# Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction

^{*}

^{†}

^{‡}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. PMV Correction

#### 2.2. vdW Volume Correction

#### 2.3. Element Count Correction

## 3. Results

#### 3.1. Identifying Rigid and Flexible Molecules Using Molecular Dynamics with GB Solvent

#### 3.2. Fitting PMVC, ECC, and PMVECC Parameters

#### 3.3. Quality of Fit

## 4. Discussion

#### 4.1. Dealing with Conformational Sampling

#### 4.2. Accuracy and Computational Efficiency of 3D-RISM/PMVECC

#### 4.3. Force Field Parameters

## 5. Materials and Methods

#### 5.1. Structure Preparation

#### 5.2. GB HFE

`igb = 2, gbsa = 1`) and vacuum (

`igb = 6`) [3,54,55] environments in the

`sander`MD engine of AmberTools 2017 [56]. For all simulations, a 1 fs time step was used, temperature was held at $298.15\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ using a Langevin thermostat with $\gamma =5\phantom{\rule{0.166667em}{0ex}}\mathrm{p}{\mathrm{s}}^{-1}$, and conformations were saved every 10,000 steps. The resulting trajectories were then post-processed in

`sander`(

`imin = 5`) using the GB with surface area implicit solvent (

`igb = 2, gbsa = 1`) and in a vacuum to obtain the potential energy of each conformation in aqueous and gas phases. HFEs were then calculated from these potential energies using pyMBAR 3.1.1 [57,58].

#### 5.3. 1D-RISM

`rism1d`in AmberTools 2021 [44,59]. The coincident extended simple point charge model (cSPC/E) was used to model water [44,60]. The dielectrically consistent RISM (DRISM) equations [61,62] were solved with a dielectric constant of 78.497 to a residual tolerance of ${10}^{-12}$ on a 16,384-point grid, with a grid spacing of $0.025\phantom{\rule{0.166667em}{0ex}}\mathsf{\AA}.$ Convergence was accelerated with the modified inversion of iterative subspace (MDIIS) method [63].

#### 5.4. 3D-RISM Calculations

`rism3d.snglpnt`of AmberTools 2021 [44,59] was used to calculate the HFE and PMV using the AMBER parameter and coordinate files provided with the FreeSolv dataset for each solute and bulk water properties from

`rism1d`. The 3D-RISM equations were solved to a residual tolerance of ${10}^{-4}$ on a grid with spacing of $0.3\phantom{\rule{0.166667em}{0ex}}\mathsf{\AA}$, accelerated by MDIIS. Lennard–Jones cutoffs with a relative tolerance of ${10}^{-4}$ were used to determine the size of the grid and analytic corrections were applied [47]. Reciprocal space long-range asymptotics were calculated with a relative tolerance of ${10}^{-5}$.

#### 5.5. Parameter Fitting

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Skyner, E.R.; McDonagh, L.J.; Groom, R.C.; Mourik, T.V.; Mitchell, O.J.B. A review of methods for the calculation of solution free energies and the modelling of systems in solution. Phys. Chem. Chem. Phys.
**2015**, 17, 6174–6191. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sharp, K.A.; Honig, B. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. J. Phys. Chem.
**1990**, 94, 7684–7692. [Google Scholar] [CrossRef] - Still, W.C.; Tempczyk, A.; Hawley, R.C.; Hendrickson, T. Semianalytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc.
**1990**, 112, 6127–6129. [Google Scholar] [CrossRef] - Kovalenko, A.; Hirata, F. Self-consistent description of a metal–water interface by the Kohn–Sham density functional theory and the three-dimensional reference interaction site model. J. Chem. Phys.
**1999**, 110, 10095–10112. [Google Scholar] [CrossRef] - Beglov, D.; Roux, B. An Integral Equation to Describe the Solvation of Polar Molecules in Liquid Water. J. Phys. Chem. B
**1997**, 101, 7821–7826. [Google Scholar] [CrossRef] - Ornstein, L.S.; Zernike, F. Accidental deviations of density and opalescence at the critical point of a single substance. Proc. Akad. Sci.
**1914**, 17, 793. [Google Scholar] - Truchon, J.F.; Pettitt, B.M.; Labute, P. A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies. J. Chem. Theory Comput.
**2014**, 10, 934–941. [Google Scholar] [CrossRef] - Sergiievskyi, V.P.; Jeanmairet, G.; Levesque, M.; Borgis, D. Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections. J. Phys. Chem. Lett.
**2014**, 5, 1935–1942. [Google Scholar] [CrossRef] [Green Version] - Palmer, D.S.; Frolov, A.I.; Ratkova, E.L.; Fedorov, M.V. Towards a universal method for calculating hydration free energies: A 3D reference interaction site model with partial molar volume correction. J. Phys. Condens. Matter
**2010**, 22, 492101. [Google Scholar] [CrossRef] - Robert, A.; Luukkonen, S.; Levesque, M. Pressure correction for solvation theories. J. Chem. Phys.
**2020**, 152, 191103. [Google Scholar] [CrossRef] - Borgis, D.; Luukkonen, S.; Belloni, L.; Jeanmairet, G. Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional. J. Chem. Phys.
**2021**, 155, 024117. [Google Scholar] [CrossRef] [PubMed] - Johnson, J.; Case, D.A.; Yamazaki, T.; Gusarov, S.; Kovalenko, A.; Luchko, T. Small molecule hydration energy and entropy from 3D-RISM. J. Phys. Condens. Matter
**2016**, 28, 344002. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Luchko, T.; Blinov, N.; Limon, G.C.; Joyce, K.P.; Kovalenko, A. SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling. J. Comput. Aided Mol. Des.
**2016**, 30, 1115–1127. [Google Scholar] [CrossRef] [PubMed] - Roy, D.; Kovalenko, A. A molecular solvation theory simulation of liquid alkyl esters of acetic acid with the 3D Reference Interaction Site Model. J. Mol. Liq.
**2021**, 344, 117763. [Google Scholar] [CrossRef] - Roy, D.; Kovalenko, A. Application of the Approximate 3D-RISM Molecular Solvation Theory to Acetonitrile as Solvent. J. Phys. Chem. B
**2020**, 124, 4590–4597. [Google Scholar] [CrossRef] - Roy, D.; Kovalenko, A. Performance of 3D-RISM-KH in Predicting Hydration Free Energy: Effect of Solute Parameters. J. Phys. Chem. A
**2019**, 123, 4087–4093. [Google Scholar] [CrossRef] [PubMed] - Roy, D.; Kovalenko, A. Benchmarking Free Energy Calculations in Liquid Aliphatic Ketone Solvents Using the 3D-RISM-KH Molecular Solvation Theory. J
**2021**, 4, 604–613. [Google Scholar] [CrossRef] - Roy, D.; Kovalenko, A. Application of the 3D-RISM-KH molecular solvation theory for DMSO as solvent. J. Comput. Aided Mol. Des.
**2019**, 33, 905–912. [Google Scholar] [CrossRef] - Roy, D.; Blinov, N.; Kovalenko, A. Predicting Accurate Solvation Free Energy in n-Octanol Using 3D-RISM-KH Molecular Theory of Solvation: Making Right Choices. J. Phys. Chem. B
**2017**, 121, 9268–9273. [Google Scholar] [CrossRef] - Sumi, T.; Mitsutake, A.; Maruyama, Y. A solvation-free-energy functional: A reference-modified density functional formulation. J. Comput. Chem.
**2015**, 36, 1359–1369. [Google Scholar] [CrossRef] [Green Version] - Luukkonen, S.; Belloni, L.; Borgis, D.; Levesque, M. Predicting Hydration Free Energies of the FreeSolv Database of Drug-like Molecules with Molecular Density Functional Theory. J. Chem. Inf. Model.
**2020**, 60, 3558–3565. [Google Scholar] [CrossRef] [PubMed] - Mobley, D.L.; Guthrie, J.P. FreeSolv: A database of experimental and calculated hydration free energies, with input files. J. Comput. Aided Mol. Des.
**2014**, 28, 711–720. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Duarte Ramos Matos, G.; Kyu, D.Y.; Loeffler, H.H.; Chodera, J.D.; Shirts, M.R.; Mobley, D.L. Approaches for Calculating Solvation Free Energies and Enthalpies Demonstrated with an Update of the FreeSolv Database. J. Chem. Eng. Data
**2017**, 62, 1559–1569. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kovalenko, A. Three-dimensional RISM Theory for Molecular Liquids and Solid-Liquid Interfaces. In Molecular Theory of Solvation; Hirata, F., Ed.; Number 24 in Understanding Chemical Reactivity; Springer: Dordrecht, The Netherlands, 2004; pp. 169–275. [Google Scholar]
- Luchko, T.; Joung, I.S.; Case, D.A. Chapter 4 Integral Equation Theory of Biomolecules and Electrolytes. In Innovations in Biomolecular Modeling and Simulations; Royal Society of Chemistry: Cambridge, UK, 2012. [Google Scholar]
- Joung, I.S.; Luchko, T.; Case, D.A. Simple electrolyte solutions: Comparison of DRISM and molecular dynamics results for alkali halide solutions. J. Chem. Phys.
**2013**, 138, 044103. [Google Scholar] [CrossRef] [Green Version] - Tsednee, T.; Luchko, T. Closure for the Ornstein-Zernike equation with pressure and free energy consistency. Phys. Rev. E
**2019**, 99, 032130. [Google Scholar] [CrossRef] [Green Version] - Kovalenko, A.; Hirata, F. Potential of Mean Force between Two Molecular Ions in a Polar Molecular Solvent: A Study by the Three-Dimensional Reference Interaction Site Model. J. Phys. Chem. B
**1999**, 103, 7942–7957. [Google Scholar] [CrossRef] - Kast, S.M.; Kloss, T. Closed-form expressions of the chemical potential for integral equation closures with certain bridge functions. J. Chem. Phys.
**2008**, 129, 236101. [Google Scholar] [CrossRef] - Kobryn, A.E.; Gusarov, S.; Kovalenko, A. A closure relation to molecular theory of solvation for macromolecules. J. Phys. Condens. Matter
**2016**, 28, 404003. [Google Scholar] [CrossRef] [Green Version] - Morita, T.; Hiroike, K. A New Approach to the Theory of Classical Fluids. I. Prog. Theor. Phys.
**1960**, 23, 1003–1027. [Google Scholar] [CrossRef] [Green Version] - Verlet, L.; Levesque, D. On the theory of classical fluids II. Physica
**1962**, 28, 1124–1142. [Google Scholar] [CrossRef] - Sergiievskyi, V.; Jeanmairet, G.; Levesque, M.; Borgis, D. Solvation free-energy pressure corrections in the three dimensional reference interaction site model. J. Chem. Phys.
**2015**, 143, 184116. [Google Scholar] [CrossRef] [PubMed] - Bondi, A. van der Waals Volumes and Radii. J. Phys. Chem.
**1964**, 68, 441–451. [Google Scholar] [CrossRef] - Mobley, D.L.; Shirts, M.; Lim, N.; Chodera, J.; Beauchamp, K.; Lee-Ping. MobleyLab/FreeSolv: Version 0.52. 2018. Available online: https://zenodo.org/record/1161245#.Y8YTVxVByUk (accessed on 16 June 2018).
- Mobley, D.L.; Dill, K.A.; Chodera, J.D. Treating Entropy and Conformational Changes in Implicit Solvent Simulations of Small Molecules. J. Phys. Chem. B
**2008**, 112, 938–946. [Google Scholar] [CrossRef] [Green Version] - Knapp, B.; Ospina, L.; Deane, C.M. Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas. J. Chem. Theory Comput.
**2018**, 14, 6127–6138. [Google Scholar] [CrossRef] [PubMed] - Bennett, C.H. Efficient estimation of free energy differences from Monte Carlo data. J. Comput. Phys.
**1976**, 22, 245–268. [Google Scholar] [CrossRef] - Omelyan, I.; Kovalenko, A. Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids. J. Chem. Phys.
**2019**, 151, 214102. [Google Scholar] [CrossRef] [Green Version] - Omelyan, I.; Kovalenko, A. MTS-MD of Biomolecules Steered with 3D-RISM-KH Mean Solvation Forces Accelerated with Generalized Solvation Force Extrapolation. J. Chem. Theory Comput.
**2015**, 11, 1875–1895. [Google Scholar] [CrossRef] - Omelyan, I.; Kovalenko, A. Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces. J. Chem. Phys.
**2013**, 139, 244106. [Google Scholar] [CrossRef] - Omelyan, I.; Kovalenko, A. Generalised canonical–isokinetic ensemble: Speeding up multiscale molecular dynamics and coupling with 3D molecular theory of solvation. Mol. Simul.
**2013**, 39, 25–48. [Google Scholar] [CrossRef] - Miyata, T.; Hirata, F. Combination of molecular dynamics method and 3D-RISM theory for conformational sampling of large flexible molecules in solution. J. Comput. Chem.
**2008**, 29, 871–882. [Google Scholar] [CrossRef] - Luchko, T.; Gusarov, S.; Roe, D.R.; Simmerling, C.; Case, D.A.; Tuszynski, J.; Kovalenko, A. Three-Dimensional Molecular Theory of Solvation Coupled with Molecular Dynamics in Amber. J. Chem. Theory Comput.
**2010**, 6, 607–624. [Google Scholar] [CrossRef] [PubMed] - Zwanzig, R.W. High-Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases. J. Chem. Phys.
**1954**, 22, 1420–1426. [Google Scholar] [CrossRef] - Anandakrishnan, R.; Drozdetski, A.; Walker, R.C.; Onufriev, A.V. Speed of Conformational Change: Comparing Explicit and Implicit Solvent Molecular Dynamics Simulations. Biophys. J.
**2015**, 108, 1153–1164. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wilson, L.; Krasny, R.; Luchko, T. Accelerating the 3D reference interaction site model theory of molecular solvation with treecode summation and cut-offs. J. Comput. Chem.
**2022**, 43, 1251–1270. [Google Scholar] [CrossRef] - Miyata, T.; Hikasa, Y. Sigma enlarging bridge correction of three dimensional Ornstein–Zernike theory for solvation free energy of polyatomic solutes immersed in Lennard-Jones monatomic solvent. AIP Adv.
**2022**, 12, 085206. [Google Scholar] [CrossRef] - Mobley, D.L.; Bayly, C.I.; Cooper, M.D.; Shirts, M.R.; Dill, K.A. Small Molecule Hydration Free Energies in Explicit Solvent: An Extensive Test of Fixed-Charge Atomistic Simulations. J. Chem. Theory Comput.
**2009**, 5, 350–358. [Google Scholar] [CrossRef] [Green Version] - Riquelme, M.; Lara, A.; Mobley, D.L.; Verstraelen, T.; Matamala, A.R.; Vöhringer-Martinez, E. Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges. J. Chem. Inf. Model.
**2018**, 58, 1779–1797. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Wolf, R.M.; Caldwell, J.W.; Kollman, P.A.; Case, D.A. Development and testing of a general amber force field. J. Comput. Chem.
**2004**, 25, 1157–1174. [Google Scholar] [CrossRef] - Jakalian, A.; Bush, B.L.; Jack, D.B.; Bayly, C.I. Fast, efficient generation of high-quality atomic charges. AM1-BCC model: I. Method. J. Comput. Chem.
**2000**, 21, 132–146. [Google Scholar] [CrossRef] - Jakalian, A.; Jack, D.B.; Bayly, C.I. Fast, efficient generation of high-quality atomic charges. AM1-BCC model: II. Parameterization and validation. J. Comput. Chem.
**2002**, 23, 1623–1641. [Google Scholar] [CrossRef] - Onufriev, A.; Bashford, D.; Case, D.A. Exploring protein native states and large-scale conformational changes with a modified generalized born model. Proteins Struct. Funct. Bioinform.
**2004**, 55, 383–394. [Google Scholar] [CrossRef] [PubMed] - Weiser, J.; Shenkin, P.S.; Still, W.C. Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO). J. Comput. Chem.
**1999**, 20, 217–230. [Google Scholar] [CrossRef] - Case, D.A.; Cerutti, D.S.; Cheatham, T.E., III; Darden, T.A.; Duke, R.E.; Giese, T.J.; Gohlke, H.; Goetz, A.W.; Greene, D.; Homeyer, N.; et al. AMBER 2017; University of California: San Francisco, CA, USA, 2017. [Google Scholar]
- Shirts, M.R.; Chodera, J.D. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys.
**2008**, 129, 124105. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Shirts, M.; Beauchamp, K.; Naden, L.; Chodera, J.; Rodríguez-Guerra, J.; Martiniani, S.; Stern, C.; Henry, M.; Fass, J.; Gowers, R.; et al. Choderalab/Pymbar: 3.1.1. 2022. Available online: https://zenodo.org/record/7383197#.Y8YTchVByUk (accessed on 1 December 2022).
- Case, D.A.; Aktulga, H.M.; Belfon, K.; Ben-Shalom, I.Y.; Brozell, S.R.; Cerutti, D.S.; Cheatham, T.E.I.; Cruzeiro, V.W.D.; Darden, T.A.; Duke, R.E.; et al. Amber 2021; University of California: San Francisco, CA, USA, 2021. [Google Scholar]
- Berendsen, H.J.C.; Grigera, J.R.; Straatsma, T.P. The missing term in effective pair potentials. J. Phys. Chem.
**1987**, 91, 6269–6271. [Google Scholar] [CrossRef] - Perkyns, J.; Pettitt, B.M. A site–site theory for finite concentration saline solutions. J. Chem. Phys.
**1992**, 97, 7656–7666. [Google Scholar] [CrossRef] - Perkyns, J.S.; Montgomery Pettitt, B. A dielectrically consistent interaction site theory for solvent—Electrolyte mixtures. Chem. Phys. Lett.
**1992**, 190, 626–630. [Google Scholar] [CrossRef] - Kovalenko, A.; Ten-no, S.; Hirata, F. Solution of three-dimensional reference interaction site model and hypernetted chain equations for simple point charge water by modified method of direct inversion in iterative subspace. J. Comput. Chem.
**1999**, 20, 928–936. [Google Scholar] [CrossRef] - Seabold, S.; Perktold, J. Statsmodels: Econometric and Statistical Modeling with Python. In Proceedings of the 9th Python in Science Conference, Austin, TX, USA, 28 June 2010; pp. 92–96. [Google Scholar] [CrossRef] [Green Version]
- McKinney, W. Data Structures for Statistical Computing in Python. In Proceedings of the 9th Python in Science Conference, Austin, TX, USA, 28 June 2010; pp. 56–61. [Google Scholar] [CrossRef]

**Figure 1.**Categorizing rigid and flexible molecules from MD simulations. The standard deviation of the combined GB and surface area from MD simulations is given on the x axis. The difference between ${E}_{\mathrm{GB}}$ calculated from just the first frame (static) and over the entire MD trajectory is given on the y axis. Histograms for both quantities are given on their respective axes. For clarity, the full range of the data is not shown, which has maximum values of ${\sigma}_{\Delta {G}_{\mathrm{GB}}}=4.0\phantom{\rule{0.166667em}{0ex}}\mathrm{kcal}/\mathrm{mol}$ and $\left(\right)open="|"\; close="|">\Delta {G}_{\mathrm{GB},\mathrm{static}}-\Delta {G}_{\mathrm{GB},\mathrm{MD}}$.

**Figure 2.**HFEs for 3D-RISM/PMVC, 3D-RISM/ECC, 3D-RISM/PMVECC, and explicit solvent using parameters from Table 1. Leave-out data were used for all plots, except for uncorrected explicit solvent calculations, which are from Refs. [22,35]. Molecules containing combinations of F, Cl, Br, P, and S atoms are plotted with multiple symbols (e.g., see labeled molecule in the bottom row). See Section 5.5 for details of the fitting procedure.

**Figure 3.**HFEs from single (original conformation) rigid and flexible datasets for GB and 3D-RISM with PMVECC.

**Table 1.**Fit parameters for PMVC, ECC, and PMVECC, averaged over all leave-one-out fits. Uncertainties in the last digit are given in parentheses, and represent the standard deviation over all leave-one-out fits. Uncertainty for the a coefficient for PMVC is $8\times {10}^{-5}\phantom{\rule{0.166667em}{0ex}}\mathrm{kcal}/\mathrm{mol}/{\mathsf{\AA}}^{3}$. Coefficient a is in kcal/mol/Å${}^{3}$. All other values are in kcal/mol. See Section 5.5 for details of the fitting procedure.

