Toward Accurate and Efficient Predictions of Entropy and Gibbs Free

Article pubs.acs.org/JPCC

Toward Accurate and Efficient Predictions of Entropy and Gibbs Free Energy of Adsorption of High Nitrogen Compounds on Carbonaceous Materials Andrea Michalkova Scott,*,† Leonid Gorb,‡ Elizabeth A. Burns,‡ Sergey N. Yashkin,§ Frances C. Hill,† and Jerzy Leszczynski∥ †

U.S. Army Engineer Research and Development Center (ERDC), Vicksburg, Mississippi 39180, United States Badger Technical Services, LLC, Vicksburg, Mississippi 39180, United States § Samara State Technical University, 443100 Samara, Russian Federation ∥ Interdisciplinary Nanotoxicity Center, Department of Chemistry and Biochemistry, Jackson State University, Jackson, Mississippi 39217, United States ‡

S Supporting Information *

ABSTRACT: The adsorption of high nitrogen compounds (HNCs) on the selected adsorption sites of carbonaceous materials from the gas phase has been investigated by ab initio quantum chemical methods at the density functional level applying both periodic and cluster approaches with M06-2X and BLYP functionals including dispersion forces (BLYPD2). Among the possible structures of the adsorption complexes, the most stable systems possess nitrogen-containing heterocycles in a parallel orientation toward the modeled carbon surface. The adsorption enthalpies, calculated using the rigid rotor-harmonic oscillator approach (RRHO), were in good agreement with available experimental data. This approach was shown to provide sufficiently accurate adsorption enthalpies from the gas phase for the HNC−carbon systems. The vibrational, rotational, and translation contributions to the adsorption entropy were also analyzed by the approach extended beyond the RRHO scheme. The effects of anharmonic vibrations and internal rotations of the adsorbate on the adsorption sites of the modeled carbon surface were estimated. The Gibbs free energies calculated using the RRHO approach were adjusted to take into account the heterogeneity of the carbon surfaces and underestimation of the adsorption enthalpies at the BLYP-D2(PBC) level. The corrected Gibbs free energy values of adsorption are negative for all of the investigated HNC−carbon systems, and they agree well with available experimental data. This suggests an effective adsorption of selected high nitrogen compounds on carbonaceous materials from the gas phase at 298.15 K. Partition coefficients for distribution of high nitrogen compounds on modeled carbon surfaces were also predicted in good agreement with the experimental results. are expensive and time-consuming.5 Computational predictions of Kd are indirect using the molecular structures of chemicals based on their correlations with the molecular descriptors (QSAR studies).6−9 A direct way to determine the Kd coefficients is to measure or compute the Gibbs free energies that govern the corresponding phase transition. These Gibbs free energies can be represented by the adsorption Gibbs free energies calculated for the partitioning of environmental contaminants between the carbonaceous material and gas phase (air) or between the carbonaceous material and solution (water bulk). A search of available literature suggests that only a few papers were published to produce values (both experimentally and computationally) for the Gibbs free energies of adsorption on carbon-containing surfaces10−14 and corresponding partition

1. INTRODUCTION Adsorption on carbonaceous materials has gained in importance recently since this phenomenon plays a significant role in several applications like crystallization,1 heterogeneous catalysis,2 and stabilization of nanoparticles.3,4 In spite of large interest in the development of new technologies for the processes mentioned above, the specific mechanisms of adsorption of the target compounds (especially organic contaminants) are still ambiguous. Evaluation of the environmental behavior of organic contaminants has become a principal goal in the assessment of the environmental risk posed by these substances. Another chemical property, which is of great importance in evaluating the fate and persistence of organic contaminants in the environment, is the soil/water partition coefficient (Kd) with the carbonaceous material selected as a component of soil. Kd determines the distribution of chemicals in the environment and so helps to estimate the ecological consequences that may follow from this distribution. Experimental studies of the Kd values (adsorption phenomena) © 2014 American Chemical Society

Received: December 12, 2013 Revised: February 12, 2014 Published: February 14, 2014 4774

dx.doi.org/10.1021/jp4121832 | J. Phys. Chem. C 2014, 118, 4774−4783

The Journal of Physical Chemistry C

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coefficients.4,15−20 This is the main reason we have started developing computational protocols to accurately calculate thermodynamic parameters of adsorption on carbon surfaces.10−13 The adsorption of benzene, polycyclic aromatic hydrocarbons (PAHs), and nitroaromatic compounds (NACs) on the carbonaceous surfaces from the gas phase and water solution was investigated at the DFT, MP2, and CCSD(T) levels of theory applying the cluster and periodic approaches.13 Computationally inexpensive and accurate prediction of thermodynamic parameters for studied adsorption phenomena were evaluated based on comparison with available experimental data. The best accuracy for the adsorption enthalpies was obtained from the calculations that include periodic boundary conditions (PBCs) and was performed at the BLYP level with inclusion of dispersion forces (BLYP-D2). However, limited experimental data on the adsorption entropies did not allow us to make definitive conclusions as to whether these computationally effective approximations can accurately predict the adsorption entropy values (TΔSads). To obtain theoretical results that correspond with experimental data, an empirical fitting of the calculated entropy values was performed. The objective of this paper is to continue our investigations utilizing efficient computational approaches to accurately predict the Gibbs free energies of adsorption. The main focus of this study is to investigate the accuracy of calculated adsorption entropies while also taking into account accurate prediction of the adsorption enthalpies. To address these issues, adsorption of various six-membered aromatic nitrogen-containing heterocyclic contaminants including pyridine, pyrimidine, and multiple azine compounds on different carbon surface models was computed. Publications regarding this subject are few. The adsorption energy values for pyridine and 1,3,5triazine interacting with graphene have already been calculated at different DFT levels (GGA and LDA, PBE-2D, PBE-D).21−25 The parallel type of adsorption was found to be preferable. Only a few experimental studies were published on the adsorption of pyridine, pyrazine, pyrimidine, and 1,3,5-triazine on different forms of carbon,26−30 in which heats of adsorption were measured for interactions with oxidized and nonoxidized activated carbon26,30 and graphitized thermal carbon black.27−30 Gas−solid chromatography was used to measure the heat of the adsorption for pyridine on various surfaces.31

