# The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

## 3. Discussion

#### 3.1. The Good

**2**,

**3**,

**4**,

**7**,

**10**,

**11**,

**12**,

**13**,

**14**,

**15**, and

**17**. Thus, for these molecules obtaining $\Delta {A}^{low\to high}$ within an indirect scheme should be fairly straightforward and should not require full simulations at the $high$ level of theory. We will focus our discussion here on molecules

**2**and

**11**.

#### 3.1.1. Molecule **2**

**2**(4-chloro-1-methyl-1H-pyrazole-3-carbaldehyde oxime, ZINC00077329), is a pyrazole oxime compound, which can be used to synthesize other pyrazole oximes that have antitumor, insecticidal, and acaricidal activities [82].

**2**, and using FEP or BAR to calculate $\Delta {A}_{gas}^{MM\to 3ob}$ is not likely to provide converged or accurate results. However, utilizing nonequilibrium ${W}^{MM\to 3ob}$ instead of $\Delta {U}^{MM\to 3ob}$ vastly improves overlap of ${P}_{mm}$ and ${P}_{3ob}$ (shown in Figure 3b) to 53.89%, and improves one-sided $\Pi $ values to 1.86 and 2.19 for JAR (fw) and JAR (bw), respectively. One point of concern regarding W distributions for

**2**is the “tail”, or small secondary peak, seen around −4 kcal/mol in ${P}_{3ob}$; however, despite this secondary peak, there appears to be more than enough configurational overlap to provide converged results.

#### 3.1.2. Molecule **11**

**11**(ZINC00138607, IUPAC name 2-[5-(2-hydroxyphenyl)-4,5-dihydro1,2,4-oxadiazol-3-yl]1-tetrahydro-1H-pyrrol-1-ylethan-1-one) contains chemical features seen in a large number of molecules within the PubChem database. Thus, correctly modeling such a molecule is imperative for providing theoretical aid to experimentalists applying some of

**11**’s chemical features in drug discovery or other application-driven investigations.

**2**, potential energy distributions coming from $MM$ and $3ob$ equilibrium simulations are disparate, with merely 0.03% overlap (Figure 4a). Additionally, $\Pi $ values (−3.26 and −3.38 for FEP (fw) and FEP (bw), respectively (see Table 2)) indicate that these potential energy distributions are not suited to providing converged FES between levels of theory. Poor convergence can also be seen in: high sample size hysteresis values (>1 kcal/mol), deviation between FEP (fw) and FEP (bw), and broadened $\Delta {U}^{MM\to 3ob}$ distributions themselves. By all metrics, FEP and BAR fail for molecule

**11**, a small molecule in gas phase with chemical features seen in many experimental contexts. However, as again seen with molecule

**2**, ${W}^{MM\to 3ob}$ distributions were far more suited for calculating converged $\Delta {A}_{gas}^{MM\to 3ob}$ (Figure 4b). $\Pi $ values were much improved compared to their equilibrium counterparts, being 0.99 and 1.68 for JAR (fw) and JAR (bw), respectively; overlap between the two distributions is also dramatically improved at 44.12%; JAR (fw) and JAR (bw) are essentially absent of sample size hysteresis, and agree with each other within ≈0.5 kcal/mol.

#### 3.2. The Bad

**1**,

**5**,

**6**,

**16**,

**18**,

**19**,

**21**, and

**22**. We focus our discussion here on molecules

**5**and

**6**, as representative examples.

#### 3.2.1. Molecule **5**

**5**(ZINC00087557, 3-phenylcyclopropane-1,2-dicrabohydrazide) contains functional groups useful in metal-organic chemistry [83], and thus has potential for future modeling focus not only in drug discovery projects but also in inorganic modeling. However, we have seen that it is quite difficult to obtain converged $\Delta {A}_{gas}^{MM\to 3ob}$ for this species even with nonequilibrium switching simulations.

**5**’s equilibrium $\Delta {U}^{MM\to 3ob}$ distributions are quite broad and exhibit little to no overlap (≈0.0%) (see Figure 6a). Convergence issues in FEP/BAR are further indicated by very low one-sided $\Pi $ values, sample size hysteresis is seen in FEP (fw), FEP(bw) and BAR, and once again magnitude differences between FEP (fw) and FEP (bw) (see Table 2). Unlike with the “Good” molecules, although nonequilibrium simulations of

**5**improved overlap and resulted in narrower distributions (Figure 6b), JAR (fw)/JAR (bw) metrics still indicate potential convergence failure and CRO results might require further validation. For example, for JAR (fw) $\Pi $ = 0.08, and JAR (bw) $\Pi $ = −0.66, both indicate unreliable one-sided distributions. Additionally, JAR (bw) exhibits sample size hysteresis ($Hyst$ = 2.26 kcal/mol), and JAR (fw) and JAR (bw) disagree by 1.66 kcal/mol. CRO results, on the other hand, do barely pass convergence metrics: sample size hysteresis is low, and overlap is sufficient for a two-sided method at 8.76%. Thus, while CRO may be able to calculate a trustworthy result, it is far from the stellar nonequilibrium convergence results seen from “Good” molecules.

