Spin Effects in sp2 Nanocarbons in the Light of Unrestricted Hartree-Fock Approach and Spin-Orbit Coupling Theory
Abstract
The paper presents the first reference to the post factum similarity of nonrelativistic unrestricted Hartree-Fock formalism and Dirac-Fock spin-orbit theory when applying for the consideration of spin effects characteristic for sp 2 nanocarbon open-shell molecules (fullerenes, carbon nanotubes, and graphene). The origin of the similarity as well as interchangeability of the approaches when determining either UHF or SOC peculiarities and parameters are discussed.
Keywords
Unpaired Electron Spin Effect Density Matrix Renormalization Group Molecule Atom Spin ContaminationNotes
Acknowledgements
The author greatly appreciate fruitful and stimulating discussions with V. Sheka, E. Rashba, J. Karwowski, R. Hoffmann, I. Mayer, E. Orlenko, P. D’yachkov, S. I. Vinitski, A. Gusev, Yu. P. Rybakov, E. Brändas, M. Nacimento, and D. Mukherjee. A particular gratitude to L. Gross, L. Buchinsky and S.V. Demishev for kind permition to use experimental data at own discretion. The work was performed under financial support of the Peoples’ Friendship University of Russia, grant: 022,203-0-000.
References
- 1.Pople JA, Nesbet RK (1954) J Chem Phys 22:571–572CrossRefGoogle Scholar
- 2.Bendikov M, Duong HM, Starkey K, Houk KN, Carter EA, Wudl F (2004) J Am Chem Soc 126:7416–7417CrossRefGoogle Scholar
- 3.Sheka EF (2003) Lecture notes in computer science, vol 2658. In: Sloot PMA, Abramson D, Bogdanov AV, Dongarra J, Zomaya AY, Gorbachev YE (eds) Computational science—ICCS 2003, Part II. Springer, Berlin, pp 386–403Google Scholar
- 4.Sheka EF (2004) Centr Europ J Phys 2:160–182Google Scholar
- 5.Sheka EF (2004) Int J Quant Chem 100:375–387CrossRefGoogle Scholar
- 6.Hachmann J, Dorando JJ, Avilés M, Chan GK-L (2007) J Chem Phys 127:134309Google Scholar
- 7.Jiang D, Dai S (2008) J Phys Chem A 112:332–335CrossRefGoogle Scholar
- 8.Qu Z, Zhang D, Liu C, Jiang Y (2009) J Phys Chem A 113:7909–7914CrossRefGoogle Scholar
- 9.Hajgató B, Szieberth D, Geerlings P, De Proft F, Deleuze MS (2009) J Chem Phys 131:224321CrossRefGoogle Scholar
- 10.Bettinger HF (2010) Pure Appl Chem 82:905–915CrossRefGoogle Scholar
- 11.Rayne S, Forest K (2011) Comput Theor Chem 976:105–112CrossRefGoogle Scholar
- 12.Gao X, Hodgson JL, Jiang D, Zhang SB, Nagase S, Miller GP, Chen Z (2011) Org Lett 13:3316–3319CrossRefGoogle Scholar
- 13.San-Fabián E, Moscardó F (2011) Eur Phys J 64:239–248Google Scholar
- 14.Rivero P, Jiménez-Hoyos CA, Scuseria GE (2013) J Phys Chem B 117:12750–12758CrossRefGoogle Scholar
- 15.Torres AE, Guadarrama P, Fomine S (2014) J Mol Model 20:2208CrossRefGoogle Scholar
- 16.Blanquart G (2015) Int J Quant Chem 115:796–801CrossRefGoogle Scholar
- 17.Ibeji CU, Ghosh D (2015) Phys Chem Chem Phys 17:9849–9856CrossRefGoogle Scholar
- 18.Sheka EF (2003)Fullerenes as polyradicals. Paper 54 presented at the internet electronic conference of molecular design. http://www.biochempress.com
