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The CMIRS Solvation Model for Methanol: Parametrization, Testing and Comparison with SMD, SM8 and COSMO-RS Natalia Moreira Silva, Peter Deglmann, and Josefredo Rodriguez Pliego J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b10249 • Publication Date (Web): 23 Nov 2016 Downloaded from http://pubs.acs.org on December 1, 2016

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The Journal of Physical Chemistry

The CMIRS Solvation Model for Methanol: Parametrization, Testing and Comparison with SMD, SM8 and COSMO-RS

Natalia M. Silvaa, Peter Deglmannb and Josefredo R. Pliego Jr.a,*

a

Departamento de Ciências Naturais, Universidade Federal de São João del-Rei

36301-160, São João del-Rei, MG, Brazil. b

Polymer Processing&Engineering, BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen, Germany

* [email protected]

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Abstract

The new continuum solvation model CMIRS (composite method for implicit representation of solvent) proposed by Pomogaeva and Chipman and implemented in GAMESS was parametrized for methanol solvent, aimed to be used for ionic reactions in solution. The model was tested for predicting single-ion solvation free energy, pKa of acids and protonated bases, and the activation free energy barriers of SN2 and SNAr reactions in methanol. A comparison was performed with other continuum models such as SMD, SM8 and COSMO-RS. For a prediction of pKa and free energy barriers, the order of performance was CMIRS > COSMO-RS > SMD > SM8. In particular, the CMIRS model is much superior to the other continuum models for predicting pKa of acids (without empirical corrections) and able to evenly describe hard ions like methoxide and charge dispersed ions like 2,4,6-trinitrophenol. Based on our results, we suggest the field-extremum contribution, present in the CMIRS, should be included in continuum solvation models, which can result in substantial improvement in the modeling of ionic reactions in solution.



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Introduction The interaction of molecules and ions with the solvent is a very important phenomenon, which is quantified by the solvation free energy.1-6 This property directly translates into the chemical potential of the solute, it is related to many different equilibria in condensed phase, like acid dissociation constants (pKa),7-12 reduction potentials,13-14 partition coefficients,15 phase equilibria and solubility,16-18 small molecule-protein interaction or hots-guest complexes,19 and the most diverse kinds of chemical equilibria and kinetics processes.20-26 Therefore, an accurate calculation of the solvation free energy is of paramount importance for theoretical and computational chemistry when dealing with systems of technical interest.27 This fact has motivated the development of a wide variety of theoretical approaches for computing the solvation free energy. In addition, challenge tests have been proposed in order to evaluate these different methods.28-39 A preeminent problem in computational chemistry is the description of ionic reactions in polar solvents. In particular, many organic reactions involve ions as reactants or ions are formed along the reaction pathway. Due to the fact that ionsolvent interactions are strong, the solvent usually has a profound effect on the reaction kinetics and thermodynamics.22 Among the different approaches for calculating the solvation free energy, continuum solvation models are very popular and widely used in the study of chemical reactions.3,

20, 23-24, 40

However, these models

exhibit a deficiency in the description of ion solvation, in particular for small or charge centered ions in protic solvents.41-42 Such a problem has recently become evident in a report by Plata and Singleton, where PCM and SMD continuum solvation models have predicted different solvent effects for an important chemical reaction in methanol solution.43 This again shows that a prediction of the solvation free energy of ions is still a challenging and non-trivial task within the modeling ionic chemical reactions in polar solvents. The Polarizable Continuum Model (PCM) has been proposed more than 30 years ago and remains in active algorithm development.44-48 Its several formulations (DPCM, CPCM, IEFPCM) make use of atom-centered spheres to generate a molecular 4 ACS Paragon Plus Environment

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shaped cavity. This method considers the molecular electronic density interacting with the dielectric, which can be a reliable description of the solute in the absence of directed interactions. Considering these attractive features, Cramer and Truhlar have used the PCM approach to develop the solvent model density (SMD) which combines the PCM method for electrostatic solvation and an atomic surface-tension based contribution for nonelectrostatic solvation.49 A closely related method is the SM8.50 In this model, atomic point charges are used to obtain the electrostatic solvation instead of continuous electronic density. The SMD method has been implemented in Gaussian, GAMESS and NWChem programs and has become widely used. Although tests with the SMD method have pointed out that it works very well for neutral molecules,30, 39, 49 its performance in the case of ions is less satisfactory. Indeed, we have found that the calculation of pKa for acids and bases in methanol using SMD (and SM8) leads to systematic deviations, even when considering an isodesmic proton exchange reaction, i.e. reactions involving the same functional group in proton exchange.12 The performance of SMD has also been tested for modeling activation barriers for ionmolecule reactions in methanol and dipolar aprotic solvents.38 It was found that the rate acceleration effect when going from protic to dipolar aprotic solvents was not described appropriately by SMD. In particular, the performance of this solvation model for dipolar aprotic solvents was disappointing, with an average error in the barriers of more than 5 kcal mol-1. Therefore, further improvements are needed. The solvation model COSMO, which represents an efficient simplification to PCM via considering an immediate (conductor like) screening outside the cavity, was developed around a decade after PCM.51 As an extension of it, COSMO-RS (Conductor like Screening Model for Real Solvents) was proposed only slightly later.18, 52 The basic approximation in COSMO-RS is that an ensemble of interacting molecules may be replaced by a corresponding ensemble of independent, pairwise interacting surface segments. This approximation results in a loss of molecular neighborhood information of these surface segments and therefore a loss of structural or steric information but at the same time in an extreme reduction in complexity of the problem. The screening charge density σ is the only descriptor determining the residual part of interaction free energies and it is assumed that a fluid mixture is fully characterized by the distribution 5 ACS Paragon Plus Environment


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function of these σ (the so called σ-profile). From this quantity, in an iteratively performed Boltzmann-like integration, residual chemical potentials are computed; apart from the “misfit” contribution which covers “normal” electrostatic interactions, a hydrogen bonding term (also depending only on the σ-profile) is added in order to account for these stronger interactions where the misfit term alone would be insufficient. Although the COSMO-RS model was initially mainly applied to questions of chemical engineering, its ability to predict vapor pressures of any substance makes it also able to be used for the computation of chemical thermodynamics and kinetics.53 Even for the case of charge non-conserving reactions a reasonable (although not perfect) agreement with the experiment has been observed.54 With the aim to improve the description of ion solvation by a dielectric continuum approach, Pomogaeva and Chipman have recently proposed the composite method for implicit representation of solvent (CMIRS).55-57 The development of the CMIRS model has been initiated by early studies by Chipman on the flaw of continuum solvation models in the case of ionic species. Chipman has shown the correlation between extreme electric-field on the solute cavity and deviations of the dielectric solvation model.58-59 The idea of Chipman was to introduce an additional term to the solvation free energy able to account for the strong specific (hydrogen bonding) solute-solvent interactions, which are not described by the dielectric continuum model.60-61

Pomogaeva and Chipman have tested the CMIRS model for water,

dimethyl sulfoxide and acetonitrile.55-56 For a water solvent and using an isodensity contour of 0.001 au, the authors have obtained the mean unsigned error of 2.36 kcal mol-1 for ionic solutes and 0.75 kcal mol-1 for neutral solutes taken from Minnesota solvation database, both using a B3LYP/6-31+G* electronic density. For comparison, the SMD method leads to a mean unsigned error of 4.9 kcal mol-1 for ions and 0.8 kcal mol-1 for neutrals using the B3LYP/6-31G* method.49 Thus, the field-extremum contribution in the CMIRS model is a substantial improvement over the pure dielectric description of electrostatic solvation. Motived by the relation between the extremum electric field and deviations of the solvation free energy in the continuum model, Liu et al have developed the SMVLE model.62 This approach combines the surface and volume polarization for electrostatic 6 ACS Paragon Plus Environment

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(SVPE) method for bulk electrostatic, the cavity-dispersion-solvent-structure (CDS) contribution and a third term to account for local electrostatics, related to the electric field on the solute cavity. The method exhibits a mean unsigned error of 3.07 kcal mol1

for ions and 0.55 kcal mol-1 for neutrals in aqueous solution. Thus, both the SMVLE

and the CMIRS models point out that additional terms to account for strong specific interaction (hydrogen bond) lead to substantial improvement of the continuum models for ions in polar solvents. In this paper, we have parametrized the CMIRS method for methanol. Our objective was to obtain a reliable continuum based solvation model able to describe ionic reactions in methanol solution. Following the parametrization of the model, we carried out some tests like prediction of pKa and barriers for SN2 and SNAr reactions. For comparison, we also performed calculations with the SMD, SM8 and COSMO-RS methods.



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The CMIRS model and parameter fitting The solvation free energy calculated by the CMIRS model is a sum of four contributions in which five parameters have to be fitted: ∆ , , , , = ∆ + ∆ + ∆ + ∆ , 1 The first term on the right side is the bulk electrostatic, calculated by the SS(V)PE method and depends on the isodensity parameter (I). The second and third term correspond to the dispersion and exchange-repulsion interactions (nonelectrostatic solvation) and depend on the parameters A and B, respectively. The last term is the field-extremum contribution and has the expression: ∆ , = | | + | | 2 In equation (2), Fmin is the lowest electric field normal to the solute cavity and accounts for hydrogen bonding from the solvent. The Fmax term represents its counterpart in order to account for hydrogen bonding from the solute to the solvent. The parameter γ is fixed in 3.6 as reported by Pomogaeva and Chipman.56 In the parametrization of the CMIRS model for methanol, our aim was to obtain a reliable model for ion solvation. Thus, we have used some parameters of Pomogaeva and Chipman for water solvent and changed only the dielectric constant (to 32.613 for methanol) and the parameters A, C and D. We have fixed the isodensity parameter in 0.001 e/bohr3 and B = 0.045576 au. For determining the A parameter (dispersion contribution), we performed a trial and error procedure with a few neutral molecules (1,1-difluoroethane, n-butanol, benzene and o-cresol) and found that a value of A = 0.0125 au is adequate to minimize the deviation from experimental data. In the case of C and D parameters, which were most relevant for our purpose, an error function (f) was defined according to the expression:

8

! , = "#∆ $% &' + ∆# $% ($% ) * − ∆,-.. , 0ℎ23 245 .627* + #∆9ℎ&

'

)

; 8 8

+ ∆#9ℎ($% * − ∆,-.. , 0ℎ23 245 .627* : 3 8

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which was minimized with respect to the parameters C and D. We found the values of 800 and 0 to be the best and physically most meaningful choice for C and D, respectively. All of these solvation calculations were done with the X3LYP/6-31(+)G(d) electronic density. The fitted parameters were then used to test the model for a methanolic environment.

Solvation free energy data for neutrals and ions In previous publications, we have obtained experimental solvation free energy data for 37 neutrals39 and 25 ions in methanol.63 In the latter case, the free energy scale excludes the net potential inside the ion cavity and is especially adequate for continuum models.4,

64-71

The solvation data for neutrals are presented in Table S1

(supporting information). For ions, we have used solvation data of 17 ions from our previous publication63 and derived more 14 ion solvation data, resulting in 31 single ion solvation free energy values (19 anions and 12 cations). The procedure for determining the experimental solvation free energy of ions has been described,63 and we have used experimental pKa in methanol,72 gas phase basicity values taken from NIST,73 the solvation free energy of the proton determined in our previous work (253.6 kcal mol-1) and the solvation free energy of the respective neutral species, determined with the SMD/X3LYP/6-31+G(d) method. We should notice that for 4hydroxybenzoic acid and 4-nitroaniline, the NIST basicity values are in considerable error and we have used theoretical values. For anions, the equation is:

' ∗ ' ∗ $ ∗ $ ) = 1.364.@ $ − ∆A + ∆ − ∆ − ∆

1.89 DE6F G4F ';

(4)

and for cations, the equation is:



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∗ ∗ ∗ ) ∆ $) = −1.364.@ $ ) + ∆A + ∆ + ∆ $ +

1.89 DE6F G4F ';

(5)

Table S2 (supporting information) presents the values used in the calculation of the solvation free energy of ions, which complements our previously reported data.

Theoretical Calculations Structure optimizations, harmonic frequencies, electronic densities for solvation free energy calculation and single point energies have been obtained at different levels, depending on the set of data to be generated. In the first set of calculations, related to generating additional “experimental“ solvation free energy of single organic ions, geometry optimization of the neutral species were done at X3LYP/6-31+G(d) level,74 followed by single point solvation free energy calculation at SMD/X3LYP/6-31+G(d) level (Table S2). The second set of calculations is related to the test of CMIRS model for solvation free energy of 37 neutral species. We have used the previously optimized structures39 (at X3LYP/6-31G(d) level) to perform single point calculations at CMIRS/X3LYP/6-31(+)G(d) level. Results are given in Table S1. The calculation of the solvation free energies of single ions is the third set of calculations. In this case, we have done geometry optimizations at the X3LYP/631+G(d) level, followed by single point solvation free energy calculations at the SMD/X3LYP/6-31+G(d) and CMIRS/X3LYP/6-31(+)G(d) levels. In the fourth set of calculations, the pKa predictions, we used geometries and frequencies obtained at the X3LYP/DZ+P(d) level and single point energies at the X3LYP/TZVPP+diff level as well as the SMD and SM8 results from our previous report.12 In this article, we performed additional solvation calculations at the CMIRS/X3LYP/631(+)G(d) and COSMO-RS level in order to test the performance of these solvation models. For HA acids, we used the proton exchange reaction with phenoxide ion as the reference species: 10 ACS Paragon Plus Environment

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HA + PhO− → A− + PhOH

(6)

meaning that pKa were obtained via the following equation: .@ $ =

∗ ∆ + .@ 9ℎ&$ 7 HIF510

For BH+ acids, the considered proton exchange reaction was: BH+ + CH3NH2

→ B + CH3NH3+

(8)

so that pKa of BH+ acids were calculated by: .@ $) =

∗ ∆ + .@ $% ($%) 9 HIF510

In a fifth set of calculations, free energy barriers of anion-molecule nucleophilic substitution reactions in methanol were studied, where we have taken six reactions from our previous report38 and included three more transition states. For these systems, we have done geometry optimizations and harmonic frequencies at the SMD/X3LYP/DZ+P(d)+diff level of theory. Higher level single point energy calculation have been done with the CCSD(T) method and a def2-TZVPP basis set for C and H and def2-TZVPPD basis sets for O, Cl, Br and S.75-76 In the case of large structures, we have used an additivity approximation using CCSD(T)/def2-SVPD and MP2/def2-TZVPPD methods. Some functionals were also tested using this extended basis set: X3LYP,74 M1177 and M08-SO.78 The solvation free energy calculations were done with the SMD/X3LYP/DZ+P(d)+diff, SM8/B3LYP/6-31G*, CMIRS/X3LYP/6-31(+)G(d) and COSMORS methods. All the X3LYP, M08-SO, M11, SMD and CMIRS calculations were done with the GAMESS program.79-80 The SM8 calculations were done with GAMESSPLUS81 and the CCSD(T) and MP2 calculations with the ORCA program.82 COSMO-RS free energies of solvation were obtained with the software COSMOtherm GmbH & Co. KG using the BP_TZVP_C30_1501.ctd parameterization. As input for this, single-point calculations at the BP86/TZVP(gas) and BP86/TZVP(COSMO, infinite dielectric constant) levels were performed with the program package TURBOMOLE.83



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Results and Discussion Testing CMIRS and SMD models for absolute solvation free energy Although this parametrization of the CMIRS model for methanol was done with the aim to apply this method for ionic reactions, it is worthwhile to know how reliable it is when describing the solvation of neutral species. We have done the calculations of solvation free energies for 37 neutral molecules and compared with experimental data taken from a recent report of our group. The results are presented in Figure 1 (and Table S1) and a comparison with experimental values indicates that the results are reasonable, with a mean unsigned error (MUE) of 1.2 kcal mol-1. We have also included the calculations with the SMD model for comparison and in this case the MUE is 0.7 kcal mol-1. The better performance of the SMD model for neutrals should be expected, considering the high parametrization of the nonelectrostatic solvation term present in SMD. Computed solvation free energies of ions are shown in Figure 1 (and Table S3) for both CMIRS and SMD models. We can see the performance of the CMIRS model is much better than SMD. Considering both anions and cations, the MUE is 5.4 kcal mol-1 for CMIRS and reaches 11.2 kcal mol-1 for SMD. In the case of mean signed error (MSE), the CMIRS model presents small positive deviations for anions and small negative deviations for cations. Thus, taking anions and cations together, the MSE becomes -0.1 kcal mol-1. In the case of SMD model, the anions have much higher deviation than cations and the final MSE is as high as 7.8 kcal mol-1. We should emphasize that the present data include hard ions like CH3O−, OH−, F− and CH3OH2+, which are difficult to describe by pure continuum models.41-42,

84

Particularly here, the field-extremum

correction is able to provide a better description of these difficult cases. It is important to consider that the SMD model was parametrized against another solvation free energy scale, which could partially explain the bad performance of this model for ions in methanol. In order to compare more consistently both these methods, we have analyzed anions and cations separately. Table S3 presents the MSE 12 ACS Paragon Plus Environment

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calculated for each set of ions and using the CMIRS and SMD models. The CMIRS model has a MSE of 4.0 kcal mol-1 for anions and -6.6 kcal mol-1 for cations, while the SMD model exhibits errors of 15.1 and -3.7 kcal mol-1, respectively. These results point out that the CMIRS model is much more reliable for describing processes in which charged species are created or destroyed, like described below: molecule1 + molecule2 → anion + caƟon In fact, the sum of MSE for cations and anions are -2.6 kcal mol-1 for the CMIRS model. On the other hand, this sum amounts to 11.4 kcal mol-1 for the SMD model, indicating this method should not be used for process like those indicated above. Another important type of process is: molecule1 + ion2 → ion1 + molecule2 To describe these processes in solution requires that the error in the solvation free energy of ions is similar. Thus, we can define the standard deviation of the solvation free energy values for anions and cations with respect to MSE. For the CMIRS model, the standard deviations are 4.1 and 3.2 kcal mol-1 for anions and cations, respectively. In the case of SMD model, the value is 4.6 kcal mol-1 for both anions and cations. These results also suggest a slightly superior performance of the CMIRS for ionic reactions in solution. The performance in chemical processes will be tested in the next sections, along with other methods like SM8 and COSMO-RS.



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-60 -80 -100 -120 -120

-100

-80

-60

-40

Experimental

Figure 1: Comparison of solvation free energies predicted by the CMIRS and SMD models. The study was performed for neutrals (green circles), anions (blue lozenges) and cations (red squares). Units in kcal mol-1.


