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Predicting Accurate Solvation Free Energy in n-Octanol Using 3DRISM-KH Molecular Theory of Solvation – Making Right Choices DIPANKAR ROY, Nikolay Blinov, and Andriy Kovalenko J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06375 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 8, 2017

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The Journal of Physical Chemistry

Predicting Accurate Solvation Free Energy in n-Octanol using 3D-RISM-KH Molecular Theory of Solvation – Making Right Choices Dipankar Roy,1,2 Nikolay Blinov,1,2 and Andriy Kovalenko1,2,* 1

Department of Mechanical Engineering, University of Alberta 10-203 Donadeo Innovation Centre for Engineering, 9211-116 Street NW Edmonton, Alberta, Canada T6G 1H9

2

National Institute for Nanotechnology, 11421 Saskatchewan Drive Edmonton, Alberta, Canada T6G 2M9

* E-mail: [email protected] Abstract Molecular theory of solvation, a.k.a. three-dimensional reference interaction site model theory of solvation with Kovalenko-Hirata closure relation (3D-RISM-KH), is an accurate and fast theory predicting solvation free energy and structure. Here we report a benchmark study of n-Octanol solvation free energy calculations using this theory. The choice of correct force field parameters is quintessential for the success of 3D-RISM theory, and we present a guideline to obtain them for n-Octanol solvent. Our best prediction of the solvation free energy on a set of 205 small organic molecules supplemented with the so-called “Universal Correction” scheme yields relative mean unsigned error of 0.94 kcal/mol against the reported database. The best agreement is obtained with the united atom (UA) type force field parameterization of n-Octanol with the van der Waals parameters of hydroxyl hydrogen reported by Kobryn et al [Kobryn, A. E.; Kovalenko, A. J. Chem. Phys. 2008, 129, 134701].

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Introduction Molecular solvation theory within the framework of integral equation formalism is proven to be accurate and fast, requiring moderate computational cost. The three-dimensional reference interaction site model (3D-RISM) with the Kovalenko-Hirata (KH) closure is the most successful generation of this theory.1-3 The success of the 3D-RISM-KH theory in reproducing hydration free energies is well documented in the literature.4 Integral equation theory of molecular liquids is developed based on statistical mechanics and an essential part of multiscale methodology for (bio)chemical systems in solution. The theory uses a molecular interaction potential force field, and via diagrammatic analysis of the solvation free energy derives integral equations for correlation functions between molecules in solution in the statistical-mechanical ensemble. The formulation of the 3D-RISM-KH theory is described in detail in literature.5-8 As a brief summary, a molecule is described in RISM theory by a six-dimensional vector (viz. three positional {r} and three orientational {} degrees of freedoms). These six degrees of freedom are incorporated in the molecular Ornstein–Zernike equation (MOZ) in terms of the pair correlation functions (PCF) of r and  of liquids. The solvation structure is represented in the form of probability density ργgγ(r) of finding interaction site γ of solvent molecules at position r around the solute molecule of arbitrary shape. The term ργ is the average number density and gγ(r) is the 3D site distribution function. The region of physical interest thus defined by values of gγ(r) < 1 (depletion in density) and gγ(r) > 1 (enhancement of density) relative to the average density at gγ(r) 1. The 3D-RISM theory coupled with the KH closure consistently accounts for both electrostatic and non-polar effects, and has an exact differential of the solvation free energy, thus allowing to analytically perform Kirkwood’s thermodynamic integration, gradually switching the solute-solvent interaction on. Several studies were undertaken to improve the accuracy of 3D-RISM by introducing a correction for cavitation energy, MD modifications, etc., ACS Paragon Plus Environment

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to name a few.9-11 One popular correction scheme is known as the universal correction (UC). It uses regression model built on the Gaussian fluctuation hydration free energy (HFE) functional and partial molar volume obtained from 3D-RISM, which was shown to produce excellent hydration free energy.12-13 For non-polar solvents, the report of successful applications of this theory is limited. This has less to do with insufficient benchmark sets but more with inadequate force field parameters and careful calibrations. Octanol is very important and interesting solvent owing to the demand of correct prediction of octanol-water partition coefficients of drugs and drug-like compounds. Very recently, a successful application of the 3D-RISM-KH theory pertaining to Octanol-Water partition coefficients and solvation free energies of a moderate set of compounds was reported.14 In this note, we intend to compare effect of force field parameters in reproducing octanol solvation free energies. We envision that our finding reported here will serve as a guideline towards RISM-KH theory applied to non-polar solvents.