2.1. Periodic Approximation. The CPMD (Car− Parrinello molecular dynamics) software32 and the plane-wave DFT method33 were employed to carry out the PBC calculations. The gradient-corrected BLYP functional34,35 was used with a plane-wave expansion of Kohn−Sham orbitals with an energy cutoff of 200 Ry. Only the Γ-point was considered for the Brillouin-zone sampling. The dispersion term was included at the PBC level using the transferable C6-coefficients of Grimme36 (notation BLYP-D2(PBC) will be used in the text and tables, where D2 is used to express inclusion of the dispersion term in the calculations). The C6/R6 pairwise additive potential was applied to account for long-range dispersion effects. This model has been shown to be successful in dealing with small molecular adducts, π···π stacking systems, and DNA base pairs.37−40 The nonconserving dual-space Gaussian pseudopotentials by Goedecker−Teter−Hutter41,42 were adopted to describe the core electrons for all atoms. Minima on the BLYP potential energy surface were located with fully relaxed atomic positions. Energies were converged to 10−5 eV in all cases. The structures were optimized until the absolute values of the Hellmann−Feynman forces acting on the atoms in the relaxed structure were less than 0.05 eV/Å. The periodic model of the carbon surface was constructed using the experimental crystal structure data of graphite.43 The bulk unit cell contains a single layer of carbon atoms since it was previously shown that a second carbon layer has a small influence on the optimized geometries and energetics of various aromatic compounds adsorbed on the carbon surfaces.13 Thus, the second carbon sheet was removed and replaced by a layer of adsorbates (one molecule per a unit cell). The initial distance between the adsorbate and surface was set up to be half of the experimental crystal lattice vector c of graphite (3.354 Å = 1/ 2c). A 20 Å vacuum space was added in the c direction. The computational supercell used for all PBC calculations was hexagonal with dimensions a = 9.844 Å, b = 9.844 Å, c = 23.354 Å as was also applied in our previous work.13 The hexagonal form of natural graphite possesses the ABABAB type stacking, which was applied to the periodic models of carbon in this paper.44,45 The AB stacking was also found to be the most favorable for adsorption of benzene and PAHs (naphthalene) on graphite.46 2.2. Cluster Approximation. The cluster models of adsorbate−carbon for further DFT calculations of the adsorption enthalpies, entropies, and Gibbs free energies were prepared using the PBC optimized structures of selected high nitrogen compounds (HNCs) interacting with the modeled carbon surface. The optimum adsorbate−surface distance was determined from the results of the PBC calculations. As was shown in our previous study,13 extension of the cluster model and addition of the second layer to the carbon surface models insignificantly improve the accuracy of the Gibbs free energies. Moreover, it was revealed that the cluster model composed of a single coronene molecule (C24H12) is sufficient to calculate thermodynamic parameters for adsorption systems on carbon surfaces. Therefore, coronene-sized cluster models were applied to simulate the carbon surface. Electroneutrality was maintained in these carbon surface models by saturating the dangling bonds with hydrogen atoms. The cluster model of a carbon surface will be denoted “c” in the text, tables, and figures. The cluster calculations were performed using the following DFT functionals: M06-2X33 as implemented in the Gaussian 09 program package E.01 version47 and BLYP34,35 with inclusion of a dispersion term (notation BLYP-D2(Cluster) will be used

2. COMPUTATIONAL DETAILS In our previous study, an approach based on a combination of two different approximations and different levels of theory was proven to be efficient to accurately calculate the Gibbs free energies for adsorption systems of PAHs and NACs on a carbon surface.10,13 On the basis of the analysis presented in the recent study,13 we have selected the most appropriate methods and basis sets to investigate the adsorption of high nitrogen compounds (HNCs) on carbon surfaces using a combined periodic and cluster approach. The calculations were performed in two steps. Periodic boundary conditions (PBCs) were applied at the DFT-D level to obtain the initial optimized structures of the studied adsorption systems and to calculate the adsorption energies. In the next step, the most stable PBC structures were used to prepare the cluster models to calculate the thermodynamic parameters (including the entropy contributions and Gibbs free energies) and partition coefficients. 4775



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3. RESULTS AND DISCUSSION Before discussing the main subject of this studythe contribution of the entropy term to the Gibbs free energy of adsorptionwe will briefly describe the structures of adsorption complexes as obtained from both PBC and cluster calculations. Moreover, the trends in changes of the interaction energies between considered contaminants and the adsorption sites of carbonaceous materials will be discussed. 3.1. Structure. Only a few theoretical studies have been published on the adsorption of nitrogen compounds on various forms of carbon.22,23,25 Using the DFT-LDA method, the most stable adsorption configuration of pyridine and 1,3,5-triazine on graphene was found to be the π−π stacking between the aromatic ring of the adsorbate and graphene surface.22,23,25 The influence of “aromaticity” has been discussed in ref 17. These findings are consistent with our results for HNCs adsorbed on the modeled carbon surfaces as described below. Figures 1−4 illustrate the optimized structures of pyridine (Pyr), pyridazine (Prdz), pyrimidine (Prm), pyrazine (Prz), 1,2,3-triazine (Tr), 1,3,5-triazine (Tr3), 1,2,4,-triazine (Tr2), 1,2,3,4-tetrazine (Tet), 1,2,3,5-tetrazine (Tet3), 1,2,4,5-tetrazine (Tet4), pentazine (Pen), and hexazine (Hex) adsorbed on the modeled carbon surface with the distances between the

in the text and tables, and D2 is used to express inclusion of a dispersion term in the calculations; see Section 2.1 for more details) as implemented in the ORCA program package.48 The 6-31+G(d,p) basis set49 was applied. The systems were fully optimized at the M06-2X/6-31+G(d,p) level of theory. The absence of imaginary frequencies in the calculated vibrational spectra determined that the obtained geometries of studied adsorption systems are true minima on the potential energy surface. Adsorption energies (ΔEads) were calculated as the difference between the total energies of the HNC−carbon systems and total energies of the isolated HNCs and carbon surface subsystems. In the case of the M06-2X calculations, the adsorption energies were not corrected by the basis set superposition error (BSSE) terms, as recommended by the authors of this functional.33 The BLYP-D2(Cluster) adsorption energies were corrected by the BSSE using the counterpoise method.50 The thermodynamic parameters including adsorption enthalpy (ΔHads), adsorption entropy (ΔSads), and Gibbs free energy (ΔGads) were calculated at room temperature (298.15 K) and 1 atm pressure utilizing the OpenThermo package.51 This software was specifically developed for statistical thermodynamics computations employing several thermodynamic approximations. Among them is the canonical rigid rotor/harmonic oscillator (RRHO) approach, which used vibrational frequencies obtained from the cluster M06-2X calculations. In previously published works,10,13 the RRHO approach as implemented in Gaussian 09 was shown to predict ΔHads with virtually experimental accuracy at both PBC and cluster levels. Thus, we have applied two other approximations only to estimate ΔSads. These approaches go beyond the RRHO method taking into account the internal rotations and anharmonicity of vibrations as follows: (1) Application of models of Isaacson and Truhlar,52−55 in which the formal expression of the harmonic partition function is used, while vibrational frequencies are calculated at the anharmonic level. The anharmonic frequencies (calculated using the Gaussian 09 package)47 considered were selected in such a way that all low frequencies, which are lower than 400 cm−1, were included. The fact that the adsorption entropy was calculated using the anharmonic frequencies is denoted in the text and tables by a capital A. (2) Application of a modified expression of rotational partition function to take into account the case of free rotations Q free rot =

2πIredkT hσ

2π

(1)

where Ired is reduced value of a moment of inertia. This expression was used in place of the classical one Q rot =

(8π 2kT )3/2 πI1I2I3 σh3

(2)

Newly obtained modified values of rotational partition function were used to calculate ΔSads. The entropy values calculated using an approximation based on harmonic frequencies will be denoted RRHO, and those computed based on anharmonic frequencies will be denoted OT-A (to account for anharmonicity) and OT-AR (to account for free rotations) in the text and tables.

Figure 1. Optimized structure of pyridine (Pyridine_c (a)), pyrazine (Pyrazine_c (b)), and pyrimine (Pyrimidine_c (c)) adsorbed on coronene, with adsorbate−surface distances [Å] obtained at the BLYPD2(PBC) and M06-2X/6-31+G(d,p) levels (in parentheses). 4776



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Figure 3. Optimized structure of 1,3,5-triazine (1,3,5-triazine_c (a)), 1,2,3,4-tetrazine (1,2,3,4-tetrazine_c (b)), and 1,2,3,5-tetrazine (1,2,3,5-tetrazine_c (c)) adsorbed on coronene, with adsorbate− surface distances [Å] obtained at the BLYP-D2(PBC) and M06-2X/631+G(d,p) levels (in parentheses).

nitrogen atoms in the target molecule. We did not observe a specific trend in decreasing of the molecule−surface distances with an increasing number of the nitrogen atoms in the adsorbate. Similar distances (3.0−3.4 Å) were calculated for pyridine adsorbed on graphene at the PBE+D2 level25 and for azines adsorbed on graphitized thermal carbon black derived from molecular statistical calculation.27 (3) The intermolecular distances are slightly shorter than found for benzene or PAHs adsorbed on coronene (∼3.5 Å (MP2/6-31G(d)56 and ∼3.4 Å (M05-2X)10), and they are almost the same as the NAC−coronene distances (∼3.3 and 3.2 Å (BLYP-D2(PBC)13). This suggests that binding is a combination of van der Waals contacts and electrostatic interactions, which include the C···N intermolecular Coulomb interactions occurring between the nitrogen atoms of the target compounds and the surface carbon atoms. From comparison of the BLYP-D2(PBC) and M06-2X results (see Figures 1−4), one can see that the molecule− surface distances are almost the same in both cases or slightly longer when the cluster approach was used. The same trend was seen in our previous study for adsorption of PAHs and NACs on the modeled carbon surfaces.10,13 On the basis of the discussion above regarding the HNC− carbon surface distances, we expect that pyridazine binds the most strongly with the carbon surface compared with the studied HNC molecules with one and two nitrogen atoms. Moreover, we predict that the adsorption on the modeled carbon surface is stronger for triazines and tetrazines having the nitrogen atoms placed next to each other than for the rest of the calculated HNC compounds.