- 19.Sheka EF, Zayets VA (2005) Russ J Phys Chem 79(12):2009–2014Google Scholar
- 20.Sheka EF (2006) J Str Chem 47:593–599CrossRefGoogle Scholar
- 21.Sheka EF (2007) Int J Quant Chem 107:2803–2816CrossRefGoogle Scholar
- 22.Sheka EF (2011) Fullerenes: Nanochemistry, Nanomagnetism, Nanomedicine, Nanophotonics, CRC Press. Taylor and Francis, Boca RatonCrossRefGoogle Scholar
- 23.Sheka EF (2011) In: Bai C, Awadelkarim OO, Kapitza S (eds) Encyclopedia of life support systems(EOLSS): Nanoscience and Nanotechnologies (Kharkin V. UNESCO EOLSS, Oxford, pp 415–444Google Scholar
- 24.Stück D, Baker TA, Zimmerman Pl, Kurlancheek W (2011) J Chem Phys 135:194306Google Scholar
- 25.Jiménez-Hoyos CA, Rodríguez-Guzmán R, Scuseria GE (2014) J Phys Chem A 118:9925–9940CrossRefGoogle Scholar
- 26.Sheka EF, Chernozatonskii LA (2007) J Phys Chem C 111:10771–10780CrossRefGoogle Scholar
- 27.Chen Z, Jiang D, Lu X, Bettinger HF, Dai S, Schleyer PR, Houk KN (2007) Org Lett 9:5449–5452CrossRefGoogle Scholar
- 28.Sheka EF, Chernozatonskii LA (2010) Int J Quant Chem 110:1466–1480Google Scholar
- 29.Sheka EF, Chernozatonskii LA (2009) arXiv:0901.3624v1
- 30.Jiang D, Sumpter B, Dai S (2007) J Chem Phys 126:134701CrossRefGoogle Scholar
- 31.Sheka EF, Chernozatonskii LA (2010) Int J Quant Chem 110:1938–1946Google Scholar
- 32.Sheka EF, Chernozatonskii LA (2010) J Exp Theor Phys 110:121–132CrossRefGoogle Scholar
- 33.Nagai H, Nakano M, Yoneda K, Kishi R, Takahashi H, Shimizu A, Kubo T, Kamada K, Ohta K, Botek E, Champagne B (2010) Chem Phys Lett 489:212–218CrossRefGoogle Scholar
- 34.Morita Y, Suzuki S, Sato K, Takui T (2011) Nat Chem 3:197–204CrossRefGoogle Scholar
- 35.Sheka EF (2012) Int J Quant Chem 112:3076–3090CrossRefGoogle Scholar
- 36.Ang LS, Sulaiman S, Mohamed-Ibragim MI (2012) Sains Malaysiana 41:445–452Google Scholar
- 37.Sheka EF (2013) Progress in theoretical chemistry and physics, vol 27. In: Hotokka M, Brändas EJ, Maruani J, Delgado-Barrio G (eds) Advances in quantum methods and applications in chemistry, physics, and biology. Springer, Berlin, pp 249–284Google Scholar
- 38.Mizukami W, Kurashige Y, Yanai T (2013) J Chem Theor Comput 9:401–407CrossRefGoogle Scholar
- 39.Plasser F, Pašalić H, Gerzabek MH, Libisch F, Reiter R, Burgdörfer J, Müller T, Shepard R, Lischka H (2013) Ang Chem. Int Ed 52:2581–2584CrossRefGoogle Scholar
- 40.Sheka EF (2014) Int J Quant Chem 114:1079–1095CrossRefGoogle Scholar
- 41.Horn S, Plasser F, Müller T, Libisch F, Burgdörfer J, Lischka H (2014) Theor Chem Acc 133:1511CrossRefGoogle Scholar
- 42.Wu C-S, Chai J-D (2015) J Chem Theory Comput 11:2003–2011CrossRefGoogle Scholar
- 43.Sheka EF (2015) Adv Quant Chem 70:111–161CrossRefGoogle Scholar
- 44.Fradera X, Sola M (2002) J Comput Chem 23:1347–1356CrossRefGoogle Scholar
- 45.Szabo A, Ostlund NS (1996) Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. McGraw-Hill, Toronto, Lancheaster, p 467Google Scholar