Computational Methods The following sections describe the computational methods and benchmark data set used for all solvation energies reported in this report. Apart from atomic coordinates, the parameters of a force field relevant to 3D-RISM-KH involve atomic charges and van der Waals’ (vdW) parameters ( in Å and  in kcal/mol). Generation of partial atomic charges is the first critical step. Classical force field methods use atomic charges computed using various quantum mechanical schemes. However, in the present exercise we intended to add up charges of all hydrogen atoms to that of the carbon atom attached with them, a process similar to that adopted for united atom (UA) parameters. This leads to partial atomic ACS Paragon Plus Environment


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charges on carbon, oxygen, and hydroxyl hydrogen atom summing up to zero. The n-octanol solvent molecule is optimized using semi-empirical AM1,15 Hartree-Fock (HF),16 and MP2 level.17-18 For all ab initio and DFT calculations, Pople’s 6-31G(d) basis set is used.19 The atomic charges are extracted from the optimized geometry at respective levels of theory. For all the calculations, we have used the lowest energy conformation of n-Octanol. It was shown previously that using other low-energy conformations for solvation energy calculations did not affect the results significantly. See reference 14 for more details. Further, we have recalculated these charges at the continuum solvation model for n-octanol solvent using the SMD solvation model.20 The choice of basis set is made based on the reported accuracy in predicting solvation free energy benchmarks for SMx solvation models.20 Further, this basis set is used for generation of partial atomic charges for small molecules in compliance to GAFF and CHARMM force fields. For comparison we have calculated atomic charges of n-Octanol using triple- basis sets (6-311G(d,p), 6-311++G(d,p), aug-cc-pvTZ) at MP2 level.21-23 All electronic structure calculations were done using the Gaussian09 suite of quantum chemical programs.24-25 As a separate experiment, we have prepared the octanol molecule using the Antechamber and GAFF force field parameters.26-27 As in the electronic structure methods, the charges of non-polar hydrogens were added to the attached carbon atom. Additionally, the TraPPE force field developed by the Siepmann group is also employed.28-29 The atomic charges in the TraPPE force field involve the atomic charges on hydroxyl oxygen, hydroxyl hydrogen, and carbon attached to the hydroxyl group. The rest of the CH2 and CH3 groups were assigned zero charge. The partial atomic charge calculation scheme adopted by the Automatic Topology Builder (ATB) server is also used.30-31 This method uses initial atomic charges calculated as per Merz-Kollman scheme using B3LYP/aug-cc-pvTZ level before converting to UA force field kind of treatment of atomic


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charges. All atomic charges used in this report are summarized in Table S1 in Supporting Information. The most important component required in the 3D-RISM-KH theory is vdW parameters. It is important to note at this juncture that most current generation force fields use zero as  and  parameters for hydroxyl hydrogens. It is essential though to use non-zero parameters for convergence of 1D-RISM calculations to generate distribution functions of solvent and to produce reliable solvation free energy. The modified versions of AMBER (GLYCAM force field, and H-bonded amides), CHARMM, OPLS(UA), and Drieding force fields incorporated non-zero vdW parameters for H-bonded polar hydrogens as special cases.32-35 We have incorporated these parameters in our report for comparison purpose. A careful calibration of polar hydroxyl hydrogen parameters pertaining to alcohols was reported from our laboratory.36 These parameters were implemented in the Amsterdam Density Functional (ADF) Modeling Suite37 of computational chemistry for methanol and ethanol and were used also in this report. The Universal Force Field (UFF) parameters were tested, too, as these parameters were developed based on valence states and connectivity of elements only.38 The united-atom variant of the OPLS force field is incorporated in this study to cover the performance of the entire spectrum of the first two generations of force fields (vide infra).39 To cover current generation force fields developed using combination of ab initio and empirical training set, we have used the vdW parameters of COMPASS force field.40 The corresponding parameters for C, O, and H were taken from the work of Wu et al.41 All the vdW parameters used in this report are summarized in Table 1.



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Table 1: Summary of the van der Waal’s parameters used in this reporta (Å) Amberb

Amber’c

CHARMMd

Driedinge

TraPPEf

GAFFg

UFFi

C[CH3]

3.600

3.600

3.600

3.8983

3.750

3.775

3.851

3.854

3.905

C[CH2]

3.600

3.600

3.600

3.8983

3.950

3.905

3.851

3.815

3.905

O

3.200

3.100

3.200

3.4046

3.020

3.070

3.500

3.580

3.07

2.886

1.807

0.0

H

2.000

2.000

1.600

3.195

0.700

h

0.700

h

COMPASSj OPLS (UA)k

(kcal/mol) Amber

Amber’

CHARMM

Drieding

TraPPE

GAFF

UFF

C[CH3]

0.0903

0.0600

0.0903

0.0951

0.1950

0.2070

0.105

0.062

0.175

C[CH2]

0.0903

0.0600

0.0903

0.0951

0.0914

0.1180

0.105

0.068

0.118

O

0.1591

0.1500

0.1591

0.0957

0.1850

0.170

0.0600

0.096

0.170

0.0001

h

0.0440

0.008

0.000

H

0.0200

0.0200

0.0498

0.046

0.046

h

COMPASSj OPLS (UA)k

Distance () in Å, and energy () in kcal/mol. bRef. 21. cRef. 22. dRef. 23. eRef. 24 . fRef. 19b. g Ref. 17. hRef. 25. iRef. 27. jRef. 31. kRef. 29. a

Benchmark database: The experimental octanol solvation energies were collected from the Minnesota Solvation Model (SMx) benchmarking reported by Marenich et al.20 The structures of solute molecules were extracted from the FreeSolv database of Mobley et al and used as such for further processing.42 For the molecules unique to the Minnesota Solvation benchmarking set, the structures were first optimized at the HF/6-31G(d) level to get the minimum structure in the respective potential energy surface. The structures of solute molecules were finally processed using Antechamber to prepare necessary input parameters for RISM calculations. The name and free energy of solvation in n-octanol are summarized in Table S2 of Supporting Information. Our dataset for n-octanol solvation free energy contains molecules covering first three rows of periodic table, thus providing an excellent opportunity to test performance of a broad range of force field parameters within the framework of the 3D-RISM-KH theory. A broad classification of molecules in the present dataset is provided in Table S3 of Supporting Information. ACS Paragon Plus Environment

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The 3D-RISM-KH calculations were performed using a uniform cubic 3D-grid of 128128128 points in the box of size 646464 Å3 to encompass solute with few solvation layers. The convergence accuracy of the modified direct inversion in the iterative subspace (MDIIS) solver was set to 10-4. The site-site susceptibility function of bulk n-Octanol solvent is obtained from the dielectrically consistent RISM theory (DRISM) and extended RISM (XRISM) theory with the KH closure, keeping in the mind the low dielectric constant of n-Octanol (10.3 at 25 ̊C).43-46 The density of octanol solvent was set to be 0.824 g/cm3 at 298.15 K. For all the 1D-RISM calculations except with TraPPE parameters, all heavy atoms as well as hydroxyl hydrogen are treated as unique sites. For calculations with TraPPE parameters the intervening six methylene groups connecting CH3- and -CH2OH terminals were treated as equivalent sites, keeping consistency with the force field parameters. To compare 3D-RISM predictions, molecular dynamics simulations were also performed for a selected system with UFF force field for n-Octanol solvent and GAFF for solute molecules using the GROMACS suite of programs.47-48

Results and Discussion As the current report thrives to compare and contrast performance of different combinations of force field parameters against benchmark octanol solvation free energy, we have summarized different combinations of force field parameters in Table 2 and designated them with labels as L1-L9 for method of generating atomic charges, and alphabet A-E based on type of vDW parameter. For instance, level L3B denotes for n-octanol, atomic charges were computed using HF/6-31G(d) method, and vdW parameters were those from AMBER force field with parameters for H-bonded hydrogen.



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Table 2: Theoretical levels used for calculations Charge Method L1 AM1 L2 AM1/n-Octanol L3 HF L4 HF/n-Octanol L5 MP2 L6 MP2/n-Octanol L7 ATB L8 GAFF

vdW Parameters A GAFF/ADF B AMBER C AMBER’ D CHARMM E DRIEDING F UFF G COMPASS

The 3D-RISM-KH theory is an excellent choice for solvents other than water, although special care needs to be taken while generating the susceptibility function of non-polar solvents using DRISM theory. In the DRISM theory, the radially dependent site-site susceptibility of solvent is decomposed into intra- and intermolecular terms, and then renormalized. While renormalization of the former represents geometry of the solvent, renormalization of the latter term in the DRISM-KH theory involves bridge functions responsible for enforcing consistency of correct dielectric constant of the liquid. The renormalization of the intermolecular term depends on the inverse characteristic size of the solvent molecule. This parameter is characteristic separation of molecules in solution below which the dielectric correction is turned off to avoid distortion of the short-range solvation structure. For n-octanol the inverse characteristic size is prescribed to be 10 Å, below which spurious ghost peaks appear.5,49 The excess chemical potentials (μ) obtained from solving the Gaussian Fluctuation (GF) functional with the 3D-RISM-KH theory have decent direct correlation to the experimental solvation free energy benchmark for almost all theoretical combinations employed, albeit with varying accuracy. More interestingly, the solvation free energy obtained from the solvation free energy correction based on partial molar volume significantly improves our predictions against benchmark database.50 The partial molar volumes of the compounds were obtained from the 3DACS Paragon Plus Environment

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RISM-KH theory, too.51 The universal correction (UC) scheme based on the 3D-RISM-KH theory and PMV (ρVmol) is used to calculate corrected solvation free energy (ΔμUC) using the equation: ΔμUC = ΔμKH + α (ρVmol) +  The constants α and β are obtained from linear regression analysis. We have tested all possible combinations between atomic charge models and vdW parameters. Some of the combinations were discarded as they either (i) produced negative isothermal compressibility of octanol solvent relaying unphysical solution to 1D-RISM integral equation, or (ii) convergence of 3D-RISM integral equation failed for several solutes at a given solvent distribution.52 Due to a very large number of computed solvation free energies in n-Octanol, all the solvation free energies were reported in Supporting Information. The most relevant part of our findings, a comparative performance of different computational levels with reference to benchmark data, is summarized in Table 3. As mentioned, the solvation free energies obtained with the UC-scheme are used to obtain the data reported in Table 3. The regression coefficients were tabulated in Supporting Information.



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Table 3: Comparison of the solvation free energy predicted by the 3D-RISM-KH theory in n Octanol solvent against our benchmark dataseta Level of Calculation b

MUSE

RMSEc MUSEb RMSEc MUSEb RMSEc b

MUSE

RMSEc MUSEb RMSEc MUSEb RMSEc MUSEb RMSEc

L1A 1.210 (1.054) 1.552 (1.352) L1B 1.239 (1.226) 1.594 (1.575) L1C 1.064 (1.254) 1.382 (1.616) L1D 1.182 -d 1.523 -d L1E 1.051 (1.195) 1.348 (1.542) L1F 1.192 (1.193) 1.532 (1.532) L1G 1.209 (1.221) 1.571 (1.591)

L2A 1.160 (1.020) 1.489 (1.314) L2B 1.188 (1.171) 1.526 (1.504) L2C 1.040 (1.598) 1.354 (2.375) L2D 1.142 (1.038) 1.469 (1.351) L2E 1.020 (1.195) 1.315 (1.542) L2F 1.154 (1.154) 1.480 (1.480) L2G 1.162 (1.170) 1.504 (1.518)

L3A 0.951 -d 1.388 -d L3B 0.922 (0.951) 1.338 (1.388) L3C (0.922)e

L4A 0.962 (1.075) 1.251 (1.411) L4B 0.966 (0.963) 1.259 (1.250) L4C (0.966)f

(1.338)e

(1.258)f

L3D 0.960 -d 1.298 -d L3E 1.458 (0.960) 2.092 (1.298) L3F 0.956 (0.966) 1.286 (1.300) L3G 0.997 (0.998) 1.384 (1.384)

L4D 0.978 (0.994) 1.259 (1.364) L4E 1.080 (0.978) 1.418 (1.258) L4F 0.979 (0.979) 1.255 (1.255) L4G 0.999 (0.990) 1.306 (1.305)

L5A 0.993 (1.031) 1.280 (1.349) L5B 0.999 (0.994) 1.293 (1.280) L5C 0.991 (1.001) 1.343 (1.294) L5D 1.004 -d 1.285 -d L5E 1.037 (1.087) 1.357 (1.482) L5F 1.006 (1.005) 1.285 (1.285) L5G 1.015 (1.016) 1.322 (1.322)

a

L6A 0.958 (1.082) 1.247 (1.421)e L6B 0.961 (0.958) 1.254 (1.246) L6C 0.999 (0.961) 1.374 (1.253) L6D 0.974 (0.996) 1.255 (1.368) L6E 1.087 (0.974) 1.428 (1.254) L6F 0.974 (0.975) 1.250 (1.50) L6G 0.986 (0.986) 1.304 (1.302)

L7A 0.949 (1.195) 1.248 (1.566) L7B 0.957 (0.948) 1.256 (1.249) L7C 1.027 (0.957) 1.434 (1.255) L7D 0.972 (1.025) 1.259 (1.427) L7E 1.200 (0.972) 1.573 (1.258) L7F 0.948 (0.948) 1.238 (1.238) L7G 0.986 (0.986) 1.333 (1.331)

L8A 1.003 (1.032) 1.291 (1.351) L8B 1.013 (1.005) 1.309 (1.292) L8C 1.246 (1.015) 1.782 (1.312) L8D 1.015 (0.993) 1.299 (1.343) L8E 1.078 (1.017) 1.412 (1.300) L8F 1.030 (1.029) 1.314 (1.314) L8G 1.014 (1.016) 1.329 (1.328)

Site-site susceptibility function of the solvent is calculated using the DRISM-KH theory. Results obtained with the XRISM-KH theory are given in parentheses. bMean unsigned error in kcal/mol. cRMS error, in kcal/mol, is calculated as √∑𝑛(𝑦̂𝑖 − 𝑦𝑖 )2 ⁄𝑛 , where (𝑦̂𝑖 − 𝑦𝑖 ) is the


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difference between the experimental and calculated solvation free energy. d XRISM-KH did not converge to desired accuracy. eNegative partial molar volumes of solutes. fNon-convergence of 3D-RISM-KH calculation and negative PMVs. A close inspection of Table 3 reveals several important facts. First, among all the charge models, partial atomic charges computed using n-Octanol/HF/6-31G(d) and n-Octanol/MP2/6-31G(d) perform uniformly well in combination with various AMBER vdW parameters for n-Octanol in predicting solvation free energy. This is true for atomic charges obtained via ATB server, and this charge model works consistently well for almost all the combinations. The aforementioned charge models with CHARMM like parameters are found to be less successful. Partial atomic charges computed from AM1-BCC performed with mixed degree of accuracy, although in combination with the force field parameters reported by Kobryn et al.36 provide excellent prediction against benchmark database. Second, for combination of various force fields’ vdW parameters, the best performers are those containing H-bonded hydrogen parameters extracted from the UFF force field followed by the AMBER and Dreiding force fields. It is important to note that the combination of GAFF parameters with that of vdW parameters calibrated for hydroxyl hydrogen is proven to be an excellent candidate for the present benchmark study. Further, we did not notice significant performance degradation in switching from DRISM to XRISM calculations. The slight differences in performance of these two theories are dependent on the charge model used. The performance of COMPASS force field parameters is not at par with that of UFF; however, in combination with ATB-charges they perform satisfactorily. The XRISM-KH calculation of the solvent susceptibility function of n-Octanol failed to converge to required accuracy (

Octanol Using 3D-RISM-KH Molecular Theory of ... - ACS Publications

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