Improved Directional Hydrogen Bonding Interactions for the Prediction

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Thermodynamics, Transport, and Fluid Mechanics

Improved Directional Hydrogen Bonding Interactions for the Prediction of Activity Coefficients with COSMO-SAC Chun-Kai Chang, Wei-Lin Chen, David T. Wu, and Shiang-Tai Lin Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02493 • Publication Date (Web): 27 Jul 2018 Downloaded from http://pubs.acs.org on July 31, 2018

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Industrial & Engineering Chemistry Research

Improved Directional Hydrogen Bonding Interactions for the Prediction of Activity Coefficients with COSMO-SAC

Chun-Kai Chang,a Wei-Lin Chen,a David T. Wu,b and Shiang-Tai Lin*a

a b

Department of Chemical Engineering, National Taiwan University, Taiwan

Department of Chemistry and Department of Chemical and Biological Engineering, Colorado School of Mines, USA

ABSTRACT In a recent work, Chen and Lin showed that the consideration of directional hydrogen bonding in the COSMO-SAC model significantly improves the description of solvation properties of associating fluids. In their method, the direction of a hydrogen bond was determined based on the VSEPR theory; however, this geometric approach does not reflect the local electronic environment of the lone pairs and cannot be applied to certain molecules such as DMSO and HF. In this work, we adopt a new scheme that determines the hydrogen bond acceptors of a molecule based on the minima in the molecular electrostatic potential (MESP). The hydrogen bonding directions thus determined result in improvements (about 5-7% for VLE) in the prediction of the COSMO-SAC model for a variety of thermodynamic properties and phase equilibria, such as vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE), infinite dilution activity coefficient (IDAC) and octanol-water partition coefficient (Kow) calculations.

Keywords: Screening charge, COSMO-SAC, COSMOSAC-DHB, MESP, hydrogen bond, phase behavior, activity coefficient, partition coefficient

ACS Paragon Plus Environment 1

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

*to whom all correspondence should be addressed. E-mail: [email protected]


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1. INTRODUCTION

The COSMO-based activity coefficient models, such as COSMO-RS1 and COSMO-SAC,2 are powerful methods for predicting phase equilibria involving liquid mixtures.3-6 In these methods, the interactions between molecules in the liquid state are determined based on the apparent screening charges induced at the molecular surface when considering the molecule as embedded in a perfect conductor.7 Since such information can be obtained from quantum mechanical solvation calculations,8,

9

the COSMO-based models are applicable to a wide

variety of chemical compounds, including organics,10-15 electrolytes,10, (IL),19-23 polymers,24,

25

16-18

and pharmaceuticals.26 However, it has been noted

ionic liquids 27, 28

that the

accuracy is reduced for mixtures containing associating fluids. Therefore, there has been a continuous effort toward improving the description of hydrogen bonding interactions.11, 27, 29

In the original COSMO-based models, the hydrogen bonds were assumed to form only between highly polarized surfaces, and the strength of the interactions was empirically assumed to be proportional to the surface charge density of the hydrogen bonding donor-acceptor pairs. Given the experimental observations that the strength of a hydrogen bond depends on the identity of the donor-acceptor pair, Hsieh et al.27 proposed to estimate the interaction strength based on the identity of the hydrogen bonding surface (O, N, or F), in addition to the screening charge densities. Such an approach indeed improves the description of associating fluids; however, at the cost of introducing additional empirical parameters. More recently, Chen and Lin11 proposed a novel idea for describing the hydrogen bonding interactions by recognizing the relative orientations of the donor and the acceptor. Specifically, a hydrogen bond is formed between a donor-acceptor pair along the direction of the electron lone pair, determined based on the Valence Shell Electron Pair Repulsion (VSEPR) theory.30 Using this approach, Chen and Lin reported a remarkable improvement in describing the solvation properties of ions and the phase equilibria of associating fluids. Despite their ACS Paragon Plus Environment 3


success, the geometric VSEPR method of determining the spatial direction of a hydrogen bond is not applicable for three types molecules: most of molecules that contain F (e.g. hydrogen fluoride and vinyl fluoride), molecules with the acceptor atoms connected to elements in the third row of the periodic table (e.g. sulfones and phosphine oxides), and O appearing in the terminal of linear functional groups (e.g. ketenes and cyanates). This is because the method proposed by Chen and Lin utilizes the bond directions for determining the lone pair directions of the acceptor atom. The location of lone pairs cannot be unambiguously defined in these three types of molecules. Furthermore, VSEPR does not explicitly account for the possible change in directions of lone pairs as a result of changes in local environment due to the presence of strongly electronegative or electropositive atoms. Some examples of these difficulties are illustrated in the first section of Supporting Information.

In addition to the geometric VSEPR approach, it has been proposed that the direction of a lone pair can be determined by physical observables, such as the molecular electron density (MED)

31-33

and molecular electrostatic potential (MESP).34-40 Using the MESP, for example,

the lone pair position is determined from the local minimum of the molecular electrostatic potential of the given molecule. In this work, we adopt the MESP approach to identify the directions of lone pairs and hydrogen bonding surfaces in the COSMO-SAC (DHB) model. We show that this new approach provides a robust and slightly more accurate description of solvation and thermodynamic properties, including VLE, LLE, IDAC and Kow. More importantly, this method is generally applicable for all types of compounds as the needed electrostatic potential can be obtained from quantum chemical calculations.


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2. THEORY 2.1.

The COSMO-SAC Model

The activity coefficient of a chemical species in a mixture can be determined from the difference in solvation free energy of the species in the mixture and in its neat liquid41 as lnγ/ =

∗ ∗ / /

+ ln

(1)

where and stand for the molar concentration of species i in a pure fluid and in a

solution, respectively. R is the gas constant and T is the temperature. The solvation free energy,

∗ Δ/ , is the work required to transfer a solute molecule i from a point in the ideal gas phase

to another point in solution j under constant temperature and pressure. Using a perfect conductor as a reference solvent, the solvation free energy can be calculated as the sum of contributions from three different terms accounting for cavity formation (cav), ideal solvation (is), dispersion interactions (dsp) and restoring energy (res), ∗ ∗ ! ΔG/ = ΔG/ + ΔG∗ + ΔG

∗"#

∗$% + ΔG/

(2)

∗ ! where ΔG/ is the Gibbs free energy of cavity formation, ΔG∗ is the ideal solvation

energy, ΔG

∗"#

∗$% is the dispersion interactions and ΔG/ is the restoring energy. Lin and

Sandler2 showed that the difference in the cavity formation energy for a solute being in the solvent and its pure state can be obtained from the Staverman-Guggenheim model 42 as ∗&'( ∗&'( / /

) = lnγ/ −ln

(3)

) where the lnγ/ term takes into consideration the molecular size and shape difference

between both solute and solvent ) ln+/ = ln

,

-

+ 0 ln .

/

1

,

+ 2 −

,

-

3 4 2

(4)

with 6 = (4 0 )/(Σ 4 0 ) , 9 = (4 : )/(Σ 4 : ) and 2 = (: − 0 ) − (: − 1) where /

.

4 , : and 0 are the mole fraction, normalized volume and surface area of molecule i,

respectively; z is the coordination number and is usually set to 10. The summations run through all species in the mixture. Substituting Eq. 2 and Eq. 3 into Eq. 1, the activity ACS Paragon Plus Environment 5


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coefficient can be expressed as ln+/ =

∗=> ∗=> < / < /

) + ln+/

(5)

where the ideal solvation and dispersion terms are cancelled because they do not depend on the composition of the solution. In the COSMO-SAC model, the restoring energy term in Eq. 5 is calculated from the summation of the segment activity coefficient, which reflects the interaction between the segments after dissecting the screening charges on the solute-solvent boundary, as ∗=> /

=@

?

>AA

ΣCD E (FG )lnΓ (FG )

(6)

where Γ (FG ) is the segment activity coefficient of a screening charge density FG ; I is

the surface area of a molecule of component i, JKLL is the effective contact area when two molecules contact each other. The term E (FG ), known as the “σ-profile”, is the ratio of the

surface area of segments whose charge density is FG to the total molecular surface area, I . For a mixture, the σ-profile becomes an area-weighted average of pure components, P (F ) =

N - ? O (C) N - ?P

(7)

The segment activity coefficient for the pure component (i) and the mixture (s) can be determined from Eq. 82 lnΓQ (FG ) = −lnΣCR E (FS )Γ (FS )exp (

W(CD ,CR ) Y

)

(8)

where

ΔZ(FG , FS ) = [\) (FG + FS )/

(9)

is the interaction energy for FG and FS . The coefficient [\) is a constant that can be

determined based on JKLL [\) =

L] ×_.a×@>AA b/c /×de

(10)

where fg is a polarization factor that can be determined from the QM calculations43 and h_

is the permittivity of vacuum. Note that JKLL is the only adjustable parameter in the basic

form of COSMO-based models and the value of JKLL is usually taken to be around 6 to 9 Å2 ACS Paragon Plus Environment 6

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depending on the kind of model applied.

2.2.

Treatments of Hydrogen Bonding Interactions

We briefly review here the treatment of hydrogen bonding interactions in the successive improvements of the COSMO based model, leading to the current MESP approach. In the case where the two segments in contact may form a hydrogen bond, Klamt29 suggested that an additional energy gain (favorable) between the two segments should be accounted for. Therefore, the segment interactions (Eq. 9) are modified to be iZ (FG , FS ) = [\) (FG + FS )/ + [jk max[0, F

− Fpq ]min[0, F"t + Fpq ]

(11)

where σpq (= 0.0084 e/Å2) is the cutoff charge density above which the segments are considered to be capable of forming a hydrogen bond. The σacc and σdon are the larger

(positive, associated with hydrogen bonding acceptor atoms) and smaller (negative, associated with hydrogen bonding donor atoms) values of σm and σn (usually within 0.025 e/Å2),

respectively. The coefficient [jk is a parameter accounting for the strength of hydrogen bonding interactions.

In Eq. 11, hydrogen bonding surfaces are identified as those possessing a charge density greater than the cutoff, σpq , and the strength of the interaction is proportional to the product of the charge excesses of the donor and acceptor segments. Hsieh et al.27 refined the description of hydrogen bonding interactions by differentiating the contributions from different hydrogen bonding groups: segments on a hydroxyl groupurface (OH) and segments on the other hydrogen bonding surface (OT), such as on ethers, carbonyls, amines, etc. The segment interaction in their model is as follows:

v v v v iZ(FG , FS ) = [\) (FG + FS )/ − [jk (FG , FS )(FG − FS )/

(12)

where the superscripts s and t stand for the type of segments and the coefficient [jk depends

on the type of donor-acceptor segments.



v [jk (FG , FS ) =

v [{|{| if } = ~ = OH and FG × FS < 0 z x [{{ if } = ~ = OT and F v × F < 0 G S

v y [{|{ if s = OH, t = OT and FG × FS < 0 x w0 otherwise

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(13)

Note that Eqs. 11 and 12 use different criteria for describing the strength of HB interactions. In Eq. 11, the strength of HB is determined based on the charge density of the donor and acceptor segments, whereas in Eq. 12 the strength is determined based on the types of hydrogen bonding surfaces, in addition to charge density. [jk in both Eq. 11 and Eq 12. are

used to assess the strength of HB interactions. [jk can be obtained from fitting to VLE or LLE data. Further details are given in the section of Computational Details. In addition, the electrostatic interaction parameter [\) is taken to be a function of temperature: [\) = I\) +

c

(14)

where AES and BES are independent of temperature.

Instead of differentiating the hydrogen bonding surfaces, Chen and Lin11 proposed to restrict the hydrogen bonding segments to those lying in the direction of lone pairs of the donor atoms (e.g., O, N, and F) and the OH, NH, and FH bonds. The lone pair vector, determined based on the VSEPR theory, and OH, NH, and FH bond vectors are used to find a hydrogen bond center (hbc) on the molecular surface, as shown in Fig. 1(a). Furthermore, the HB-surface regions are identified as those located within a certain cutoff distance (RHB cut ) of the hydrogen bond center, as shown in Fig. 1(b) and 1(c).


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(a)

(b)

-0.025 e/Å2

-0.025

(c)

HB surface on O/N/F HB surface on H

Fig. 1. The hydrogen bond centers (yellow balls) (a) identified based on VSEPR for water, the spatial distribution of COSMO charge density (b), and the HB surface regions of water from COSMO-SAC (DHB)/VSEPR (c). ACS Paragon Plus Environment 9


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With the directional hydrogen bonding (DHB) approach, the strength of segment interactions is then determined as the following: ∆W(σm , σn ) = (AES +

BES T2

)(σm + σn )2 + Chb max[0, σacc - σhb ]min[0,σdon + σhb ]

(15)

Note that the temperature dependence is introduced as in the 2010 model and the form of the hydrogen bonding interaction is the same as in the original model. Significant improvements in the prediction accuracy of phase equilibria for associating fluids were observed when the DHB approach was used. It is worth mentioning that a fewer number of parameters are needed in the DHB approach compared to the 2010 model.

