions, which include harmonic potentials to describe bond stretching and angle bending as well as various cosine series to describe dihedral angles and improper torsion angles. The developers of both models provide the end user a means to obtain point charges via a fit to the molecules electrostatic charge

I. INTRODUCTION Naphthalene and its derivatives are ubiquitous in the petroleum industry. They are present in crude oil and serve as the building blocks for larger asphaltene molecules. They are precursors to the synthesis of several important chemicals such as pesticides, dyes, and industrial solvents. These molecules also form an essential component of several drug formulations and play a crucial role in the pharmaceutical industry. Therefore, a detailed description of their thermodynamic properties is of interest. The phase behavior of naphthalene derivatives is particularly relevant. Within the petroleum industry, separation processes such as distillation are commonly used to fractionate crude oil. Detailed knowledge of the phase behavior of the individual components provides a basis for predicting the phase behavior of the complex mixtures common to crude oil. Accurate descriptions of the saturation properties of petroleum fractions enable one to optimize the performance of unit operations, thereby leading to an efficient use of resources. In this work, we examine the extent to which molecular simulation provides accurate predictions of the saturation properties of naphthalene derivatives. Molecular simulation represents a promising tool for determining the thermophysical properties of organic molecules. One of the key inputs for a classical molecular simulation is the force field, which provides a quantitative description of the intra- and intermolecular interactions for a collection of molecules.1 To obtain accurate property predictions over a wide range of conditions for many species, one needs a robust © 2014 American Chemical Society

Received: Revised: Accepted: Published: 16072

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saturation properties of interest, provide simulation details, and describe the process used to obtain GAFF and CGenFF parameters. Next, we present our simulation results for the molecular models and discuss the extent to which they capture trends provided by experimental data and engineering correlations. Finally, we provide a few concluding remarks.

distribution, which is obtained via a quantum mechanical calculation. Lennard-Jones parameters are typically deduced by fitting to properties such as room-temperature liquid densities and heats of vaporization. The approximations invoked by these modeling schemes include the omission of explicit multibody interactions and polarizability. The Siepmann group has pursued the development of the transferable potentials for phase equilibria force field (TraPPE).8−10 TraPPE has been developed with the aim to maintain transferability of the parameters within a given homologous series. This force field shares the same basic functional form as GAFF and CGenFF. The key distinction is that the Lennard-Jones parameters are fit using liquid−vapor phase equilibrium data. For example, model parameters are often adjusted to reproduce saturated liquid densities, vapor pressures, and critical properties. One of the drawbacks of TraPPE is that the parameter set is limited relative to GAFF and CGenFF. There remain several function groups to parametrize. Recently, Rai and Siepmann extended the explicit hydrogen (TraPPE-EH) version of the force field to describe substituted benzene and polycyclic aromatic compounds.8 In fact, they examined several of the compounds that we consider in our work, and therefore we are now in a position to compare the performance of GAFF, CGenFF, and TraPPE for select naphthalene derivatives. One question that naturally arises is how well these force fields perform with respect to the prediction of liquid−vapor saturation properties, wherein relevant conditions vary over a wide range of temperature and density. Given the approach used to develop TraPPE, the expectation is that this force field will provide a relatively good description of saturation properties. How well GAFF and CGenFF will perform is less certain. Martin previously addressed this question for several small organic molecules, including ethane, 2-methylbutane, ethanol, isobutene, isopropanol, and pentane.11 He considered TraPPE, the AMBER param96 force field (a precursor to GAFF),5 the CHARMM22 force field (a precursor to CGenFF),3 and a few other models. Martin concluded that CHARMM and TraPPE generally provided the most accurate predictions of saturation properties. He noted that CHARMM proved superior in predicting vapor densities, while TraPPE provided higher quality liquid density predictions. While the AMBER force field rated slightly worse overall, Martin noted its favorable performance with respect to capturing saturated vapor densities. In this work, we compare the performance of GAFF, CGenFF, and TraPPE in the prediction of liquid−vapor saturation properties of naphthalene, tetralin, trans-decalin, quinolone, 1-methylnaphthalene, 1-naphthol, indole, benzo[b]furan, and benzo[b]thiophene. We perform calculations with GAFF and CGenFF to determine saturated densities, vapor pressures, enthalpies of vaporization, and critical properties. These results are compared with TraPPE data from the recent study of Rai and Siepmann8 as well as experimental data and commonly used correlations. We utilize a histogram-based approach12 to obtain coexistence properties over a relatively wide range of temperature. We first complete a series of grand canonical simulations to directly obtain estimates of saturation properties at relatively high temperature. We then use an expanded ensemble procedure that allows us to trace the saturation curve over the entire temperature range of interest. This work is organized as follows. In the following section we describe the molecular simulation methods used to compute

