Abstract
Ritz variational principle has been utilized to study the structural properties of the valence electron of the endohedrally captured H, Li and Na atom in fullerene C\(_{36}\) and C\(_{60}\) cages. The cage environment is incorporated by considering a spherical shell model potential. On the other hand, the interaction between the core and the valence electron corresponding to Li and Na atom has been mimicked by another model potential. The effect of the fullerene C\(_{36}\) and C\(_{60}\) cages on the total energy eigenvalue and different energy components contributing to the total energy (e.g. kinetic energy, Coulombic part of the potential energy, total cage potential etc.) has been studied for all H, Li and Na atoms. The position space as well as momentum space geometrical properties, variance, and Pearson correlation coefficient are also included in the present work. We have estimated the one-electron radial charge density in both position and momentum space which are clearly depicting the effect of the cage on the valence electron of H, Li and Na atom. Further, we have shown the effect of the fullerene cages on both position and momentum space Shannon, Fisher and disequilibrium entropies corresponding to all the above-mentioned atoms.
Similar content being viewed by others
Data availability statement
All data that support the findings of this study are included within the article (and any supplementary information files).
References
K. Sen, Electronic Structure of Quantum Confined Atoms and Molecules (Springer, Cham, 2014). https://doi.org/10.1007/978-3-319-09982-8
V. Aquilanti, C. Montgomery, H.E. ans Ramachandran, N. Sathyamurthy, Eur. Phys. J. D 75, 187 (2021). https://doi.org/10.1140/epjd/s10053-021-00197-2
E. Ley Koo, Revista Mexicana de Física 64, 326–363 (2018). https://doi.org/10.31349/RevMexFis.64.326
J.K. Saha, S. Bhattacharyya, T.K. Mukherjee, Phys. Plasmas 23, 092704 (2016). https://doi.org/10.1063/1.4962508
W. Jaskólski, Phys. Rep. 271, 1 (1996)
D.J. Norris, A.L. Efros, S.C. Erwin, Science 319, 1776 (2008). https://doi.org/10.1126/science.1143802
A.P. Alivisatos, Science 271, 933 (1996). https://doi.org/10.1126/science.271.5251.933
N.L. Rosi, J. Eckert, M. Eddaoudi, D.T. Vodak, J. Kim, M. O’Keeffe, O.M. Yaghi, Science 300, 1127 (2003). https://doi.org/10.1126/science.1083440
J. Sabin, E. Brandas, S.C. editors, The Theory of Confined Quantum Systems Parts I and II, Vol. 57, Advances in Quantum Chemistry (Academic Press, 2009)
L. Türker, Int. J. Hydrog. Energy 32, 1933 (2007). https://doi.org/10.1016/j.ijhydene.2006.10.043
C. Laughlin, S.-I. Chu, J. Phys. A Math. Theor. 42, 265004 (2009). https://doi.org/10.1088/1751-8113/42/26/265004
S. Bhattacharyya, J.K. Saha, P.K. Mukherjee, T.K. Mukherjee, Phys. Scr. 87, 065305 (2013). https://doi.org/10.1088/0031-8949/87/06/065305
R. Chandra, B. Dutta, J.K. Saha, S. Bhattacharyya, T.K. Mukherjee, Int. Quantum Chem. 118, e25597 (2018). https://doi.org/10.1002/qua.25597
M.N. Guimarães, F.V. Prudente, J. Phys. B At. Mol. Opt. Phys. 38, 2811 (2005). https://doi.org/10.1088/0953-4075/38/15/017
S. Dutta, J. Saha, S. Bhattacharyya, T. Mukherjee, Asian J. Phys. 25, 1339 (2016)
S. Mondal, K. Sen, J.K. Saha, Phys. Rev. A 105, 032821 (2022). https://doi.org/10.1103/PhysRevA.105.032821
P.C. Deshmukh, J. Jose, H.R. Varma, S.T. Manson, Eur. Phys. J. D 75, 166 (2021). https://doi.org/10.1140/epjd/s10053-021-00151-2
