Next Article in Journal
Hand Gesture Recognition with Symmetric Pattern under Diverse Illuminated Conditions Using Artificial Neural Network
Previous Article in Journal
Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions
Previous Article in Special Issue
Computational Exploration of Functionalized Rhombellanes: Building Blocks and Double-Shell Structures
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Editorial

Postface for Applied Designs in Chemical Structures with High Symmetry

1
Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj, Romania
2
Chemical Doctoral School, Babes-Bolyai University, Cluj-Napoca, 400028 Cluj, Romania
Symmetry 2022, 14(10), 2044; https://doi.org/10.3390/sym14102044
Submission received: 22 July 2022 / Accepted: 27 September 2022 / Published: 30 September 2022
(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)
Probably the best example to start with with regard to structures with high symmetry (SHS) is C 60 fullerene (buckminsterfullerene) [1], a synthetic form of carbon resembling footballs [2]. Inside of an applicability domain with structure–property relationships applied, designs may serve as tools for the in silico construction of chemical SHS, as well as for the characterization of structure, the classification of series of structures, and property prediction [3]. Investigation into these structures helps us to better understand their natural tendencies to stabilize matter into chemicals, as well as to further develop new classes of highly symmetric chemical compounds. Several experimental [4,5] and theoretical tools [6,7,8] are now available for this task.
“Applied Designs in Chemical Structures with High Symmetry” (ADCSHS) is a collection of twelve articles.

1. Contributions

Rhombellane was defined by Diudea [9] in the context of distinguishing between cycles, rings, and strong rings. Having in mind the real interest for new potent drug carriers, the potential of these new topologies to be implemented as real chemical structures has been explored further in [10]. ADCSHS gives a group of five papers on this topic ([11,12,13,14,15]). In [11], by using the rhombellane framework, several dual-layer covalent assemblies were designed as potential drug delivery systems. Following a computational study, the authors concluded that the aromatic moieties through stacking interactions, as well as the hydrogen bond donor and acceptor groups on the surface layer, significantly contribute to the ligand binding capacity. They also noted that the immobilization of compounds with pharmaceutical potential could be further enhanced by attachment of functional groups to the aromatic rings. In a subsequent docking study [12], the immobilization of oxindole derivatives was evaluated against immobilization on C 60 , where, in one instance, an increase up to 4–5 times of the binding constant was noticed.
Docking provides preferred orientation, affinity, and interaction of a ligand in the binding site of a host molecule, and several computer programs are dedicated to do this task. ADCSHS provides two papers on this topic (Refs. [16,17] docking to enzymes’ active sites). With the use of AutoDock (v.4 [18] and Vina [19] in [13] and in [14,15,16,17]), Dr. Szefler and Dr. Czelen docked several ligands (cisplatin in [13], polyethylenimines derivatives in [14], ChEMBL474807 in [15], oxindole derivatives in [16]) to different hosts (rhombellane homeomorphs and C 60 in [13,14,15], nanotubes in [15], 1E9H (CDK2, PDB [20]) and 3QVR (GOx, PDB [21]) enzymes active sites in [16] and in [17]) when similar binding affinities were observed. However, some distinct conclusions were drawn; thus, the highest values of both binding affinity and binding constant were found in the case of carbon nanotubes [15] when compared with the other alternatives (rhombellane homeomorphs and C 60 fullerene).
COSMO (from COnductor-like Screening MOdel) is a method which has become popular in recent years [22,23] for calculating the electrostatic interaction of a molecule with a solvent [24]. Some challenges and possible solutions in the case of fullerenes are provided in [25]. It was documented in [25] that, from the perspective of the COSMO-RS approach, in the case of C 60 , it is indispensable to distinguish calorimetric contributions to Gibbs free energy of fusion from the fluidization term; classification of solvents into groups with similar values of fluidization term proved to significantly increase the accuracy of the predicted solubility.
In the search for improving the explanatory power of structure–activity relationships, in [26], starting from binding constants of 1:1 β -cyclodextrin complexes with different organic compounds, the authors apply a previously reported approach [27] of non-linear multivariate adaptive regression splines (implemented in STATISTICA v.12 software) on common molecular descriptors calculated from simplified molecular input line entry specification. The study included internal and external validation, which indicated good accuracy of the model, while inclusion of the XlogP (polarity-related descriptor) gives the physical support of the model since the cyclodextrin cavity is hydrophobic.
Some of the research carried out under the framework of the GEMNS project (Self-navigated integrin receptors seeking ’thermally-smart’ multifunctional few-layer graphene-encapsulated magnetic nanoparticles for molecular MRI-guided anticancer treatments in ’real time’ personalized nanomedicine) from the EuroNanoMed-II, PN III, ERA-NET program (ID 57, Grant no. 8/2015, Director Prof. Mircea V. Diudea) was highlighted in [28]. The authors of [28], combining data from Chemoffice (v. 2005) software with tools from Mathematica (v. 5.0) software constructed QSAR models using the AutoQSAR (v. 2009) software. Hypotheses were derived from QSARs, and finally, a merged (combined from two) hypothesis was formulated. Based on their study, the authors concluded that a mathematical model based on Riemann surfaces can be built in order to screen and characterize polymers with gene transfer properties.
At over fifty years since its formulation [29], density functional theory is has become a very powerful tool for molecular and materials modeling. As a typical case study of its capabilities, in [30], dimensionless ratio, elastic constants, shear modulus, Young’s modulus, bulk modulus, ductile–brittle transition, material anisotropy, and Poisson’s ratio, as functions of applied pressure, are calculated for TiV alloys with symmetric structures under high pressure. The authors of [30] were able to extract from their computations a series of important specific information, for example, that the symmetric crystal structure of the TiV alloy produces structural phase transitions when the applied pressure exceeds 42.05 GPa, which was found to be the critical pressure of the structural phase transition.
Molecular conformation as a subproblem of the geometrical shaping of molecules is essential for the expression of biological activity, and two typical examples are sugars [31] and amino acids [32]. In [33], the author stresses the connection between geometrical orthogonalization and molecular alignment. In [33], it is shown that while the eigenproblem arises when topological adjacencies are represented into the Hessian, molecular alignment is achieved when projections of the geometrical adjacencies follow a transformation which maximizes its principal components.

2. Perspectives

As later studies showed [34,35], similarity invokes symmetry (and vice versa) in certain details, and there is plenty of research on the formulation of the eigenproblem in chemistry. Moving from the molecular level to macroscopic level requires a change in perspective regarding the objects subjected to the symmetry analysis [36,37]. Molecular clusters are an interesting case of similarity symmetry, the topology being taken to the next level [38].
Even if the primary use of symmetry is to predict or explain properties such as dipole moment and allowed spectroscopic transitions, there is an increasing number of studies [39,40,41,42,43] recognizing and documenting the role of symmetry in the biological manifestations of chemical compounds since the control of the symmetry in synthetic molecules increases the ability to provide therapies with minimal side effects.

Funding

This research received no external funding.

Acknowledgments

Since most of the papers from ADCSHS are written by authors who know, collaborated with, or were guided by Mircea V. Diudea (b. 11 November 1950; d. 25 June 2019), a memoriam is in its place here. Mircea Vasile Diudea received his B.Sc. and M.Sc. in Chemistry from the Faculty of Chemistry, Babeş-Bolyai University of Cluj-Napoca (1974), and his Ph.D. in Chemistry (1977) from the Institute of Chemistry Cluj-Napoca. He started to work as chemist at ‘Terapia’ drug factory (in 1974), then as a researcher at the Chemical-Pharmaceutical Institute of Cluj-Napoca (in 1980), finally taking a position at the Department of Chemistry from Babeş-Bolyai University (in 1987). He was the founder and the president of the European Society of Mathematical Chemistry (ESMC). Writing over 450 papers (most of them on molecular topology) and several books, including [44,45], Diudea succeeded in having a positive and emancipative influence on others. He kept correspondence and had fruitful collaborations with other well-known scientists in his field, resulting in the following works: [46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64], to enumerate just a few of the results of his fruitful collaborations. Twenty-seven students graduated under his supervision. The author of this editorial is grateful for the help received from M. V. Diudea, as his former Advisor (in Chemistry), being the first of his graduates enrolled in his open PhD positions.Symmetry 14 02044 g001

Conflicts of Interest

The author declares no conflict of interest.

References

  1. Kroto, H.; Heath, J.; O’Brien, S.; Curl, R.F.; Smalley, R.E. C60: Buckminsterfullerene. Nature 1985, 318, 162–163. [Google Scholar] [CrossRef]
  2. Jones, D.E.H. Hollow molecules. New Sci. 1966, 32, 245. [Google Scholar]
  3. Jäntschi, L.; Bálint, D.; Pruteanu, L.L.; Bolboacă, S.D. Elemental factorial study on one-cage pentagonal face nanostructure congeners. Mater. Discov. 2016, 5, 14–21. [Google Scholar] [CrossRef]
  4. Koichi, S.; Koshino, H.; Satoh, H. Handling of Highly Symmetric Molecules for Chemical Structure Elucidation in a CAST/CNMR System. J. Comput. Chem. Jpn. 2015, 14, 193–195. [Google Scholar] [CrossRef]
  5. Tranquada, J.M. Topological Doping and Superconductivity in Cuprates: An Experimental Perspective. Symmetry 2021, 13, 2365. [Google Scholar] [CrossRef]
  6. Buda, A.B.; Mislow, K. A Hausdorff chirality measure. J. Am. Chem. Soc. 1992, 114, 6006–6012. [Google Scholar] [CrossRef]
  7. Echeverría, G.; Alvarez, S. Application of Symmetry Operation Measures in Structural Inorganic Chemistry. Inorg. Chem. 2008, 47, 10965–10970. [Google Scholar] [CrossRef]
  8. Nadimi-Shahraki, M.H.; Taghian, S.; Mirjalili, S.; Ewees, A.A.; Abualigah, L.; Abd Elaziz, M. MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm. Symmetry 2021, 13, 2388. [Google Scholar] [CrossRef]
  9. Diudea, M.V. Hypercube Related Polytopes. Iran. J. Math. Chem. 2018, 9, 1–8. [Google Scholar]
  10. Diudea, M.V.; Lungu, C.N.; Nagy, C.L. Cube-Rhombellane Related Structures: A Drug Perspective. Molecules 2018, 23, 2533. [Google Scholar] [CrossRef]
  11. Nagy, K.; Szefler, B.; Nagy, C.L. Computational Exploration of Functionalized Rhombellanes: Building Blocks and Double-Shell Structures. Symmetry 2020, 12, 343. [Google Scholar] [CrossRef]
  12. Czelen, P.; Szefler, B. The Immobilization of Oxindole Derivatives with Use of Cube Rhombellane Homeomorphs. Symmetry 2019, 11, 900. [Google Scholar] [CrossRef] [Green Version]
  13. Szefler, B.; Czelen, P. Docking of Cisplatin on Fullerene Derivatives and Some Cube Rhombellane Functionalized Homeomorphs. Symmetry 2019, 11, 874. [Google Scholar] [CrossRef]
  14. Szefler, B.; Czelen, P. Docking of Polyethylenimines Derivatives on Cube Rhombellane Functionalized Homeomorphs. Symmetry 2019, 11, 1048. [Google Scholar] [CrossRef]
  15. Czelen, P.; Szefler, B. The Immobilization of ChEMBL474807 Molecules Using Different Classes of Nanostructures. Symmetry 2019, 11, 980. [Google Scholar] [CrossRef]
  16. Czelen, P. Investigation of the Inhibition Potential of New Oxindole Derivatives and Assessment of Their Usefulness for Targeted Therapy. Symmetry 2019, 11, 974. [Google Scholar] [CrossRef]
  17. Szefler, B. Docking Linear Ligands to Glucose Oxidase. Symmetry 2019, 11, 901. [Google Scholar] [CrossRef]
  18. Morris, G.M.; Huey, R.; Lindstrom, W.; Sanner, M.F.; Belew, R.K.; Goodsell, D.S.; Olson, A.J. Autodock4 and AutoDockTools4: Automated docking with selective receptor flexibility. J. Comput. Chem. 2009, 30, 2785–2791. [Google Scholar] [CrossRef]
  19. Trott, O.; Olson, A.J. AutoDock Vina: Improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. J. Comput. Chem. 2010, 31, 455–461. [Google Scholar] [CrossRef]
  20. wwPDB Foundation. wwPDB Foundation. PDB Entry—1E9H. Protein Data Bank 2011. [Google Scholar]
  21. wwPDB Foundation. PDB Entry—3QVR. Protein Data Bank 2011. [Google Scholar]
  22. Rezaei Motlagh, S.; Harun, R.; Awang Biak, D.R.; Hussain, S.A.; Wan Ab Karim Ghani, W.A.; Khezri, R.; Wilfred, C.D.; Elgharbawy, A.A.M. Screening of Suitable Ionic Liquids as Green Solvents for Extraction of Eicosapentaenoic Acid (EPA) from Microalgae Biomass Using COSMO-RS Model. Molecules 2019, 24, 713. [Google Scholar] [CrossRef] [PubMed]
  23. Sherwood, J.; Granelli, J.; McElroy, C.R.; Clark, J.H. A Method of Calculating the Kamlet-Abboud-Taft Solvatochromic Parameters Using COSMO-RS. Molecules 2019, 24, 2209. [Google Scholar] [CrossRef] [PubMed]
  24. Klamt, A.; Schüürmann, G. COSMO: A new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc. Perkin Trans. 2 1993, 2, 799–805. [Google Scholar] [CrossRef]
  25. Cysewski, P. Application of the Consonance Solvent Concept for Accurate Prediction of Buckminster Solubility in 180 Net Solvents using COSMO-RS Approach. Symmetry 2019, 11, 828. [Google Scholar] [CrossRef]
  26. Cysewski, P.; Przybylek, M. Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String. Symmetry 2019, 11, 922. [Google Scholar] [CrossRef]
  27. Przybylek, M.; Recki, L.; Mroczynska, K.; Jelinski, T.; Cysewski, P. Experimental and theoretical solubility advantage screening of bi-component solid curcumin formulations. J. Drug Deliv. Sci. Technol. 2019, 50, 125–135. [Google Scholar] [CrossRef]
  28. Lungu, C.N.; Grudzinski, I.P. Riemann-Symmetric-Space-Based Models in Screening for Gene Transfer Polymers. Symmetry 2019, 11, 1466. [Google Scholar] [CrossRef]
  29. Becke, A.D. Perspective: Fifty years of density-functional theory in chemical physics. J. Chem. Phys. 2014, 140, 18A301. [Google Scholar] [CrossRef]
  30. Yu, F.; Liu, Y. DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure. Symmetry 2019, 11, 972. [Google Scholar] [CrossRef]
  31. Janežič, D.; Jäntschi, L.; Bolboacă, S.D. Sugars and Sweeteners: Structure, Properties and In Silico Modeling. Curr. Med. Chem. 2020, 27, 5–22. [Google Scholar] [CrossRef]
  32. Hovmöller, S.; Zhou, T.; Ohlson, T. Conformations of amino acids in proteins. Acta Crystallogr. D Biol. Crystallogr. 2002, 58, 768–776. [Google Scholar] [CrossRef]
  33. Jäntschi, L. The Eigenproblem Translated for Alignment of Molecules. Symmetry 2019, 11, 1027. [Google Scholar] [CrossRef]
  34. Cheong, S.W. SOS: Symmetry-operational similarity. NPJ Quantum Mater. 2019, 4, 53. [Google Scholar] [CrossRef] [Green Version]
  35. Joiţa, D.-M.; Tomescu, M.A.; Bàlint, D.; Jäntschi, L. An Application of the Eigenproblem for Biochemical Similarity. Symmetry 2021, 13, 1849. [Google Scholar] [CrossRef]
  36. Petukhov, S.V. Non-Euclidean geometries and algorithms of living bodies. Comput. Math. Appl. 1989, 17, 505–534. [Google Scholar] [CrossRef]
  37. Martinetz, T.; Schulten, K. Topology representing networks. Neural Netw. 1994, 7, 507–522. [Google Scholar] [CrossRef]
  38. Jäntschi, L.; Bolboacă, S.D. Conformational study of C24 cyclic polyyne clusters. Int. J. Quantum Chem. 2018, 118, e25614. [Google Scholar] [CrossRef]
  39. Feder-Kubis, J.; Czerwoniec, P.; Lewandowski, P.; Pospieszny, H.; Smiglak, M. Ionic Liquids with Natural Origin Component: A Path to New Plant Protection Products. ACS Sustain. Chem. Eng. 2020, 8, 842–852. [Google Scholar] [CrossRef]