**5**, we see that ${\chi}_{2}$ and ${\chi}_{3}$ could be causing convergence issues in FEP, BAR, and JAR (Figure 7). For example, consider $MM$ and $3ob$ dihedral populations in ${\chi}_{2}$ and ${\chi}_{3}$. These populations have distinct minimum angles at the two levels of theory, which doubtless are contributing to convergence failure when using FEP/BAR. However, when conducting $MM\to 3ob$ switching simulations, the barriers to rotation from $MM$ preferred dihedral conformations to $3ob$ preferred dihedral conformations may be too high to traverse during the shorter nonequilibrium switching simulations (i.e., 1 ps). Although the switching simulation dihedral populations are more similar to their respective target level of theories, there are still discrepancies. For example, considering

**5**’s ${\chi}_{3}$, we see $MM$ predicts two low energy angles at 60${}^{\circ}$ and −140${}^{\circ}$ while $3ob$ predicts one low energy dihedral value at 140${}^{\circ}$. After $MM\to 3ob$ switching simulations, the two peaks predicted by $MM$ relax to one larger peak vaguely encompassing the low energy region in $3ob$ simulations, although this low energy dihedral peak does not have the same population density as seen from $3ob$ equilibrium simulations. It is likely that longer switching simulations may be needed to allow these dihedral degrees of freedom to completely relax. However, by pooling both ${W}^{MM\to 3ob}$ and ${W}^{3ob\to MM}$ values, we were able to obtain marginally converged CRO results.

#### 3.2.2. Molecule **6**

**6**(ZINC00095858, ethyl N-[(2-chlorophenyl)sulfonyl]carbamate) is a flexible small molecule with thousands of similar structures available in the PubChem Database, thus ensuring accurate FES modeling of

**6**could be beneficial for modeling many other small molecules.

**5**, FEP and BAR results for

**6**are unreliable: $\Delta {U}^{MM\to 3ob}$ distributions are broad and non-overlapping (Figure 8a), $\Pi $ values are poor, sample size hysteresis for FEP (fw) and FEP (bw) is high, and FEP (fw) and FEP (bw) differ by ≈21 kcal/mol (see Table 2). Unfortunately, as with with FEP, JAR (fw) and JAR (bw) results are also not immediately trustworthy, with one-sided $\Pi $ values of −0.65 and −0.47 for JAR (fw) and JAR (bw), respectively, and discrepancy between JAR (fw) and JAR (bw) of ≈5 kcal/mol (see Table 3). However, by utilizing data from both $MM\to 3ob$ and $3ob\to MM$ switching simulations, i.e., CRO, we were able to calculate a marginally converged $\Delta {A}_{gas}^{MM\to 3ob}$. Overlap between nonequilibrium work distributions (23.95%) is much improved compared to $\Delta {U}^{MM\to 3ob}$ distributions (0.00%).

**6**, ${\chi}_{3}$ may be distinct enough to cause convergence errors, certainly with FEP/BAR as $trans$-${\chi}_{3}$ is vastly overrepresented from $MM$ simulations. This may also be the case in JAR (fw) and JAR (bw) results, as $MM\to 3ob$ switching simulations are unable to replicate the near degeneracy of the $trans$- and $gauche$-${\chi}_{3}$ conformations as seen in $3ob$ simulations. However, pooling together all switching simulations may provide enough $gauche$-${\chi}_{3}$ conformations to achieve convergence.

#### 3.3. The Ugly

**8**,

**9**, and

**20**. We focus our discussion here on molecules

**8**and

**9**.

#### 3.3.1. Molecule **8**

**8**(ZINC ID 00107778, 4,6-dichloro-2H-chromene-3-carbaldehyde oxime) is another oxime species similar to molecule

**2**. As mentioned above, oxime species have been used recently as promising anti-cancer agents, and thus the computational community should ensure our methods can properly model such compounds [82,84,85,86].

**8**should result in marginally converged $\Delta {A}_{gas}^{MM\to 3ob}$, and yet other analyses of $\Delta U$ distributions indicate these are unreliable datasets. Even though ${W}^{MM\to 3ob}$ distributions do overlap considerably better than $\Delta {U}^{MM\to 3ob}$, at 24.92%, $\Pi $ evaluations of ${W}^{MM\to 3ob}$ (fw and bw) distributions indicate only marginally improved reliability, and not enough to be sufficiently confident in JAR or even CRO results. Additionally, the W distributions in Figure 10b seem to be oddly polymodal. Considering the difficulties in convergence observed, we conducted longer switching simulations (5 ps) in the hopes of improving convergence by allowing longer relaxation times. Data from 5 ps switching simulations are given in Table 3 in row “

**8 (5 ps)**”, and distributions are shown in Figure 10c. Unfortunately, even conducting 5 ps switching simulations did not allow for significantly improved ${W}^{MM\to 3ob}$ distributions.