Figure 2. Optimized structure of pyridazine (Pyridazine_c (a)), 1,2,3triazine (1,2,3-triazine_c (b)), and 1,2,4-triazine (1,2,4-triazine_c (c)) adsorbed on coronene, with adsorbate−surface distances [Å] obtained at the BLYP-D2(PBC) and M06-2X/6-31+G(d,p) levels (in parentheses).

adsorbate and surface obtained using both periodic and cluster approximations (in parentheses). Analogous to the conclusions of our recently published study of the adsorption of NACs and PAHs on carbon,13 we consider the results obtained at the BLYP-D2(PBC) level to be the most accurate among the applied approaches. Thus, first we discuss the results related to the optimized geometries of calculated HNC−carbon systems obtained at this level of theory. The main findings regarding the optimized structures of calculated complexes obtained at the BLYP-D2(PBC) level can be summarized in the following way: (1) HNCs are aligned in a parallel orientation toward the carbon surface (see Figures 1−4) forming the π−π systems. This agrees with the conclusion of another theoretical study where adsorption of pyridine on graphene occurred mainly through π−π chemistry.22 The only exception is the Hex_c system, where the hexazine molecule is found to split into three N2 molecules (see Figure 4). Because 3N2−carbon does not represent the adsorption system of six-membered aromatic nitrogen-containing heterocycles interacting with carbon, Hex_c will not be considered in further analysis of the energetic and thermodynamic parameters. (2) The distances between the target molecule and adsorbent vary based on the number and location of the 4777



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and experimental data. The following trends can be seen from the adsorption enthalpy values of calculated HNC−carbon systems obtained at the BLYP-D2(PBC) level: (1) The adsorption enthalpies increase with an increasing number of the nitrogen atoms in the adsorbate up to four nitrogen atoms. The reason can be that the presence of the nitrogen atoms in the aromatic ring decreases the π-electron density of the carbon atoms in aromatic heterocyclic compounds. This causes reduction of the π−π repulsion with the carbon surface, thereby leading to stronger adsorption. This effect was found to increase with an increasing number of the nitrogen atoms in the aromatic ring. The same finding was reported in several other theoretical studies of the adsorption of nitrogen aromatic compounds on graphene.22−24 (2) The mutual positions of the nitrogen atoms in the adsorbate are shown to affect the adsorption enthalpies of the studied systems more significantly than their actual number. A similar finding was reported in the experimental study of pyridine, pyrimidine, pyrazine, and 1,3,5-triazine adsorption on graphitized thermal carbon black.27 (3) The adsorption enthalpy values are larger for HNC interacting with the carbon surfaces than that between benzene and modeled carbon.10,13 This result suggests that pyridine shows additional electrostatic interactions with the carbon surface as was also reported for the adsorption of pyridine and benzene on graphitized carbon black. (4) The binding in all of the calculated HCN−carbon systems was found to be weaker than the binding of NACs to the carbon surfaces,10,13 where also a significant charge transfer occurs between the adsorbate and adsorbent.57 The ΔEads results from the cluster calculations at the M06-2X level correspond very well with the results from the BLYPD2(PBC) calculations. On the other hand, the BSSE-corrected adsorption energies obtained using the BLYP-D2(cluster) method are slightly smaller than the BLYP-D2(PBC) ΔEads values. The experimentally measured adsorption enthalpies are available only for pyridine, pyrimidine, pyrazine, and 1,3,5triazine adsorbed on graphitized carbon black.27−29 As one can see from Table 1, the BLYP-D2(PBC) and M06-2X interaction enthalpies are lower than the experimental data by ∼2 kcal/ mol. There can be two reasons for such a computational

Figure 4. Optimized structure of 1,2,4,5-tetrazine (1,2,4,5-tetrazine_c (a)), pentazine (Pentazine_c (b)), and hexazine (Hexazine_c (c)) adsorbed on coronene with adsorbate−surface distances [Å] obtained at the BLYP-D2(PBC) and M06-2X/6-31+G(d,p) levels (in parentheses).

3.2. Adsorption Energies and Enthalpies. As we have already mentioned, the results of our recently published paper on the adsorption of PAHs and NACs on the carbon surfaces suggest the BLYP-D2(PBC) binding energies are the most accurate among all approximations considered.13 Thus, these results are discussed first and then compared with the M06-2X

Table 1. Adsorption Energies (ΔEads) and Enthalpies (ΔHads) [kcal/mol] for Adsorption of High Nitrogen Compounds on the Modeled Carbon Surfaces from the Gas Phase and Available Experimental Adsorption Enthalpies BLYP-D2 (cluster)b

BLYP-D2(PBC) method/system

ΔEads

ΔHads

Pyr_c Prz_c Prm_c Prdz_c Tr_c Tr2_c Tr3_c Tet_c Tet3_c Tet4_c Pen_c

−8.6 −8.4 −9.4 −10.2 −11.4 −11.0 −8.3 −13.2 −7.5 −7.3 −10.9

−6.5 −6.4 −8.0 −8.4 −9.2 −9.1 −6.8 −11.8 −5.8 −5.6 −8.1

a

M06-2Xc

exp

ΔEads

ΔEads

ΔHads

ΔHadsd

−7.7 −8.2 −7.6 −9.3 −8.3 −7.9 −6.8 −8.4 −7.9 −8.0 −7.5

−9.1 −9.2 −9.3 −10.1 −11.1 −10.1 −8.3 −11.4 −10.5 −9.9 −10.9

−7.0 −7.2 −7.9 −8.3 −8.9 −8.2 −6.8 −10.0 −8.8 −8.1 −9.2

−9.9 to −10.427−29 −9.327 −9.427−29

−8.6 to −8.927

ΔHads calculated from BLYP-D2(PBC) adsorption energies by addition of the zero-point energy from the M06-2X calculations. bBSSE corrected value. cBSSE uncorrected value. dInteraction enthalpies are determined in refs 27−29 at a constant volume rather than at a constant pressure; therefore, 0.6 kcal/mol (RT, T = 298.15 K) has been added according to the equation ΔH = ΔU + RT.

a

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ΔS = ΔStrans + ΔSrot + ΔSvib

underestimation. Despite that the BLYP-D2(PBC) method was parametrized to reproduce the interaction energies of similar systems at the CCSD(T)/CBS level,36,37 a recent publication by Boese and Sauer58 suggests a systematic underestimation (ca. 1−2 kcal/mol) of the BLYP-D2(PBC) binding energies for the adsorption on oxide surfaces. In addition, adsorption energy and enthalpy values are known to depend on the heterogeneity of the carbonaceous materials. In particular, all experimental data listed in Table 1 were obtained on graphitized thermal carbon black Sterling MT. However, in the experimental publication59 it is clearly stated that the best representation of an ideal graphite phase (the model considered in this study) contains different graphitized thermal carbon blackCarbopack C HT. This causes the experimentally measured binding energies of polar substances adsorbed on this material to be systematically lower by ∼1−2 kcal/mol compared with the data obtained using Sterling MT. In particular, the adsorption enthalpy of nitrobenzene adsorbed on Carbopack C HT is reported to be −11.7 kcal/mol.59 This number corresponds well with the binding energy calculated in a previous study by our group at the BLYP-D2(PBC) level (−11.6 kcal/mol) (RT value is included, see Table 1).13 To obtain direct conformation of this statement the experimental measurement of the adsorption energy for pyridine interacting with Carbopack C HT instead of with Sterling MT has been performed under the same experimental conditions as in ref 27. The observations show that the adsorption energy for pyridine−Sterling MT is lower by ca. 1 kcal/mol when compared with the value for the pyridine−Carbopack C HT system. 3.3. Entropy. In this section we analyze the accuracy of different approaches to predict the adsorption entropy values based on comparison with available experimentally measured data. In this regard, it should be noted that adsorption of a molecule on a surface of any material results in a decrease in freedom of motion of such a molecule and increases the order of the system. In other words, there is an entropy loss reflecting that free translational and rotational degrees of freedom are converted into bound motions.60 There are six degrees of freedom that are mostly affected by the formation of intermolecular complexes. Three of these degrees of freedom are the relative translational motions of two subsystems. The remaining three are the rotational degrees of freedom that correspond to their relative orientation (appearance of intermolecular vibrational modes, i.e., vibration of the target molecule on the adsorption site). During the adsorption these six degrees of freedom convert into ‘‘oscillations’’ within the adsorption potential of the complex, which is characterized by a larger amount of low frequencies due to a larger number of fluctuations of the adsorbed molecule around its equilibrium state. In general, these oscillations are “soft”; i.e., their frequencies are low, with average energies per mode of the order of kT, where k is the Boltzmann’s constant and T is an absolute temperature. In addition, these low frequencies have strong anharmonic character.61−63 The above description characterizes the adsorption process as considered at the RRHO level. In reality the situation is more complicated since adsorption can be accompanied by free or hindered rotations of adsorbate around the adsorption site and by the appearance of some translational degrees of freedom due to the ability of the adsorbed molecule to migrate from one adsorbed center to another one. Therefore, we have analyzed the contributions to the entropy in the framework of traditional decomposition

(3)

and more sophisticated approximations than RRHO have been applied. Total adsorption entropy values (TΔSads) and available experimental data as well as vibrational (TΔSvib), rotational (TΔSrot), and translational (TΔStrans) adsorption entropy terms for all calculated HNC−carbon systems calculated using the harmonic (RRHO) and anharmonic frequencies at the M06-2X level are given in Tables 2 and 3. Notations OT-A and OT-AR Table 2. Total T*ΔSads Values [kcal/mol] for Adsorption of High Nitrogen Compounds on the Modeled Carbon Surface from the Gas Phase method/system

RRHOa

OT-Ab

OT-ARc

exp


−8.5 −8.1 −8.8 −8.6 −8.4 −8.1 −7.4 −10.8 −10.0 −8.8 −10.7

−6.8 −9.2 −7.3 −9.1 −4.6 −8.6 −10.1 −11.9 −6.2 −5.2 −9.8

−3.8 −6.2 −4.4 −6.2 −1.7 −5.7 −7.2 −8.9 −3.2 −2.2 −7.0

−7.5 to −7.727 (298 K) −7.3 to −7.727 (298 K) −7.4 to −7.727 (298 K)

−7.1 to −7.727 (298 K)

a

RRHO - T*(ΔSads) calculated using the OpenThermo software based on the harmonic frequencies for the optimized structures from the M06-2X/6-31+G(d,p) calculations. bOT-A - T*(ΔSads) calculated using the OpenThermo software based on the anharmonic frequencies for the optimized structures from the M06-2X/6-31+G(d,p) calculations. cOT-AR -T*(ΔSads) calculated using the OpenThermo software based on the anharmonic frequencies with inclusion of rotations for the optimized structures from the M06-2X/6-31+G(d,p) calculations.

Table 3. Vibrational (T*ΔSvib), Rotational (T*ΔSrot), and Translational (T*ΔStrans) Values [kcal/mol] (M06-2X/631G+(d,p)) for Adsorption of High Nitrogen Compounds on the Modeled Carbon Surfaces from the Gas Phase T*ΔSvib a

T*ΔSrot

method/system

RRHO

OT-A


8.4 8.3 8.0 8.2 8.4 9.1 8.7 6.1 6.9 7.7 6.1

10.1 7.2 9.5 7.7 12.2 8.6 6.0 5.0 10.7 11.3 7.0

b

a

RRHO

OT-AR

−5.5 −5.0 −5.4 −5.4 −5.4 −5.8 −4.7 −5.4 −5.4 −5.0 −5.3

−2.2 −2.0 −2.5 −2.5 −2.5 −3.0 −1.8 −2.4 −2.4 −2.0 −2.5

T*ΔStrans c

RRHO −11.4 −11.4 −11.4 −11.4 −11.4 −11.4 −11.4 −11.5 −11.5 −11.5 −11.5

a RRHO - T*ΔSvib, T*ΔSrot, and T*ΔStrans calculated using the OpenThermo software based on the harmonic frequencies for the optimized structures from the M06-2X/6-31+G(d,p) calculations. b OT-A - T*ΔSvib calculated using the OpenThermo software based on the anharmonic frequencies for the optimized structures from the M06-2X/6-31+G(d,p) calculations. cOT-AR - T*ΔSrot calculated using the OpenThermo software based on the anharmonic frequencies with inclusion of rotations for the optimized structures from the M062X/6-31+G(d,p) calculations.

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To analyze how the presence of hindered or even free rotations influences the TΔSads value, the energy profiles of such internal rotations were calculated for all of the studied complexes at the M06-2X level. These energy profiles are presented in Figures S1 and S2 in the Supporting Information. The “transition states” were located from these plots, which give the total energy dependence for the rotation angle change. In the next step, the structures corresponding to the “transition states” were additionally optimized using the geometrical constraints to obtain the final values of the energy barriers. They are presented in Table S6 in the Supporting Information. They suggest that all of the considered adsorption complexes possess very small barriers for the internal rotation in the range of 0.0−0.8 kcal/mol. To take into account this observation, expression 1 has been used to adjust the rotational entropy term for all of the HNC−carbon adsorption systems. The adsorption entropy values obtained using this approach based on the anharmonic frequencies are denoted OT-AR in the text and Tables 2 and 3. As expected, the presence of additional rotational degrees of freedom results in less negative OT-AR TΔSrot values (ca. 3 kcal/mol, Table 3) leading to less negative TΔSads when compared with the RRHO entropy values. The third entropy term, which can also be modified if other approaches than the RRHO scheme are applied, is the contribution from translations (TΔStrans). However, the size of considered cluster models does not allow investigation of this phenomenon. Nevertheless, the comparative analysis of the data presented in Tables 2 and 3 and Tables S2 and S3 in the Supporting Information suggests that the TΔSads values can be predicted accurately using the computational techniques only if the contributions in the expression 3 are accurately balanced. We have found such a balance in two cases: when the RRHO scheme was applied to calculate the adsorption HNC−carbon complexes and in the case of water dimer when the experimentally measured frequencies were applied to the M06-2X calculated geometry. 3.4. Gibbs Free Energy. The calculated Gibbs free energies of adsorption from the gas phase (ΔGads) for the interactions of all of the HNC compounds with the modeled carbon surfaces are given in Table 4. They were calculated from the ΔHads and TΔSads values obtained using the RRHO level values based on the harmonic vibrational frequencies. To obtain the ΔGads values that correspond in the best way to the adsorption on graphitized carbon black Sterling MT as described in Section 3.2 we have subtracted 2 kcal/mol to fit the ΔHads values (for more explanation see Section 3.2) and another 1 kcal/mol to fit the TΔSads values (for more details see Section 3.2). The Gibbs free energies of adsorption from the gas phase adjusted by this method are denoted ΔGadj ads, and they are presented in the second column of Table 4. The ΔGadj ads values are all negative (−1.4 to −3.1 kcal/mol). They are close to the experimental range of the Gibbs free energies of adsorption of various NACs on the carbon nanotubes (from −0.6 to −2.3 kcal/mol at 293 K),14 and they show good agreement with the experimental data for adsorption of pyridine, pyrazine, pyrimidine, and 1,3,5triazine on graphite.27−29 Thus, we predict the effective binding for all studied six-membered nitrogen-containing heterocycles on the considered carbon surface model from the gas phase at room temperature. The Gibbs free energy values were converted into the values of equilibrium constants. These constants characterize the equilibrium partitioning of the contaminants between the

are used to distinguish between different approaches used to calculate the adsorption entropy values. When one compares the TΔSads values in Table 2, surprisingly the results obtained at the RRHO level overestimate the experimental data only slightly. Thus, it can be suggested that this approach can be used to quite accurately reproduce the experimental results. In the discussion below we analyze different entropy contributions calculated at the non-RRHO level. As follows from the data presented in Tables 2 and 3, the replacement of harmonic frequencies (RRHO data) by their anharmonic counterparts (OT-A data) leads to 0.5−3.8 kcal/mol change of the TΔSads and TΔSvib values. These changes can be confirmed by differences in the anharmonic and harmonic frequencies (see Table S1 in the Supporting Information, in which low harmonic and anharmonic frequencies (lower than 200 cm−1) for all studied HNC−carbon systems are presented). These frequencies differ by more than 20 cm−1 for all calculated HNC−carbon complexes. There are no published experimental values of low vibrational frequencies for any of the considered HNC−carbon systems. Also, due to computational cost, it is not currently possible to calculate the anharmonic frequencies for studied HNC−carbon systems at any more sophisticated level than DFT even given the current power of supercomputers. Thus, we have selected a water dimer as our benchmark intermolecular complex to provide a detailed comparison of harmonic, anharmonic (calculated at different computational levels), and experimentally observed vibrational frequencies. These values are presented in Table S2 in the Supporting Information, and the total entropy values for water dimer calculated using the M06-2X optimized geometry and published CCSD(T) and experimental frequencies are presented in Table S3 in the Supporting Information. We observe similar tendencies for water dimer as was found for the HNC−carbon systems. The frequencies calculated at the anharmonic level differ significantly from harmonic vibrational frequencies, and the TΔSvib value was found to increase by about 2 kcal/mol at the M06-2X and M06-2X//Exp levels. The anharmonic frequencies are blue-shifted, providing more positive values of TΔSvib in the case of M06-2X and experimental data. This means that the calculations using the experimental and anharmonic frequencies predict more disordered considered species than those calculated at the harmonic level. Thus, it can be concluded that the anharmonic mode affects the vibrational entropy term significantly by increasing its positive value. As a second, more appropriate model, which may improve the entropy analysis of studied HNC−carbon systems, the sandwich conformer of the benzene dimer was selected. However, there are neither experimentally measured thermodynamic parameters nor low harmonic and anharmonic frequencies published for this type of benzene dimer.64,65 Thus, we were not able to use the sandwich conformer of the benzene dimer as our benchmark system. Another component, which can contribute in a different way to the total adsorption entropy value, is the rotational entropy term (TΔSrot). The contribution of this entropy component was recently analyzed in two papers published by Sauer’s group.66,67 It was reported that for hindered internal rotations special attention needs to be paid to calculations of the rotational partition functions since the calculations of these values using the harmonic-oscillator approximation can lead to significant errors. 4780



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black Sterling MT (adj log Kd) differ from the experimental log Kd by less than one logarithmic unit. This is actually the standard accuracy for the quantum-chemical predictions of the physicochemical properties (such as vapor pressure, Henry’s law constants, water solubility, octanol/water partition coefficients) for various environmental contaminants.68

Table 4. Gibbs Free Energy from the Gas Phase (ΔGads, kcal/mol) and log Kd (Kd, Partition Coefficient) for Adsorption of High Nitrogen Compounds on the Modeled Carbon Surface (M06-2X/6-31+G(d,p) Level) method/ system Pyr_c Prz_c Prm_c

ΔGads

a

1.5 0.9 0.9

b ΔGadj ads

−1.5 −2.1 −2.1

Prdz_c Tr_c Tr2_c Tr3_c

0.3 0.7 −0.1 0.6

−2.7 −2.3 −3.1 −2.4

Tet_c Tet3_c Tet4_c Pen_c

0.8 1.2 0.7 1.6

−2.2 −1.8 −2.3 −1.4

exp −2.427 (298 −2.027 (298 −2.027 (298 −1.427 (298 -

adj log Kdd

exp

−1.1

1.1

1.727 (298 K)

−0.6

1.5

1.527 (298 K)

−0.6

1.5

1.527 (298 K)

−0.2 −0.5 0.1 −0.4

2.0 1.7 2.3 1.8

1.127 (298 K)

−0.6 −0.9 −0.5 −1.1

1.6 1.3 1.7 1.0

-

log K) K) K)

K)

Kdc

4. CONCLUSIONS In this paper we continued our investigations into how to attain efficient computational approaches to predict accurately the Gibbs free energies of adsorption. We have focused on the adsorption entropies and Gibbs free energies calculated in the gas phase. Adsorption of various heterocyclic high nitrogen contaminants (HNC) including pyridine, pyrimidine, and multiple azine compounds on models of carbonaceous materials was studied. Both cluster and periodic approaches were employed using the M06-2X and BLYP DFT functionals with inclusion of dispersion forces. The most stable structures of the calculated complexes were reported, in which the preferred orientation was found to be when the adsorbate was placed in a parallel orientation toward the carbon surface. Predicted adsorption enthalpies for the HNC−carbon systems agree with available experimental data with a small difference of about 2 kcal/mol. We believe that this difference is caused by underestimation of the adsorption energy at the BLYP-D2(PBC) level and by real heterogeneity of the carbon surface. An analysis of the role of vibrational, rotational, and translational contributions to the value of the adsorption entropy term (TΔSads) suggests that the rigid rotor-harmonic oscillator approximation (RRHO) provides accurate TΔSads values (probably due to the compensation of errors). We also found that consideration of both anharmonic vibrational frequencies and hindered rotations results in less negative TΔSads values. This finding suggests that the adsorption states are more disordered than predicted at the RRHO level. Finally, the adsorption Gibbs free energies and partition coefficients for distribution of HNCs between carbon and air were predicted by fitting to the experimental data for the adsorption on graphitized carbon black Sterling MT. Application of this adjustment leads to negative Gibbs free energy values for adsorption of all studied HNCs on the considered carbon surface model from the gas phase. This suggests an effective adsorption of these compounds on the selected adsorption sites of modeled carbon from the gas phase at room temperature.

ΔGads - calculated using the OpenThermo software based on the harmonic frequencies and rigid-rotor harmonic oscillator (RRHO) approach for the optimized structures from the M06-2X/6-31+G(d,p) calculations. bΔGadj ads - calculated using the OpenThermo software based on the harmonic frequencies and rigid-rotor harmonic oscillator (RRHO) approach for the optimized structures from the M06-2X/631+G(d,p) calculations adjusted to fit the adsorption on carbon black Sterling MT. clog Kd − log Kd calculated based on ΔGads using the OpenThermo software based on the harmonic frequencies and rigidrotor harmonic oscillator (RRHO) approach for the optimized structures from the M06-2X/6-31+G(d,p) calculations. dadj log Kd − log Kd calculated based on ΔGadj ads using the OpenThermo software based on the harmonic frequencies and rigid-rotor harmonic oscillator (RRHO) approach for the optimized structures from the M06-2X/631+G(d,p) calculations adjusted to fit the adsorption on carbon black Sterling MT. a

adsorbent and air. These partition coefficients were calculated using the following formula Cphase1 ⎛ ΔG ⎞ ⎟ = Kd = exp⎜ − ⎝ RT ⎠ Cphase2

ΔG are the ΔGads and ΔGadj ads values presented in Table 4 obtained using the RRHO approach (ΔGads) and the values that mimic the best the adsorption on graphitized carbon black Sterling MT (ΔGadj ads). Cphase1 and Cphase2 are the equilibrium concentrations of the chemical after the distribution between the phases; R is the universal gas constant; and T is temperature. We will use the notation log Kd for the values calculated using ΔGads and adj log Kd for the values calculated using ΔGadj ads. The log Kd and adj log Kd values for distribution of all studied six-membered nitrogen-containing heterocycles between air and carbon are summarized in Table 4. The adj log Kd values are positive for all studied HNC−carbon systems (1.0 (pentazine−carbon) − 2.3 (1,2,4-triazine−carbon)). On the basis of good agreement of the calculated adsorption entropies and Gibbs free energies, we believe these log Kd values are quite accurate. As one can see from Table 4, the calculated adj log Kd values for the pyrazine− and pyrimidine−carbon systems agree very well with the experimental data. For two other systems (pyridine− and 1,3,5-trazine−carbon) the data fitted to carbon

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S4, which present low vibrational harmonic and anharmonic frequencies for all calculated high nitrogen compound (HNC) carbon systems (Table S1) and for water dimer with available MP2, CCSD(T), and experimental data (Tables S2); the vibrational, rotational, translational, and total entropy values calculated using the M06-2X optimized geometry and CCSD(T) and experimental vibrational frequencies for water dimer (Tables S3); and the energy barrier values to correct the rotational entropy term obtained at the M06-2X/6-31+G(d,p) level for all HNC−carbon systems (Table S4). Figures S1 and S2 illustrate the graphs from calculations of the energy barrier values to correct the rotational entropy term obtained at the M06-2X/6-31+G(d,p) level for all HNC−carbon systems. This material is available free of charge via the Internet at http://pubs.acs.org. 4781



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 001-601-6343637. Fax: 001-601-634-2742. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We would like to thank Mr. Konstantin Tokarev for his help with the creation and usage of the OpenThermo code. This work was facilitated by support from the High Performance Computing Major Shared Resource Center at the ERDC (Vicksburg, MS) and the Office of Naval Research grant No. N00034-03-1-0116. The use of trade, product, or firm names in this report is for descriptive purposes only and does not imply endorsement by the U.S. Government. Results in this study were funded and obtained from research conducted under the Environmental Quality Technology Program of the United States Army Corps of Engineers by the US Army ERDC. Permission was granted by the Chief of Engineers to publish this information. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

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Toward Accurate and Efficient Predictions of Entropy and Gibbs Free

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