II. MOLECULAR SIMULATIONS Simulation Methods. We require a means to compute the properties of molecules that possess topologies characterized by relatively rigid ring structures. The approach that we use has been detailed in earlier reports12 from our group, and therefore we limit our discussion here to an overview of the techniques that we employ. We construct phase diagrams via a general two-step histogram-based approach.12 In the first step, we use grand canonical (GC) simulation to locate saturation points at a minimum of two relatively high temperatures. More specifically, GC simulation is used to determine the density probability distribution of a system at a given temperature and activity, and subsequently histogram reweighting13 is employed to locate the coexistence point. This approach provides a socalled “direct” method for determining saturation properties. The aforementioned density probability distribution covers a range of states that span from the homogeneous vapor to homogeneous liquid, including a myriad of inhomogeneous states at intermediate densities.14,15 This probability distribution typically spans several orders of magnitude and can be difficult to capture. In earlier work,16 we demonstrated that transition matrix Monte Carlo provides an efficient means for computing density probability distributions for “simple” molecules. For molecules with complex topologies and/or interactions, additional challenges come into play. For example, large molecules generally prove difficult to insert and remove from a dense liquid. To address these challenges, we incorporate additional advanced sampling techniques within the histogram-based scheme to arrive at a general method for computing bulk saturation properties.12 Specific strategies that we employ include reservoir grand canonical Monte Carlo (MC),17 a growth expanded ensemble scheme,18 and hybrid MC methods19 to sample the intramolecular degrees of freedom of molecules. We are interested in collecting coexistence data over a wide range of temperature. Applying the direct approach becomes computationally demanding and proves inefficient. Therefore, we employ an indirect scheme to trace saturation lines over a wide range of temperature.12 A schematic of the approach is provided in Figure 1. To initiate the calculation, we use coexistence data obtained with the direct GC-based method described above to formulate a guess of how properties vary along the liquid−vapor saturation line. We now work within an isothermal−isobaric ensemble (NPT), and therefore generate an estimate for how temperature and pressure vary along the saturation line by assuming that the logarithm of the vapor pressure ln Psat varies linearly with reciprocal temperature 1/T. States along this path are sampled via isothermal−isobaric expanded ensemble (NPT-TEE) simulations.12,20 Within these simulations, one creates a series of subensembles that map to specific state points (e.g., 500 subensembles) along the estimate for the saturation line. In this work, we use a scheme in which the subensembles are separated by uniform increments in 1/T. Separate NPT-TEE simulations are completed for the liquid and vapor phases. Thus, we avoid sampling the inhomogeneous states encountered in direct GC simulation at intermediate 16073

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complete reservoir MC moves to refresh the reservoir configurations. The computational cost associated with maintaining the reservoir typically does not exceed 10% of the total computational effort. The Lo and Palmer potential21 is employed to describe the manner in which a partial molecule interacts with the rest of the system during the growth expanded ensemble process. The number of growth stages employed spans linearly from one at low density to approximately ten for dense liquid conditions. We generally take the latter number to be commensurate with the number of heavy atoms in a molecule. A spherical cutoff coupled with a mean-field correction is used to account for long-range Lennard-Jones interactions.1 The Ewald summation is used to compute electrostatic interactions.1 Lennard-Jones interactions and the real-space contribution to the Ewald summation are cutoff at a distance of 16 Å. The algorithm described by Frenkel and Smit1 with a precision of 5 × 10−5 is used to determine the damping factor and number of lattice vectors associated with the Ewald summation. NPT-TEE Simulations. We employ a cubic simulation cell consisting of 150 molecules. The MC move mix includes molecular displacements and rotations, HMC, and HMC-One moves, volume change attempts, and subensemble change attempts. Volume changes are selected with a probability of approximately 1/2N, and subensemble changes are attempted with a probability of 1%. The remaining moves are distributed using the “equal computational cost” approach noted above. The spherical cutoff distance for the Lennard-Jones and realspace Ewald contribution is taken to be a constant fraction of the simulation cell length, usually 25%. Simulations are performed over a broad range of β = 1/kBT (kB is Boltzmann’s constant) with a discretization of Δβ = 2.0 × 1017 J−1. Critical and Boiling Points. The critical temperature Tc is estimated by extrapolating the difference between saturated liquid and vapor densities to zero using the density scaling law22 with a scaling exponent of 0.326. The critical density ρc and pressure Pc are extrapolated using the law of rectilinear diameters23 and the Clausius−Clapeyron equation,24 respectively. This analysis is completed with the 200 highest temperature data points resulting from the NPT-TEE simulations. The boiling temperature Tb is determined via interpolation using the two NPT-TEE points bracketing Psat = 1 atm. Statistical Uncertainties. Statistical uncertainties are determined by performing four independent sets of simulations. The standard deviation of the results from the four simulation sets is taken as an estimate of the statistical uncertainty. Force Fields. In this work we perform simulations using two models: CGenFF7 and GAFF.6 These force fields have similar functional forms and provide parameters for bonded as well as nonbonded interactions. To obtain parameters for a particular molecule, we first optimize its geometry in vacuum at the B3PW91 level of Kohn−Sham density functional theory (DFT) and the 6-31+G** basis set using the commercially available Q-Chem software (version 4.0).25 The optimized structure is then used to identify atom types, bonds, bending angles, and torsion angles present within the molecule as well as to calculate partial charges. The force field parameters and the compatible atomic charges for GAFF are obtained using the Antechamber program.26 whereas those for CGenFF are obtained using the Paramchem Web site.27 We use the AM1BCC method,28 available in Antechamber, to calculate partial charges for GAFF. This method is computationally less

Figure 1. Calculation of liquid−vapor saturation properties from GC and NPT-TEE simulations. Vapor pressures for quinolone are plotted as a function of reciprocal temperature. Blue circles represent data from direct GC simulations. Dashed black and red lines denote the initial linear guess and final (converged) values, respectively. Dashed lines are constructed by connecting the data from 1255 subensembles employed within the NPT-TEE scheme.

densities. These simulations provide the relative Gibbs free energy along the P(T) path sampled. These data, along with a direct coexistence point, are used to ascertain the accuracy of the linear ln Psat − 1/T guess used to initiate the calculation. As one might suspect, this guess typically proves reasonable at relatively high temperature but often misses considerably at low temperature. We now modify the Psat(T) relationship. The NPT-TEE simulations provide the density probability distributions sampled in each subensemble. These distributions are used within a histogram reweighting scheme to estimate the change in the Gibbs free energy upon modification of the pressure. A new estimate for Psat at a given temperature is deduced by determining the pressure for which the difference in Gibbs free energy between the liquid and vapor phases is zero. This modified Psat(T) relationship is now used within a new set of NPT-TEE simulations, and the modification scheme is again used to revise the Psat(T) relationship. The modification cycle is repeated until Psat(T) converges, which typically requires just one iteration beyond the initial linear guess. GC Simulation Details. We employ a cubic simulation cell of 1 × 105 Å3 and span a particle number range from zero to approximately 400 molecules. The MC move mix includes molecular displacements and rotations, hybrid MC (HMC) moves (both HMC and HMC-One12), as well as molecular insertions (or growth) and deletions (or reductions). Insertions/deletions are selected with 60% probability, and the displacement, rotation, HMC, and HMC-One moves are partitioned such that the computational time invested in each move is roughly equal. The reservoir includes 500 molecules in an ideal gas state. At the outset of a simulation, we use a single molecular configuration to populate the reservoir and subsequently equilibrate the molecular configurations before initiating the primary simulation. During a GC simulation, we regularly 16074