**8**’s dihedral populations may provide insight into this molecule’s convergence issues: although ${\chi}_{1}$ is fairly consistent between $MM$ and $3ob$ distributions, ${\chi}_{2}$ is quite distinct between $MM$ and $3ob$ (see Figure 11). $MM$ and $3ob$ simulations agree there is a low energy $cis$-${\chi}_{2}$ conformation, however $3ob$ simulations also predict the $gauche$- and $trans$-${\chi}_{2}$ conformation is populated, while $MM$ simulations do not visit this region. It should also be noted, as described in the Methods, equilibrium simulations were launched by initiating randomized dihedrals to ensure thorough dihedral sampling. Even after randomizing ${\chi}_{2}$, $MM$ simulations did not visit $trans$ regions that were shown to be energetically stable in $3ob$ simulations. Furthermore, even after $MM\to 3ob$ switching simulations of 1 ps and 5 ps, $MM$ configurations are not able to relax into the $trans$- and $gauche$-${\chi}_{2}$ conformations predicted by $3ob$. Thus, the barrier to rotation around ${\chi}_{2}$ must be too high to overcome, even during longer/slower switching protocols. This is a case where intramolecular force matching may improve $low$-level classical parameters and thus overlap to the higher level of theory.

**8**is truly one of the toughest convergence cases in our HiPen dataset.

#### 3.3.2. Molecule **9**

**9**(ZINC ID 00123162, 1-phenyl-1,2,3-butanetrione 2-[N-(4-chlorophenyl)hydrazone]) contains chemical features seen in thousands of molecules available in the PubChem database, and therefore ensuring appropriate FES modeling with

**9**could ensure appropriate FES modeling of many other compounds in the near future.

**9**: FEP (fw), FEP (bw), and BAR exhibited sample size hysteresis; FEP (fw) and FEP (bw) did not agree in magnitude; $\Pi $ values did not indicate well-behaved $\Delta U$ distributions at −4.27 and −4.77 for FEP (fw) and FEP (bw), respectively; and finally forward and backward $\Delta U$ distributions exhibited only 0.02% overlap (see Figure 12a). Additionally, 1 ps nonequilibrium switching protocol did not improve according to convergence criteria as would be expected: JAR (fw, 1 ps), JAR (bw, 1 ps), and CRO (1 ps) exhibit considerable sample size hysteresis; JAR (fw, 1 ps) and JAR (bw, 1 ps) differ in magnitude by ≈11 kcal/mol; and $\Pi $ values are −4.64 and −2.48, for JAR (fw, 1 ps) and JAR (bw, 1 ps), respectively, with 22.83% overlap (see Figure 12b). As such, we once again conducted longer nonequilibrium switching simulations (5 ps). Much like with

**8**, such longer nonequilibrium switching simulations only marginally improved results compared to 1 ps switching simulations. JAR (fw, 5 ps) and JAR (bw, 5 ps) still do not agree in magnitude, although JAR (fw, 5 ps) agrees with CRO (5 ps), and JAR (bw, 5 ps) exhibits ≈10 kcal/mol in sample size hysteresis. Calculated $\Pi $ values (−1.24 and −2.95, for JAR (fw, 5 ps) and JAR (bw, 5 ps), respectively) indicate W distributions after 5 ps are still not well behaved.

**9**, we again hoped to pin-point convergence issues in dihedral degrees of freedom, Figure 13. As can be seen in Figure 13a,b, ${\chi}_{1}$ and ${\chi}_{2}$ distributions between equilibrium $MM$ and $3ob$ simulations are fairly similar, low energy dihedral conformations are consistent between levels of theory and relative populations between such angles are also consistent. However, for ${\chi}_{3}$, ${\chi}_{4}$, ${\chi}_{5}$, and ${\chi}_{6}$, there are large discrepancies between $MM$ and $3ob$ regarding the low energy dihedral values and their relative populations, such discrepancy is especially clear in ${\chi}_{6}$ (Figure 13g). Furthermore, such discrepancies are not completely resolved within 1, or even 5 ps nonequilibrium switching simulations, as is the case for ${\chi}_{3}$ and ${\chi}_{4}$. Thus, these dihedrals likely represent the roadblock to converged $\Delta {A}^{low\to high}$ for

**9**and further likely require intramolecular force matching to be resolved.

## 4. Materials and Methods

#### 4.1. Equilibrium Simulations

^{−1}was applied to all atoms, and random velocities were added at each step corresponding to a temperature bath of 300 K.

**MM simulations:**For each molecule, ten LD simulations were carried out, which were started from different initial random velocities. Additionally, to enhance sampling, we employed different starting coordinates if/when the molecule contained rotatable bonds (cf. Figure 2). First, all rotatable bonds were randomized. Next, 1000 steps of Adopted Basis Newton–Raphson minimization were carried out while restraining the dihedral angles harmonically ($k=100$ kcal/mol/A

^{2}) to their randomized value(s). Finally, restraints were removed and 10 ps of LD were carried out as equilibration. As molecules were simulated in the gas phase, all nonbonded interactions were calculated explicitly during the simulation; neither switching nor shifting functions were applied. Following these preparation steps, 10 million steps of LD were carried out with a timestep of 1 fs; this corresponds to 10 ns per run, and a cumulative simulation length of 100 ns for the ten runs per molecule. Restart files (containing both coordinates and velocities) were saved every 100 steps, resulting in 1 million coordinate and velocity sets per molecule. For use in FEP and BAR, the energies for each coordinate set were computed at both the MM and SCC-DFTB/3ob levels of theory. We further computed the instantaneous dihedral angles of all rotatable bonds considered.

**SCC-DFTB3/3ob simulations:**All simulations employing the SCC-DFTB/3ob potential energy function, were conducted according to a protocol closely mirroring what was just described for the MM simulations. However, in the case of SCC-DFTB/3ob simulations, the simulation length per run (again, 10 runs per molecule) was only 1 ns (a timestep of 1 fs was used); the cumulative simulation length, therefore, was 10 ns. Coordinate and velocity information was saved every 100 steps resulting in a total of 100,000 restart files. As in the MM case, for each of the coordinate sets we computed the energy at the force field and SCC-DFT3/3ob levels of theory, as well as the instantaneous values of the dihedrals of the rotatable bonds.

#### 4.2. Nonequilibrium “Switching” Simulations

**MM to 3ob Switching simulations:**$MM\to 3ob$ switching simulations were launched from every 10,000th $MM$ simulation step, i.e., from snapshots saved at 10 ps intervals during the $MM$ equilibrium simulations. Per molecule, this resulted in a total of 10,000 $MM\to 3ob$ nonequilibrium switches. Unless otherwise noted, all switching simulations were conducted for 1 ps (1000 steps). ${W}^{MM\to 3ob}$ was recorded per switch and post-processed using JAR and CRO. For each of the final coordinates, we also computed the dihedral angles of the rotatable bonds.

**3ob to MM Switching simulations:**$3ob\to MM$ switching simulations were launched from every 1000th $3ob$ simulation step, or every 1 ps. Per molecule, this resulted in a total of 10,000 $3ob\to MM$ nonequilibrium simulations. Unless otherwise noted, all switching simulations were conducted for 1 ps (1000 steps). ${W}^{3ob\to MM}$ was recorded per switch and post-processed according to JAR and CRO. As was done at the end of the $MM\to 3ob$ switching simulations, dihedral angle values were recorded.

## 5. Conclusions

**8**and

**9**. We intend to use these data in the near future for further method development as well as evaluating the same criterion/metrics in solvent phase free energy simulations. Furthermore, we hope this dataset will prove as useful to FES practitioners in providing standardized results as the BEGDB and MNDB2.0 datasets are to the quantum mechanical calculation community.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MM | Molecular Mechanics |

QM | Quantum Mechanics |

SQM | Semiempirical Quantum Mechanics |

QM/MM | Quantum Mechanical/Molecular Mechanical hybrid methods |

SQM/MM | Semiempirical Quantum Mechanical/Molecular Mechanical hybrid methods |

FEP | Free Energy Perturbation |

BAR | Bennett’s Acceptance Ratio |

JAR | Jarzynski’s equation |

CRO | Crooks’ equation |

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Sample Availability: Samples of the compounds are not available from the authors. |

**Figure 1.**The indirect cycle underlying (S)QM/MM FES. “0” and “1” denote the two physical end states, e.g., a molecule in gas phase and solution, or a ligand in the free state and bound to a receptor.

**Figure 2.**The HiPen dataset modeled herein. Dihedrals that were probed or randomized (see Methods) in this work have been identified for each molecule.

