Funct. Mater. 2021; 28 (4): 743-750

doi:https://doi.org/10.15407/fm28.04.743

Estimating spin gap in conjugated nanomolecules by spin-flip configuration-interaction-singles approach

A.V.Luzanov

STC "Institute for Single Crystals", National Academy of Science of Ukraine, 60 Nauky Ave., 61001 Kharkiv, Ukraine

Abstract: 

For solids and molecular structures, the spin gap, Δs, is usually defined as the lowest electronic transition energy with a minimal nonzero change of the ground-state total spin. Here we apply π-electron semiempirical schemes to estimate Δs in nanosized conjugated systems of graphene quantum-dot and chain-like types. Namely, the spin-flip configuration interaction singles (SF-CIS) and appropriately specified Heisenberg spin-Hamiltonian (HSH) models are employed. It is shown by comparison with results of the exact π-electron theory that the simplest version of SF-CIS reasonably reproduces Δs in small-size problems, thus providing a justifiction for using the method in related problems. A particular attention is given to ferromagnetic oligomeric systems based on phenalenyl and triangulene subunits. The conjunction of SF-CIS and HSH approaches gives an efficient numerical scheme for estimating Δs in very large chain-like magnetic structures.

Keywords: 
π-electrons, graphene molecules, polyradicals, organic ferromagnet, exchange integral, Heisenberg's spin Hamiltonian.
References: 
1. A.D.Guclu, P.Potasz, M.Korkusinski, P.Hawrylak, Graphene Quantum Dots, New York, Springer (2014).
https://doi.org/10.1007/978-3-662-44611-9
 
2. A.Narita, X.-Y.Wang, X.Feng, K.Mullen, Chem. Soc. Rev., 44, 6616 (2015).
https://doi.org/10.1039/C5CS00183H
 
3. From Polyphenylenes to Nanographenes and Graphene Nanoribbons, ed. by K.Mullen, X.Feng, Springer Switzerland (2017).
 
4. J.-L.Bredas, Mater. Horiz., 1, 17 (2014).
https://doi.org/10.1039/C3MH00098B
 
5. M.Pope, C.E.Swenberg, Electronic Processes in Organic Crystals and Polymers, Oxford University Press, Oxford (1999).
 
6. S.Nishimoto, M.Takahashi, Y.Ohta, J. Phys. Soc. Jpn., 69, 1594 (2000).
https://doi.org/10.1143/JPSJ.69.1594
 
7. C.Raghu, Y.A.Pati, S.Ramasesha, Phys. Rev. B, 66, 035116 (2002).
https://doi.org/10.1103/PhysRevB.66.035116
 
8. D.P.Goli, S.Prodhan, S.Mazumdar, S.Ramasesha, Phys. Rev. B, 94, 035139 (2016).
https://doi.org/10.1103/PhysRevB.94.035139
 
9. J.Hachmann, J.J.Dorando, M.Aviles, G.K.-L.Chan, J. Chem. Phys., 127, 134309 (2007).
https://doi.org/10.1063/1.2768362
 
10. M.A.Hajj, J.-P.Malrieu, J. Chem Phys., 127, 144902 (2007).
https://doi.org/10.1063/1.2764028
 
11. S.Dutta, K.Wakabayashi, Sci. Rep., 2, 519 (2012).
https://doi.org/10.1038/srep00519
 
12. M.Das, J. Chem. Phys., 140, 124317 (2014).
https://doi.org/10.1063/1.4869582
 
13. M.Das, J. Chem. Phys., 143, 064704 (2015).
https://doi.org/10.1063/1.4928571
 
14. A.Valentim, G.A.Bocan, J.D.Fuhr et al., Phys. Chem. Chem. Phys., 22, 5882 (2020).
https://doi.org/10.1039/C9CP06065K
 
15. D.I.Lyakh, M.Musial, V.F.Lotrich, R.J.Bartlett, Chem. Rev., 112, 182 (2012).
https://doi.org/10.1021/cr2001417
 
16. H.Koch, H.A.Jensen, P.Jorgensen, T.Helgaker, J. Chem. Phys., 93, 3345 (1990).
https://doi.org/10.1063/1.458815
 
17. A.I.Krylov, Chem. Phys. Lett., 350, 522 (2001).
https://doi.org/10.1016/S0009-2614(01)01316-1
 
18. A.I.Krylov, Acc. Chem. Res., 39, 83 (2006).
https://doi.org/10.1021/ar0402006
 
19. D.Casanova, A.I.Krylov, Phys. Chem. Chem. Phys., 22, 4326 (2020).
https://doi.org/10.1039/C9CP06507E
 
20. D.C.Mattis, The Theory of Magnetism, Harper and Row, Inc., New York (1965).
 
21. A.V.Luzanov, Theor. Experim. Chem., 17, 227 (1982)
https://doi.org/10.1007/BF00519488
 
Theor. Experim. Chem., 27, 356 (1991).
https://doi.org/10.1007/BF01372507
 
22. A.V.Luzanov, Funct. Mater., 22, 514 ( 2015).
 
23. A.V.Luzanov, J. Struct. Chem., 45, 729 (2004).
https://doi.org/10.1007/s10947-005-0052-3
 
24. M.M.Mestechkin, G.E.Whyman, V.Klimo, J.Tino, Spin-Extended Hartree-Fock Method and Its Application to Molecules, Naukova Dumka, Kiev (1983) [in Russian].
 
25. A.V.Luzanov, V.V.Ivanov,Theor. Exp. Chem., 26, 363 (1991)
https://doi.org/10.1007/BF00530247
 
26. G.Gire, Y.A.Pati, S.Ramasesha, J. Phys. Chem., 123, 5257 (2019).
https://doi.org/10.1021/acs.jpca.9b02196
 
27. D.Klein, A.T.Balaban, Open. Org.Chem. J., 5, 27 (2011).
https://doi.org/10.2174/1874364101105010027
 
28. M.D.Watson, A.Fechtenkotter, K.Mullen, Chem. Rev., 101, 1267 (2001).
https://doi.org/10.1021/cr990322p
 
29. A.C.Grimsdale, K.Mullen, Angew. Chem. Int. Ed., 44, 5592 (2005).
https://doi.org/10.1002/anie.200500805
 
30. M.Grzybowski, B.Sadowski, H.Butenschon, D.T.Gryko, Angew. Chem. Int. Ed., 59, 2998 (2020).
https://doi.org/10.1002/anie.201904934
 
31. S.Mishra, D.Beyer, R.Berger et al., J. Am. Chem. Soc., 142, 1147 (2020).
https://doi.org/10.1021/jacs.9b09212
 
32. U.Beser, M.Kustler, M.Maghsoumi et al., J. Am. Chem. Soc., 138, 4322 (2016).
https://doi.org/10.1021/jacs.6b01181
 
33. T.P.Troy, T.W.Schmidt, Mon. Not. R. Astron. Soc., 371, L41 (2006).
https://doi.org/10.1111/j.1745-3933.2006.00204.x
 
34. K.Tahara, Y.Tobe, Chem. Rev., 106, 5274 (2006).
https://doi.org/10.1021/cr050556a
 
35. S.Compernolle, L.Chibotaru, A.Ceulemans, J. Chem. Phys., 119, 2854 (2003).
https://doi.org/10.1063/1.1587691
 
36. M.Mestechkin, J. Chem. Phys., 122, 186 (2005).
https://doi.org/10.1063/1.1844311
 
37. P.Povie, Y.Segawa, T.Nashihara et al., Science, 356, 172 (2017).
https://doi.org/10.1126/science.aam8158
 
38. A.L.Buchachenko, Russ. Chem. Rev., 60, 2439 (2011).
https://doi.org/10.1007/s11172-011-0378-2
 
39. J.S.Miller, Material Today, 17, 224 (2014).
https://doi.org/10.1016/j.mattod.2014.04.023
 
40. Y.Aoki, Y.Orimoto, A.Imamura, Quantum Chemical Approach for Organic Ferromagnetic Material Design, Springer, Cham (2017).
https://doi.org/10.1007/978-3-319-49829-4
 
41. J.Liu, X.Feng, Angew. Chem. Int. Ed., 59, 23386 (2020).
https://doi.org/10.1002/anie.202008838
 
42. Y.Morita, S.Suzuki, K.Sato, T.Takue, Nature Chem., 3, 197 (2011).
https://doi.org/10.1038/nchem.985
 
43. Q.Deng, J.-D.Chai, ACS Omega, 4, 14202 (2019).
https://doi.org/10.1021/acsomega.9b01259
 
44. J.Su, M.Telychko, S.Song, J.Lu, Angew. Chem. Int. Ed., 59, 7558 (2019).
 
45. J.Li, S.Sanz, J.Castro-Esteban et al., Phys. Rev. Lett., 124, 177201 (2020).
https://doi.org/10.1103/PhysRevLett.124.177201
 
46. V.O.Cheranovkii, V.Slavin, E.V.Ezerskaya et al., Crystals, 9, 251 (2019).
https://doi.org/10.3390/cryst9050251
 
47. N.Mataga, Theor. Chim. Acta, 10, 372 (1968).
https://doi.org/10.1007/BF00526505
 
48. A.A.Ovchinnikov, Theor. Chim. Acta, 47, 297 (1978).
https://doi.org/10.1007/BF00549259
 
49. G.D.O'Connor, T.P.Troy, D.A.Roberts et al., J. Am. Chem., 133, 14454 (2011).
https://doi.org/10.1021/ja206322n
 
50. E.Lieb, D.Mattis, J. Math. Phys., 3, 749 (1962)
https://doi.org/10.1063/1.1724276
 
E.Lieb, Phys. Rev. Lett., 62, 1201 (1989).
https://doi.org/10.1103/PhysRevLett.62.1201
 
51. W.Marshall, Proc. Roy. Soc.. A., 232, 48 (1955).
https://doi.org/10.1098/rspa.1955.0200
 
52. H.-J.Mikeska, A.K.Kolezhuk, Lect. Notes Phys., 645, 1 (2004).
https://doi.org/10.1007/BFb0119591
 
53. A.Das, T.Muller, F.Plasser et al., J. Phys. Chem., 120, 1625 (2016).
https://doi.org/10.1021/acs.jpca.5b12393
 
54. D.C.Mattis, The Theory of Magnetism I, Statics and Dynamics, Springer, Heidelberg (1981).
https://doi.org/10.1007/978-3-642-83238-3
 
55. J.van Kranendonk, Physica, 21, 749 (1955).
https://doi.org/10.1016/S0031-8914(55)91888-7
 
56. C.K.Majumdar, G.Mukhopadyay, A.K.Rajagopal, Pramana J. Phys., 1, 135 (1973).
https://doi.org/10.1007/BF02846659
 
57. M.Fiedler, Czechoslovak Math. J., 23, 298 (1973).
https://doi.org/10.21136/CMJ.1973.101168
 
58. W.N.Anderson Jr, T.D.Morley, Lin.Multilin, Algebra, 18, 2 (1985).
https://doi.org/10.1080/03081088508817681
 
59. P.V.Mieghem, Graph Spectra for Complex Networks, Cambridge University Press, Cambridge (2011).
 
60. M.A.Klopotek, arXiv:1707.05210v5 [math.CA] 30 Aug 2019.
 
61. S.Bose, Phys. Rev. Lett., 91, 207901 (2003).
https://doi.org/10.1103/PhysRevLett.91.207901
 

Current number: