# The PM6-FGC Method: Improved Corrections for Amines and Amides

^{*}

## Abstract

**:**

_{2}group in amines and amides, caused by the inadequate selection of the model compound used to represent these functional groups (an NH

_{3}molecule). In this work, methylamine and acetamide are used as representatives of amine and amide groups, respectively. This new selection leads to significant improvements in the calculation of noncovalent interactions in the validation set.

## 1. Introduction

_{2}groups in amines and, tentatively, in amides. We evaluated IPECs for the six different pair combinations of these molecules, considering orientations of the interacting molecules that emphasize the atom–pair interactions in the complexes.

_{2}group in amines and amides (see [21] for extra details). The aim of the present study is to improve the method by handling and solving these shortcomings.

## 2. Results and Discussion

_{3}NH

_{2}–CH

_{3}NH

_{2}, CH

_{3}CONH

_{2}–CH

_{3}CONH

_{2}, CH

_{3}NH

_{2}–CH

_{3}CONH

_{2}, CH

_{3}NH

_{2}–CH

_{4}, CH

_{3}NH

_{2}–HCOOH, CH

_{3}CONH

_{2}–CH

_{4}, and CH

_{3}CONH

_{2}–CH

_{3}COOH. For each complex, we carried out a series of independent fits, adjusting all the parameters simultaneously. The final parameters, resulting from our best fits, are given in the Supplementary Materials, in the form of a Python dictionary. Notice that, for each complex, the total number of parameters involved in the fits is five times the number of different types of pairwise interactions.

#### 2.1. Methylamine Dimer

#### 2.2. Acetamide Dimer

#### 2.3. Methylamine—Acetamide Complex

_{3}NH

_{2}–CH

_{3}CONH

_{2}complex is 24, which is equal to the number of different types of pairwise interactions in this system. We show in Figure 4 the IPECs of eight orientations; the remaining IPECs are depicted in Figures S3 and S4 of the Supplementary Materials. Among the orientations considered for this complex, orientation 13 exhibits the strongest attractive interaction, with a well depth of 28.9 kJ/mol at the DFT level, which is consistent with formation of a hydrogen bond between an amide hydrogen and the amine nitrogen of the partner molecule. For this orientation, both corrected methods reproduce the reference IPEC quite well. By contrast, and as expected, the PM6 method significantly underestimates the strength of the hydrogen bonding interaction.

#### 2.4. Methylamine—Methane Complex

_{3}NH

_{2}–CH

_{4}complex is eight. This is the number of orientations we considered for this complex. Figure 5 shows the IPECs for four selected orientations. The IPECs for the remaining orientations are depicted in Figure S5 of the Supplementary Materials. As can be seen, although the PM6-D3H4 curves for orientations 1 and 5 show small disagreement with the reference IPECs, both corrected methods describe the intermolecular interaction satisfactorily. The PM6 curves deviate significantly from the reference DFT data, especially in orientations 4 and 8, in which hydrogen atoms face each other.

#### 2.5. Methylamine—Formic Acid Complex

_{3}–HCOOH complex in our previous work [21]. As for the complexes discussed earlier in this paper, the improvement of our approach over the PM6 and PM6-D3H4 methods is clear. Considering all the orientations of this complex, the MAEs calculated for interaction energies below 5 kJ/mol are 1.76 kJ/mol (PM6), 1.88 kJ/mol (PM6-D3H4), and 0.38 kJ/mol (PM6-FGC). For this system, the PM6 value is slightly lower than that calculated for the PM6-D3H4 method, and the same occurs for the other upper limits of the interaction energies (Table S1).

#### 2.6. Acetamide—Methane Complex

_{3}NH

_{2}–CH

_{4}complex, both corrected methods afford results in good or reasonably good agreement with the reference IPECs. The improvement of PM6-FGC over the PM6-D3H4 method is reflected in the values of the calculated MAEs (Table S1). Considering all the orientations and interaction energies below 5 kJ/mol, the MAE of our method (0.15 kJ/mol) is four times smaller than that of the PM6-D3H4 method (0.61 kJ/mol).

#### 2.7. Acetamide—Acetic Acid Complex

_{3}NH

_{2}–HCOOH complex, Figure 6). For orientation 35, wherein the carboxyl hydrogen faces a methyl hydrogen of the partner molecule, the PM6-FGC curve around an H⋯H distance of 2 Å deviates somewhat from the reference curve. This deviation results from the strange behaviour of the PM6 Hamiltonian, whose curve shows a maximum at an H⋯H distance of 2.1 Å and a minimum at 1.5 Å. Nevertheless, in general, the performance of our method is reasonably good, and the improvement over the other SQM approaches is clear. The calculated MAEs, for energies below 5 kJ/mol, are 2.71, 1.72, and 0.51 kJ/mol for PM6, PM6-D3H4, and PM6-FGC, respectively (see Table S1 of the Supplementary Materials).

#### 2.8. Validation of the PM6-FGC Method

_{3}as the representative for both amine and amide groups, which resulted in a drastic approximation for amides. Particularly, this led to a remarkable error for the global minimum of the acetamide dimer. It is important to mention that, in this work, we have included the most stable configuration of the acetamide dimer in the training set, but not the orientation of the methylamine dimer considered in the S66 database (complex 10, see Figure S10). Finally, the interaction energies calculated for complexes 46 and 62 with our previous corrections were found to be in better agreement with the benchmark data than those evaluated with the present corrections. This is probably a result of error compensation.

## 3. Methods and Computational Details

_{3}molecule as representative. We chose three molecules in all, specifically, methane, formic acid, and ammonia, which resulted in six bimolecular complexes needed to get the parameters. The corrections obtained from NH

_{3}/CH

_{4}fittings could model –NH

_{2}/alkane interactions, but the use of ammonia as representative proved not to be adequate enough to reproduce other interactions of the –NH

_{2}group in amines and amides (see for instance the results shown in Table 1 for some complexes of methylamine, N-methylacetamide and acetamide). Therefore, to try to solve these limitations, in the present investigation, we decided to use methylamine and acetamide as representatives, instead of ammonia. In addition, and with the purpose of exploring parameter transferability, we also considered the acetic acid molecule.

_{ij}is the interatomic distance between atoms i and j. The parameters A

_{ij}, B

_{ij}, C

_{ij}and D

_{ij}depend on the nature of the considered pair of atoms. The parameters A

_{ij}and C

_{ij}may be either positive or negative. In our previous work [21], we constrained the D

_{ij}parameters to be integers. In this study, to get additional, although small, flexibility, these parameters were considered real (positive) numbers instead. ${f}_{\mathrm{cut}}\left({r}_{ij}\right)$ is a cutoff function introduced to remove the correction at very short r

_{ij}distances:

_{ij}is a parameter that controls the strength of the damping for the interaction between atoms i and j, and d

_{ij}is the distance at which the cutoff function takes the value ½. As in our previous study, we set s

_{ij}= 10. The functional form of our corrections, i.e., Equation (1), was justified in our proof-of-concept work [21]. As shown in that paper, the differences between the reference and the PM6 IPECs have, in general, the form of typical intermolecular potential energy curves or the form of decaying exponentials with negative amplitudes, in agreement with Equation (1).

^{2}:

_{i}, y

_{i}) represents one of the N data points, a is the collective variable formed by the total number of fitting parameters and f (x

_{i};

**a**) is the value of the model function at x

_{i}(i.e., a particular geometry of the interacting molecules). The square of the difference between y

_{i}(i.e., a B3LYP-D3–PM6 energy difference) and the corresponding model value, calculated with Equations (1) and (2), may be multiplied by a weighting factor (w

_{i}), assigned to each data point. The use of a genetic algorithm has the advantage of efficiently exploring the search space and provides near optimal solutions when the number of fitting parameters is large. Since genetic algorithms may lead to many solutions that can be equally valid, our corrections should be viewed more as whole functional group corrections, rather than as individual pairwise corrections.

## 4. Summary and Conclusions

_{2}groups. For this reason, in the present study, we performed new parameterizations, using methylamine and acetamide as representatives of the amine and amide functional groups. The results of this work show a clear improvement over our previous parameterization and reinforce the importance of considering sufficient orientations of the interacting molecules in the reference database. We plan to extend the method to other functional groups relevant to biological compounds and implement the corrections in the MOPAC program. A Python script to calculate PM6-FGC corrections is available upon request.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## References