**Figure 3.**(

**a**) Molecule

**2**’s potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**2**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 4.**(

**a**) Molecule

**11**’s potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**11**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 5.**Dihedral populations for

**11**’s dihedral degrees of freedom (see Figure 2 for dihedral labels).

**Figure 6.**(

**a**) Molecule

**5**’s potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**5**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 7.**Dihedral populations for

**5**’s dihedral degrees of freedom (see Figure 2 for dihedral labels).

**Figure 8.**(

**a**) Molecule

**6**’s Potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**6**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 9.**Dihedral populations for

**6**’s dihedral degrees of freedom (see Figure 2 for dihedral labels).

**Figure 10.**(

**a**) Molecule

**8**’s potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**8**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions from 1 ps switching simulations plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis. (

**c**) Molecule

**8**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions from 5 ps switching simulations plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 11.**Dihedral populations for

**8**’s dihedral degrees of freedom (see Figure 2 for dihedral labels).

**Figure 12.**(

**a**) Molecule

**9**’s potential energy “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions plotted as “offset” from the $\overline{\Delta {U}^{MM\to 3ob}}$ to simplify the x-axis. (

**b**) Molecule

**9**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions from 1 ps switching simulations plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis. (

**c**) Molecule

**9**’s nonequilibrium work “forward” (${P}_{mm}$) and “backward” (${P}_{3ob}$) distributions from 5 ps switching simulations plotted as “offset” from the $\overline{{W}^{MM\to 3ob}}$ to simplify the x-axis.

**Figure 13.**Dihedral populations for

**9**’s dihedral degrees of freedom (see Figure 2 for dihedral labels).

**Table 1.**ZINC Database ID’s for each HiPen molecule; the total number of atoms (${N}_{tot}$) and total number of heavy atoms (${N}_{heavy}$) per molecule; ParamChem reported CGenFF penalties; calculated $\Delta A$ “offset” for each molecule in the dataset should be added or subtracted (to positive and negative $\Delta A$’s respectively) to every $\Delta A$ listed in Table 2 and Table 3 to give the total calculated $\Delta A$.

ZINC ID | ${\mathit{N}}_{\mathit{tot}}/{\mathit{N}}_{\mathit{Heavy}}$ | CGenFF Penalties | Offset (kcal/mol) | ||
---|---|---|---|---|---|

Param | Charge | ||||

1 | 00061095 | 36/21 | 432.10 | 200.99 | 29,000 |

2 | 00077329 | 16/10 | 378.50 | 347.24 | 15,000 |

3 | 00079729 | 18/13 | 683.00 | 207.72 | 17,000 |

4 | 00086442 | 21/12 | 312.50 | 283.62 | 19,000 |

5 | 00087557 | 31/17 | 378.50 | 347.31 | 25,000 |

6 | 00095858 | 25/16 | 567.90 | 361.40 | 25,000 |

7 | 00107550 | 21/11 | 378.50 | 347.29 | 16,000 |

8 | 00107778 | 22/15 | 378.50 | 347.29 | 21,000 |

9 | 00123162 | 34/21 | 385.50 | 217.28 | 29,000 |

10 | 00133435 | 34/22 | 470.50 | 27.14 | 28,000 |

11 | 00138607 | 36/20 | 336.00 | 261.56 | 29,000 |

12 | 00140610 | 20/12 | 449.00 | 214.90 | 17,000 |

13 | 00164361 | 23/14 | 424.00 | 194.49 | 20,000 |

14 | 00167648 | 44/26 | 436.50 | 226.60 | 35,000 |

15 | 00169358 | 26/16 | 540.40 | 142.16 | 22,000 |

16 | 01755198 | 28/12 | 329.00 | 21.11 | 19,000 |

17 | 01867000 | 32/18 | 470.50 | 5.82 | 22,000 |

18 | 03127671 | 41/24 | 329.00 | 25.20 | 34,000 |

19 | 04344392 | 52/29 | 329.00 | 24.78 | 40,000 |

20 | 04363792 | 28/21 | 698.00 | 185.49 | 28,000 |

21 | 06568023 | 30/18 | 329.00 | 21.60 | 25,000 |

22 | 33381936 | 33/21 | 545.50 | 395.62 | 30,000 |

**Table 2.**Equilibrium results. $\Delta {A}^{MM\to 3ob}$ calculated with FEP (fw), FEP (bw), and BAR, as well as calculated convergence metrics. For each $\Delta A$, we divide the total dataset into 10 blocks, calculate $\Delta {A}_{i}$ from each of these i blocks, and compare the average of those $\Delta {A}_{i}$ to $\Delta A$ calculated from the total dataset (giving $Hyst$), and we also report the standard deviation of these $\Delta {A}_{i}$ (${\sigma}_{\Delta A}$). To determine the reliability of $\Delta U$ distributions for calculating $\Delta A$ we report: $\overline{\Delta U}$, the standard deviation of $\Delta U$’s (${\sigma}_{\Delta U}$) as narrower distributions are likely to provide converged results, and finally we report one-sided $\Pi $ which, when >0.5, likely indicates the $\Delta U$ distribution is resultant from sufficient and unbiased sampling. Finally, we report percentage overlap in $\Delta U$ between forward and backward distributions.

