Home Metal–ligand bonding and noncovalent interactions of mutated myoglobin proteins: a quantum mechanical study
Article
Licensed
Unlicensed Requires Authentication

Metal–ligand bonding and noncovalent interactions of mutated myoglobin proteins: a quantum mechanical study

  • Juliana J. Antonio and Elfi Kraka ORCID logo EMAIL logo
Published/Copyright: September 4, 2025
Pure and Applied Chemistry
From the journal Pure and Applied Chemistry Volume 97 Issue 10

Abstract

Metal–ligand bonding and noncovalent interactions (NCIs), such as hydrogen bonding or π–π interactions, play a crucial role in determining the structure, function, and selectivity of both biological and artificial metalloproteins. In this study, we employed a hybrid quantum mechanics/molecular mechanics (QM/MM) approach to investigate the ligation of water or cyanide in a mutated myoglobin system, in which the native heme scaffold was replaced with M-salophen or M-salen Schiff base complexes (M = Cr, Mn, Fe). Using our local vibrational mode analysis, particularly local vibrational mode force constants as intrinsic bond strength parameters, complemented with electron density and natural orbital analyses we explored the role of metal–ligand bonding and NCIs in different environments within the myoglobin pocket. Our analysis revealed that metal–ligand bonding, for both water and cyanide ligands, is strongest in the delta form of distal histidine and favors salophen prosthetic groups, as indicated by an overall increase in metal–ligand bond strength. Hydrogen bonding between the distal histidine and ligand also exhibited greater strength in the delta form; however, this effect was more pronounced with salen prosthetic groups. Additionally, the NCIs within the active pocket of the protein were found to be variable, highlighting the adaptability of local force constants. In summary, our data underscore the potential of computational methodologies in guiding the rational design of artificial metalloproteins for tailored applications, with local vibrational mode analysis serving as a powerful tool for bond strength assessment.

Keywords: π-π interactions; hydrogen bonding; local vibrational force constants; local vibrational mode analysis; metal–ligand bonding; myoglobin; non-covalent interactions; QM/MM; quantum science and technology
Corresponding author: Elfi Kraka, Department of Chemistry, Computational and Theoretical Chemistry Group (CATCO), Southern Methodist University, 3215 Daniel Ave, Dallas, TX 75275-0314, USA, e-mail:
Article note: A collection of invited papers to celebrate the UN’s proclamation of 2025 as the International Year of Quantum Science and Technology.

Funding source: National Science Foundation, NSF

Award Identifier / Grant number: CHE2102461

Award Identifier / Grant number: DGE-2034834

Acknowledgments

Computational resources provided by SMU’s O’Donnell Institute of Data Science and High Performance Computing.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: All other authors state no conflict of interest.

  6. Research funding: This work was supported by the National Science Foundation, Grant CHE2102461, and the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-2034834.

  7. Data availability: All data are available via the manuscript and/or the supporting Information.

References

1. Vornholt, T.; Leiss-Maier, F.; Jeong, W. J.; Zeymer, C.; Song, W. J.; Roelfes, G.; Ward, T. R. Artificial Metalloenzymes. Nat. Rev. Methods Primers 2024, 4, 78. https://doi.org/10.1038/s43586-024-00356-w.Search in Google Scholar

2. Brouwer, B.; Della-Felice, F.; Illies, J. H.; Iglesias-Moncayo, E.; Roelfes, G.; Drienovská, I. Noncanonical Amino Acids: Bringing New-to-Nature Functionalities to Biocatalysis. Chem. Rev. 2024, 124, 10877–10923. https://doi.org/10.1021/acs.chemrev.4c00136.Search in Google Scholar

3. Vornholt, T.; Christoffel, F.; Pellizzoni, M. M.; Panke, S.; Ward, T. R.; Jeschek, M. Systematic Engineering of Artificial Metalloenzymes for New-to-Nature Reactions. Sci. Adv. 2021, 7, eabe4208. https://doi.org/10.1126/sciadv.abe4208.Search in Google Scholar

4. Bloomer, B. J.; Clark, D. S.; Hartwig, J. F. Progress, Challenges, and Opportunities with Artificial Metalloenzymes in Biosynthesis. Biochem 2023, 62, 221–228. https://doi.org/10.1021/acs.biochem.1c00829.Search in Google Scholar

5. Gao, L.; Zhang, Y.; Zhao, L.; Niu, W.; Tang, Y.; Gao, F.; Cai, P.; Yuan, Q.; Wang, X.; Jiang, H.; Gao, X. An Artificial Metalloenzyme for Catalytic Cancer-Specific DNA Cleavage and Operando Imaging. Sci. Adv. 2020, 6, eabb1421. https://doi.org/10.1126/sciadv.abb1421.Search in Google Scholar

6. Davis, H. J.; Ward, T. R. Artificial Metalloenzymes: Challenges and Opportunities. ACS Cent. Sci. 2019, 5, 1120–1136. https://doi.org/10.1021/acscentsci.9b00397.Search in Google Scholar

7. Alonso-Cotchico, L.; Rodriguez-Guerra, J.; Lledos, A.; Marechal, J. D. Molecular Modeling for Artificial Metalloenzyme Design and Optimization. Acc. Chem. Res. 2020, 53, 986–905. https://doi.org/10.1021/acs.accounts.0c00031.Search in Google Scholar

8. Jeong, W. J.; Yu, J.; Song, W. J. Proteins as Diverse, Efficient, and Evolvable Scaffolds for Artificial Metalloenzymes. Chem. Commun. 2020, 56, 9586. https://doi.org/10.1039/D0CC03137B.Search in Google Scholar

9. Maity, B.; Taher, M.; Mazumdar, S.; Ueno, T. Artificial Metalloenzymes Based on Protein Assembly. Coord. Chem. Rev. 2022, 469, 214593. https://doi.org/10.1016/j.ccr.2022.214593.Search in Google Scholar

10. Matsuo, T.; Hirota, S. Artificial Enzymes with Protein Scaffolds: Structural Design and Modification. Bioorg. Med. Chem. 2014, 22, 5638–5656. https://doi.org/10.1016/j.bmc.2014.06.021.Search in Google Scholar

11. Shafaat, H. S.; Manesis, A. C.; Yerbulekova, A. How to Build a Metalloenzyme: Lessons from a Protein-Based Model of Acetyl Coenzyme A Synthase. Acc. Chem. Res. 2023, 56, 984–993. https://doi.org/10.1021/acs.accounts.2c00824.Search in Google Scholar

12. Bhardwaj, M.; Kamble, P.; Mundhe, P.; Jindal, M.; Thakur, P.; Bajaj, P. Multifaceted Personality and Roles of Heme Enzymes in Industrial Biotechnology. 3 Biotech 2023, 13, 389. https://doi.org/10.1007/s13205-023-03804-8.Search in Google Scholar

13. Lemon, C. M. Diversifying the Functions of Heme Proteins with Non-Porphyrin Cofactors. J. Inorg. Biochem. 2023, 246, 112282. https://doi.org/10.1016/j.jinorgbio.2023.112282.Search in Google Scholar

14. Oohora, K.; Hayashi, T. Myoglobins Engineered with Artificial Cofactors Serve as Artificial Metalloenzymes and Models of Natural Enzymes. Dalton Trans. 2021, 50, 1940–1949. https://doi.org/10.1039/D0DT03597A.Search in Google Scholar

15. Kato, S.; Abe, M.; Gröger, H.; Hayashi, T. Reconstitution of Myoglobin with Iron Porphycene Generates an Artificial Aldoxime Dehydratase with Expanded Catalytic Activities. ACS Catal. 2024, 14, 13081–13087. https://doi.org/10.1021/acscatal.4c03220.Search in Google Scholar

16. Singh, P.; Yadav, P.; Sodhi, K. K.; Tomer, A.; Mehta, S. B. Advancement in the Synthesis of Metal Complexes with Special Emphasis on Schiff Base Ligands and Their Important Biological Aspects. Results Chem. 2024, 101222. https://doi.org/10.1016/j.rechem.2023.101222.Search in Google Scholar

17. Shahraki, S. Schiff Base Compounds as Artificial Metalloenzymes. Colloids Surf., B 2022, 218, 112727. https://doi.org/10.1016/j.colsurfb.2022.112727.Search in Google Scholar

18. Ueno, T.; Ohashi, M.; Kono, M.; Kondo, K.; Suzuki, A.; Yamane, T.; Watanabe, Y. Crystal Structures of Artificial Metalloproteins: Tight Binding of FeIII(Schiff-Base) by Mutation of Ala71 to Gly in Apo-Myoglobin. Inorg. Chem. 2004, 43, 2852–2858. https://doi.org/10.1021/ic0498539.Search in Google Scholar

19. Ueno, T.; Koshiyama, T.; Ohashi, M.; Kondo, K.; Kono, M.; Suzuki, A.; Yamane, T.; Watanabe, Y. Coordinated Design of Cofactor and Active Site Structures in Development of New Protein Catalysts. J. Am. Chem. Soc. 2005, 127, 6556–6562. https://doi.org/10.1021/ja045995q.Search in Google Scholar

20. Ohashi, M.; Koshiyama, T.; Ueno, T.; Yanase, M.; Fujii, H.; Watanabe, Y. Preparation of Artificial Metalloenzymes by Insertion of Chromium(III) Schiff Base Complexes into Apomyoglobin Mutants. Angew. Chem., Int. Ed. 2003, 42, 1005–1008. https://doi.org/10.1002/anie.200390256.Search in Google Scholar

21. Hirota, S.; Lin, Y.-W. Design of Artifcial Metalloproteins/Metalloenzymes by Tuning Noncovalent Interactions. J. Biol. Inorg. Chem. 2018, 23, 7–25. https://doi.org/10.1007/s00775-017-1506-8.Search in Google Scholar

22. Kraka, E.; Zou, W.; Tao, Y. Decoding Chemical Information from Vibrational Spectroscopy Data: Local Vibrational Mode Theory. WIREs: Comput. Mol. Sci. 2020, 10, 1480. https://doi.org/10.1002/wcms.1480.Search in Google Scholar

23. Kraka, E.; Quintano, M.; La Force, H. W.; Antonio, J. J.; Freindorf, M. The Local Vibrational Mode Theory and Its Place in the Vibrational Spectroscopy Arena. J. Phys. Chem. A 2022, 126, 8781–8798. https://doi.org/10.1021/acs.jpca.2c05962.Search in Google Scholar

24. Kelley, J. D.; Leventhal, J. J. Normal Modes and Coordinates. In Problems in Classical and Quantum Mechanics: Extracting the Underlying Concepts; Springer International Publishing, 2017; pp 95–117.Search in Google Scholar

25. Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra; McGraw-Hill: New York, 1955.Search in Google Scholar

26. Wilson, E. B. Some Mathematical Methods for the Study of Molecular Vibrations. J. Chem. Phys. 1941, 9, 76–84. https://doi.org/10.1063/1.1750829.Search in Google Scholar

27. Barone, V.; Alessandrini, S.; Biczysko, M.; Cheeseman, J. R.; Clary, D. C.; McCoy, A. B.; DiRisio, R. J.; Neese, F.; Melosso, M.; Puzzarini, C. Computational Molecular Spectroscopy. Nat. Rev. Methods Primers 2021, 1, 38. https://doi.org/10.1038/s43586-021-00034-1.Search in Google Scholar

28. Peluzo, B. M. T. C.; Makoś, M. Z.; Moura, R. T.Jr.; Freindorf, M.; Kraka, E. Linear Versus Bent Uranium(II) Metallocenes – A Local Vibrational Mode Study. Inorg. Chem. 2023, 62, 12510–12524. https://doi.org/10.1021/acs.inorgchem.3c01761.Search in Google Scholar

29. Antonio, J. J.; Kraka, E. Metal–Ring Interactions in Group 2 ansa-metallocenes: Assessed with the Local Vibrational Mode Theory. Phys. Chem. Chem. Phys. 2024, 26, 15143–15155. https://doi.org/10.1039/d4cp00225c.Search in Google Scholar

30. Antonio, J. J.; Kraka, E. Non-Covalent π–interactions in Mutated aquomet-Myoglobin Proteins: A QM/MM and Local Vibrational Mode Study. Biochemistry 2023, 62, 2325–2337. https://doi.org/10.1021/acs.biochem.3c00192.Search in Google Scholar

31. Freindorf, M.; Antonio, J.; Kraka, E. Hydrogen Sulfide Ligation in Hemoglobin I of Lucina pectinata – a QM/MM and Local Mode Study. J. Phys. Chem. A 2023, 127, 8316–8329. https://doi.org/10.1021/acs.jpca.3c04399.Search in Google Scholar

32. Freindorf, M.; Antonio, J.; Kraka, E. Iron–Histidine Bonding in Bishistidyl Hemoproteins – a Local Vibrational Mode Study. J. Comput. Chem. 2024, 45, 574–588. https://doi.org/10.1002/jcc.27267.Search in Google Scholar

33. Freindorf, M.; Kraka, E. A Closer Look at the FeS Heme Bonds in Azatobacter Vinelandii Bacterioferritin: QM/MM and Local Mode Analysis. J. Comput. Chem. 2025, 46, e70012; https://doi.org/10.1002/jcc.70012.Search in Google Scholar

34. Freindorf, M.K. F.; Fleming, K.; Kraka, E. Iron-Histidine Coordination in Cytochrome b5: A Local Vibrational Mode Study. ChemPhysChem 2025, 26, e202401098; https://doi.org/10.1002/cphc.202401098.Search in Google Scholar

35. Freindorf, M.; Kraka, E. Metal-ligand and Hydrogen Bonding in the Active Site of Fe(III)-, Mn(III)- and Co(III)-myoglobins. Dalton Trans. 2025, 54, 4096–4111; https://doi.org/10.1039/D4DT03246B.Search in Google Scholar

36. Verma, N.; Tao, Y.; Zou, W.; Chen, X.; Chen, X.; Freindorf, M.; Kraka, E. A Critical Evaluation of Vibrational Stark Effect (VSE) Probes with the Local Vibrational Mode Theory. Sensors 2020, 20, 2358. https://doi.org/10.3390/s20082358.Search in Google Scholar

37. Machado, F. C.; Quintano, M.; Santos, C. V.Jr.; Neto, A. N. C.; Kraka, E.; Longo, R. L.; Moura, R. T.Jr. Theoretical Insights into the Vibrational Spectra and Chemical Bonding of Ln(III) Complexes with a Tripodal N4O3 Ligand Along the Lanthanide Series. Phys. Chem. Chem. Phys. 2025, 27, 17984–1803. https://doi.org/10.1039/d4cp03677h.Search in Google Scholar

38. Quintano, M.; Delgado, A. A. A.; MouraJr.R. T.; Freindorf, M.; Kraka, E. Local Mode Analysis of Characteristic Vibrational Coupling in Nucleobases and Watson–Crick Base Pairs of DNA. Electron. Struct. 2022, 4, 044005-1–044005-17. https://doi.org/10.1088/2516-1075/acaa7a.Search in Google Scholar

39. Quintano, M.; Moura, R. T.Jr.; Kraka, E. Exploring Jahn-Teller Distortions: A Local Vibrational Mode Perspective. J. Mol. Model. 2024, 30, 102-1–102-12. https://doi.org/10.1007/s00894-024-05882-8.Search in Google Scholar

40. Cremer, D.; Kraka, E. From Molecular Vibrations to Bonding, Chemical Reactions, and Reaction Mechanism. Curr. Org. Chem. 2010, 14, 1524–1560. https://doi.org/10.2174/138527210793563233.Search in Google Scholar

41. Kraka, E.; Larsson, J. A.; Cremer, D. Generalization of the Badger Rule Based on the Use of Adibatic Vibrational Modes. In Computational Spectroscopy; Grunenberg, J., Ed.; Wiley: New York, 2010; pp 105–149.Search in Google Scholar

42. Mayer, I. Charge, Bond Brder an Valence in the Ab Initio Theory. Chem. Phys. Lett. 1983, 97, 270–274. https://doi.org/10.1016/0009-2614(83)80005-0.Search in Google Scholar

43. Mayer, I. Bond Orders and Valences from ab Initio Wave Functions. Int. J. Quantum Chem. 1986, 29, 477–483. https://doi.org/10.1002/qua.560290320.Search in Google Scholar

44. Mayer, I. Bond Order and Valence Indices: A Personal Account. J. Comput. Chem. 2007, 28, 204–221. https://doi.org/10.1002/jcc.20494.Search in Google Scholar

45. Bader, R. F. W. Atoms in Molecules. Acc. Chem. Res. 1985, 18, 9–15. https://doi.org/10.1021/ar00109a003.Search in Google Scholar

46. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, 1995.Search in Google Scholar

47. Popelier, P. Atoms in Molecules: An Introduction; Prentice-Hall: Harlow, England, 2000.Search in Google Scholar

48. Cremer, D.; Kraka, E. Chemical Bonds Without Bonding Electron Density? Does the Difference Electron-Density Analysis Suffice for a Description of the Chemical Bond? Angew. Chem., Int. Ed. 1984, 23, 627–628. https://doi.org/10.1002/anie.198406271.Search in Google Scholar

49. Cremer, D.; Kraka, E. A Description of the Chemical Bond in Terms of Local Properties of Electron Density and Energy. Croat. Chem. Acta 1984, 57, 1259–1281.Search in Google Scholar

50. Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735–746. https://doi.org/10.1063/1.449486.Search in Google Scholar

51. Eswar, N.; Webb, B.; Marti‐Renom, M. A.; Madhusudhan, M.; Eramian, D.; Shen, M.-y.; Pieper, U.; Sali, A. Comparative Protein Structure Modeling Using Modeller. Curr. Protoc. Bioinf. 2006, 15, 5.6.1–5.6.30. https://doi.org/10.1002/0471250953.bi0506s15.Search in Google Scholar

52. Meng, E. C.; Goddard, T. D.; Pettersen, E. F.; Couch, G. S.; Pearson, Z. J.; Morris, J. H.; Ferrin, T. E. UCSF ChimeraX: Tools for Structure Building and Analysis. Protein Sci. 2023, 32, e4792. https://doi.org/10.1002/pro.4792.Search in Google Scholar

53. Scouras, A. D.; Daggett, V. The Dynameomics Rotamer Library: Amino Acid Side Chain Conformations and Dynamics from Comprehensive Molecular Dynamics Simulations in Water. Protein Sci. 2011, 20, 341–352. https://doi.org/10.1002/pro.565.Search in Google Scholar

54. Li, P.; Merz, K. M. J. MCPB.py: A Python Based Metal Center Parameter Builder. J. Chem. Inf. Model. 2016, 56, 599–604. https://doi.org/10.1021/acs.jcim.5b00674.Search in Google Scholar

55. Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped atom-atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615–6620. https://doi.org/10.1039/B810189B.Search in Google Scholar

56. Ditchfield, R.; Hehre, W.; Pople, J. Self-Consistent Molecular-Orbital Methods. IX. an Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971, 54, 724–728. https://doi.org/10.1063/1.1674902.Search in Google Scholar

57. Hariharan, P.; Pople, J. The Influence of Polarization Functions on Molecular Orbital Hydrogenation Energies. Thermochim. Acta 1973, 28, 213–222. https://doi.org/10.1007/BF00533485.Search in Google Scholar

58. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A.Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian16 Revision C.01; Gaussian Inc: Wallingford CT, 2016.Search in Google Scholar

59. Seminario, J. M. Calculation of Intramolecular Force Fields from Second-Derivative Tensors. Int. J. Quantum Chem. 1996, 60, 1271–1277. https://doi.org/10.1002/(SICI)1097-461X(1996)60:7%3C1271::AID-QUA8%3E3.0.CO;2-W.Search in Google Scholar

60. Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comput. Chem. 1984, 5, 129–145. https://doi.org/10.1002/jcc.540050204.Search in Google Scholar

61. Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The RESP Model. J. Phys. Chem. 1993, 97, 10269–10280. https://doi.org/10.1021/j100142a004.Search in Google Scholar

62. Tian, C.; Kasavajhala, K.; Belfon, K. A. A.; Raguette, L.; Huang, H.; Migues, A. N.; Bickel, J.; Wang, Y.; Pincay, J.; Wu, Q.; Simmerling, C. ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained Against Quantum Mechanics Energy Surfaces in Solution. J. Chem. Theory Comput. 2020, 16, 528–552. https://doi.org/10.1021/acs.jctc.9b00591.Search in Google Scholar

63. Anandakrishnan, R.; Aguilar, B.; Onufriev, A. V. H++ 3.0: Automating pK Prediction and the Preparation of Biomolecular Structures for Atomistic Molecular Modeling and Simulations. Nucleic Acids Res. 2012, 40, 537–541. https://doi.org/10.1093/nar/gks375.Search in Google Scholar

64. Gordon, J. C.; Myers, J. B.; Folta, T.; Shoja, V.; Heath, L. S.; Onufriev, A. H++: A Server for Estimating P Ka S and Adding Missing Hydrogens to Macromolecules. Nucleic Acids Res. 2005, 33, 368–371. https://doi.org/10.1093/nar/gki464.Search in Google Scholar

65. Myers, J.; Grothaus, G.; Narayanan, S.; Onufriev, A. A Simple Clustering Algorithm Can be Accurate Enough for Use in Calculations of pKs in Macromolecules. Proteins: Struct., Funct., Bioinf. 2006, 63, 928–938. https://doi.org/10.1002/prot.20922.Search in Google Scholar

66. Case, D.; Aktulga, H.; Belfon, K.; Ben-Shalom, I.; Berryman, J.; Brozell, S.; Cerutti, D.; III, T. C.; Cisneros, G.; Cruzeiro, V.; Darden, T.; Forouzesh, N.; Ghazimirsaeed, M.; Giambaşu, G.; Giese, T.; Gilson, M.; Gohlke, H.; Goetz, A.; Harris, J.; Huang, S. I. Z.; Izmailov, S.; Kasavajhala, K.; Kaymak, M.; Kovalenko, A.; Kurtzman, T.; Lee, T.; Li, P.; Li, Z.; Lin, C.; Liu, J.; Luchko, T.; Luo, R.; Machado, M.; Manathunga, M.; Merz, K.; Miao, Y.; Mikhailovskii, O.; Monard, G.; Nguyen, H.; O’Hearn, K.; Onufriev, A.; Pan, F.; Pantano, S.; Rahnamoun, A.; Roe, D.; Roitberg, A.; Sagui, C.; Schott-Verdugo, S.; Shajan, A.; Shen, J.; Simmerling, C.; Skrynnikov, N.; Smith, J.; Swails, J.; Walker, R.; Wang, J.; Wang, J.; Wu, X.; Wu, Y.; Xiong, Y.; Xue, Y.; York, D.; Zhao, C.; Zhu, Q.; Kollman, P. AMBER 2024; University of California: San Francisco, USA, 2024.Search in Google Scholar

67. Tao, P.; Schlegel, H. B. A Toolkit to Assist ONIOM Calculations. J. Comput. Chem. 2010, 31, 2363–2369. https://doi.org/10.1002/jcc.21524.Search in Google Scholar

68. Vreven, T.; Frisch, M. J.; Kudin, K. N.; Schlegel, H. B.; Morokuma, K. Geometry Optimization with QM/MM Methods II: Explicit Quadratic Coupling. Mol. Phys. 2006, 104, 701–714. https://doi.org/10.1080/00268970500417846.Search in Google Scholar

69. Bacskay, G. B. A Quadratically Convergent Hartree – Fock (QC-SCF) Method. Application to Closed Shell Systems. Chem. Phys. 1981, 61, 385–404. https://doi.org/10.1016/0301-0104(81)85156-7.Search in Google Scholar

70. Zou, W.; Moura, R.Jr.; Santos, C. V.Jr.; Quintano, M.; Bodo, F.; Freindorf, M.; Cremer, D.; Kraka, E. LModeA2025, Computational and Theoretical Chemistry Group (CATCO); Southern Methodist University: Dallas, TX, USA, 2025.Search in Google Scholar

71. Keith, T. A. AIMAll (Version 19.10.12); TK Gristmill Software: Overland Park KS, USA, 2019.Search in Google Scholar

72. Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Karafiloglou, P.; Landis, C. R.; Weinhold, F. NBO 7.0. Theoretical Chemistry Institute; University of Wisconsin: Madison, 2018.Search in Google Scholar

73. Kraka, E.; Cremer, D. Chemical Implication of Local Features of the Electron Density Distribution. In Theoretical Models of Chemical Bonding. The Concept of the Chemical Bond; Maksic, Z. B., Ed.; Springer Verlag: Heidelberg, Vol. 2, 1990; pp 453–542.Search in Google Scholar

74. Kraka, E.; Cremer, D. Dieter Cremer’s Contribution to the Field of Theoretical Chemistry. Int. J. Quantum Chem. 2019, 119, e25849. https://doi.org/10.1002/qua.25849.Search in Google Scholar

75. Tao, Y.; Zou, W.; Nanayakkara, S.; Freindorf, M.; Kraka, E. A Revised Formulation of the Generalized Subsystem Vibrational Analysis (GSVA). Theor. Chem. Acc. 2021, 140, 31-1–31-5. https://doi.org/10.1007/s00214-021-02727-y.Search in Google Scholar

76. Moura, R. T.Jr.; Quintano, M.; Antonio, J. J.; Freindorf, M.; Kraka, E. Automatic Generation of Local Vibrational Mode Parameters: from Small to Large Molecules and QM/MM Systems. J. Phys. Chem. A 2022, 126, 9313–9331. https://doi.org/10.1021/acs.jpca.2c07871.Search in Google Scholar

77. Quintano, M.; Moura, R. T.Jr.; Kraka, E. Frontier Article: Local Vibrational Mode Theory Meets Graph Theory: Complete and Non-Redundant Local Mode Sets. Chem. Phys. Lett. 2024, 849, 141416-1–1141416-13. https://doi.org/10.1016/j.cplett.2024.141416.Search in Google Scholar

78. Ding, K.; Yin, S.; Li, Z.; Jiang, S.; Yang, Y.; Zhou, W.; Zhang, Y.; Huang, B. Observing Noncovalent Interactions in Experimental Electron Density for Macromolecular Systems: A Novel Perspective for Protein – Ligand Interaction Research. J. Chem. Inf. Model. 2022, 62, 1734–1743. https://doi.org/10.1021/acs.jcim.1c01406.Search in Google Scholar

79. Van Stappen, C.; Deng, Y.; Liu, Y.; Heidari, H.; Wang, J.-X.; Zhou, Y.; Ledray, A. P.; Lu, Y. Designing Artificial Metalloenzymes by Tuning of the Environment Beyond the Primary Coordination Sphere. Chem. Rev. 2022, 122, 11974–12045. https://doi.org/10.1021/acs.chemrev.2c00106.Search in Google Scholar

80. Adhav, V. A.; Saikrishnan, K. The Realm of Unconventional Noncovalent Interactions in Proteins: Their Significance in Structure and Function. ACS Omega 2023, 8, 22268–22284. https://doi.org/10.1021/acsomega.3c00205.Search in Google Scholar

81. Jeong, W. J.; Lee, J.; Eom, H.; Song, W. J. A Specific Guide for Metalloenzyme Designers: Introduction and Evolution of Metal-Coordination Spheres Embedded in Protein Environments. Acc. Chem. Res. 2023, 56, 2416–2425. https://doi.org/10.1021/acs.accounts.3c00336.Search in Google Scholar

82. Kumbhar, S.; Fischer, F. D.; Waller, M. P. Assessment of Weak Intermolecular Interactions Across QM/MM Noncovalent Boundaries. J. Chem. Inf. Model. 2012, 52, 93–98. https://doi.org/10.1021/ci200406s.Search in Google Scholar

83. Humphrey, W.; Dalke, A.; Schulten, K. VMD – Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33–38. https://doi.org/10.1016/0263-7855(96)00018-5.Search in Google Scholar

84. Cremer, D.; Pople, J. A. General Definition of Ring Puckering Coordinates. J. Am. Chem. Soc. 1975, 97, 1354–1358; https://doi.org/10.1021/ja00839a011.Search in Google Scholar

85. Böselt, L.; Thürlemann, M.; Riniker, S. Machine Learning in QM/MM Molecular Dynamics Simulations of Condensed-Phase Systems. J. Chem. Theory Comput. 2021, 17, 2641–2658. https://doi.org/10.1021/acs.jctc.0c01112.Search in Google Scholar

86. Bereau, T.; DiStasio, R. A.Jr.; Tkatchenko, A.; von Lilienfeld, O. A. Non-Covalent Interactions Across Organic and Biological Subsets of Chemical Space: Physics-Based Potentials Parametrized from Machine Learning. J. Chem. Phys. 2018, 148, 241706. https://doi.org/10.1063/1.5009502.Search in Google Scholar

87. Cao, Y.; Romero, J.; Olson, J. P.; Degroote, M.; Johnson, P. D.; Kieferová, M.; Kivlichan, I. D.; Menke, T.; Peropadre, B.; Sawaya, N. P. D.; Sim, S.; Veis, L.; Aspuru-Guzik, A. Quantum Chemistry in the Age of Quantum Computing. Chem. Rev. 2019, 119, 10856–10915. https://doi.org/10.1021/acs.chemrev.8b00803.Search in Google Scholar

Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/pac-2025-0454).

Received: 2025-03-06
Accepted: 2025-06-03
Published Online: 2025-09-04
Published in Print: 2025-10-27

© 2025 IUPAC & De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Review Articles
  3. Minimum energy path methods and reactivity for enzyme reaction mechanisms: a perspective
  4. The quantum revolution in enzymatic chemistry: combining quantum and classical mechanics to understand biochemical processes
  5. A quantum chemical perspective of photoactivated biological functions
  6. Does chemistry need more physics?
  7. Rotational dynamics of ATP synthase: mechanical constraints and energy dissipative channels
  8. Transforming dreams into reality: a fairy-tale wedding of chemistry with quantum mechanics
  9. The quantum chemistry revolution and the instrumental revolution as evidenced by the Nobel Prizes in chemistry
  10. Influence of symmetry on the second-order NLO properties: insights from the few state approximations
  11. The dichotomy between chemical concepts and numbers after almost 100 years of quantum chemistry: conceptual density functional theory as a case study
  12. How ‘de facto variational’ are fully iterative, approximate iterative, and quasiperturbative coupled cluster methods near equilibrium geometries?
  13. Electronic structure of methyl radical photodissociation
  14. Bridging experiment and theory: a computational exploration of UMG-SP3 dynamics
  15. Research Articles
  16. O–Li⋯O and C–Li⋯C lithium bonds in small closed shell and open shell systems as analogues of hydrogen bonds
  17. Metal–ligand bonding and noncovalent interactions of mutated myoglobin proteins: a quantum mechanical study
https://doi.org/10.1515/pac-2025-0454
Keywords for this article
π-π interactions; hydrogen bonding; local vibrational force constants; local vibrational mode analysis; metal–ligand bonding; myoglobin; non-covalent interactions; QM/MM; quantum science and technology

Articles in the same Issue

  1. Frontmatter
  2. Review Articles
  3. Minimum energy path methods and reactivity for enzyme reaction mechanisms: a perspective
  4. The quantum revolution in enzymatic chemistry: combining quantum and classical mechanics to understand biochemical processes
  5. A quantum chemical perspective of photoactivated biological functions
  6. Does chemistry need more physics?
  7. Rotational dynamics of ATP synthase: mechanical constraints and energy dissipative channels
  8. Transforming dreams into reality: a fairy-tale wedding of chemistry with quantum mechanics
  9. The quantum chemistry revolution and the instrumental revolution as evidenced by the Nobel Prizes in chemistry
  10. Influence of symmetry on the second-order NLO properties: insights from the few state approximations
  11. The dichotomy between chemical concepts and numbers after almost 100 years of quantum chemistry: conceptual density functional theory as a case study
  12. How ‘de facto variational’ are fully iterative, approximate iterative, and quasiperturbative coupled cluster methods near equilibrium geometries?
  13. Electronic structure of methyl radical photodissociation
  14. Bridging experiment and theory: a computational exploration of UMG-SP3 dynamics
  15. Research Articles
  16. O–Li⋯O and C–Li⋯C lithium bonds in small closed shell and open shell systems as analogues of hydrogen bonds
  17. Metal–ligand bonding and noncovalent interactions of mutated myoglobin proteins: a quantum mechanical study
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 3.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0454/pdf
Scroll to top button