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Theoretical calculation of pKa The correct prediction of ionization of acids and bases in polar solution is a very important test of solvation models. In addition, pKa is an essential property to understand solution phase chemistry. As a consequence, theoretical calculation of pKa has received a considerable attention in the past thirty years.10-12, 14, 41, 85-95 Recently, our group has investigated the performance of the SMD and SM8 models for predicting pKa of phenols, carboxylic acids and amines in methanol solution.12 We have used the proton exchange approach for each set of acids and bases. A systematic deviation of the pKa values was observed, even using isodesmic reactions. However, it was possible to derive a simple linear correction function and thus to obtain an accurate prediction of pKa values. In this paper, our aim is to perform a harder test of the models. Thus, we have chosen 20 HA acids (phenols, carboxylic acids and methanol) with a wide range of pKa values, from 3.6 to 18.6. We have used equations (6) and (7) to compute pKa and the results are in Table S4 and Figure 2. The SMD method exhibits the same trends observed in our previous study, with a systematic deviation from experimental data. The RMSE is very high, 4.4 pKa units for a set of 20 HA acids. In the case of SM8, the RMSE is smaller, just 3.3. The most sophisticated COSMO-RS methods also has a poor performance, with a RMSE of 4.0. These results, using a proton exchange reaction, point out a flaw of the SMD, SM8 and COSMO-RS approaches to treat different ions evenly. While the previous continuum models are not reliable, the CMIRS method shows an outstanding performance, with a RMSE of only 1.1 pKa units. This method is obviously able to correct the inability of the dielectric continuum solvation to treat ions with different charge dispersion. For example, the error in the pKa of CH3OH (the highest pKa) is 3.35, whereas the error for 2,4,6-trinitro-phenol (the lowest pKa value) is only 0.98 (both predicted values being too positive). For comparison, the SMD method has deviations of 7.00 and -5.72 pKa units, respectively, which point out a very serious flaw of SMD. Even COSMO-RS exhibits deviations (in the opposite directions) of 1.78 and -3.97 pKa units, respectively.



30

SMD RMSE = 4.4

25

pKa (theor)

20 15 10 5 0 -5 -5

0

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pKa (exp)

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RMSE = 3.3

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pKa (theor)

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15 10 5 0 -5 -5

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30

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pKa (exp)

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CMIRS 25

RMSE = 1.1

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pKa (theor)

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15 10 5 0 -5 -5

0

5

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pKa (exp)

Figure 2: Comparison of predicted with experimental pKa for phenols, carboxylic acids and methanol in methanol solution using four different solvation models. Gas phase contribution at the X3LYP/TZVPP+diff//X3LYP/DZ+P(d) level. RMSE = root of mean squared error.



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In the case of BH+ acids, we have used equations (8) and (9) to calculate pKa and the results are in Figure 3 and Table S5. The parametrization of the CMIRS method for cations has not included an extremum electric field term. As a consequence, all of the methods have exhibited a similar performance, although the CMIRS is slightly better. Because the performances are close to each other (RMSE in the range of 3.3 to 4.3), we have gathered the results of the four methods in the same graphic. It is evident from the trends that more acidic BH+ ions are systematically not stabilized enough by the continuum methods, leading to an overestimation of the decrease of pKa. The extreme cases are protonated methanol (CH3OH2+) and protonated 2-nitro-aniline, with deviations as large as -9.9 and -5.6 units, respectively, when using the SMD method. In the case of CMIRS, the deviations are -7.8 and -5.6 units, respectively. It should be noted that for both pKa test series, also a novel parameterization of COSMO-RS (BP_TZVPD_FINE_C30_1501) was tried, which is based on screening charges and energies computed with a larger basis set. The obtained performance was slightly better for the BH+ acids whereas it was even worse for HA acids indicating that the problem to evenly describe strongly localized and delocalized charges (in particular negative charges) has not been solved in recent COSMO-RS method developments.


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15 CMIRS

10

COSMO-RS

SM8

SMD

5

pKa(theor)

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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10

15

pKa(exp) Figure 3: Comparison of predicted with experimental pKa for BH+ acids (protonated amines and derivatives and protonated methanol) in methanol solution using four different solvation models. Gas phase contribution at the X3LYP/TZVPP+diff//X3LYP/DZ+P(d) level. The RMSE is 4.2, 4.3, 4.0 and 3.3 for SMD, SM8, COSMO-RS and CMIRS methods, respectively.

Free Energy Barriers for SN2 and SNAr Reactions Nucleophilic substitution reactions are classical organic reactions. In particular, anion-molecule SN2 and SNAr reactions exhibit a very solvent dependent free energy barrier and thus constitute an interesting test of solvation models. We have selected nine such reactions in methanol solution, including six reactions previously investigated by the SMD model. These reactions as well as results are given in Tables 1 and 2. Table 1 shows the difference of electronic energy when going from the reactants to the transition states in several levels of theory. We have used the CCSD(T)/def2-TZVPPD method as our benchmark and benchmarked some functionals like X3LYP, M11 and M08-SO with the def2-TZVPPD basis set. Our results point out the M08-SO has a good performance, with a RMSE of only 1.6 kcal mol-1 from CCSD(T). The M11 and X3LYP methods present higher deviations, 2.5 and 2.8 kcal mol-1,



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respectively. A similarly good performance was also observed for the M08-HX method in the study of a classical Knoevenagel reaction.96

Table 1: Energy and free energy barriers for nucleophilic substitution reactions. ∆Ea Number

SN2 or SNAr Reaction

X3LYP

M11

M08-SO

CCSD(T)

∆G*mb

1

CH3Cl + N3−

0.11

6.48

4.08

2.53

8.12

2

CH3Cl + SCN−

7.23

13.43

10.70

10.32

16.13

3

CH3Br + Cl−

-6.10

-2.96

-3.93

-2.16

1.93

2.85

5.52

2.93

5.21

12.37

−

4

CH3CHBrCH3 + PhS

5

CH3CH2CH2CH2Cl + PhS−

3.38

7.31

4.40

4.49

13.93

6

2-bromo-pyridine + MeO−

-11.22

-13.18

-13.69

-15.44

-6.74

-19.74

-17.17

-17.67

-17.36

-8.79

−

7

CH3Br + MeO

8

CH3CHBrCH3 + MeO−

-16.63

-15.37

-16.79

-14.32

-5.82

9

PhCH2Cl + MeO−

-17.95

-11.97

-14.49

-15.79

-6.79

2.8

2.5

1.6

RMSE

c

a –Electronic energy barriers with four different methods using the def2-TZVPPD basis set. Energy barriers are in kcal mol-1. b – Molecular contribution to the free energy barrier, including electronic, vibrational, rotational and translational terms. Harmonic frequencies at the SMD/X3LYP/DZ+P(d)+diff level. c – RMSE in relation to CCSD(T) method.

The results show a considerable difference in the performance of the solvation models. The SMD method shows a performance similar to our previous report, with RMSE of 2.8 kcal mol-1. On the other hand, the SM8 method performs poorly with a RMSE of 5.1 kcal mol-1. Indeed, it is observed that the SM8 method systematically overestimates the activation barriers. In the case of the COSMO-RS method, a good performance is obtained with an RMSE of only 2.1 kcal mol-1. To our surprise, the CMIRS method is quite similar to the COSMO-RS one, with an RMSE of 2.5 kcal mol-1 (excluding reaction 5, because the CMIRS calculation has not converged). Considering the fact that many reactions involve the hard methoxide ion, this close performance of COSMO-RS and CMIRS was unexpected, although it has to be noted that an error cancellation is even possible for these cases if the reaction proceeds via an early 20 ACS Paragon Plus Environment

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transition state in which the negative charge is almost as “naked” as in the anionic reactant.

Table 2: Free energy barriers for nucleophilic substitution reactions in methanol solution. ∆G‡sola Number

SN2 or SNAr Reaction

SMD

SM8

COSMO-RS

CMIRS

Expb

1

CH3Cl + N3−

22.85

28.07

23.80

24.58

25.77

26.49

28.95

24.53

28.34

25.37

23.93

32.95

26.28

22.81

24.55

26.77

30.36

24.08

25.78

22.64

25.56

28.44

25.63

-

23.40

−

2

CH3Cl + SCN

3

CH3Br + Cl

−

4

CH3CHBrCH3 + PhS−

5

CH3CH2CH2CH2Cl + PhS

− −

6

2-bromo-pyridine + MeO

24.20

28.33

24.92

27.96

28.78

7

CH3Br + MeO−

21.00

26.23

19.75

24.75

22.64

8

CH3CHBrCH3 + MeO−

27.42

31.69

24.68

29.19

25.23

20.27

26.00

22.85

25.86

23.73

2.8

5.1

2.1

2.5

9

PhCH2Cl + MeO

RMSEc

−

a – Free energy barrier in solution. Free energy berries are in kcal mol-1 and refer to a standard state of 1 mol L-1. b – Reactions taken from references 38, 97. c – RMSE with respect to experimental data.

From these results, an overall accuracy of the methods in the order CMIRS > COSMO-RS > SMD > SM8 can be concluded. We can make recommendations for using the solvation models in the modeling ionic reactions in solution. Thus, the SM8 model has turned out to perform worst among the tested methods and should be avoided. However, it should be noted that there are reports of other situations where the SM8 method could be recommended; for example, we have found that description of zwitterionic isomers of hydroxylamine can be accurately described by SM8, while SMD has failed.98-99 The SMD method has also performed poorly in pKa prediction, although the results for the activation barriers are more reasonable. However, because the deviations in pKa are systematic, it is possible to apply simple empirical corrections to 21 ACS Paragon Plus Environment


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predict reliable pKa,12 so that using such schemes a reliable treatment of reactive ionic systems is possible in polar solvents.96 For pKa prediction, the COSMO-RS solvation model exhibits a similar trend as SMD. Absolute pKa are not predicted on spot which is a consequence of the fact that the slope of the correlation line between predicted and experimental pKa is not one; this phenomenon has already been described earlier.93 Also for COSMO-RS it can be concluded that the absence of a term that (like in CMIRS) covers solvent dependent contributions from particularly high surface charges leads to this effect. Our results point out that the CMIRS method exhibits the best performance for the investigated problems. In particular, the prediction of pKa of neutral HA acids is very reliable and emphasizes the benefits from an extremum electric field correction. The results are slightly less accurate for activation barriers and in the case of BH+ acids, where in the latter case the absence of such an electric field correction leads to the higher error. In addition, the parameterization done in this study is not complete and further fit of the parameters can lead to improved results. In this point, we should call the attention for a very recent publication by You and Herbert.100 These authors have presented the CMIRS version 1.1 and have point out an error in the dispersion term of the CMIRS version 1.0 (used in this work). Fortunately, the exchange and dispersion terms can be adjusted in order to compensate this error, as You and Herbert have found comparing the mean unsigned error of the solvation free energy of neutrals in cyclohexane for both versions. It should furthermore be noted that for the solvation models SM8, SMD and COSMO-RS, microsolvation could represent one way to mitigate some of the problems discussed above. At least for aqueous pKa prediction, a correlation line much closer than one has been obtained when adding one or two explicit water molecules.101-102 Also for a methanol medium, which represents a hydrogen bonding environment as well, it could be expected that the addition of a few solvent molecules leads to improved results.


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Conclusion A parametrization of the CMIRS continuum model for methanol solvent was proposed and tested against neutral and singly charged ion solvation free energy values. The results point out the CMIRS model is able describe processes in which charged species are created or eliminated. In addition, the performance of the model for pKa and activation free energy barriers of SN2 and SNAr reactions was also evaluated and compared with the SMD, SM8 and COSMO-RS models. We have found the CMIRS method has an overall better performance than other continuum models. Furthermore, our results suggest the inclusion of field-extremum correction in continuum models should lead to improved performance in the modeling of ionic reactions in liquid phase.

Supporting Information Additional Tables and the coordinates of the optimized structures.

Acknowledgments The authors thank the agencies CNPq, FAPEMIG, and CAPES for support.

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