FEP (fw) | FEP (bw) | BAR | Overlap (%) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | $\overline{\mathbf{\Delta}\mathit{U}}$ | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{U}}$ | $\mathbf{\Pi}$ | $\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | $\overline{\mathbf{\Delta}\mathit{U}}$ | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{U}}$ | $\mathbf{\Pi}$ | $\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | $\mathbf{\Delta}\mathit{U}$ | |

1 | −301.11 | 4.08 | 5.29 | −282.47 | 7.89 | −3.14 | 305.82 | 1.87 | 2.02 | 322.87 | 7.30 | −3.29 | −303.34 | −0.15 | 3.15 | 0.04 |

2 | −255.52 | 0.19 | 0.51 | −245.10 | 4.29 | −1.15 | 258.88 | 0.29 | 0.60 | 268.72 | 5.28 | −1.47 | −256.87 | −0.05 | 0.11 | 0.28 |

3 | −412.88 | 0.35 | 0.65 | −402.47 | 3.49 | −1.17 | 416.38 | 0.54 | 0.78 | 428.26 | 4.86 | −2.06 | −414.19 | −0.01 | 0.01 | 0.12 |

4 | −254.51 | 0.43 | 0.69 | −239.09 | 5.66 | −2.43 | 259.24 | 0.51 | 0.84 | 269.67 | 4.34 | −1.64 | −256.34 | 0.00 | 0.03 | 0.06 |

5 | −589.94 | 2.30 | 2.38 | −570.06 | 5.78 | −3.41 | 604.61 | 2.25 | 2.49 | 626.49 | 7.84 | −4.29 | −596.97 | 0.48 | 0.25 | 0.00 |

6 | −109.58 | 2.58 | 2.59 | −86.31 | 7.14 | −4.07 | 130.57 | 4.83 | 4.41 | 162.27 | 10.42 | −6.04 | −118.33 | 0.56 | 2.35 | 0.00 |

7 | −992.13 | 0.33 | 0.67 | −982.02 | 3.94 | −1.06 | 994.96 | 4.83 | 12.05 | 1011.88 | 19.05 | −3.26 | −993.15 | 0.21 | 0.49 | 0.28 |

8 | −994.00 | 4.16 | 4.03 | −982.45 | 4.39 | −1.46 | 988.29 | 9.09 | 5.74 | 1009.22 | 7.77 | −4.10 | −992.02 | 1.03 | 14.08 | 3.72 |

9 | −447.42 | 2.99 | 3.12 | −423.12 | 9.04 | −4.27 | 451.15 | 8.94 | 4.93 | 475.54 | 6.40 | −4.77 | −449.44 | 1.02 | 5.61 | 0.02 |

10 | −336.30 | 0.84 | 0.99 | −320.41 | 5.46 | −2.54 | 341.91 | 0.31 | 0.72 | 352.24 | 4.10 | −1.61 | −337.98 | 0.11 | 0.07 | 0.04 |

11 | −460.25 | 1.37 | 1.30 | −441.09 | 7.09 | −3.26 | 464.90 | 1.43 | 1.15 | 482.37 | 8.89 | −3.38 | −461.88 | 0.11 | 0.07 | 0.02 |

12 | −70.74 | 2.17 | 1.31 | −54.33 | 4.82 | −2.66 | 84.97 | 0.85 | 1.21 | 115.59 | 11.07 | −5.86 | −77.20 | 0.25 | 0.02 | 0.00 |

13 | −556.49 | 2.79 | 1.67 | −547.25 | 5.39 | −3.27 | 571.83 | 1.37 | 1.32 | 587.80 | 5.62 | −3.28 | −567.59 | 0.18 | 0.15 | 0.01 |

14 | −80.28 | 0.79 | 0.97 | −65.97 | 4.62 | −2.17 | 85.55 | 0.78 | 0.77 | 100.32 | 6.15 | −2.89 | −82.62 | 0.12 | 0.10 | 0.03 |

15 | −406.76 | 0.18 | 0.46 | −398.31 | 3.39 | −0.56 | 408.29 | 0.32 | 0.54 | 419.87 | 5.52 | −2.04 | −407.59 | 0.02 | 0.00 | 0.51 |

16 | −633.17 | 1.32 | 1.57 | −621.65 | 4.28 | −1.45 | 638.22 | 2.26 | 2.73 | 664.09 | 8.08 | −5.12 | −636.14 | 0.72 | 0.68 | 0.05 |

17 | −673.11 | 0.21 | 0.55 | −664.21 | 3.29 | −0.70 | 672.67 | −0.13 | 0.71 | 682.01 | 3.11 | −1.71 | −673.41 | −0.03 | 0.01 | 0.69 |

18 | −518.20 | 1.82 | 1.80 | −501.32 | 5.34 | −2.76 | 525.15 | 4.99 | 4.91 | 551.31 | 9.84 | −5.09 | −520.79 | 0.90 | 3.94 | 0.10 |

19 | −879.27 | 3.54 | 2.13 | −857.72 | 6.10 | −3.74 | 892.96 | 1.86 | 2.43 | 918.55 | 9.50 | −4.99 | −885.39 | 0.51 | 0.21 | 0.00 |

20 | −691.39 | 3.08 | 4.83 | −676.22 | 6.43 | −2.37 | 713.26 | 0.83 | 1.34 | 753.13 | 14.99 | −7.29 | −702.33 | 0.83 | 1.13 | 0.00 |

21 | −70.62 | 2.52 | 1.58 | −59.20 | 3.66 | −1.43 | 69.86 | 1.10 | 1.30 | 87.37 | 8.66 | −3.39 | −69.33 | 0.25 | 0.84 | 0.37 |

22 | −177.51 | 0.73 | 0.97 | −165.15 | 4.25 | −1.68 | 181.81 | 0.82 | 1.04 | 213.38 | 37.01 | −6.02 | −179.19 | 0.14 | 0.22 | 0.07 |

**Table 3.**Nonequilibrium results. $\Delta {A}^{MM\to 3ob}$ calculated with JAR (fw), JAR (bw), and CRO, as well as calculated convergence metrics. For each $\Delta A$, we divide the total dataset into 10 blocks, calculate $\Delta {A}_{i}$ from each of these i blocks, and compare the average of those $\Delta {A}_{i}$ to $\Delta A$ calculated from the total dataset (giving $Hyst$), and we also report the standard deviation of these $\Delta {A}_{i}$ (${\sigma}_{\Delta A}$). To determine the reliability of W distributions for calculating $\Delta A$, we report: $\overline{W}$, the standard deviation of W’s (${\sigma}_{W}$) as narrower distributions are likely to provide converged results, and finally we report one-sided $\Pi $ which, when >0.5, likely indicates the W distribution is resultant from sufficient and unbiased sampling. Finally, we report percentage overlap in W between forward and backward distributions.

JAR (fw) | JAR (bw) | CRO | Overlap (%) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | $\overline{\mathit{W}}$ | ${\mathit{\sigma}}_{\mathit{W}}$ | $\mathbf{\Pi}$ | $\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | $\overline{\mathit{W}}$ | ${\mathit{\sigma}}_{\mathit{W}}$ | $\mathbf{\Pi}$ | $\mathbf{\Delta}\mathit{A}$ | Hyst | ${\mathit{\sigma}}_{\mathbf{\Delta}\mathit{A}}$ | W | |

1 | −305.97 | 2.92 | 3.87 | −299.85 | 5.07 | −0.80 | 300.95 | 0.47 | 0.39 | 302.15 | 1.97 | 1.60 | −301.61 | 0.53 | 4.44 | 32.71 |

2 | −272.53 | 0.21 | 0.48 | −271.48 | 0.60 | 1.86 | 271.88 | 0.13 | 0.48 | 272.59 | 1.59 | 2.19 | −271.84 | 0.09 | 0.08 | 53.89 |

3 | −408.69 | 0.00 | 0.03 | −408.18 | 0.90 | 2.40 | 408.63 | 0.00 | 0.05 | 409.03 | 0.63 | 2.57 | −408.66 | 0.00 | 0.00 | 56.68 |

4 | −271.25 | 0.00 | 0.03 | −271.10 | 0.41 | 3.02 | 271.15 | 0.00 | 0.02 | 271.31 | 0.49 | 3.00 | −271.20 | 0.00 | 0.00 | 79.52 |

5 | −539.16 | 0.58 | 0.98 | −535.17 | 1.98 | 0.08 | 537.50 | 2.26 | 2.71 | 543.25 | 3.18 | −0.66 | −538.78 | 0.36 | 0.37 | 8.76 |

6 | −143.51 | 3.69 | 2.10 | −137.78 | 2.08 | −0.65 | 138.57 | 1.46 | 2.12 | 143.83 | 3.12 | −0.47 | −140.17 | 0.41 | 1.70 | 23.95 |

7 | −999.40 | 0.42 | 0.69 | −998.41 | 0.69 | 1.91 | 998.80 | 1.37 | 2.82 | 1000.98 | 3.29 | 1.03 | −999.02 | 0.42 | 0.28 | 44.88 |

8 | −995.50 | 3.54 | 3.79 | −990.77 | 4.06 | −0.25 | 989.35 | 6.99 | 4.61 | 998.13 | 4.05 | −1.69 | −995.41 | 0.90 | 9.68 | 24.92 |

8 (5 ps) | −995.88 | 2.90 | 3.74 | −991.48 | 4.16 | −0.18 | 989.36 | 7.05 | 3.29 | 997.91 | 3.78 | −1.71 | −995.87 | 0.68 | 1.60 | 27.70 |

9 | −426.22 | 1.72 | 1.95 | −414.69 | 8.21 | −2.48 | 415.08 | 7.74 | 5.19 | 428.09 | 4.12 | −2.87 | −423.89 | 0.91 | 8.28 | 22.83 |

9 (5 ps) | −426.53 | −0.28 | 1.04 | −419.30 | 7.09 | −1.24 | 412.65 | 9.23 | 5.75 | 425.23 | 4.45 | −2.95 | −425.45 | 1.22 | 6.82 | 60.27 |

10 | −285.45 | 0.02 | 0.15 | −284.78 | 0.82 | 2.25 | 285.36 | 0.00 | 0.03 | 286.22 | 1.18 | 2.03 | −285.41 | 0.01 | 0.00 | 46.14 |

11 | −510.05 | 0.02 | 0.17 | −507.81 | 2.93 | 0.99 | 509.50 | 0.23 | 0.41 | 510.72 | 0.96 | 1.68 | −509.92 | 0.03 | 0.01 | 44.12 |

12 | −81.64 | 0.00 | 0.03 | −81.37 | 0.55 | 2.78 | 81.48 | 0.00 | 0.03 | 81.77 | 0.63 | 2.73 | −81.56 | 0.00 | 0.00 | 72.35 |

13 | −558.93 | 0.00 | 0.02 | −558.82 | 0.36 | 3.13 | 558.80 | 0.00 | 0.01 | 558.91 | 0.36 | 3.12 | −558.86 | 0.00 | 0.00 | 84.07 |

14 | −61.10 | 0.00 | 0.05 | −60.35 | 0.91 | 2.08 | 60.95 | −0.01 | 0.09 | 61.75 | 0.99 | 1.97 | −61.03 | 0.02 | 0.00 | 45.35 |

15 | −408.64 | 0.00 | 0.02 | −408.50 | 0.39 | 2.63 | 408.56 | 0.00 | 0.00 | 408.70 | 0.42 | 3.03 | −408.59 | 0.01 | 0.00 | 76.59 |

16 | −604.94 | 1.73 | 2.59 | −600.37 | 2.46 | −0.55 | 599.77 | 2.54 | 0.82 | 607.38 | 4.70 | −1.37 | −602.79 | 0.52 | 2.78 | 33.53 |

17 | −672.92 | 0.00 | 0.02 | −672.79 | 0.38 | 3.08 | 672.88 | 0.00 | 0.01 | 673.01 | 0.41 | 3.07 | −672.90 | 0.00 | 0.00 | 76.92 |

18 | −533.65 | 2.30 | 2.30 | −527.81 | 2.42 | −0.69 | 529.28 | 2.69 | 3.09 | 536.11 | 5.43 | −1.05 | −530.42 | 0.61 | 3.72 | 26.08 |

19 | −912.05 | 4.65 | 3.21 | −904.31 | 3.36 | −1.53 | 906.22 | 0.00 | 0.81 | 909.91 | 3.03 | 0.05 | −907.05 | 0.45 | 1.40 | 25.82 |

20 | −704.48 | 2.63 | 4.45 | −699.99 | 4.35 | −0.18 | 697.46 | 5.67 | 3.51 | 706.31 | 2.49 | −1.72 | −704.26 | 0.77 | 7.32 | 13.21 |

21 | −55.94 | 1.36 | 1.40 | −53.45 | 1.12 | 0.82 | 53.51 | −0.02 | 0.04 | 54.19 | 1.09 | 2.05 | −53.70 | 0.09 | 0.53 | 60.60 |

22 | −172.40 | 6.19 | 3.39 | −162.42 | 1.51 | −2.45 | 165.24 | 0.37 | 0.78 | 171.36 | 7.48 | −0.80 | −165.13 | 0.11 | 0.20 | 9.71 |

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## Share and Cite

**MDPI and ACS Style**

Kearns, F.L.; Warrensford, L.; Boresch, S.; Woodcock, H.L.
The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations. *Molecules* **2019**, *24*, 681.
https://doi.org/10.3390/molecules24040681

**AMA Style**

Kearns FL, Warrensford L, Boresch S, Woodcock HL.
The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations. *Molecules*. 2019; 24(4):681.
https://doi.org/10.3390/molecules24040681

**Chicago/Turabian Style**

Kearns, Fiona L., Luke Warrensford, Stefan Boresch, and H. Lee Woodcock.
2019. "The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations" *Molecules* 24, no. 4: 681.
https://doi.org/10.3390/molecules24040681