Keywords
Reduced Density Matrix Functional Theory
Hydrogen Clusters
Natural Orbitals
Metal-Insulator Transition
How to Cite
Abstract
The metal–insulator transition (MIT) is a fundamental phenomenon in condensed matter physics and a hallmark of strong electronic correlations. Hydrogen-based systems offer a simple yet powerful model for investigating the MIT, as their insulating behavior arises purely from electron–electron interactions. In this work, we study finite hydrogen clusters with cubic geometries using Natural Orbital Functional Theory (NOFT), a method capable of accurately describing correlated systems beyond mean-field approaches. We focus on two key signatures of the MIT: the fundamental energy gap and the harmonic average of the atomic one-particle reduced density matrix. Our results show that NOFT captures the transition from insulating to metallic behavior as the interatomic distance decreases. By extrapolating the energy gap to the thermodynamic limit, we estimate a critical distance rc ~1.2 Å, in excellent agreement with quantum Monte Carlo benchmarks. These findings demonstrate the reliability of NOFT for describing strong correlation effects in large-scale models.
References
[1] N. F. Mott, Rev Mod Phys 40, 677 (1968).
[2] M. Imada, A. Fujimori and Y. Tokura, Rev Mod Phys 70, 1039 (1998).
[3] A. B. Georgescu, P. Ren, A. R. Toland, S. Zhang, K. D. Miller, D. W. Apley, E. A. Olivetti, N. Wagner and J. M. Rondinelli, Chem Mater 33, 5591 (2021).
[4] Y. J. Lee, Y. Kim, H. Gim, K. Hong and H. W. Jang, Adv Mater 36, 2305353 (2024).
[5] J. H. de Boer and E. J. W. Verwey, Proc Phys Soc 49, 59 (1937).
[6] B. H. Brandow, Int J Quantum Chem Symp 10, 417 (1976).
[7] S. Kettemann, Ann Phys 456, 169306 (2023).
[8] G. Bellomia, C. Mejuto-Zaera, M. Capone and A. Amaricci, Phys Rev B 109, 115104 (2024).
[9] B. Lowe, B. Field, J. Hellerstedt, J. Ceddia, H. L. Nourse, B. J. Powell, N. V. Medhekar and A. Schiffrin, Nat Commun 15, 3559 (2024).
[10] D. M. Ceperley and B. J. Alder, Phys Rev B Condens Matter 36, 2092 (1987).
[11] M. A. Morales, C. Pierleoni, E. Schwegler and D. M. Ceperley, Proc Natl Acad Sci U S A 107, 12799 (2010).
[12] I. Silvera, Proc Natl Acad Sci USA 107, 12743 (2010).
[13] J. McMinis, M. A. Morales, D. M. Ceperley and J. Kim, J Chem Phys 143, 194703 (2015).
[14] M. Motta, C. Genovese, F. Ma, Z.-H. Cui, R. Sawaya, G. K.-L. Chan, N. Chepiga, P. Helms, C. Jiménez-Hoyos, A. J. Millis, U. Ray, E. Ronca, H. Shi, S. Sorella, E. M. Stoudenmire, S. R. White and S. Zhang, Phys Rev X 10, 031058 (2020).
[15] E. J. Landinez-Borda, K. O. Berard, A. Lopez and B. M. Rubenstein, Faraday Discuss 254, 500 (2024).
[16] P. Hohenberg and W. Kohn, Phys Rev 136, B864 (1964).
[17] W. Kohn and L. Sham, Phys Rev 140, A1133 (1965).
[18] A. I. Liechtenstein, V. I. Anisimov and J. Zaanen, Phys Rev B 52, R5467 (1995). [19] F. Aryasetiawan and O. Gunnarsson, Phys Rev Lett 74, 3221 (1995).
[20] C. Rödl, F. Fuchs, J. Furthmüller and F. Bechstedt, Phys Rev B 79, 235114 (2009).
[21] J. Kunˇe, A. V. Lukoyanov, V. I. Anisimov, R. T. Scalettar and W. E. Pickett, Nat Mater 7, 198 (2008).
[22] O. Miura and T. Fujiwara, Phys Rev B 77, 195124 (2008).
[23] M. Piris, Adv Chem Phys 134, 387 (2007).
[24] M. Piris, Adv Quantum Chem 90, 15 (2024).
[25] S. Sharma, J. K. Dewhurst, S. Shallcross and E. K. U. Gross, Phys Rev Lett 110, 116403 (2013).
[26] Y. Shinohara, S. Sharma, S. Shallcross, N. N. Lathiotakis and E. K. U. Gross, J Chem Theory Comp 11, 4895 (2015).
[27] T. L. Gilbert, Phys Rev B 12, 2111 (1975).
[28] M. Levy, Proc Natl Acad Sci USA 76, 6062 (1979).
[29] S. M. Valone, J Chem Phys 73, 1344 (1980).
[30] C. Schilling, J Chem Phys 149, 231102 (2018).
[31] P. O. Löwdin, Phys Rev 97, 1474 (1955).
[32] J. F. H. Lew-Yee, M. Piris and J. M. del Campo, J Chem Phys 154, 064102 (2021).
[33] X. Lopez, F. Ruipérez, M. Piris, J. M. Matxain and J. M. Ugalde, ChemPhysChem 12, 1061 (2011).
[34] F. Ruipérez, M. Piris, J. M. Ugalde and J. M. Matxain, Phys Chem Chem Phys 15, 2055 (2013).
[35] E. Ramos-Cordoba, X. Lopez, M. Piris and E. Matito, J Chem Phys 143, 164112 (2015).
[36] X. Lopez and M. Piris, Theor Chem Acc 138, 89 (2019).
[37] I. Mitxelena and M. Piris, J Phys Condens Matter 32, 17LT01 (2020).
[38] I. Mitxelena and M. Piris, J Chem Phys 152, 064108 (2020).
[39] I. Mitxelena and M. Piris, J Chem Phys 156, 214102 (2022).
[40] I. Mitxelena and M. Piris, J Chem Phys 160, 204106 (2024).
[41] P. Pulay, Int J Quantum Chem 111, 3273 (2011).
[42] M. Piris, X. Lopez and J. M. Ugalde, J Phys Chem Lett 15, 12138 (2024).
[43] J. Liebert and C. Schilling, SciPost Phys 14, 120 (2023).
[44] L. Ding, C.-L. Hong and C. Schilling, Quantum 8, 1525 (2024).
[45] M. Piris, Chem Sci 15, 17284 (2024).
[46] M. Piris, Int J Quantum Chem 113, 620 (2013).
[47] M. Piris, Phys Rev Lett 119, 063002 (2017).
[48] M. Piris, Phys Rev Lett 127, 233001 (2021).
[49] L. Franco, J. F. H. Lew-Yee and J. M. del Campo, AIP Advances 13, 065213 (2023).
[50] J. F. H. Lew-Yee, J. M. del Campo and M. Piris, J Chem Theory Comput 19, 211 (2023).
[51] L. Franco, R. Rojas-Hernández, I. A. Bonfil-Rivera, E. Orgaz and J. M. del Campo, Phys Chem Chem Phys (2025).
[52] J. F. H. Lew-Yee, I. A. Bonfil-Rivera, M. Piris and J. M. del Campo, J Chem Theory Comput 20, 2140 (2024).
[53] A. Rivero-Santamaría and M. Piris, J Chem Phys 160, 071102 (2024).
[54] J. F. H. Lew-Yee, M. Piris and J. M. Campo, J Chem Phys 158, 084110 (2023).
[55] J. F. H. Lew-Yee and M. Piris, J Chem Theory Comp 21, 2402 (2025).
[56] M. Piris and I. Mitxelena, Comput Phys Commun 259, 107651 (2021).
[57] L. Franco, I. A. Bonfil-Rivera, J. F. Huan Lew-Yee, M. Piris, J. M. del Campo and R. A. Vargas-Hernández, J Chem Phys 160, 244107 (2024).
[58] J. F. H. Lew-Yee, J. M. del Campo and M. Piris, Phys Rev Lett (in press, 2025).
[59] A. J. Coleman, Rev Mod Phys 35, 668 (1963).
[60] M. Piris, G. G. N. Angilella and C. Amovilli, eds., Many-body approaches Differ. scales a Tribut. to N. H. March Occas. his 90th Birthd., chapter 22, 261–278 (Springer, New York, 2018).
[61] D. A. Mazziotti, Chem Rev 112, 244 (2012).
[62] M. Piris, R. Carbó-Dorca and T. Chakraborty, eds., Quantum Chemistry at the Dawn of the 21st Century. Series: Innovations in Computational Chemistry, chapter 22, 593–620 (Apple Academic Press, 2018).
[63] M. Piris, Phys Rev A 100, 32508 (2019).
[64] I. Mitxelena, M. Rodríguez-Mayorga and M. Piris, Eur Phys J B 91, 109 (2018).
[65] M. Piris, J Math Chem 25, 47 (1999).
[66] R. Ditchfield, W. J. Hehre and J. A. Pople, J Chem Phys 54, 724 (1971).
[67] A. V. Sinitskiy, L. Greenman and D. A. Mazziotti, J Chem Phys 133, 014104 (2010).
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