- Řezáč, J.; Fanfrlík, J.; Salahub, D.; Hobza, P. Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes. J. Chem. Theory Comput.
**2009**, 5, 1749–1760. [Google Scholar] [CrossRef] - Korth, M.; Pitoňák, M.; Řezáč, J.; Hobza, P. A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods. J. Chem. Theory Comput.
**2010**, 6, 344–352. [Google Scholar] [CrossRef] [PubMed] - Řezáč, J.; Hobza, P. A halogen-bonding correction for the semiempirical PM6 method. Chem. Phys. Lett.
**2011**, 506, 286–289. [Google Scholar] [CrossRef] - Řezáč, J.; Hobza, P. Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods. J. Chem. Theory Comput.
**2012**, 8, 141–151. [Google Scholar] [CrossRef] - Stewart, J.J.P. Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements. J. Mol. Model.
**2007**, 13, 1173–1213. [Google Scholar] [CrossRef] [Green Version] - Korth, M. Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields. J. Chem. Theory Comput.
**2010**, 6, 3808–3816. [Google Scholar] [CrossRef] - Kromann, J.C.; Christensen, A.S.; Steinmann, C.; Korth, M.; Jensen, J.H. A third-generation dispersion and third-generation hydrogen bonding corrected PM6 method: PM6-D3H+. PeerJ
**2014**, 2, e449. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fiedler, L.; Gao, J.; Truhlar, D.G. Polarized Molecular Orbital Model Chemistry. 1. Ab Initio Foundations. J. Chem. Theory Comput.
**2011**, 7, 852–856. [Google Scholar] [CrossRef] [PubMed] - Zhang, P.; Fiedler, L.; Leverentz, H.R.; Truhlar, D.G.; Gao, J. Polarized Molecular Orbital Model Chemistry. 2. The PMO Method. J. Chem. Theory Comput.
**2011**, 7, 857–867, Erratum in J. Chem. Theory Comput.**2012**, 8, 2983–2983. [Google Scholar] [CrossRef] - Isegawa, M.; Fiedler, L.; Leverentz, H.R.; Wang, Y.; Nachimuthu, S.; Gao, J.; Truhlar, D.G. Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry. J. Chem. Theory Comput.
**2013**, 9, 33–45. [Google Scholar] [CrossRef] [Green Version] - Fiedler, L.; Leverentz, H.R.; Nachimuthu, S.; Friedrich, J.; Truhlar, D.G. Nitrogen and Sulfur Compounds in Atmospheric Aerosols: A New Parametrization of Polarized Molecular Orbital Model Chemistry and Its Validation against Converged CCSD(T) Calculations for Large Clusters. J. Chem. Theory Comput.
**2014**, 10, 3129–3139. [Google Scholar] [CrossRef] [PubMed] - Grimme, S. Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comp. Chem.
**2004**, 25, 1463–1473. [Google Scholar] [CrossRef] [PubMed] - Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comp. Chem.
**2006**, 27, 1787–1799. [Google Scholar] [CrossRef] [PubMed] - Kolb, M.; Thiel, W. Beyond the MNDO model: Methodical considerations and numerical results. J. Comp. Chem.
**1993**, 14, 775–789. [Google Scholar] [CrossRef] - Weber, W.; Thiel, W. Orthogonalization corrections for semiempirical methods. Theor. Chem. Acc.
**2000**, 103, 495–506. [Google Scholar] [CrossRef] - Dral, P.O.; Wu, X.; Spörkel, L.; Koslowski, A.; Weber, W.; Steiger, R.; Scholten, M.; Thiel, W. Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters. J. Chem. Theory Comput.
**2016**, 12, 1082–1096. [Google Scholar] [CrossRef] - Dral, P.O.; Wu, X.; Thiel, W. Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections. J. Chem. Theory Comput.
**2019**, 15, 1743–1760. [Google Scholar] [CrossRef] [Green Version] - Dewar, M.J.S.; Zoebisch, E.G.; Healy, E.F.; Stewart, J.J.P. Development and use of quantum mechanical molecular models. 76. AM1: A new general purpose quantum mechanical molecular model. [Erratum to document cited in CA103(2):11627f]. J. Am. Chem. Soc.
**1993**, 115, 5348. [Google Scholar] [CrossRef] - Řezáč, J.; Riley, K.E.; Hobza, P. S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures. J. Chem. Theory Comput.
**2011**, 7, 2427–2438, Erratum in J. Chem. Theory Comput.**2014**, 10, 1359–1360. [Google Scholar] [CrossRef] - Řezáč, J.; Riley, K.E.; Hobza, P. Extensions of the S66 Data Set: More Accurate Interaction Energies and Angular-Displaced Nonequilibrium Geometries. J. Chem. Theory Comput.
**2011**, 7, 3466–3470. [Google Scholar] [CrossRef] - Pérez-Tabero, S.; Fernández, B. Cabaleiro-Lago, E.M.; Martínez-Núñez, E.; Vázquez, S.A., New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling. J. Chem. Theory Comput.
**2021**, 17, 5556–5567. [Google Scholar] [CrossRef] [PubMed] - Hostaš, J.; Řezáč, J.; Hobza, P. On the performance of the semiempirical quantum mechanical PM6 and PM7 methods for noncovalent interactions. Chem. Phys. Lett.
**2013**, 568, 161–166. [Google Scholar] [CrossRef] - Grimme, S.; Hansen, A.; Brandenburg, J.G.; Bannwarth, C. Dispersion-Corrected Mean-Field Electronic Structure Methods. Chem. Rev.
**2016**, 116, 5105–5154. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sure, R.; Grimme, S. Comprehensive Benchmark of Association (Free) Energies of Realistic Host–Guest Complexes. J. Chem. Theory Comput.
**2015**, 11, 3785–3801. [Google Scholar] [CrossRef] - Brandenburg, J.G.; Hochheim, M.; Bredow, T.; Grimme, S. Low-Cost Quantum Chemical Methods for Noncovalent Interactions. J. Phys. Chem. Lett.
**2014**, 5, 4275–4284. [Google Scholar] [CrossRef] - Gonzalez-Lafont, A.; Truong, T.N.; Truhlar, D.G. Direct dynamics calculations with NDDO (neglect of diatomic differential overlap) molecular orbital theory with specific reaction parameters. J. Chem. Phys.
**1991**, 95, 4618–4627. [Google Scholar] [CrossRef] - Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys.
**1993**, 98, 5648–5652. [Google Scholar] [CrossRef] [Green Version] - Becke, A.D. Density-functional thermochemistry. I. The effect of the exchange-only gradient correction. J. Chem. Phys.
**1992**, 96, 2155–2160. [Google Scholar] [CrossRef] - Becke, A.D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A
**1988**, 38, 3098–3100. [Google Scholar] [CrossRef] - Johnson, E.R.; Becke, A.D. A post-Hartree–Fock model of intermolecular interactions. J. Chem. Phys.
**2005**, 123, 024101. [Google Scholar] [CrossRef] - Becke, A.D.; Johnson, E.R. A density-functional model of the dispersion interaction. J. Chem. Phys.
**2005**, 123, 154101. [Google Scholar] [CrossRef] [PubMed] - Johnson, E.R.; Becke, A.D. A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections. J. Chem. Phys.
**2006**, 124, 174104. [Google Scholar] [CrossRef] [PubMed] - Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys.
**2005**, 7, 3297–3305. [Google Scholar] [CrossRef] - Pople, J.A.; Head-Gordon, M.; Raghavachari, K. Quadratic configuration interaction. A general technique for determining electron correlation energies. J. Chem. Phys.
**1987**, 87, 5968–5975. [Google Scholar] [CrossRef] - Kendall, R.A.; Dunning, J.T.H.; Harrison, R.J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys.
**1992**, 96, 6796–6806. [Google Scholar] [CrossRef] [Green Version] - Meroueh, O.; Hase, W.L. Dynamics of energy transfer in peptide-Surface collisions. J. Am. Chem. Soc.
**2002**, 124, 1524–1531. [Google Scholar] [CrossRef] - Wang, J.; Hase, W.L. Intermolecular Potential To Represent Collisions of Protonated Peptide Ions with Fluorinated Alkane Surfaces. J. Chem. Phys. B
**2005**, 109, 8320–8324. [Google Scholar] [CrossRef] - Deb, B.; Hu, W.; Song, K.; Hase, W.L. An analytical potential energy function to model protonated peptide soft-landing experiments. The CH3NH3+/CH4 interactions. Phys. Chem. Chem. Phys.
**2008**, 10, 4565–4572. [Google Scholar] [CrossRef] - Nogueira, J.J.; Sánchez-Coronilla, A.; Marques, J.M.C.; Hase, W.L.; Martínez-Núñez, E.; Vázquez, S.A. Intermolecular potentials for simulations of collisions of SiNCS+ and (CH3)2SiNCS+ ions with fluorinated self-assembled monolayers. Chem. Phys.
**2012**, 399, 193–204. [Google Scholar] [CrossRef] - Pratihar, S.; Kohale, S.C.; Vázquez, S.A.; Hase, W.L. Intermolecular Potential for Binding of Protonated Peptide Ions with Perfluorinated Hydrocarbon Surfaces. J. Chem. Phys. B
**2014**, 118, 5577–5588. [Google Scholar] [CrossRef] - Řezáč, J.; Hobza, P. Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit? J. Chem. Theory Comput.
**2013**, 9, 2151–2155. [Google Scholar] [CrossRef] [PubMed] - Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M. Estimated MP2 and CCSD(T) interaction energies of n-alkane dimers at the basis set limit: Comparison of the methods of Helgaker et al. and Feller. J. Chem. Phys.
**2006**, 124, 114304. [Google Scholar] [CrossRef] [PubMed] - Goerigk, L.; Hansen, A.; Bauer, C.; Ehrlich, S.; Najibi, A.; Grimme, S. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem. Chem. Phys.
**2017**, 19, 32184–32215. [Google Scholar] [CrossRef] [Green Version] - Hawkins, D.M. The Problem of Overfitting. J. Chem. Inf. Comput. Sci.
**2004**, 44, 1–12. [Google Scholar] [CrossRef] - Martínez-Núñez, E. An automated method to find transition states using chemical dynamics simulations. J. Comp. Chem.
**2015**, 36, 222–234. [Google Scholar] [CrossRef] [PubMed] - Martinez-Nunez, E. An automated transition state search using classical trajectories initialized at multiple minima. Phys. Chem. Chem. Phys.
**2015**, 17, 14912–14921. [Google Scholar] [CrossRef] - Rodríguez, A.; Rodríguez-Fernández, R.; Vázquez, S.A.; Barnes, G.L.; Stewart, J.J.P.; Martínez-Núñez, E. tsscds2018: A code for automated discovery of chemical reaction mechanisms and solving the kinetics. J. Comp. Chem.
**2018**, 39, 1922–1930. [Google Scholar] [CrossRef] [PubMed] - Kopec, S.; Martínez-Núñez, E.; Soto, J.; Peláez, D. vdW-TSSCDS—An automated and global procedure for the computation of stationary points on intermolecular potential energy surfaces. Int. J. Quantum Chem.
**2019**, 119, e26008. [Google Scholar] [CrossRef] - Martínez-Núñez, E.; Barnes, G.L.; Glowacki, D.R.; Kopec, S.; Peláez, D.; Rodríguez, A.; Rodríguez-Fernández, R.; Shannon, R.J.; Stewart, J.J.P.; Tahoces, P.G.; et al. AutoMeKin2021: An open-source program for automated reaction discovery. J. Comp. Chem.
**2021**, 42, 2036–2048. [Google Scholar] [CrossRef] - Stewart, J.J.P. MOPAC2016, 16.307; Steward Computational Chemistry. Available online: http://openmopac.net/ (accessed on 1 April 2021).
- Boys, S.F.; Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys.
**1970**, 19, 553–566. [Google Scholar] [CrossRef] - Simon, S.; Duran, M.; Dannenberg, J.J. How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers? J. Chem. Phys.
**1996**, 105, 11024–11031. [Google Scholar] [CrossRef] [Green Version] - Neese, F. Software update: The ORCA program system, version 4.0. WIREs Comput. Mol. Sci.
**2018**, 8, e1327. [Google Scholar] - Neese, F.; Wennmohs, F.; Becker, U.; Riplinger, C. The ORCA quantum chemistry program package. J. Chem. Phys.
**2020**, 152, 224108. [Google Scholar] [CrossRef] [PubMed] - Marques, J.M.C.; Prudente, F.V.; Pereira, F.B.; Almeida, M.M.; Maniero, A.M.; Fellows, C.E. A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data. J. Phys. B At. Mol. Opt. Phys.
**2008**, 41, 085103. [Google Scholar] [CrossRef] - Almeida, M.M.; Prudente, F.V.; Fellows, C.E.; Marques, J.M.C.; Perieira, F.B. Direct fit of spectroscopic data of diatomic molecules by using genetic algorithms: II. The ground state of RbCs. J. Phys. B At. Mol. Opt. Phys.
**2011**, 44, 225102. [Google Scholar] [CrossRef] - Rodríguez-Fernández, R.; Pereira, F.B.; Marques, J.M.C.; Martínez-Núñez, E.; Vázquez, S.A. GAFit: A general-purpose, user-friendly program for fitting potential energy surfaces. Comput. Phys. Commun.
**2017**, 217, 89–98. [Google Scholar] [CrossRef] - Buckingham, R.A. The classical equation of state of gaseous helium, neon and argon. Proc. R. Soc. Lond. A
**1938**, 168, 264–283. [Google Scholar]

**Figure 1.**(

**a**) Model compounds and atom types considered for the parameterizations, and (

**b**) atom-type transferability to dialanine.

**Figure 4.**Comparison of IPECs for eight selected orientations of the CH

_{3}NH

_{2}–CH

_{3}CONH

_{2}complex.

**Figure 8.**Comparison of IPECs for eight selected orientations of the CH

_{3}CONH

_{2}/CH

_{3}COOH complex.

**Figure 9.**Linear correlations obtained for the dialanine dimer. For comparison, we include the PM6-FGC results evaluated with our previous corrections [21].

**Figure 10.**Linear correlations obtained for the diglycine dimer. For comparison, we include the PM6-FGC results evaluated with our previous corrections [21].

**Figure 11.**Linear correlations obtained for the diglycine trimer. For comparison, we include the PM6-FGC results evaluated with our previous corrections [21].

Complex ^{a} | CCSD(T)/CBS ^{b} | B3LYP-D3 | PM6 | PM6-D3H4 | PM6-FGC ^{c} | PM6-FGC ^{d} |
---|---|---|---|---|---|---|

(10) CH_{3}NH_{2}–CH_{3}NH_{2} | −17.41 | −18.04 | −7.70 | −19.00 | −13.10 | −14.10 |

(11) CH_{3}NH_{2}–peptide | −22.68 | −22.71 | −16.11 | −25.69 | −18.79 | −19.02 |

(14) peptide–CH_{3}NH_{2} | −31.17 | −32.98 | −17.49 | −31.42 | −27.61 | −32.32 |

(15) peptide–peptide | −36.11 | −36.74 | −24.73 | −36.82 | −30.12 | −37.92 |

(21) CH_{3}CONH_{2}–CH_{3}CONH_{2} | −68.03 | −70.09 | −51.80 | −70.71 | −49.58 | −70.95 |

(46) peptide–pentane | −17.82 | −17.21 | −5.27 | −17.20 | −17.57 | −15.06 |

(62) pentane–CH_{3}CONH_{2} | −14.77 | −14.46 | −6.44 | −16.48 | −14.81 | −13.47 |

MAE | 0.87 | 11.21 | 1.51 | 5.21 | 2.42 |

**Table 2.**Statistical parameters

^{a}of the linear correlations using B3LYP-D3/def2-TZVP interaction energies as the reference.

Diglycine Dimer | Dialanine Dimer | Diglycine Trimer | ||||
---|---|---|---|---|---|---|

MAE | MBE | MAE | MBE | MAE | MBE | |

PM6 | 17.9 | −15.0 | 14.3 | −14.0 | 10.8 | −5.1 |

PM6-D3H4 | 18.6 | 15.5 | 20.3 | 19.5 | 25.3 | 25.3 |

PM6-FGC | 4.0 (6.0) | −0.6 (3.2) | 4.9 (8.7) | 1.9 (8.7) | 5.9 (9.1) | 4.6 (8.7) |

^{a}MAE and MBE values are given in kJ/mol. Values in parentheses correspond to the parameterization performed in our previous work [21].

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Ríos-García, M.; Fernández, B.; Rodríguez-Otero, J.; Cabaleiro-Lago, E.M.; Vázquez, S.A.
The PM6-FGC Method: Improved Corrections for Amines and Amides. *Molecules* **2022**, *27*, 1678.
https://doi.org/10.3390/molecules27051678

**AMA Style**

Ríos-García M, Fernández B, Rodríguez-Otero J, Cabaleiro-Lago EM, Vázquez SA.
The PM6-FGC Method: Improved Corrections for Amines and Amides. *Molecules*. 2022; 27(5):1678.
https://doi.org/10.3390/molecules27051678

**Chicago/Turabian Style**

Ríos-García, Martiño, Berta Fernández, Jesús Rodríguez-Otero, Enrique M. Cabaleiro-Lago, and Saulo A. Vázquez.
2022. "The PM6-FGC Method: Improved Corrections for Amines and Amides" *Molecules* 27, no. 5: 1678.
https://doi.org/10.3390/molecules27051678