O.V. Pupysheva, A.A. Farajian, B.I. Yakobson, Nano Lett. 8, 767 (2008). https://doi.org/10.1021/nl071436g
W. Harneit, C. Boehme, S. Schaefer, K. Huebener, K. Fostiropoulos, K. Lips, Phys. Rev. Lett. 98, 216601 (2007). https://doi.org/10.1103/PhysRevLett.98.216601
C. Ju, D. Suter, J. Du, Phys. Rev. A 75, 012318 (2007). https://doi.org/10.1103/PhysRevA.75.012318
J.B. Melanko, M.E. Pearce, A.K. Salem, Nanotubes, nanorods, nanofibers, and fullerenes for nanoscale drug delivery, in Nanotechnology in Drug Delivery, edited by M.M. de Villiers, P. Aramwit, G.S. Kwon (Springer, New York, 2009), pp. 105–127. https://doi.org/10.1007/978-0-387-77668-2_4
R.H. Zadik, Y. Takabayashi, G. Klupp, R.H. Colman, A.Y. Ganin, A. Potočnik, P. Jeglič, D. Arčon, P. Matus, K. Kamarás, Y. Kasahara, Y. Iwasa, A.N. Fitch, Y. Ohishi, G. Garbarino, K. Kato, M.J. Rosseinsky, K. Prassides, Sci. Adv. 1, e1500059 (2015). https://doi.org/10.1126/sciadv.1500059
H. Imahori, S. Fukuzumi, Adv. Funct. Mater. 14, 525 (2004). https://doi.org/10.1002/adfm.200305172
A. Cortés-Santiago, R. Vargas, J. Garza, J. Mex. Chem. Soc. 56, 270 (2012)
T. Debnath, J.K. Saha, T. Banu, T. Ash, A.K. Das, Theor. Chem. Acc. 135, 167 (2016). https://doi.org/10.1007/s00214-016-1919-4
T. Debnath, T. Ash, J.K. Saha, A.K. Das, Chem. Sel. 2, 4039 (2017). https://doi.org/10.1002/slct.201700307
J.P. Connerade, V.K. Dolmatov, P.A. Lakshmi, S.T. Manson, J. Phys. B At. Mol. Opt. Phys. 32, L239 (1999). https://doi.org/10.1088/0953-4075/32/10/101
E.M. Nascimento, F.V. Prudente, M.N. Guimarães, A.M. Maniero, J. Phys. B At. Mol. Opt. Phys.D 44, 015003 (2010). https://doi.org/10.1088/0953-4075/44/1/015003
O. Motapon, S.A. Ndengue, K.D. Sen, Int. J. Quantum Chem. 111, 4425 (2011). https://doi.org/10.1002/qua.22996
C.Y. Lin, Y.K. Ho, J. Phys. B At. Mol. Opt. Phys. 45, 145001 (2012). https://doi.org/10.1088/0953-4075/45/14/145001
V.K. Dolmatov, J.L. King, J.C. Oglesby, J. Phys. B At. Mol. Opt. Phys. 45, 105102 (2012). https://doi.org/10.1088/0953-4075/45/10/105102
C.Y. Lin, Y.K. Ho, Few-Body Syst. 54, 425 (2013). https://doi.org/10.1007/s00601-012-0405-3
L. Wu, S. Zhang, B. Li, Phys. Lett. A 384, 126033 (2020). https://doi.org/10.1016/j.physleta.2019.126033
K.A. Dubey, K. Srikanth, T.R. Rao, J. Jose, J. Phys. Commun. 4, 075016 (2020). https://doi.org/10.1088/2399-6528/aba476
S. Saha, J. Jose, Int. J. Quantum Chem. 120, e26374 (2020). https://doi.org/10.1002/qua.26374
D.M. Mitnik, J. Randazzo, G. Gasaneo, Phys. Rev. A 78, 062501 (2008). https://doi.org/10.1103/PhysRevA.78.062501
S.H. Patil, K.D. Sen, Y.P. Varshni, Can. J. Phys. 83, 919 (2005). https://doi.org/10.1139/p05-023
A.V. Korol, A.V. Solov’yov, J. Phys. B At. Mol. Opt. Phys. 43, 201004 (2010). https://doi.org/10.1088/0953-4075/43/20/201004
C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948a). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
R. González-Férez, J.S. Dehesa, Eur. Phys. J. D 32, 39 (2005). https://doi.org/10.1140/epjd/e2004-00182-3
R. López-Ruiz, H. Mancini, X. Calbet, Phys. Lett. A 209, 321 (1995). https://doi.org/10.1016/0375-9601(95)00867-5
C. Aslangul, R. Constanciel, R. Daudel, P. Kottis, Aspects of the localizability of electrons in atoms and molecules: loge theory and related methods, edited by P.-O. Löwdin, Advances in Quantum Chemistry, Vol. 6 (Academic Press, 1972), pp. 93–141. https://doi.org/10.1016/S0065-3276(08)60542-0
A. Nagy, Chem. Phys. Lett. 556, 355 (2013). https://doi.org/10.1016/j.cplett.2012.11.065
A.S. Hyman, S.I. Yaniger, J.F. Liebman, Int. J. Quantum Chem. 14, 757 (1978). https://doi.org/10.1002/qua.560140608
M.J. Puska, R.M. Nieminen, Phys. Rev. A 47, 1181 (1993). https://doi.org/10.1103/PhysRevA.47.1181
M. Amusia, A. Baltenkov, B. Krakov, Phys. Lett. A 243, 99 (1998). https://doi.org/10.1016/S0375-9601(98)00158-3
A.V. Verkhovtsev, R.G. Polozkov, V.K. Ivanov, A.V. Korol, A.V. Solov’yov, J. Phys. B At. Mol. Opt. Phys. 45, 215101 (2012). https://doi.org/10.1088/0953-4075/45/21/215101
S. Sahoo, Y.K. Ho, Phys. Plasmas 13, 063301 (2006). https://doi.org/10.1063/1.2200290
A. Hibbert (Academic Press, 1982), pp. 309–340
C. Laughlin, G. Victor, (Academic Press, 1989), pp. 163–194
M. Marinescu, H.R. Sadeghpour, A. Dalgarno, Phys. Rev. A 49, 982 (1994). https://doi.org/10.1103/PhysRevA.49.982
W. Schweizer, P. Faßbinder, R. González-Fèrez, At. Data Nucl. Data Tables 72, 33 (1999). https://doi.org/10.1006/adnd.1999.0808
S. Sahoo, Y.K. Ho, J. Phys. B At. Mol. Opt. Phy. 33, 5151 (2000). https://doi.org/10.1088/0953-4075/33/22/316
S. Sahoo, Y.K. Ho, Chin. J. Phys. 43, 66 (2005)
Y.B. Xu, M.Q. Tan, U. Becker, Phys. Rev. Lett. 76, 3538 (1996). https://doi.org/10.1103/PhysRevLett.76.3538
V. Dolmatov, A. Baltenkov, J.-P. Connerade, S. Manson, Radiation Physics and Chemistry 70, 417 (2004). https://doi.org/10.1016/j.radphyschem.2003.12.024
A.N. Grum-Grzhimailo, E.V. Gryzlova, S.I. Strakhova, J. Phys. B At. Mol. Opt. Phys. 44, 235005 (2011). https://doi.org/10.1088/0953-4075/44/23/235005
C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948b). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
R.A. Fisher, Breakthroughs in Statistics: Methodology and Distribution (Springer, New York, 1992), pp. 66–70. https://doi.org/10.1007/978-1-4612-4380-9_6
S. Nordebo, M. Gustafsson, B. Nilsson, Inverse Probl. 23, 859 (2007). https://doi.org/10.1088/0266-5611/23/3/001
I. Bialynicki-Birula, Ł. Rudnicki, Entropic uncertainty relations in quantum physics, in Statistical Complexity: Applications in Electronic Structure, edited by K. Sen (Springer, Dordrecht, 2011), pp. 1–34. https://doi.org/10.1007/978-90-481-3890-6_1
I. Białynicki-Birula, J. Mycielski, Commun. Math. Phys. 44, 129 (1975). https://doi.org/10.1007/BF01608825
S. Chowdhury, N. Mukherjee, A.K. Roy, Quantum Rep. 5, 459 (2023). https://doi.org/10.3390/quantum5020030
Acknowledgements
Anjan Sadhukhan acknowledges the partial financial support from National Science and Technology Council (NSTC), Taiwan under Grant Number NSTC 111-2811-M-A49-558. Jayanta K. Saha acknowledges partial financial support from DHESTBT, Govt. of West Bengal, India under Grant Number 249 (Sanc.)/ST/P/S &T/16G-26/2017 and Science and Engineering Research Board (SERB), Govt. of India under file number CRG/2022/003547. KDS thanks INSA, New Delhi, for the award of a senior scientist fellowship. SM is grateful for the financial help from UGC-CSIR, Govt. of India under File Number 16-6 (DEC. 2017)/2018 (NET/CSIR). The authors are thankful to anonymous reviewer for making useful suggestions which led to substantial improvement in the presentation of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Mondal, S., Sadhukhan, A., Sen, K. et al. Structural properties and quantum information measures of H, Li and Na atoms endohedrally captured in C\(_{36}\) and C\(_{60}\) cages. Eur. Phys. J. Plus 138, 576 (2023). https://doi.org/10.1140/epjp/s13360-023-04188-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-023-04188-7