Rather than using the VSEPR theory, here we propose to use the MESP to determine the lone pair direction.34, 37-40 The vector pointing from the donor atom to the local minimum in the MESP is considered as the lone pair direction, and its intersection at the molecular surface is the hydrogen bond center. The local potential minima can be found by searching the values in the potential field determined with quantum chemical calculations (evaluated on 3-dimensional spatial grids). Each of the local minima found is regarded as a lone pair site. All other subsequent calculations are the same as those in the VSEPR approach (illustrated in Fig. 1.).

(a)

(b)

(c)

HB surface on O/N/F

HB surface on H

Fig. 2 The hydrogen bond centers identified based on VSEPR (yellow balls) and MESP ACS Paragon Plus Environment 10

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(green balls) for water (a), respectively, and the HB surface region of water from COSMO-SAC (DHB)/VSEPR (b) and COSMO-SAC (DHB)/MESP (c). Note that the hydrogen bond centers for proton donors (green balls near hydrogen atoms) are the same for VSEPR and MESP.

One advantage of MESP over VSEPR in determining the lone pair vector is illustrated in Fig. 3 for HF, DMSO and methylisocyanate. For these compounds, it is not possible to determine the specific lone pair vectors based on VSEP due to the lack of auxiliary bonds. In contrast, the lone pair directions can be obtained based on MESP without any auxiliary bond directions. Further details about auxiliary bond directions and the difficulty of arranging lone pair positions are discussed in the Supporting Information. The hydrogen bond centers determined from MESP for these compounds are illustrated in Fig. 3.

(a)

(b)

(c)

Fig. 3. The hydrogen bond centers determined based on MESP for HF (a), DMSO (b) and methylisocyanate (c). The green balls represent the hydrogen bond centers and the black ones represent electrostatic potential local minima. The VSEPR fails to provide the lone pair direction for these compounds.

The difference in the treatment of hydrogen bonding segments is reflected in the σ-profile, “fingerprint” of the molecule. Fig. 4 compares the water σ-profiles resulting from different COSMO-based models. To better illustrate the differences in each COSMO-based models, the ACS Paragon Plus Environment 11


σ-profiles are separated into two parts, the contribution from non hydrogen-bonding segments (non hydrogen-bonding level σ -profile) and the contribution from hydrogen-bonding segments (hydrogen-bonding level σ-profile). Note that one can obtain the same σ-profile after summing up the two contributions for the same molecule. It can be seen that different treatments result in the same hydrogen bonding σ-profiles for extreme charge densities (e.g., |σ|>0.016 e/Å2), indicating all 4 methods consider the most polarized segments as hydrogen bonding surfaces. For change density |σ| around 0.015 e/Å2, the 2002, VSEPR and MESP approaches identify a higher portion of surface regions as a hydrogen bonding surface. The

most significant differences in the hydrogen bonding σ-profiles are observed for |σ| 2010 > VSEPR ~ MESP. . (a)

1.4

2002

1.2

2010 DHB (VSEPR)

1

DHB (MESP)

0.8

Ai (Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.6 0.4 0.2

-0.025

-0.015

0 -0.005 0.005 σ (e/Å2)


0.015

0.025

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(b)

3.5 3 2.5 2

Ai (Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5 1 0.5

-0.025

-0.015

0 -0.005 0.005 σ (e/Å2)

0.015

0.025

Fig. 4. σ-profile from non hydrogen-bonding (a) and hydrogen-bonding (b) surfaces of water using different COSMO-SAC models.

3. COMPUTATIONAL DETAILS

The Amsterdam Density Functional (ADF) software44-46 is used for all quantum chemical calculations. The equilibrium geometry of a molecule is obtained using the GGA Becke Perdew functional and TZP basis set. The spatial distribution of the electrostatic potential is then calculated (using the “densf” utility) on Cartesian grids with medium resolution. A local minimum in the MESP is determined by comparing the potential value on a grid point (located at the center of a local 3x3x3 grid) with its 26 neighboring grid points. Each of the local minima found is regarded as a lone pair site. The COSMO47 calculation is then performed to obtain screening segment charge density on the molecular surface. The calculation procedure for the activity coefficient is the same as that in our previous work.11

In order to evaluate the performance of the COSMO-SAC model among different quantum ACS Paragon Plus Environment 13


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calculation methods, it is necessary to re-optimize the parameters in COSMO-SAC. As in our

previous work,15 f# is the first parameter to optimize based on internal consistency for the

averaging process. Secondly, we optimized the parameters in COSMO-SAC 2002, aeff and Chb, using VLE data of 1118 binary systems. Thirdly, the two parameters in COSMO-SAC 2010, AES and BES, were fitted to LLE of 71 non-HB binary systems, and the three HB interaction parameters, COH-OH, COT-OT and COH-OT were fitted to 309, 60 and 190 VLE binary systems. Lastly, the HB interaction parameters (RHB cut and Chb) in COSMO-SAC (DHB) were optimized based on VLE data of 586 binary mixtures that contain hydrogen bond interactions (e.g. water, alcohols and amines). The following objective function, based on root mean square (RMS) errors for the VLE data, is used for parameter optimization.

RMSVLE =

0.5 0.5 calc exp 2 1 M pi -pi M calc exp 2 ∑i=1yi -yi + ∑i=1 exp (16) M M pi 1

where y and p are the mole fraction in the vapor phase and pressure, respectively. The superscript exp and calc stand for the experimental data and calculated values, and M is the number of data points. The re-optimized parameters for different variations of the COSMO-SAC model are summarized in Table 1.

Table 1. Parameters in different COSMO-SAC models considered in this work. Parameter

COSMO-SAC

COSMO-SAC

COSMO-SAC

COSMO-SAC

f#

2002

2010

(DHB)/VSEPR

(DHB)/MESP

0.7167

-

-

-

AES (kcal/mol

-

11841.67

11841.67

11841.67

-

2.79 × 10

2.79 × 10

2.79 × 10

Å4/e2) BES (kcal/mol


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Å4/e2 K2) Chb (kcal/mol

100664

-

33306.83

34234.17

COH-OH

-

3551.10

-

-

COT-OT

-

1077.26

-

-

COH-OT

-

3099.31

-

-

0.0063

0.0063

Å4/e2)

σ (e/Å2) σ_ (e/Å2)

0.0084

RHB cut (Å)

-

0.0070

-

-

-

-

1.4432

1.3871

aeff (Å2)

5.8447

5.8447

5.8447

5.8447

fdecay (-)

3.5722

3.5722

3.5722

3.5722

r (Å2)

66.69

66.69

66.69

66.69

q (Å3)

79.53

79.53

79.53

79.53

The liquid-liquid equilibrium (LLE), the infinite dilution activity coefficients (IDAC) and octanol-water partition coefficients (Kow) are used to assess the predictive capability of the two types of COSMO-SAC (DHB) models. The experimental data for VLE, LLE and IDAC were obtained from the DECHEMA Chemistry Data Series48 while the Kow data were obtained from the CRC handbook.49

4. RESULTS & DISCUSSION

4.1.

Comparison of COSMO-SAC(DHB) using MESP versus VSEPR

The VLE is commonly used to examine the performance of different models over the entire ACS Paragon Plus Environment 15


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concentration range. The accuracy of VLE is evaluated by the average absolute relative deviation in vapor pressure (AARD-P) and average absolute deviation in mole fraction in the vapor phase (AAD-y). Eqs. 17 and 18 show the definition of AARD-P and AAD-y, respectively. Mi AARD-P = ∑N i=1 ∑j=1 1

pcalc - pexp

1

N Mi

pexp

× 100%

(17)

exp Mi calc AAD-y = ∑N i=1 ∑j=1 yi - yi × 100% 1

1

(18)

N Mi

where N is number of VLE mixtures and Mi is the number of data points in the ith mixture. The results are summarized in Table 2.