PMVC | ECC | PMVECC | Explicit Solvent ECC | |
---|---|---|---|---|

a | −0.15 | −0.130(1) | ||

b | −0.04(1) | 0.00(1) | ||

H | −1.199(1) | −0.225(5) | −0.098(1) | |

N | −1.573(6) | −0.392(7) | 0.091(5) | |

C | −1.667(1) | −0.148(8) | 0.114(1) | |

O | −1.277(3) | 0.069(9) | 0.088(3) | |

F | −2.082(4) | −0.05(1) | 0.076(2) | |

Cl | −4.695(4) | −1.19(2) | −0.456(2) | |

Br | −5.544(7) | −1.06(2) | −0.412(6) | |

I | −6.27(1) | −0.79(3) | −0.25(1) | |

P | −1.03(3) | 2.04(3) | 2.93(3) | |

S | −3.18(1) | 0.09(2) | 0.32(1) |

**Table 2.**Hydration free energies calculated with 3D-RISM and an explicit solvent [22] with PMVC, ECC, and PMVECC corrections using parameters from Table 1. Leave-out data were used to calculate statistics, except for uncorrected explicit solvent calculations, which used data from Ref. [22] with the same bootstrap procedure. All values are given in kcal/mol. Uncertainties in the last digit are given in parentheses and represent the standard error of the mean. See Section 5.5 for details of the fitting procedure.

Slope | MUE | MSE | RMSE | ${\mathit{R}}^{2}$ | Max Error | ||
---|---|---|---|---|---|---|---|

Rigid | |||||||

3D-RISM/PMVC | 0.93(4) | 0.86(6) | −0.29(7) | 1.3(1) | 0.75(4) | 6.6 | |

3D-RISM/ECC | 0.92(4) | 1.02(6) | −0.51(8) | 1.37(8) | 0.76(3) | 5.9 | |

3D-RISM/PMVECC | 0.92(2) | 0.61(3) | 0.05(5) | 0.83(6) | 0.89(2) | 4.4 | |

Explicit solvent | 0.96(3) | 0.85(4) | −0.59(6) | 1.11(6) | 0.86(2) | 4.6 | |

Explicit solvent, ECC | 0.91(2) | 0.66(3) | −0.14(5) | 0.86(4) | 0.88(1) | 3.1 | |

Flexible | |||||||

3D-RISM/PMVC | 0.98(4) | 1.53(8) | 0.2(1) | 2.1(1) | 0.75(3) | 9.6 | |

3D-RISM/ECC | 1.07(4) | 1.56(7) | 0.0(1) | 2.1(1) | 0.78(3) | 9.8 | |

3D-RISM/PMVECC | 0.95(5) | 1.35(6) | −0.04(9) | 1.8(1) | 0.79(3) | 9.4 | |

Explicit solvent | 0.97(4) | 1.34(7) | −0.09(0) | 1.8(1) | 0.79(3) | 10.8 | |

Explicit solvent, ECC | 0.91(4) | 1.17(6) | −0.13(9) | 1.7(1) | 0.81(3) | 7.8 | |

Total | |||||||

3D-RISM/PMVC | 1.01(3) | 1.22(5) | 0.00(7) | 1.77(9) | 0.83(2) | 9.6 | |

3D-RISM/ECC | 1.06(2) | 1.32(5) | −0.21(7) | 1.80(8) | 0.84(2) | 9.8 | |

3D-RISM/PMVECC | 0.96(3) | 1.01(4) | 0.00(6) | 1.44(7) | 0.87(1) | 9.4 | |

Explicit solvent | 1.02(3) | 1.11(4) | −0.32(6) | 1.53(8) | 0.87(1) | 10.8 | |

Explicit solvent, ECC | 0.94(2) | 0.94(4) | −0.13(5) | 1.35(8) | 0.88(1) | 7.8 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Casillas, L.; Grigorian, V.M.; Luchko, T.
Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction. *Molecules* **2023**, *28*, 925.
https://doi.org/10.3390/molecules28030925

**AMA Style**

Casillas L, Grigorian VM, Luchko T.
Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction. *Molecules*. 2023; 28(3):925.
https://doi.org/10.3390/molecules28030925

**Chicago/Turabian Style**

Casillas, Lizet, Vahe M. Grigorian, and Tyler Luchko.
2023. "Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction" *Molecules* 28, no. 3: 925.
https://doi.org/10.3390/molecules28030925