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Figure 2. Saturated liquid and vapor densities for the nine compounds studied in this work. Solid blue and red lines denote data obtained using GAFF and CGenFF, respectively. Green circles denote the Gibbs ensemble data obtained by Rai and Siepmann using TRaPPE.8 Dashed black lines denote the correlation for liquid density provided in Yaws’ Thermophysical Properties of Chemicals and Hydrocarbons.31 Black squares represent the experimental liquid densities obtained by Tsonopoulos and Amber.33 Open black, cyan, and violet diamonds represent experimental liquid densities from the Hazardous Substances Data Bank,34 Grzyll et al.,35 and Hales and Townsend,36 respectively. Filled blue, red, and green diamonds show critical points for GAFF (this work), CGenFF (this work), and TRaPPE (Rai and Siepmann8), respectively. Critical points obtained from the NIST Chemistry WebBook30 (experimental measurements33,37−47) are shown as filled black diamonds or black horizontal dashed lines when only the critical temperature is available.

not attempted to determine the location of the melting point for the model systems studied here, so we cannot fully characterize the stability of the low-temperature states we probe. That being said, it is often possible within molecular simulation to push beyond the melting point to study the properties of the supercooled liquid. We begin by examining the vapor−liquid equilibrium (VLE) properties of naphthalene. Rai and Siepmann8 used this compound to obtain parameters within their fitting procedure for the TraPPE model, and therefore the expectation is that this model will provide a good description of the VLE data for naphthalene. The CGenFF and GAFF models underestimate the critical temperature by 6 and 10%, respectively, while the TraPPE model captures this property to within experimental uncertainty. The CGenFF and GAFF models also underestimate the boiling temperature by 4 and 7%, respectively, while the TraPPE model captures this property to within experimental uncertainty. This deviation in Tb corresponds to CGenFF and GAFF estimates of the vapor pressure at the experimental boiling temperature that exceed 1 atm by factors of 1.5 and 2.1, respectively. All of the models do a reasonable

expensive and provides partial atomic charges that resemble those obtained from the restrained electrostatic potential (RESP), which is another method available in Antechamber. The Paramchem Web site uses a bond-charge increment scheme to estimate the partial atomic charges for CGenFF.29

III. RESULTS AND DISCUSSION Figures 2, 3, and 4 provide the saturated densities, vapor pressures, and enthalpies of vaporization, respectively, for the components studied here. The figures contain simulation data for CGenFF, GAFF, and TraPPE8 as well as experimental data available from the NIST Chemistry WebBook,30 Yaws’ Thermophysical Properties of Chemicals and Hydrocarbons,31 Yaws’ Critical Property Data for Chemical Engineers and Chemists,32 specific gravity estimates from Tsonopoulos and Ambrose,33 and others.34−36 We also compile within Table 1 data for select properties. Note that in some cases we present liquid−vapor saturation data at temperatures lower than the experimental melting temperature. For all conditions reported, the condensed phase remains a liquid; i.e., we do not observe any instances of crystallization at lower temperatures. We have 16075

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Figure 3. Vapor pressures for the nine compounds studied in this work. Dashed black lines denote the correlation for vapor pressure provided in Yaws’ Critical Property Data for Chemical Engineers and Chemists.32 Open black circles and triangles denote the normal boiling points and reduced pressure boiling points, respectively, from NIST Chemistry WebBook30 (experimental measurements48−71). The other lines and symbols are defined in the same manner as in Figure 2.

compound has been well studied experimentally relative to the other molecules featured here. The CGenFF, GAFF, and TraPPE models provide a reasonably good and consistent description of the phase behavior. The TraPPE model overestimates Tc and Tb, while CGenFF and GAFF underestimate these properties. The deviations from experiment in model predictions for Tc and Tb do not exceed 5%. The models also provide values for ρliq and ΔHvap that are in reasonably good agreement with experimental values and the Yaws’ correlations.31 Looking closer, GAFF clearly provides the best description of Psat, TraPPE provides the best description of ρliq, and GAFF and CGenFF outperform TraPPE in describing ΔHvap. Experimental data for 1-methylnaphthalene and 1-naphthol are relatively scarce. Regarding 1-methylnaphthalene, CGenFF and GAFF underestimate Tc by 3 and 9%, respectively, and Tb by 3 and 6%, respectively. Relative to Yaws’ correlation,32 CGenFF and GAFF provide Psat estimates that are consistently high. Both the CGenFF and GAFF estimates for ρliq and ΔHvap at room temperature are within 1 and 7% of experimental values. Turning to 1-naphthol, we note that CGenFF and GAFF generate Psat curves that are nearly identical, with both models capturing Tb to within 3%. We now turn our attention to molecules containing fused five- and six-membered rings: indole, benzo[b]furan, and

job of capturing the saturated liquid densities and enthalpies of vaporization, particularly at relatively low temperature. We note that there appears to be an issue with the saturated liquid density correlation for naphthalene provided by Yaws’ Thermophysical Properties of Chemicals and Hydrocarbons,31 as the relevant curve deviates significantly from both experimental data and simulation estimates. Tetralin and trans-decalin form a natural sequence with naphthalene, with the aromaticity increasing from decalin to tetralin to naphthalene. Experimental data30 indicate that the critical and boiling point temperatures increase with increasing aromaticity. The CGenFF force field captures this qualitative trend reasonably well, whereas the GAFF force field predicts a minimum in these temperatures with increasing aromaticity. The primary difference is found in the description of transdecalin. While CGenFF and GAFF provide a relatively consistent description of naphthalene and tetralin, the two models differ considerably for trans-decalin. For example, the difference is particularly noticeable when comparing estimates for ΔHvap. That being said, GAFF appears to give the best overall description of trans-decalin, providing saturated liquid densities and vapor pressures that agree well with the Yaws’ correlations.31,32 The quinoline molecule contains two six-membered rings with one of the rings featuring a nitrogen substitution. The 16076

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Figure 4. Enthalpies of vaporization for the nine compounds studied in this work. Black open circles denote values at 298 K provided by NIST Chemistry WebBook30 (experimental measurements72,73). The other lines and symbols are defined in the same manner as in Figure 2.

pressure. Again, this trend is particularly noticeable for the molecules with two fused six-membered rings. The saturated liquid densities at relatively low temperature (room temperature or melting temperature) are generally within 2−3% of the experimental value. Before concluding, we briefly consider the vapor pressure of the molecules studied here within the context of environmental concerns. Knowledge of vapor pressure of a compound is required to understand its partitioning between liquid and vapor phases.74 Typically, the ratio of concentrations of a particular compound in liquid and vapor phases is expressed as a function of its partial pressure, which in turn is proportional to its vapor pressure. Such partitioning influences the uptake of compounds by the particulate matter present in the atmosphere and the absorption of molecules in the lungs, and therefore impacts one’s health. This is a particularly relevant issue for polyaromatic hydrocarbons (PAHs) because they are considered environmental contaminants. Note that in many cases, PAHs are solids at room temperature, and therefore one is interested in the vapor pressure of a supercooled liquid.74,75 In the past decades, the vapor pressures of various PAHs have been measured using gas chromatography. 75−77 These approaches have been successful in measuring the supercooled vapor pressures of low-volatility compounds. Their main limitation is the requirement of reference or calibration compounds, whose vapor pressures are accurately known.76 Recently, Ahmed and Sandler used molecular dynamics simulations to estimate supercooled vapor pressures of nitroaromatic compounds.78 More specifically, they employed isothermal isobaric ensemble simulations to calculate the Gibbs

benzo[b]thiophene. For indole, CGenFF and TraPPE provide relatively similar descriptions of the saturation properties, whereas GAFF often differs significantly. Relative to the Yaws’ correlation,31 the three models provide values for ρliq that are approximately 6−15% lower, with GAFF estimates much closer to Yaws’ correlation than those for CGenFF and TraPPE. GAFF outperforms the other models in describing Psat, particularly at lower temperatures. In contrast, CGenFF and TraPPE estimates for ΔHvap are in better agreement with Yaws’ correlation. CGenFF and GAFF again differ significantly in their overall description of benzo[b]furan. In this case, CGenFF outperforms GAFF, with CGenFF providing a better description of Psat and ΔHvap. The difference between CGenFF and GAFF is even more pronounced when considering benzo[b]thiophene. For this molecule, TraPPE provides the best description of ρliq, Psat, and ΔHvap. CGenFF provides an adequate description of ρliq but severely overestimates ΔHvap and underestimates Psat. In contrast, GAFF generally underestimates ΔHvap, overestimates Psat, and provides a ρliq curve with a curvature that is considerably different from that exhibited by Yaws’ correlation, CGenFF, and TraPPE. We now consider the general trends exhibited by CGenFF and GAFF. These models typically underestimate Tc and Tb. For example, for the six molecules with two fused sixmembered rings, the Tc and Tb values for trans-decalin provide the only exceptions. We note that there is also considerable diversity in the offset of Tb values with respect to experiment for the three molecules with fused five- and six-membered rings. Given that CGenFF and GAFF generally underestimate Tb, it follows that the models generally overestimate the vapor 16077

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Table 1. Critical Parameters, Normal Boiling Points, and Liquid Densities Obtained with Use of Different Force Fields and from Experimenta compound naphthalene

tetralin

trans-decalin

indole

benzo[b]furan

benzo[b]thiophene

quinoline

1-methylnaphthalene

1-naphthol

model

Tc (K)

ρc (kg/m3)

pc (MPa)

Tb (K)

ρ1 (kg/m3)

ΔHvap at 298 K unless specified (kJ/mol)

GAFF CGenFF TraPPE-EH expt GAFF CGenFF expt GAFF CGenFF Expt GAFF CGenFF TraPPE-EH expt GAFF CGenFF expt GAFF CGenFF TraPPE-EH expt GAFF CGenFF TraPPE-EH expt GAFF CGenFF expt GAFF CGenFF expt

6731 7042 7503 7466 6644 6671 7201 6966 6357 6873 7531 7383 7674 790* 6870 6651

3293 33812 3203 3156 3004 3361 33013 2732 2816

3.80 3.91

9791 (355 K) 9611 (355 K)

51.253 (355 K) 51.661 (355 K)

3411 2691 3094 272* 3581 2911

5.72 3.61

4571 4701 4902 4905 4540 4401 480 4710 4350 4603 5170 5070 5042 527 4561 4421 447 4530 5281 4946 494 5050 4921 5321 5112 4840 4981 5157 5410 5380 552

⟨976⟩ (355 K) 9571 (289 K) 9641 (289 K) [973] (289 K) 7502 (436 K) 7382 (436 K) 759* (436 K) 10911 (355 K) 10101 (355 K)

56.64* (355 K) 55.207 55.289 551 52.48171 50.1634 48.521 69.599 (355 K) 62.7311 (355 K)

1170* (355 K) 11301 (298 K) 10471 (298 K) ((1091)) (298 K) 10951 (355 K) 10911 (355 K)

59.53* (355 K) 57.598 54.373 48.42 50.5215 (355 K) 63.403 (355 K)

1101* (355 K) 10311 (355 K) 10291 (355 K)

51.61* (355 K) 62.7949 60.876

6920 7891 7714 754* 7644 7452 8054 7823 7043 7462 7721 8024 8052

4123 3171 3554 385* 3312 3281 3374 3172 3101 3441 3351

4.11 3.62 7.21 3.71 3.32 3.32

4.3* 4.60 3.90 4.81 4.10 4.1* 4.62 5.11 5.83 3.81 4.31 3.61 4.82 4.61

1047* (355 K) 10281 (289 K) 10121 (289 K) [1023] (289 K) 11012 10651 ((1095)) (372 K)

59.3120 61.417 60.767 57.3242 76.6032 75.1816

a

TRaPPE data are taken from the work of Rai and Siepmann.8 Square brackets, angle brackets, double parentheses, and asterisk symbols denote experimental data from Tsonopoulos and Ambrose,33 Hales and Townsend,36 Hazardous substance databank,34 and Yaws’ Thermophysical Properties of Chemicals and Hydrocarbons.31 The rest of the experimental data are taken from the NIST Chemistry WebBook.30

IV. CONCLUSION We examined the ability of GAFF and CGenFF to capture the liquid−vapor saturation properties of several naphthalene derivatives. Molecular simulation was used to construct phase diagrams for nine compounds, with six molecules containing two fused six-membered rings and three molecules containing fused five- and six-membered rings. We employed a two-step histogram-based procedure, wherein grand canonical simulation was used to directly locate two or more coexistence points at relatively high temperature and an isothermal−isobaric temperature expanded ensemble technique was used to trace saturation curves to relatively low temperature. Our results were compared to experimental data, engineering correlations, and Gibbs ensemble results for TraPPE from the recent work of Rai and Siepmann. The results gathered here indicate that GAFF and CGenFF provide reasonable descriptions of the liquid−vapor saturation properties of naphthalene derivatives. Neither of the two force fields clearly proved superior to the other. However, when considering their performance relative to TraPPE, we find that TraPPE generally outperforms both GAFF and CGenFF. For example, for the four common molecules for which data are available (naphthalene, quinolone, indole, and benzo[b]thiophene), GAFF, CGenFF, and TraPPE capture the critical

free energy of transferring a molecule from its vapor phase to liquid phase. This Gibbs free energy was then used to estimate the supercooled vapor pressures. The advantage of the simulation approach used here is that it permits rigorous calculation of supercooled vapor pressures to relatively low temperatures. Nucleation of the solid phase often proves difficult within molecular simulations, and therefore one can often probe temperatures well below the freezing point. Here, we compare trends in supercooled vapor pressures calculated by employing the GAFF and CGenFF force fields. Such a study can help in understanding the applicability of these force fields for studying the environmental impact of PAHs. Figure 5 provides room-temperature vapor pressure for the PAHs studied here. For those cases in which we did not extend NPT-TEE simulations to temperatures as low as 298 K, an extrapolation was performed by fitting a polynomial of degree 4 or 6 to ln Psat as a function of 1/T. Note that the minimum temperature used in NPT-TEE simulations for most PAHs was 300 K, and therefore the pressures are extrapolated over a narrow temperature range. The results indicate that the calculated vapor pressures depend strongly on the force field. Moreover, the two force fields show different trends with respect to aromaticity and the type of heteroatoms. 16078

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Research and the Rensselaer Polytechnic Institute Computational Center for Nanotechnology Innovations.

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Figure 5. Vapor pressures at 298 K for the nine compounds studied in this work. Filled blue bars and patterned red bars denote values calculated using GAFF and CGenFF force fields, respectively.

temperature to within average errors of 5.0, 5.4, and 2.2%, respectively, and the boiling temperature to within average errors of 4.5, 4.6, and 2.1%, respectively. This result is not surprising, as the force field development strategy employed for TraPPE is designed such that the molecular models accurately capture saturation properties. Finally, we note that GAFF and CGenFF tend to underestimate the critical and boiling temperatures and overestimate vapor pressures. The results from this study suggest that GAFF and CGenFF provide reasonable force fields for describing the phase behavior of systems relevant to the oil and gas industry. For example, these models could be used to study the phase behavior of complex molecules (e.g., asphaltenes), phase separation within multicomponent fluids (e.g., crude oil), and interfacial phenomena related to oil−water systems. Finally, we note that the molecular simulation methods employed here proved efficient and enabled the construction of phase diagrams over a wide range of temperature.

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ASSOCIATED CONTENT

S Supporting Information *

Data presented in Figures 1−5. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: jerring@buffalo.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support of Shell India Markets Private Ltd. Computational resources were provided in part by the University at Buffalo Center for Computational 16079

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