Table 2. Prediction accuracy of COSMO-SAC models for VLE, LLE, IDAC and Kow VLE

LLE

AARD-

AAD-

P (%)

y (%)

7.92

IDAC

Kow

RMSLLE

Npts

Nsys

RMSIDAC

RMS

3.06

0.0776

2080

143

0.669

0.480

6.08

2.67

0.0929

2389

164

0.795

0.698

6.26

2.67

0.0933

2345

164

0.587

0.480

5.80

2.53

0.0932

2393

167

0.598

0.462

431

291

COSMO-SAC 2002 COSMO-SAC 2010 COSMO-SAC (DHB)/VSEPR COSMO-SAC (DHB)/MESP Number of 586

190

binary pairs


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The performance in VLE from different models falls in the order: COSMO-SAC (DHB) based on MESP > COSMO-SAC 2010 > COSMO-SAC (DHB) based on VSEPR > COSMO-SAC 2002. The overall AARD-P from COSMO-SAC (DHB)/MESP is improved by 26.8%, 4.61% and 7.35% compared to COSMO-SAC 2002, COSMO-SAC 2010 and COSMO-SAC (DHB)/ VSEPR, respectively. The AAD-y from COSMO-SAC (DHB)/MESP is reduced by 17.32% in comparison with COSMO-SAC 2002 and by 5.24% when compared with both COSMO-SAC 2010 and COSMO-SAC (DHB)/VSEPR. The substantial improvement in AARD-P indicates that COSMO-SAC (DHB)/MESP is much more successful in predicting vapor pressures.

Fig. 5 demonstrates the VLE of a few binary mixtures: (a) ethanol (1) – water (2) at 348.15K (b) 2-methyl-1-propanol – DMSO at 353.15K (c) difluoro methane – hydrogen fluoride at 283.15K. Species that cannot be evaluated based on the VSEPR theory are marked in bold face. In general, COSMO-SAC (DHB)/MESP performs better than the other models, as seen in Fig. 5 (a) and (b). As for case (c), COSMO-SAC 2010 performs the best, perhaps because of the use of different hydrogen bond interactions. Also worth mentioning is that the VSEPR method is not applicable for DMSO, difluoromethane and hydrogen fluoride. Although COSMO-SAC (DHB)/MESP may not always be the best choice for individual systems, it does give the overall best results.



(a) 1E+05 9E+04 8E+04 7E+04 6E+04 P (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5E+04 4E+04 3E+04 2E+04 1E+04 0E+00 0

0.2

0.4

0.6 x1, y1


0.8

1

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(b)

3.50E+04 3.00E+04 2.50E+04

P (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.00E+04 1.50E+04 1.00E+04 5.00E+03 0.00E+00 0

0.2

0.4

0.6 x1, y1


0.8

1


Page 20 of 37

(c)

Fig 5. Comparison of predicted VLE phase diagram for three example binary systems: (a) ethanol (1) – water (2) at 348.15K, (b) 2-methyl-1-propanol (1) – DMSO (2) at 353.15K, and (c) difluoro methane (1) – hydrogen fluoride (2) at 283.15K. Open circles are experimental data.

The LLE can be used to assess the predictive performance between partially miscible fluids. The performance for LLE can be evaluated in several ways. One is to count the number of converged and phase separated points, which is denoted as computable data points, and the second measure is the root mean square error. K-g §@§ RMS££¤ = ( ∑¦ − 4 ) ¨¥4

©

/ c

¥

¦

(19)

where N is the number of computable data points in the LLE mixture. Despite a slight improvement in RMS from MESP, i.e., the performance based on VSEPR (0.0933) and MESP (0.0932)

are

very

similar,

noticeable

improvements


can

be

seen

in

the

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water-3-methyl-1-butanol binary mixture, as shown in Fig. 6(a). Furthermore, more data points (2393 compared to 2345) and systems (167 compared to 164) exhibit LLE based on MESP, indicating the effectiveness of using the MESP for identifying and characterizing hydrogen bonds. Fig. 6(b) presents an example where correct phase separation is predicted only with COSMO-SAC (DHB)/MESP.

(a)



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(b)

Fig. 6. The LLE of (a) water (1) - 3-methyl-1-butanol (2) and (b) water(1) succinonitrile (2) binary systems. Open circles are experimental data. The IDAC is useful for examining the solvation behavior of a solute in a solvent. The predictive performance for IDAC is evaluated by the root mean square error

exp calc RMSIDAC = ∑N i=1lnγi - lnγi 1

2 0.5

(20)

N

A greater deviation occurs in IDAC when water is infinitely dilute in alkanes. The deviation for such a kind of systems is more prominent in MESP than that in VSEPR, as seen in Fig. 6. Therefore, the overall RMS of IDAC in MESP is higher than that in VSEPR. However, MESP is more accurate than VSEPR for predicting IDAC after excluding such a type of systems. Table 3 compares the RMS in IDAC for infinite dilution of water in alkane systems and the other systems. ACS Paragon Plus Environment 22

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Table 3. RMS error of IDAC from VSEPR and MESP methods for different systems

RMSIDAC

RMSIDAC

RMSIDAC

(water-alkanes)

(others)

(overall)

2.36

0.48

0.587

2.50

0.47

0.598

52

2291

2343

COSMOSAC-DHB (VSEPR) COSMOSAC-DHB (MESP) Data points

Kow is another property useful for examining the solvation behavior of a solute in another solvent. The performance in Kow is evaluated by the root mean square error / _.·

K-g §@§ ®¯° ± ² = ∑¦ ¨¥2³´µ¶ − 2³´µ¶ ¥

¦

(21)

For Kow, MESP also performs better than VSEPR by 3.8% in RMS error (0.462 compared to 0.480).

4.2.

Comparison

of

hydrogen

bond

surfaces

in

COSMO-SAC

(DHB)/VSEPR and COSMO-SAC (DHB)/MESP For typical compounds whose lone pair sites can be determined both by VSEPR and MESP, we find little difference in their appearance of corresponding surface area within the cutoff radius from the corresponding hydrogen bond center, as shown in Table 4. To better quantify the differences of the hydrogen bonding surface regions, we define two variables: the fraction of hydrogen bonding surface (η) and the effective surface charge density (FKLL,v ). The fraction of hydrogen bonding surface is a measure of how well the hydrogen bond center (hbc) and the ACS Paragon Plus Environment 23


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cutoff radius (RHB cut ) captures segments with charge density greater than the cutoff value (Fjk ), i.e., η=

¹º» (&¼½ &C¿À ) ¹º» (&¼½ )

(22)

where Apq (§Áv ) is the area of a circle centered at the hbc with a radius of RHB cut , i.e.,

ÄÄÄÄÄÄÂk Ã < RHB Apq (§Áv ) = Σσm s(rÂσm ) if ÃrÂσm - hbc cut j-th

(23)

and Ahb (R cut &σhb ) is the area within Apq (§Áv ) that possesses a charge density greater than Fjk

ÄÄÄÄÄÄÂ j-th σhb k

(24)

The j-th hydrogen bond center on a hydrogen bonding acceptor atom k is determined as ÄÄÄÄÄÄÂk = P ÄÄÄÂk + R k × D Ï j-th hbc k j-th

(25)

Ï j-th is the unit vector ÄÄÄÂk and R k are the position and radius of atom k respectively. D where P k

Ï j-th is the unit vector from atom k toward the hydrogen bond center. In the MESP approach, D k pointing from the center of atom k to the j-th potential minima.

The value of η is an indication of how effective the hydrogen bond center identified by VSEPR or MESP can be used to capture the high charge density surfaces within the cutoff radius RHB cut . Fig. 7 compares the value of η from the two methods. Although having a smaller RHB cut value with MESP (see Table 1), the hydrogen bonding segment fraction (η) from MESP is larger than that from VSEPR (most circles located at the upper left half in Fig. 7). The results indicate that the hydrogen bond center determined by MESP more effectively includes most of the polarized segments around hydrogen bonding donor atoms.

A second measure of the difference in the hydrogen bonding segment is the effective surface charge density (FKLL,v ) defined as ACS Paragon Plus Environment 24

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FKLL,v =

∑Ð½ Ñ½ $ÄÂÐ½ ∑Ð½ $ÄÂÐ½

vj | if :ÂC½ − ÄÄÄÄÄÄÄÂ ÒÓY < §Áv JÔÕ |Fv | > Fjk

(26)

where the subscript t is either HB donor (don) or HB acceptor (acc). The effective charge density indicates the extent of “polarization” of the hydrogen bonding surfaces. Fig. 8 compares this quantity for HB acceptor (FKLL,@§§ ) and donor (FKLL,ÖS ) from the two methods. In can be seen that VSEPR and MESP give very similar results, with MESP showing a slightly polarized hydrogen bonding surface. Combined with the finding of a larger HB interaction parameter Chb in MESP (see Table 1), the results indicate that HB character from MESP is stronger than that from VSEPR.

Table 4. The comparison of HB segments determined by COSMO-SAC (DHB) /VSEPR and COSMO-SAC (DHB)/MESP for some typical example molecules (green ball: MESP, yellow ball: VSEPR) Molecule

Geometry

COSMO-surf

HB surface

HB surface

σ-profile

(atom

structure

ace

(VSEPR)

(MESP)

(hb level)

type) 3

(O: sp3)

2

Ai (Å2)

Water

HB surface on O/N/F -0.025

-0.025

2

0.025 e/Å

1 0 0 σ (e/Å2)

0.025

HB surface on H

4

(N: sp3)

3 Ai (Å2)

Amine

-0.025

2 1 0 -0.005 σ (e/Å2)

0.015

4

Acetone Ai (Å2)

(O: sp2)

2

0 -0.025

0 σ (e/Å2)

0.025

5

N-Methyl

4

formamide

Ai (Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

(N: sp )

3 2 1

(O: sp2)

0 -0.025


0 2) σ (e/Å

0.025


4

Acetonitrile

3 Ai (Å2)

(N: sp)

2 1 0

-0.025

Hydrogen

0 σ (e/Å2)

0.025

10

fluoride Ai (Å2)

8

3

(F: sp )

6 4 2 0

-0.025

DMSO

0 σ 5 (e/Å2)

0.025

4 Ai (Å2)

(O: sp2)

3 2 1 0

-0.025

Methyl

0 σ (e/Å2)

0.025

10 8

(N: sp2 )

6

Ai (Å2)

Isocyanate (O: sp2)

4 2

-0.025

0 0 σ (e/Å2)

1 0.9 0.8 0.7 η (MESP)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 37

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.2

0.4 0.6 η (VSEPR)

0.8

1

Fig. 7. Comparison of the fraction of hydrogen bonding surface from MESP and VSEPR.


0.025

Page 27 of 37

(a)

σeff, acc (MESP) (e/Å2)

0.02

0.015

0.01

0.005 0.005

0.01 0.015 σeff, acc (VSEPR) (e/Å2)

0.02

(b)

0.02

|σeff, don | (MESP) (e/Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.015

0.01

0.005 0.005

0.01

0.015 |σeff, don | (VSEPR) (e/Å2)

0.02

Fig. 8. Comparison of the effective HB surface charge density: (a) acceptor (b) donor



5. CONCLUSION A new method for identifying hydrogen bonding segments for the COSMO-SAC model is developed in this work. In this method, the hydrogen bonding segments are limited to the surface regions nearby the electron lone pairs and the proton acceptor. The local minima in the molecular electrostatic potential (MESP) are found to be an effective indication of the lone pair directions. The hydrogen bonding segments thus identified result in improved prediction of fluid thermodynamic properties (IDAC, Kow) and phase equilibria (VLE, LLE) over a wide range of mixture types, temperatures and compositions. More importantly, this new approach is applicable for all types of chemical species; whereas an earlier approach based on the VSEPR theory was limited to chemical species with clear hybridization character. We believe that the COSMO-SAC model with hydrogen bonding segments determined from MESP assigned lone pairs is a powerful method for thermodynamic property prediction of associating fluids.


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Supporting Information Summary of challenges in identifying lone pair locations with VSEPR and detailed results of VLE, Kow, and IDAC predictions for hydrogen bonding containing systems are provided in the supporting information.

ACKNOWLEDGEMENT This research was partially supported by the Ministry of Science and Technology of Taiwan (MOST 104-2221-E-002-186-MY3 and 106-2811-E-002-020) and National Taiwan University (NTU-CDP-107L7827). The computation resources from the National Center for High-Performance Computing of Taiwan and the Computing and Information Networking Center of the National Taiwan University are acknowledged. C.K. and S.T. are thankful to Prof. Gadre and his group from IIT Kanpur for providing some MESP samples that helped us in developing our program for identifying the lone pair directions. The authors also acknowledge Dr. Erik van Lenthe at Software for Chemistry & Materials B.V. (SCM) for the discussion regarding using NBO for identifying lone pairs.



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TOC graphics


Improved Directional Hydrogen Bonding Interactions for the Prediction

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