- 46.Kitagawa Y, Saito T, Nakanishi Y, Kataoka Y, Matsui T, Kawakami T, Okumura M, Yamaguchi K (2009) J Phys Chem A 113:15041–15046CrossRefGoogle Scholar
- 47.Lewars E (2011) Computational chemistry. introduction to the theory and applications of molecular and quantum mechanics, 2nd edn. Springer, Heidelberg, pp 535Google Scholar
- 48.Dehareng D, Dive G (2000) Int J Compt Chem 21:483–504CrossRefGoogle Scholar
- 49.Cizek J, Paldus J (1967) J Chem Phys 47:3976–3985CrossRefGoogle Scholar
- 50.Hubač I, Čàrski P (1983) Int J Quant Chem 24:141–148CrossRefGoogle Scholar
- 51.Kaplan I (2007) Int J Quant Chem 107:2595–603Google Scholar
- 52.Jacob CR, Reiher M (2012) Int J Quant Chem 112:3661–3684CrossRefGoogle Scholar
- 53.K, Fueno T, Yamaguchi K (1978) Theor Chim Acta 48:175–83Google Scholar
- 54.Zayets VA (1990) CLUSTER-Z1: quantum-chemical software for calculations in the s, p-basis. Institute of Surface Chemistry National Academy of Sciences, Ukraine, KievGoogle Scholar
- 55.Staroverov VN, Davidson ER (2000) Chem Phys Lett 330:161–168CrossRefGoogle Scholar
- 56.Gross L, Mohn F, Moll N, Liljeroth P, Meyer G (2009) Science 325:1110–1114CrossRefGoogle Scholar
- 57.Smallest possible five-ringed structure made: ‘Olympicene’ molecule built using clever synthetic organic chemistry.www.sciencedaily.com/releases/2012/05/120528100253.htm
- 58.Levy N, Burke SA, Meaker KL, Panlasigui M, Zettl A, Guinea F, Castro Neto AH, Crommie MF (2010) Science, 329(5991):544–547Google Scholar
- 59.Georgiou T, Britnell L, Blake P, Gorbachev RV, Gholinia A, Geim AK, Casiraghi C, Novoselov KS (2011) Appl Phys Let 99:093103CrossRefGoogle Scholar
- 60.Sheka EF, Popova NA, Popova VA, Nikitina EA, Shaymardanova LKh (2011) J Mol Mod 17:1121–1131CrossRefGoogle Scholar
- 61.Sheka EF, Popova VA, Popova NA (2013) Progress in theoretical chemistry and physics, vol 27. In: Hotokka M, Brändas EJ, Maruani J, Delgado-Barrio G (eds) Advances in quantum methods and applications in chemistry, physics, and biology. Springer, Berlin, pp 285–299Google Scholar
- 62.Kim K-J, Blanter YM, Ahn K-H (2011) Phys Rev B 84:081401(R)CrossRefGoogle Scholar
- 63.Mañes JL (2007) Phys Rev B 76:045430CrossRefGoogle Scholar
- 64.Pentsak EO, Kashin AS, Polynski MV, Kvashnina KO, Glatzel P, Ananikov VP (2015) Chem Sci 6:3302–3313CrossRefGoogle Scholar
- 65.Zhang Y, Fu Q, Cui Y, Mu R, Jin L, Bao X (2013) Phys Chem Chem Phys 15:19042–19048CrossRefGoogle Scholar
- 66.Osváth Z, Deák A, Kertész K, Molnár Gy, Vértesy G, Zámbó D, Hwang C, Biró LP (2015) Nanoscale 7:5503−5509Google Scholar
- 67.Löwdin P-O (1958) Adv Chem Phys 2:209–322Google Scholar
- 68.Bučinský L, Malček M, Biskupič S, Jayatilaka D, Büchel GE, Arion VB (2015) Comp Theor Chem 1065:27–41CrossRefGoogle Scholar
- 69.Marian CM (2001) In: Lipkowitz KB, Boyd DB (eds) Reviews in computational chemistry, vol 17, pp 99–204Google Scholar
- 70.Iliaš M, Kellö V, Urban M (2010) Acta Phys Slov 60:259–391Google Scholar
- 71.Mück LA (2012) Highly accurate quantum chemistry: spin-orbit splittings via multireference coupled-cluster methods and applications in heavy-atom main-group chemistry. DN dissertation at Johannes Gutenberg-Universität in MainzGoogle Scholar
- 72.Mϋck LA, Gauss J (2012) J Chem Phys 136:111103Google Scholar
- 73.Marian CM (2012) WIREs Comput Mol Sci 2:187–203Google Scholar
- 74.Reiher M, Wolf A (2014) Relativistic quantum chemistry: the fundamental theory of molecular science, 2nd edn, WilleyGoogle Scholar
- 75.Epifanovsky E, Klein K, Stopkowicz S, Gauss J, Krylov AI (2015) J Phys Chem 143:064102Google Scholar
- 76.Magarill LI, Chaplik AV (1999) J Exp Theor Phys 88:815–818Google Scholar
- 77.Orlandi G, Negri F (2002) Photochem Photobiol Sci 1:289–308Google Scholar
- 78.Razbirin BS, Rozhkova NN, Sheka EF, Nelson DK, Starukhin AN (2014) J Exp Theor Phys 118:735–746Google Scholar
- 79.Sheka EF (2011) Nanosci Nanotech Let 3:28–33Google Scholar
- 80.SáFar GAM, Gontijo RN, Fantini C, Martins DCS (2015) Idemori im, Pinheiro MVB, Krambrock K. J Phys Chem C 119:4344–4350Google Scholar
- 81.Liu H, Ryu S, Chen Z, Steigerwald ML, Nuckolls C, Brus LE (2009) J Am Chem Soc 131:17099–17101Google Scholar
- 82.Belousova IM, Videnichev DA, Kislyakov IM, Krisko TM, Rozhkova NN, Rozhkov S (2015) Opt Mat Express 5:169–175Google Scholar
- 83.Mayer I (1986) Int. J. Quant. Chem 29:73–84Google Scholar
- 84.Demishev SV, Pronin AA, Sluchanko NE, Weckhuysen L, Moshchalkov VV, Spitsina NG, Yagubskii ÉB (1999) JETP Lett 69:785–791Google Scholar
- 85.Demishev SV, Sluchanko NE, Weckhuysen L, Moshchalkov VV, Ohta H, Okubo S, Oshima Y, Spitsina NG (2002) Phys Sol State 44:441–443Google Scholar
- 86.Mayer I (2007) Chem Phys Let 440:357–359Google Scholar
- 87.Mayer I (2012) Chem Phys Let 539–540:172–174Google Scholar
- 88.Orlenko EV, Sheka EF, Orlenko FE (2016) Eur Phys J D 70:59Google Scholar
- 89.Sheka EF, Orlenko EV (2015) arXiv 1511.04327 [cond-mat. mes-hall]Google Scholar
- 90.Johnson RD, Yannoni CS, Dorn HC, Salem JR, Bethune DS (1992) Science 255:1235–1238Google Scholar
- 91.Tada K, Haruyama J, Yang HX, Chshiev M, Matsui T, Fukuyama H (2011) Phys Rev Lett 107:217203Google Scholar
- 92.Sheka EF (2013) Carbon materials: chemistry and physics, vol 7. In: Ashrafi AR, Cataldo F, Iranmanesh A, Ori O (eds) Topological modelling of nanostructures and extended systems. Springer, Berlin, pp 137–197Google Scholar
- 93.Rossky PJ, Karplus M (1980) J Chem Phys 73:6196–6214Google Scholar
- 94.Hubač I, Čàrski P (1980) Phys Rev A 22:2392–2399Google Scholar
- 95.Havriliak SJ, Yarkony DR (1985) J Chem Phys 83:1168–1172Google Scholar
- 96.I.Hubač, P. Čàrski Int J Quant Chem 24:141–148Google Scholar
- 97.Steele GA, Pei F, Laird EA, Jol JM, Meerwaldt HB, Kouwenhoven LP (2013) Nat Commun 4:1573Google Scholar
- 98.Marchenko D, Varykhalov A, Scholz MR, Bihlmayer G, Rashba EI, Rybkin A, Shikin AM, Rader O (2012) Nature Commun 3:1232Google Scholar