  40. Morimoto, J.; Miyamoto, K.; Ichikawa, Y.; Uchiyama, M.; Makishima, M.; Hashimoto, Y.; Ishikawa, M. Improvement in aqueous solubility of achiral symmetric cyclofenil by modification to a chiral asymmetric analog. Sci. Rep. 2021, 11, 12697. [Google Scholar] [CrossRef]
  41. Filisola-Villaseñor, J.G.; Aranda-Barradas, M.E.; Miranda-Castro, S.P.; Mendieta-Wejebe, J.E.; Valdez Guerrero, A.S.; Guillen Castro, S.A.; Martínez Castillo, M.; Tamay-Cach, F.; Álvarez-Almazán, S. Impact of Molecular Symmetry/Asymmetry on Insulin-Sensitizing Treatments for Type 2 Diabetes. Symmetry 2022, 14, 1240. [Google Scholar] [CrossRef]
  42. Bravanjalin Subi, E.; Arul Dhas, D.; Balachandran, S.; Hubert Joe, I. Crystal Growth, Structural, Vibrational, Effects of Hydrogen Bonding(C-H…O and C-H…N), Chemical Reactivity, Antimicrobial Activity, Inhibitory Effects and Molecular Dynamic Simulation of 4-Methoxy-N-(Nitrobenzylidene)-Aniline. Polycycl. Aromat. Compd. 2022, 1–55, Online first. [Google Scholar] [CrossRef]
  43. Sipe, S.N.; Lancaster, E.B.; Butalewicz, J.P.; Whitman, C.P.; Brodbelt, J.S. Symmetry of 4-Oxalocrotonate Tautomerase Trimers Influences Unfolding and Fragmentation in the Gas Phase. J. Am. Chem. Soc. 2022, 1–8, Online first. [Google Scholar] [CrossRef] [PubMed]
  44. Diudea, M.V.; Jäntschi, L.; Gutman, I. Molecular Topology, 2nd ed.; Nova Science Publishers: New York, NY, USA, 2001; ISBN 1-56072-957-0. Available online: http://lori.academicdirect.ro/books/pdf/2001_moltop.pdf (accessed on 28 September 2022).
  45. Diudea, M.V. Nanomolecules and Nanostructures–Polynomials and Indices; Princeps Edition; University of Kragujevac and Faculty of Science Kragujevac: Kragujevac, Serbia, 2010; ISBN 978-86-6009-005-0. [Google Scholar]
  46. Silberg, I.A.; Farcasan, V.; Diudea, M. Free radicals of phenothiazine and related compounds. III. Selective Chlorination of Phenothiazines with Copper (II) Chloride. J. Prakt. Chem. 1976, 318, 353–358. [Google Scholar] [CrossRef]
  47. Diudea, M.V.; Silaghi-Dumitrescu, I. Molecular topology. 1. Valence group electronegativity as a vertex discriminator. Rev. Roum. Chim. 1989, 34, 1175–1182. [Google Scholar]
  48. Balaban, A.T.; Diudea, M.V. Real number vertex invariants: Regressive distance sums and related topological indexes. J. Chem. Inf. Comput. Sci. 1993, 33, 421–428. [Google Scholar] [CrossRef]
  49. Diudea, M.V.; Horvath, D.; Bonchev, D. Molecular topology. 14. MOLORD algorithm and real number subgraph invariants. Croat. Chem. Acta 1995, 68, 131–148. Available online: http://hrcak.srce.hr/clanak/260305 (accessed on 28 September 2022).
  50. Ivanciuc, O.; Ivanciuc, T.; Diudea, M.V. Molecular graph matrices and derived structural descriptors. SAR QSAR Environ. Res. 1997, 7, 63–87. [Google Scholar] [CrossRef]
  51. Diudea, M.V.; Randić, M. Matrix Operator, W(M1,M2,M3), and Schultz-Type Indices. J. Chem. Inf. Comput. Sci. 1997, 37, 1095–1100. [Google Scholar] [CrossRef]
  52. Diudea, M.V.; Gutman, I. Wiener-type topological indices. Croat. Chem. Acta 1998, 71, 21–51. Available online: http://hrcak.srce.hr/clanak/195337 (accessed on 28 September 2022).
  53. Jäntschi, L.; Katona, G.; Diudea, M.V. Modeling molecular properties by Cluj indices. MATCH Commun. Math. Comput. Chem. 2000, 41, 151–188. Available online: http://lori.academicdirect.org/?pdf=7 (accessed on 28 September 2022).
  54. Diudea, M.V.; Kiss, A.A.; Estrada, E.; Guevara, N. Connectivity-, Wiener- and Harary-type indices of dendrimers. Croat. Chem. Acta 2000, 73, 367–381. Available online: http://hrcak.srce.hr/clanak/195000 (accessed on 28 September 2022).
  55. Diudea, M.V.; Graovac, A. Generation and graph-theoretical properties of C4-tori. MATCH Commun. Math. Comput. Chem. 2001, 44, 93–102. Available online: http://match.pmf.kg.ac.rs/electronic_versions/Match44/match44_93-102.pdf (accessed on 28 September 2022).
  56. Diudea, M.V.; Kirby, E.C. The energetic stability of tori and single-wall tubes. Fullerene Sci. Technol. 2001, 9, 445–465. [Google Scholar] [CrossRef]
  57. John, P.E.; Diudea, M.V. Wiener index of zig-zag polyhex nanotubes. Croat. Chem. Acta 2004, 77, 127–132. Available online: http://hrcak.srce.hr/clanak/151137 (accessed on 28 September 2022).
  58. King, R.B.; Diudea, M.V. The chirality of icosahedral fullerenes: A comparison of the tripling (leapfrog), quadrupling (chamfering), and septupling (capra) transformations. J. Math. Chem. 2006, 39, 597–604. [Google Scholar] [CrossRef]
  59. Vizitiu, A.E.; Diudea, M.V.; Nikolić, S.; Janežič, D. Retro-leapfrog and related retro map operations. J. Chem. Inf. Model. 2006, 46, 2574–2578. [Google Scholar] [CrossRef]
  60. Graur, F.; Elisei, R.; Szasz, A.; Neagoş, H.C.; Mureşan, A.; Furcea, L.; Neagoe, I.; Braicu, C.; Katona, G.; Diudea, M. Ethical issues in nanomedicine. In Proceedings of the International Conference on Advancements of Medicine and Health Care through Technology, IFMBE, Cluj-Napoca, Romania, 29 August–2 September 2011; pp. 9–12. [Google Scholar]
  61. Ashrafi, A.R.; Shabani, H.; Diudea, M.V. Balaban index of dendrimers. MATCH Commun. Math. Comput. Chem. 2013, 69, 151–158. Available online: http://match.pmf.kg.ac.rs/electronic_versions/Match69/n1/match69n1_151-158.pdf (accessed on 28 September 2022).
  62. Diudea, M.V.; Rosenfeld, V.R. The truncation of a cage graph. J. Math. Chem. 2017, 55, 1014–1020. [Google Scholar] [CrossRef]
  63. Szefler, B.; Czelen, P.; Diudea, M.V. Docking of indolizine derivatives on cube rhombellane functionalized homeomorphs. Stud. Univ. Babes-Bolyai Chem. 2018, 63, 7–18. [Google Scholar] [CrossRef]
  64. Majumdar, S.; Basak, S.C.; Lungu, C.N.; Diudea, M.V.; Grunwald, G.D. Mathematical structural descriptors and mutagenicity assessment: A study with congeneric and diverse datasets. SAR QSAR Environ. Res. 2018, 29, 579–590. [Google Scholar] [CrossRef]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Jäntschi, L. Postface for Applied Designs in Chemical Structures with High Symmetry. Symmetry 2022, 14, 2044. https://doi.org/10.3390/sym14102044

AMA Style

Jäntschi L. Postface for Applied Designs in Chemical Structures with High Symmetry. Symmetry. 2022; 14(10):2044. https://doi.org/10.3390/sym14102044

Chicago/Turabian Style

Jäntschi, Lorentz. 2022. "Postface for Applied Designs in Chemical Structures with High Symmetry" Symmetry 14, no. 10: 2044. https://doi.org/10.3390/sym14102044

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop